%PDF-1.3 %忏嫌 1 0 obj << /Width 1 /Filter[/CCITTFaxDecode] /ImageMask true /Subtype/Image /Type/XObject /Length 4 /BitsPerComponent 1 /Height 1 /Decode[1 0] /DecodeParms[<>] >> stream €€endstream endobj 2 0 obj << /Length 4523 >> stream /GS4 gs BT /F0 1 Tf 20.66256 0 0 20.66256 110.64 634.8 Tm 0 g [(Mortgage)-301(Inno)23(v)52(ation)-302(and)-301(the)-302(F)75(oreclosure)-295(Bo)-23(om)]TJ /F1 1 Tf 14.34624 0 0 14.34624 157.08 599.28 Tm [(Dean)-326(Corbae)]TJ -3.53821 -1.24632 TD [(Univ)26(ersit)25(y)-300(of)-318(T)84(exas)-325(at)-317(Austin)]TJ 18.1511 1.24632 TD [(Erw)25(an)-309(Quin)26(tin)]TJ /F2 1 Tf 9.96264 0 0 9.96264 462.96 604.56 Tm <03>Tj /F1 1 Tf 14.34624 0 0 14.34624 318.84 581.4 Tm [(F)84(ederal)-317(Reserv)26(e)-318(Bank)-325(of)-318(Dallas)]TJ -4.75944 -1.95731 TD [(Decem)25(b)-25(er)-326(19,)-308(2008)]TJ /F3 1 Tf 10.90909 0 0 10.90909 284.64 496.32 Tm (Abstract)Tj /F4 1 Tf -15.312 -1.848 TD [(W)88(e)-385(presen)33(t)-374(a)-374(simple)-363(quan)33(titativ)33(e)-407(mo)-33(del)-363(where)-363(agen)33(ts)-396(with)-363(di\013eren)33(t)-374(c)33(haracteristics)]TJ -1.496 -1.243 TD [(select)-451(from)-418(a)-440(set)-429(of)-440(p)-33(ossible)-418(mortgage)-451(con)33(tracts)-451(and)-429(c)33(ho)-33(ose)-440(whether)-418(to)-440(subsequen)33(tly)]TJ T* [(default)-363(on)-374(their)-363(pa)33(ymen)33(ts)-374(giv)33(en)-385(realizations)-385(of)-374(idiosyncratic)-385(income)-374(and)-363(housing)-352(price)]TJ T* [(sho)-33(c)33(ks.)-660(Tw)33(o)-418(broad)-396(t)33(yp)-33(es)-407(of)-407(mortgage)-429(con)33(tracts)-429(are)-407(considered:)-594(\fxed)-396(rate)-418(mortgages)]TJ T* [((FRM))-484(whic)33(h)-462(require)-473(a)-473(do)33(wnpa)33(ymen)33(t)-473(and)-462(mortgages)-484(whic)33(h)-473(ha)33(v)33(e)-473(v)55(ariable)-484(pa)33(ymen)33(ts)]TJ T* [(that)-451(tend)-451(to)-462(b)-33(e)-440(bac)33(kloaded.)-814(One)-440(suc)33(h)-451(example)-451(is)-451(an)-451(in)33(terest)-462(only)-451(mortgage)-473((IOM))]TJ T* [(whic)33(h)-396(requires)-396(no)-396(do)33(wnpa)33(ymen)33(t)-407(and)-385(pa)33(ymen)33(ts)-407(of)-407(in)33(terest)-407(only)-396(for)-407(a)-396(giv)33(en)-407(n)33(um)33(b)-33(er)-385(of)]TJ T* [(mo)-33(del)-385(p)-33(erio)-33(ds.)-605(W)88(e)-396(assume)-396(a)-385(comp)-33(etitiv)33(e)-418(mortgage)-407(mark)33(et)-407(where)-385(eac)33(h)-396(con)33(tract)-418(m)33(ust)]TJ T* [(earn)-319(zero)-319(exp)-33(ected)-319(pro\fts)-308(giv)33(en)-330(the)-319(c)33(haracteristics)-341(of)-319(households)-308(that)-330(select)-330(in)33(to)-330(it)-319(and)]TJ T* [(the)-429(p)-33(ossibilit)33(y)-429(of)-429(default.)-737(W)88(e)-440(\frst)-418(calibrate)-440(a)-429(b)-33(enc)33(hmark)-418(mo)-33(del)-429(with)-429(FRMs)-429(only)-429(to)]TJ T* [(data)-451(prior)-429(to)-451(2000.)-781(In)-429(the)-440(b)-33(enc)33(hmark)-429(equilibrium,)-462(p)-33(eople)-440(with)-440(lo)33(w)-451(income)-440(and)-440(lo)33(w)]TJ 0 -1.232 TD [(assets)-407(cannot)-407(a\013ord)-396(to)-407(buy)-385(houses,)-418(and)-396(in)33(terest)-407(rates)-407(on)-396(mortgages)-418(are)-407(decreasing)-407(in)]TJ 0 -1.243 TD [(initial)-319(income)-319(and)-308(assets.)-451(W)88(e)-319(then)-308(in)33(tro)-33(duce)-308(IOM)-308(mortgages)-330(whic)33(h)-308(attract)-330(equilibrium)]TJ T* [(selection)-495(b)33(y)-473(the)-473(lo)33(w)-484(income,)-517(lo)33(w)-473(asset,)-528(high-default)-473(risk)-473(part)-462(of)-484(the)-473(econom)33(y)88(.)-880(The)]TJ T* [(in)33(tro)-33(duction)-484(of)-484(IOMs)-484(causes)-484(foreclosure)-495(rates)-495(to)-484(rise)-484(mark)33(edly)-495(b)-33(ecause)-484(they)-484(induce)]TJ T* [(participation)-407(b)33(y)-407(the)-396(\\subprime")-385(segmen)33(t)-418(of)-396(the)-407(mark)33(et,)-429(and)-385(b)-33(ecause)-407(households)-385(who)]TJ T* [(c)33(ho)-33(ose)-341(IOMs)-330(build)-330(little)-352(home)-330(equit)33(y)-341(early)-341(in)-341(the)-330(con)33(tract.)]TJ /F5 1 Tf 11.95517 0 0 11.95517 196.68 184.44 Tm [(V)90(ery)-371(preliminary)89(,)-392(commen)29(ts)-380(w)30(elcome.)]TJ ET q 189.36 0 0 -0.48 71.988 132.708 cm /Im1 Do Q BT /F6 1 Tf 6.97385 0 0 6.97385 85.32 124.92 Tm <03>Tj /F7 1 Tf 9.96264 0 0 9.96264 89.88 121.2 Tm [(E-mail:)-590(corbae@eco.utexas.edu,)-397(erw)24(an.quin)24(tin@dal.frb.org.)-640(W)85(e)-421(esp)-25(ecially)-396(wish)-410(to)-410(thank)-410(Daphne)-409(Chen)]TJ -1.7947 -1.1925 TD [(who)-277(has)-265(pro)24(vided)-265(outstanding)-279(researc)24(h)-253(assistance.)-411(The)-276(views)-265(expressed)-266(in)-289(this)-278(pap)-24(er)-265(are)-277(not)-278(necessarily)-253(those)]TJ 0 -1.2045 TD [(of)-337(the)-338(F)84(ederal)-313(Reserv)24(e)-325(Bank)-324(of)-326(Dallas)-325(or)-326(the)-337(F)84(ederal)-325(Reserv)24(e)-313(System.)]TJ /F8 1 Tf 11.95517 0 0 11.95517 305.64 67.44 Tm (1)Tj ET endstream endobj 3 0 obj << /SA false /Type/ExtGState >> endobj 4 0 obj << /Length 8035 >> stream /GS4 gs BT /F9 1 Tf 17.21544 0 0 17.21544 72 683.16 Tm 0 g [(1)-1122(In)27(tro)-27(duction)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 656.88 Tm [(Since)-290(2003)-271(there)-291(has)-291(b)-30(een)-291(a)-281(signi\fcan)31(t)-292(rise)-291(in)-292(non)31(traditional)-282((non-FRM))-273(mortgages)-291(as)-281(w)30(ell)-291(as)]TJ 0 -1.21454 TD [(a)-241(signi\fcan)31(t)-262(rise)-261(in)-251(residen)30(tial)-262(loan)-250(delinquency)-270(rates)-252(in)-251(the)-251(United)-260(States)-252($see)-261(\fgure)-251(1.$)-402(Man)30(y)]TJ 0 -1.2045 TD [(of)-351(the)-362(inno)31(v)50(ations)-362(in)-351(mortgages)-362(w)30(ere)-361(designed)-371(to)-351(substan)29(tially)-372(reduce)-371(the)-361(initial)-352(obligations)]TJ T* [(of)-291(b)-30(orro)29(w)31(ers.)-442(These)-311(inno)31(v)50(ations)-302(made)-301(it)-301(p)-30(ossible)-302(for)-291(more)-301(households)-312(to)-291(obtain)-301(the)-301(\fnancing)]TJ 0 -1.21454 TD [(necessary)-341(to)-312(purc)30(hase)-331(a)-321(house)-321(and)-321(in)-321(other)-312(pap)-30(ers)-321($e.g.)-442(Cham)31(b)-30(ers,)-332(et.)-432(al.)-431(\(2007$\))-312(ha)30(v)30(e)-330(b)-31(een)]TJ 0 -1.2045 TD [(asso)-31(ciated)-330(with)-342(the)-331(rise)-332(in)-331(homeo)31(wnership.)]TJ 1.46548 -1.21454 TD [(Our)-291(ob)-50(jectiv)30(e)-311(is)-291(to)-292(quan)31(tify)-302(the)-291(imp)-30(ortance)-301(of)-281(mortgage)-281(inno)30(v)50(ation)-301(for)-281(the)-291(recen)30(t)-301(\rare-up)]TJ -1.46548 -1.2045 TD [(in)-361(foreclosure)-362(rates.)-542(Sp)-31(eci\fcally)82(,)-381(w)30(e)-361(answ)30(er)-371(the)-362(follo)31(wing)-361(questions.)-553(First,)-363(ho)30(w)-371(m)30(uc)31(h)-372(of)-351(the)]TJ T* [(rise)-282(in)-281(foreclosures)-291(can)-281(b)-30(e)-280(attributable)-283(solely)-290(to)-272(inno)30(v)51(ation)-281(in)-282(mortgage)-270(con)30(tracts?)-432(Ho)30(w)-280(m)30(uc)30(h)]TJ 0 -1.21454 TD [(do)-30(es)-361(mortgage)-352(inno)31(v)50(ation)-362(magnify)-361(the)-361(e\013ect)-361(of)-351(do)30(wn)31(turns)-383(in)-362(house)-361(v)50(alues)-371(on)-351(default)-361(rates?)]TJ 0 -1.2045 TD [(What)-381(is)-392(the)-382(w)31(elfare)-391(gain)-382(asso)-30(ciated)-391(with)-382(mortgage)-381(inno)30(v)50(ation?)-602(T)81(o)-381(answ)30(er)-392(these)-391(questions,)]TJ T* [(w)30(e)-411(\frst)-402(describ)-31(e)-411(a)-391(mo)-30(del)-401(that)-392(mimics)-412(salien)30(t)-412(features)-402(of)-391(the)-402(US)-401(housing)-402(mark)30(et)-412(up)-401(to)-392(the)]TJ 0 -1.21454 TD [(turn)-322(of)-311(the)-332(cen)31(tury)80(.)-442(W)81(e)-331(consider)-331(an)-321(econom)31(y)-331(where)-331(households)-331(v)50(alue)-331(b)-30(oth)-311(consumption)-332(and)]TJ 0 -1.2045 TD [(housing)-321(services)-342(and)-321(mo)30(v)31(e)-331(sto)-31(c)31(hastically)-332(through)-322(sev)31(eral)-332(stages)-321(of)-311(life.)-442(F)80(or)-311(simplicit)29(y)80(,)-341(agen)31(ts)]TJ 0 -1.21454 TD [(who)-391(are)-391(y)30(oung)-391(are)-392(constrained)-391(to)-392(obtain)-382(housing)-401(services)-412(from)-382(the)-391(ren)30(tal)-392(mark)30(et)-402(and)-391(split)]TJ 0 -1.2045 TD [(their)-382(remaining)-381(income)-391(b)-30(et)30(w)31(een)-401(consumption)-392(and)-381(the)-382(accum)31(ulation)-391(of)-372(liquid)-381(assets.)-614(Giv)31(en)]TJ T* [(the)-341(idiosyncratic)-362(income)-350(sho)-31(c)31(ks,)-362(despite)-361(the)-342(fact)-341(that)-332(households)-362(b)-30(egin)-340(life)-341(ex-an)30(te)-351(iden)30(tical)]TJ 0 -1.21454 TD 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[(States.)-442(Un)30(til)-322(the)-321(con)31(tract)-322(matures,)-332(agen)30(ts)-332(can)-320(c)30(ho)-30(ose)-321(to)-311(terminate)-332(the)-321(con)30(tract)-321(in)-322(an)31(y)-322(giv)31(en)]TJ 0 -1.2045 TD [(p)-30(erio)-30(d.)-693(If)-412(termination)-422(o)-30(ccurs,)-442(the)-421(house)-422(is)-422(sold)-422(and)-411(agen)31(ts)-423(receiv)31(e)-431(an)30(y)-421(pro)-31(ceeds)-431(in)-411(excess)]TJ T* [(of)-381(the)-392(outstanding)-392(loan)-381(principal.)]TJ /F11 1 Tf 7.97011 0 0 7.97011 246.12 314.52 Tm (1)Tj /F8 1 Tf 11.95517 0 0 11.95517 258.24 310.2 Tm [(Tw)31(o)-391(ev)30(en)31(ts)-413(trigger)-382(the)-391(c)30(hoice)-390(to)-382(terminate:)-563(an)-391(adv)30(erse)]TJ -15.5782 -1.21454 TD [(income)-330(sho)-31(c)31(k)-321(whic)30(h)-331(mak)31(es)-332(it)-321(imp)-31(ossible)-331(for)-312(agen)31(ts)-322(to)-321(meet)-321(their)-322(curren)30(t)-332(pa)31(ymen)30(t)-332(or)-311(a)-311(sho)-30(c)30(k)]TJ 0 -1.2045 TD 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119.4167 309.8134 Tm (0.8)Tj ET 136.1667 350.48 m 138 350.48 l S 298.8333 350.48 m 296.9167 350.48 l S BT /F13 1 Tf 10 0 0 10 127.75 346.8134 Tm (1)Tj ET 136.1667 350.48 m 298.8333 350.48 l S 136.1667 165.3134 m 298.8333 165.3134 l S 298.8333 165.3134 m 298.8333 350.48 l S 136.1667 165.3134 m 136.1667 350.48 l S q 136.1667 165.23 162.75 185.25 re W n 2 w 138.1667 233.8967 m 142.25 233.8967 l 146.3334 231.98 l 150.3334 237.5634 l 154.4167 231.98 l 158.5 228.3134 l 162.5834 226.48 l 166.6667 231.98 l 170.6667 231.98 l 174.7501 220.8967 l 178.8334 243.1467 l 182.9167 244.98 l 187 239.3967 l 191 252.3967 l 195.0834 250.5634 l 199.1668 252.3967 l 203.2501 248.6467 l 207.3335 256.0634 l 211.3335 246.8134 l 215.4168 243.1467 l 219.5001 241.3134 l 223.5835 231.98 l 227.6668 244.9801 l 231.6668 250.5634 l 235.7502 250.5634 l 239.8335 237.5634 l 243.9168 243.1467 l 248.0002 250.5634 l 252.0002 243.1467 l 256.0835 235.73 l 260.1668 241.3134 l 264.2502 243.1467 l 268.3335 243.1467 l 272.3335 239.3967 l 276.4168 252.3967 l 280.5002 270.8967 l 284.5835 274.5634 l 288.6669 274.5634 l 292.6669 309.8134 l 296.7502 328.3134 l 298.9169 340.8134 l S Q BT /F13 1 Tf 10 0 0 10 145.8333 358.3967 Tm (Foreclosure rates, all mortgages)Tj ET 1 g 353.5 165.3134 162.6667 185.1667 re f 1 G 353.5 165.3134 m 353.5 350.48 l 516.1667 350.48 l 516.1667 165.3134 l 353.5 165.3134 l S 0 G 353.5 350.48 m 516.1667 350.48 l S 353.5 165.3134 m 516.1667 165.3134 l S 516.1667 165.3134 m 516.1667 350.48 l S 353.5 165.3134 m 353.5 350.48 l S 353.5 165.3134 m 516.1667 165.3134 l S 353.5 165.3134 m 353.5 350.48 l S 353.5 165.3134 m 353.5 167.23 l S 353.5 350.48 m 353.5 348.6467 l S BT /F13 1 Tf 10 0 0 10 342.4167 153.23 Tm 0 g (1998)Tj ET 386 165.3134 m 386 167.23 l S 386 350.48 m 386 348.6467 l S BT /F13 1 Tf 10 0 0 10 374.9167 153.23 Tm (2000)Tj ET 418.5 165.3134 m 418.5 167.23 l S 418.5 350.48 m 418.5 348.6467 l S BT /F13 1 Tf 10 0 0 10 407.4167 153.23 Tm (2002)Tj ET 451.0833 165.3134 m 451.0833 167.23 l S 451.0833 350.48 m 451.0833 348.6467 l S BT /F13 1 Tf 10 0 0 10 440 153.23 Tm (2004)Tj ET 483.5833 165.3134 m 483.5833 167.23 l S 483.5833 350.48 m 483.5833 348.6467 l S BT /F13 1 Tf 10 0 0 10 472.5 153.23 Tm (2006)Tj ET 516.1667 165.3134 m 516.1667 167.23 l S 516.1667 350.48 m 516.1667 348.6467 l S BT /F13 1 Tf 10 0 0 10 505.0834 153.23 Tm (2008)Tj ET 353.5 165.3134 m 355.3333 165.3134 l S 516.1667 165.3134 m 514.25 165.3134 l S BT /F13 1 Tf 10 0 0 10 345.0833 161.6467 Tm (0)Tj ET 353.5 188.48 m 355.3333 188.48 l S 516.1667 188.48 m 514.25 188.48 l S BT /F13 1 Tf 10 0 0 10 345.0833 184.8134 Tm (1)Tj ET 353.5 211.6467 m 355.3333 211.6467 l S 516.1667 211.6467 m 514.25 211.6467 l S BT /F13 1 Tf 10 0 0 10 345.0833 207.98 Tm (2)Tj ET 353.5 234.8134 m 355.3333 234.8134 l S 516.1667 234.8134 m 514.25 234.8134 l S BT /F13 1 Tf 10 0 0 10 345.0833 231.1467 Tm (3)Tj ET 353.5 257.8967 m 355.3333 257.8967 l S 516.1667 257.8967 m 514.25 257.8967 l S BT /F13 1 Tf 10 0 0 10 345.0833 254.23 Tm (4)Tj ET 353.5 281.0634 m 355.3333 281.0634 l S 516.1667 281.0634 m 514.25 281.0634 l S BT /F13 1 Tf 10 0 0 10 345.0833 277.3967 Tm (5)Tj ET 353.5 304.23 m 355.3333 304.23 l S 516.1667 304.23 m 514.25 304.23 l S BT /F13 1 Tf 10 0 0 10 345.0833 300.5634 Tm (6)Tj ET 353.5 327.3967 m 355.3333 327.3967 l S 516.1667 327.3967 m 514.25 327.3967 l S BT /F13 1 Tf 10 0 0 10 345.0833 323.73 Tm (7)Tj ET 353.5 350.48 m 355.3333 350.48 l S 516.1667 350.48 m 514.25 350.48 l S BT /F13 1 Tf 10 0 0 10 345.0833 346.8134 Tm (8)Tj ET 353.5 350.48 m 516.1667 350.48 l S 353.5 165.3134 m 516.1667 165.3134 l S 516.1667 165.3134 m 516.1667 350.48 l S 353.5 165.3134 m 353.5 350.48 l S q 353.5 165.23 162.75 185.25 re W n 2 w 355.5 169.3134 m 359.5833 169.48 l 363.6667 169.0634 l 367.6667 169.3134 l 371.75 168.5634 l 375.8334 168.3967 l 379.9167 168.1467 l 384 167.8967 l 388 168.1467 l 392.0834 167.8967 l 396.1667 167.8967 l 400.2501 167.8967 l 404.3334 168.3967 l 408.3334 168.5634 l 412.4167 169.0634 l 416.5001 169.0634 l 420.5834 168.8133 l 424.6667 168.5633 l 428.6667 168.5633 l 432.7501 168.1467 l 436.8334 168.5633 l 440.9167 168.8133 l 445 168.8133 l 449 168.8133 l 453.0834 168.8133 l 457.1668 168.8133 l 461.2501 168.8133 l 465.3334 169.3133 l 469.3334 168.8133 l 473.4168 169.0634 l 477.5001 168.8133 l 481.5835 168.8133 l 485.6668 168.3967 l 489.6668 168.5634 l 493.7501 168.3967 l 497.8334 169.0634 l 501.9168 169.3134 l 506 169.48 l 510.0002 170.48 l 514.0835 170.48 l 516.2502 171.3134 l S [0.5 4 ]0 d 355.5 175.0634 m 359.5833 175.0634 l 363.6667 174.8133 l 367.6667 175.3133 l 371.75 172.98 l 375.8334 173.6467 l 379.9167 172.5633 l 384 171.5633 l 388 172.3133 l 392.0834 171.5633 l 396.1667 171.5633 l 400.2501 171.1467 l 404.3334 172.98 l 408.3334 174.1467 l 412.4167 174.3967 l 416.5001 175.5633 l 420.5834 173.23 l 424.6667 172.3133 l 428.6667 171.5633 l 432.7501 171.1467 l 436.8334 170.6467 l 440.9167 170.48 l 445 171.3967 l 449 170.6467 l 453.0834 169.73 l 457.1668 169.0633 l 461.2501 169.3133 l 465.3334 169.73 l 469.3334 169.3133 l 473.4168 169.48 l 477.5001 169.98 l 481.5835 169.98 l 485.6668 170.23 l 489.6668 171.5633 l 493.7501 172.3133 l 497.8334 174.8133 l 501.9168 177.6467 l 506 179.73 l 510.0002 188.98 l 514.0835 189.8967 l 516.2502 195.8134 l S []0 d 1 0 0 RG 355.5 184.3134 m 359.5833 197.73 l 363.6667 192.8967 l 367.6667 200.3134 l 371.75 210.48 l 375.8334 200.73 l 379.9167 199.3967 l 384 203.5633 l 388 214.8967 l 392.0834 190.3133 l 396.1667 238.73 l 400.2501 236.6467 l 404.3334 226.48 l 408.3334 224.3967 l 412.4167 221.1467 l 416.5001 208.8967 l 420.5834 211.3967 l 424.6667 230.6467 l 428.6667 209.0633 l 432.7501 204.48 l 436.8334 203.3134 l 440.9167 189.23 l 445 199.6467 l 449 210.73 l 453.0834 213.23 l 457.1668 190.8134 l 461.2501 193.1467 l 465.3334 197.0634 l 469.3334 194.98 l 473.4168 188.23 l 477.5001 188.73 l 481.5835 189.6467 l 485.6668 192.6467 l 489.6668 188.48 l 493.7501 187.8134 l 497.8334 190.5634 l 501.9168 195.48 l 506 196.5634 l 510.0002 197.3134 l 514.0835 200.5634 l 516.2502 203.8967 l S [0.5 4 ]0 d 355.5 203.8134 m 359.5833 196.3967 l 363.6667 199.3967 l 367.6667 203.98 l 371.75 205.8967 l 375.8334 221.3967 l 379.9167 210.48 l 384 209.0634 l 388 211.1467 l 392.0834 202.3967 l 396.1667 228.98 l 400.2501 237.1467 l 404.3334 222.98 l 408.3334 223.23 l 412.4167 214.23 l 416.5001 213.23 l 420.5834 219.98 l 424.6667 225.98 l 428.6667 215.1467 l 432.7501 210.98 l 436.8334 211.1467 l 440.9167 200.98 l 445 211.6467 l 449 214.8967 l 453.0834 207.23 l 457.1668 195.8967 l 461.2501 198.6467 l 465.3334 200.0634 l 469.3334 200.3134 l 473.4168 198.8967 l 477.5001 201.48 l 481.5835 201.23 l 485.6668 209.3134 l 489.6668 211.8967 l 493.7501 216.0634 l 497.8334 227.8134 l 501.9168 240.1467 l 506 254.23 l 510.0002 274.5634 l 514.0835 287.8134 l 516.2502 300.5634 l S Q BT /F13 1 Tf 10 0 0 10 396.0833 358.3967 Tm (Foreclosure rates)Tj ET 1 g 358.4167 293.3134 110.1667 52.1667 re f 1 G 358.4167 293.3134 m 358.4167 345.48 l 468.5833 345.48 l 468.5833 293.3134 l 358.4166 293.3134 l S 0 G 358.4167 345.48 m 468.5833 345.48 l S 358.4167 293.3134 m 468.5833 293.3134 l S 468.5833 293.3134 m 468.5833 345.48 l S 358.4167 293.3134 m 358.4167 345.48 l S 358.4167 293.3134 m 468.5833 293.3134 l S 358.4167 293.3134 m 358.4167 345.48 l S 358.4167 345.48 m 468.5833 345.48 l S 358.4167 293.3134 m 468.5833 293.3134 l S 468.5833 293.3134 m 468.5833 345.48 l S 358.4167 293.3134 m 358.4167 345.48 l S BT /F13 1 Tf 10 0 0 10 397.6667 334.3134 Tm 0 g (Prime FRM)Tj ET q 358.4167 293.23 110.25 52.25 re W n 2 w 364.4167 337.8134 m 394.5833 337.8134 l S Q BT /F13 1 Tf 10 0 0 10 397.6667 321.98 Tm (Prime ARM)Tj ET q 358.4167 293.23 110.25 52.25 re W n [0.5 4 ]0 d 2 w 364.4167 325.5634 m 394.5833 325.5634 l S Q BT /F13 1 Tf 10 0 0 10 397.6667 309.73 Tm (Subprime FRM)Tj ET q 358.4167 293.23 110.25 52.25 re W n 2 w 1 0 0 RG 364.4167 313.3134 m 394.5833 313.3134 l S Q BT /F13 1 Tf 10 0 0 10 397.6667 297.3967 Tm (Subprime ARM)Tj ET q 358.4167 293.23 110.25 52.25 re W n [0.5 4 ]0 d 2 w 1 0 0 RG 364.4167 301.0634 m 394.5833 301.0634 l S Q 1 g 353.5 422.5633 162.6667 185.1667 re f 1 G 353.5 422.5634 m 353.5 607.73 l 516.1667 607.73 l 516.1667 422.5633 l 353.5 422.5633 l S 0 G 353.5 607.73 m 516.1667 607.73 l S 353.5 422.5634 m 516.1667 422.5634 l S 516.1667 422.5634 m 516.1667 607.73 l S 353.5 422.5634 m 353.5 607.73 l S 353.5 422.5634 m 516.1667 422.5634 l S 353.5 422.5634 m 353.5 607.73 l S 353.5 422.5634 m 353.5 424.48 l S 353.5 607.73 m 353.5 605.8967 l S BT /F13 1 Tf 10 0 0 10 342.4167 410.48 Tm 0 g (1998)Tj ET 386 422.5634 m 386 424.48 l S 386 607.73 m 386 605.8967 l S BT /F13 1 Tf 10 0 0 10 374.9167 410.48 Tm (2000)Tj ET 418.5 422.5634 m 418.5 424.48 l S 418.5 607.73 m 418.5 605.8967 l S BT /F13 1 Tf 10 0 0 10 407.4167 410.48 Tm (2002)Tj ET 451.0833 422.5634 m 451.0833 424.48 l S 451.0833 607.73 m 451.0833 605.8967 l S BT /F13 1 Tf 10 0 0 10 440 410.48 Tm (2004)Tj ET 483.5833 422.5634 m 483.5833 424.48 l S 483.5833 607.73 m 483.5833 605.8967 l S BT /F13 1 Tf 10 0 0 10 472.5 410.48 Tm (2006)Tj ET 516.1667 422.5634 m 516.1667 424.48 l S 516.1667 607.73 m 516.1667 605.8967 l S BT /F13 1 Tf 10 0 0 10 505.0834 410.48 Tm (2008)Tj ET 353.5 422.5634 m 355.3333 422.5634 l S 516.1667 422.5634 m 514.25 422.5634 l S BT /F13 1 Tf 10 0 0 10 345.0833 418.8967 Tm (0)Tj ET 353.5 459.6467 m 355.3333 459.6467 l S 516.1667 459.6467 m 514.25 459.6467 l S BT /F13 1 Tf 10 0 0 10 331.1667 455.98 Tm (0.02)Tj ET 353.5 496.6467 m 355.3333 496.6467 l S 516.1667 496.6467 m 514.25 496.6467 l S BT /F13 1 Tf 10 0 0 10 331.1667 492.98 Tm (0.04)Tj ET 353.5 533.73 m 355.3333 533.73 l S 516.1667 533.73 m 514.25 533.73 l S BT /F13 1 Tf 10 0 0 10 331.1667 530.0634 Tm (0.06)Tj ET 353.5 570.73 m 355.3333 570.73 l S 516.1667 570.73 m 514.25 570.73 l S BT /F13 1 Tf 10 0 0 10 331.1667 567.0634 Tm (0.08)Tj ET 353.5 607.73 m 355.3333 607.73 l S 516.1667 607.73 m 514.25 607.73 l S BT /F13 1 Tf 10 0 0 10 336.75 604.0634 Tm (0.1)Tj ET 353.5 607.73 m 516.1667 607.73 l S 353.5 422.5634 m 516.1667 422.5634 l S 516.1667 422.5634 m 516.1667 607.73 l S 353.5 422.5634 m 353.5 607.73 l S q 353.5 422.48 162.75 185.25 re W n 2 w 1 0 0 RG 355.5 434.73 m 359.5833 441.23 l 363.6667 444.1467 l 367.6667 442.1467 l 371.75 440.23 l 375.8334 441.1467 l 379.9167 439.3967 l 384 439.3967 l 388 441.8134 l 392.0834 447.3134 l 396.1667 453.3967 l 400.2501 455.3967 l 404.3334 454.5634 l 408.3334 451.3134 l 412.4167 456.9801 l 416.5001 455.73 l 420.5834 458.23 l 424.6667 463.3967 l 428.6667 465.2301 l 432.7501 463.23 l 436.8334 467.1467 l 440.9167 468.9801 l 445 469.5634 l 449 508.6467 l 453.0834 527.1467 l 457.1668 537.23 l 461.2501 548.7301 l 465.3334 563.3134 l 469.3334 573.3134 l 473.4168 580.4801 l 477.5001 577.8134 l 481.5835 581.0635 l 485.6668 582.0635 l 489.6668 581.5635 l 493.7501 580.5635 l 497.8334 578.2302 l 501.9168 576.9802 l 506 573.0635 l 510.0002 560.8135 l 514.0835 552.8969 l 516.2502 549.3969 l S [0.5 4 ]0 d 355.5 463.8134 m 359.5833 483.8134 l 363.6667 489.98 l 367.6667 473.6467 l 371.75 471.98 l 375.8334 471.3134 l 379.9167 463.98 l 384 459.98 l 388 464.3967 l 392.0834 463.6467 l 396.1667 466.8134 l 400.2501 470.8134 l 404.3334 469.98 l 408.3334 464.1467 l 412.4167 463.3967 l 416.5001 464.4801 l 420.5834 464.6467 l 424.6667 474.3134 l 428.6667 472.9801 l 432.7501 479.4801 l 436.8334 482.5634 l 440.9167 482.6467 l 445 483.3967 l 449 528.5634 l 453.0834 536.3967 l 457.1668 536.3967 l 461.2501 532.2301 l 465.3334 534.6467 l 469.3334 547.0634 l 473.4168 546.48 l 477.5001 537.8967 l 481.5835 535.8133 l 485.6668 534.6467 l 489.6668 535.1467 l 493.7501 533.8133 l 497.8334 538.23 l 501.9168 535.98 l 506 556.3966 l 510.0002 551.0633 l 514.0835 550.3133 l 516.2502 549.48 l S Q BT /F13 1 Tf 10 0 0 10 377.6667 615.6467 Tm (Shares of Mortgage stock)Tj ET 1 g 358.4167 574.8967 110.1667 27.8333 re f 1 G 358.4167 574.8967 m 358.4167 602.73 l 468.5833 602.73 l 468.5833 574.8967 l 358.4166 574.8967 l S 0 G 358.4167 602.73 m 468.5833 602.73 l S 358.4167 574.8967 m 468.5833 574.8967 l S 468.5833 574.8967 m 468.5833 602.73 l S 358.4167 574.8967 m 358.4167 602.73 l S 358.4167 574.8967 m 468.5833 574.8967 l S 358.4167 574.8967 m 358.4167 602.73 l S 358.4167 602.73 m 468.5833 602.73 l S 358.4167 574.8967 m 468.5833 574.8967 l S 468.5833 574.8967 m 468.5833 602.73 l S 358.4167 574.8967 m 358.4167 602.73 l S BT /F13 1 Tf 10 0 0 10 397.6667 591.48 Tm 0 g (Subprime FRM)Tj ET q 358.4167 574.8134 110.25 27.9166 re W n 2 w 1 0 0 RG 364.4167 595.0634 m 394.5833 595.0634 l S Q BT /F13 1 Tf 10 0 0 10 397.6667 579.0634 Tm (Subprime ARM)Tj ET q 358.4167 574.8134 110.25 27.9166 re W n [0.5 4 ]0 d 2 w 1 0 0 RG 364.4167 582.6467 m 394.5833 582.6467 l S Q 1 g 136.1667 422.5633 162.6667 185.1667 re f 1 G 136.1667 422.5634 m 136.1667 607.73 l 298.8333 607.73 l 298.8333 422.5633 l 136.1667 422.5633 l S 0 G 136.1667 607.73 m 298.8333 607.73 l S 136.1667 422.5634 m 298.8333 422.5634 l S 298.8333 422.5634 m 298.8333 607.73 l S 136.1667 422.5634 m 136.1667 607.73 l S 136.1667 422.5634 m 298.8333 422.5634 l S 136.1667 422.5634 m 136.1667 607.73 l S 136.1667 422.5634 m 136.1667 424.48 l S 136.1667 607.73 m 136.1667 605.8967 l S BT /F13 1 Tf 10 0 0 10 125.0833 410.48 Tm 0 g (1998)Tj ET 168.6667 422.5634 m 168.6667 424.48 l S 168.6667 607.73 m 168.6667 605.8967 l S BT /F13 1 Tf 10 0 0 10 157.5833 410.48 Tm (2000)Tj ET 201.1667 422.5634 m 201.1667 424.48 l S 201.1667 607.73 m 201.1667 605.8967 l S BT /F13 1 Tf 10 0 0 10 190.0833 410.48 Tm (2002)Tj ET 233.75 422.5634 m 233.75 424.48 l S 233.75 607.73 m 233.75 605.8967 l S BT /F13 1 Tf 10 0 0 10 222.6667 410.48 Tm (2004)Tj ET 266.25 422.5634 m 266.25 424.48 l S 266.25 607.73 m 266.25 605.8967 l S BT /F13 1 Tf 10 0 0 10 255.1667 410.48 Tm (2006)Tj ET 298.8333 422.5634 m 298.8333 424.48 l S 298.8333 607.73 m 298.8333 605.8967 l S BT /F13 1 Tf 10 0 0 10 287.75 410.48 Tm (2008)Tj ET 136.1667 422.6467 m 138 422.6467 l S 298.8333 422.6467 m 296.9167 422.6467 l S BT /F13 1 Tf 10 0 0 10 119.4167 418.98 Tm (0.7)Tj ET 136.1667 468.8967 m 138 468.8967 l S 298.8333 468.8967 m 296.9167 468.8967 l S BT /F13 1 Tf 10 0 0 10 113.8333 465.23 Tm (0.75)Tj ET 136.1667 515.1467 m 138 515.1467 l S 298.8333 515.1467 m 296.9167 515.1467 l S BT /F13 1 Tf 10 0 0 10 119.4167 511.48 Tm (0.8)Tj ET 136.1667 561.48 m 138 561.48 l S 298.8333 561.48 m 296.9167 561.48 l S BT /F13 1 Tf 10 0 0 10 113.8333 557.8134 Tm (0.85)Tj ET 136.1667 607.73 m 298.8333 607.73 l S 136.1667 422.5634 m 298.8333 422.5634 l S 298.8333 422.5634 m 298.8333 607.73 l S 136.1667 422.5634 m 136.1667 607.73 l S q 136.1667 422.48 162.75 185.25 re W n 2 w 138.1667 541.0634 m 142.25 538.8134 l 146.3334 552.73 l 150.3334 570.23 l 154.4167 561.1467 l 158.5 562.1468 l 162.5834 558.3968 l 166.6667 562.1468 l 170.6667 576.0634 l 174.7501 571.1468 l 178.8334 568.4801 l 182.9167 570.1467 l 187 576.6467 l 191 568.9801 l 195.0834 568.8134 l 199.1668 572.2301 l 203.2501 571.9801 l 207.3335 576.23 l 211.3335 570.4801 l 215.4168 570.8967 l 219.5001 566.1467 l 223.5835 563.7301 l 227.6668 559.1468 l 231.6668 526.3968 l 235.7502 523.1468 l 239.8335 509.6468 l 243.9168 499.8134 l 248.0002 486.1468 l 252.0002 476.1468 l 256.0835 466.9801 l 260.1668 462.2301 l 264.2502 458.9801 l 268.3335 451.3134 l 272.3335 456.3968 l 276.4168 457.4801 l 280.5002 459.3135 l 284.5835 461.4801 l 288.6669 469.7301 l 292.6669 483.1468 l 296.7502 483.8968 l 298.9169 486.3968 l S Q BT /F13 1 Tf 10 0 0 10 138.3333 615.6467 Tm (FRMs as a fraction of all mortgages)Tj ET Q q BT /F10 1 Tf 11.95517 0 0 11.95517 72 78 Tm [(Sour)51(c)50(es:)-421(Haver)-299(analytics,)-301(National)-290(Delinquency)-290(Survey)-300($Mortgage)-299(Bankers)-279(Asso)52(ciation$,)-301(and)]TJ 0 -1.2045 TD [(Statistic)50(al)-351(A)20(bstr)52(act)-351(of)-342(the)-351(Unite)51(d)-351(States.)]TJ /F8 1 Tf 19.54301 0.3212 TD (3)Tj ET Q endstream endobj 6 0 obj << /Length 8537 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 72 683.16 Tm 0 g [(household's)-301(income)-291(and)-291(asset)-291(p)-31(osition)-281(at)-281(the)-292(time)-291(they)-291(tak)30(e)-291(out)-281(the)-291(mortgage)-281(and)-281(price)-291(these)]TJ 0 -1.21454 TD [(con)31(tracts)-343(under)-331(the)-331(assumption)-343(of)-321(comp)-30(etitiv)30(e)-341(mark)30(ets.)]TJ 1.46548 -1.2045 TD [(Since)-300(high)-291(early)-301(pa)30(ymen)30(ts)-312(are)-291(prohibitiv)30(ely)-311(costly)-301(for)-282(asset)-301(and)-291(income)-291(p)-30(o)-30(or)-281(agen)31(ts,)-312(there)]TJ -1.46548 -1.2045 TD [(is)-292(a)-290(natural)-292(role)-291(to)-281(pla)30(y)-301(in)-291(our)-292(econom)31(y)-301(for)-291(mortgage)-281(inno)30(v)51(ation)-292(in)-291(the)-301(form)-281(of)-292(con)31(tracts)-302(that)]TJ 0 -1.21454 TD [(do)-341(not)-332(fron)30(t-load)-332(pa)31(ymen)30(ts.)-503(W)81(e)-341(\fnd)-341(that)-342(in)-342(an)-341(econom)31(y)-351(calibrated)-351(to)-331(matc)30(h)-352(k)31(ey)-351(asp)-31(ects)-351(of)]TJ 0 -1.2045 TD [(the)-291(US)-281(housing)-291(mark)30(et)-302(prior)-281(to)-282(2003)-270(where)-300(FRMs)-282(are)-291(the)-281(predominan)30(t)-302(form)-281(of)-281(con)30(tracts,)-302(the)]TJ T* [(in)30(tro)-31(duction)-331(of)-321(a)-321(mortgage)-321(that)-332(appro)30(ximates)-342(the)-321(features)-342(of)-321(in)30(terest-only)-342(mortgages)-322((IOM))]TJ 0 -1.21454 TD [(has)-362(drastic)-352(e\013ects)-371(on)-351(b)-30(oth)-352(home-o)31(wnership)-372(rates)-362(and)-351(default)-362(rates.)-522(In)-352(particular,)-362(asset)-362(and)]TJ 0 -1.2045 TD [(income)-411(p)-30(o)-30(or)-391(households)-422($those)-413(who)-411(could)-401(b)-30(e)-411(in)30(terpreted)-422(as)-402(subprime$)-422(endogenously)-421(select)]TJ 0 -1.21453 TD [(in)30(to)-362(IOMs.)-563(Again,)-370(since)-382(w)31(e)-371(allo)30(w)-371(con)31(tracts)-373(to)-361(dep)-30(end)-371(on)-361(the)-372(household's)-381(income)-371(and)-371(asset)]TJ 0 -1.2045 TD [(p)-30(osition)-252(at)-251(the)-251(time)-261(they)-261(tak)30(e)-261(out)-251(the)-251(mortgage,)-271(the)-251(selection)-270(issue)-262(means)-261(that)-251(these)-271(con)30(tracts)]TJ T* [(b)-30(ear)-402(higher)-401(in)30(terest)-422(rates)-403(than)-401(FRM)-402(con)30(tracts.)-663(Since)-421(IOM)-402(mortgages)-402(bac)31(k-load)-402(pa)31(ymen)30(ts)]TJ 0 -1.21454 TD [(this)-422(implies)-442(that)-412(the)-422(future)-422(IOM)-422(pa)30(ymen)30(ts)-442(o)30(v)30(er)-431(a)-422(shorter)-422(horizon)-422(will)-421(b)-30(e)-421(higher)-422(than)-422(the)]TJ 0 -1.2045 TD [(pa)30(ymen)31(ts)-372(of)-332(\\longer")-340(FRM)-342(mortgages)-352(thereb)30(y)-361(making)-341(it)-352(more)-341(lik)30(ely)-361(they)-351(will)-351(b)-30(e)-351(sub)-51(ject)-361(to)]TJ 0 -1.21454 TD [(b)-30(oth)-372(in)30(v)30(olun)31(tary)-402(default)-372($arising)-382(from)-372(an)-381(empt)30(y)-392(budget)-381(set$)-382(and)-382(v)30(olun)31(tary)-382(default)-382($arising)]TJ 0 -1.2045 TD [(from)-322(the)-331(decision)-341(to)-331(w)30(alk)-331(a)31(w)30(a)30(y)-341(from)-322(a)-331(mortgage)-321(on)-321(a)-331(house)-331(with)-331(negativ)30(e)-341(equit)30(y$.)]TJ 1.46548 -1.2045 TD [(These)-310(\fndings)-312(ha)30(v)30(e)-300(a)-291(n)30(um)30(b)-30(er)-311(of)-291(implications)-312(for)-281(ho)30(w)-301(one)-300(should)-302(in)30(terpret)-312(curren)30(t)-302(ev)31(en)31(ts.)]TJ -1.46548 -1.21454 TD [(Mortgage)-392(inno)31(v)50(ation)-392(serv)30(es)-422(an)-391(imp)-30(ortan)29(t)-391(purp)-31(ose)-401(and,)-412(in)-401(a)-392(mo)-30(del)-391(that)-392(abstracts)-403(from)-392(the)]TJ 0 -1.2045 TD [(p)-30(ossibilit)29(y)-301(of)-271(spillo)30(v)30(ers)-312(from)-281(housing)-282(\fnance)-290(to)-281(the)-281(\fnancial)-291(system)-302(at)-281(large,)-291(can)-280(raise)-282(w)31(elfare)]TJ T* [(b)30(y)-452(expanding)-451(the)-451(range)-442(of)-431(c)30(hoices)-461(for)-442(a)-441(n)30(um)30(b)-31(er)-451(of)-442(households,)-492(particularly)-442(agen)31(ts)-453(at)-442(the)]TJ 0 -1.21454 TD [(b)-30(ottom)-282(of)-281(the)-291(asset)-292(and)-291(income)-290(distributions.)-444(The)-300(nature)-281(of)-281(these)-302(inno)31(v)50(ations,)-302(ho)30(w)31(ev)30(er,)-321(do)-30(es)]TJ 0 -1.2045 TD [(mak)30(e)-421(an)-411(increase)-421(in)-422(default)-412(rates)-412(una)30(v)31(oidable)-431(since)-422(agen)31(ts)-422(are)-412(m)30(uc)31(h)-432(slo)30(w)31(er)-422(to)-412(accum)31(ulate)]TJ 0 -1.21454 TD [(home)-331(equit)30(y)81(.)]TJ 1.46548 -1.2045 TD [(W)81(e)-311(pro)30(vide)-321(an)-311(exp)-30(erimen)31(t)-322(to)-301(sho)29(w)-320(that)-302(a)-311(correlated)-311(rise)-312(in)-311(the)-311(probabilit)29(y)-321(of)-301(house)-311(v)50(alue)]TJ -1.46548 -1.2045 TD [(sho)-30(c)30(ks)-352(causes)-351(a)-331(large)-331(increase)-351(in)-341(default)-331(rates)-342(in)-342(an)-331(econom)31(y)-351(with)-341(mortgages)-332(that)-332(bac)31(k-load)]TJ 0 -1.21454 TD [(pa)30(ymen)31(ts.)-704(The)-411(resem)30(blance)-430(with)-412(curren)30(t)-422(ev)31(en)30(ts)-432(is)-412(not)-402(purely)-422(fortuitous,)-423(in)-411(our)-402(view,)-441(and)]TJ 0 -1.2045 TD [(mak)30(es)-251(mo)-30(dels)-231(suc)30(h)-250(as)-232(ours)-231(useful)-241(to)-31(ols)-221(for)-231(designing)-241(safeguards)-231(against)-231(the)-241(collapse)-231(of)-230(\fnancial)]TJ T* [(systems)-353(in)-331(mo)-30(dern)-331(economies.)]TJ 1.46548 -1.21454 TD [(Our)-372(pap)-30(er)-371(is)-382(closely)-381(related)-381(to)-362(sev)30(eral)-391(studies)-392(of)-362(the)-371(recen)31(t)-392(ev)30(olution)-381(of)-362(the)-381(US)-371(housing)]TJ -1.46548 -1.2045 TD [(mark)30(et)-452(and)-441(mortgage)-442(c)31(hoice.)]TJ /F11 1 Tf 7.97011 0 0 7.97011 223.92 268.56 Tm (2)Tj /F8 1 Tf 11.95517 0 0 11.95517 238.2 264.24 Tm [(First)-443(is)-442(the)-452(pap)-30(er)-442(b)30(y)-451(Cham)30(b)-30(ers)-462(et)-442(al.)-783((2007))-431(whic)30(h,)-481(in)-452(a)]TJ -13.90194 -1.21454 TD [(mo)-30(del)-471(without)-483(the)-471(p)-31(ossibilit)29(y)-491(of)-462(default,)-512(argues)-472(that)-472(the)-472(dev)30(elopmen)31(t)-502(of)-462(mortgages)-472(with)]TJ 0 -1.2045 TD [(gradually)-472(increasing)-471(pa)30(ymen)31(ts)-493(has)-472(had)-462(a)-461(p)-31(ositiv)30(e)-481(impact)-472(on)-472(participation)-462(in)-472(the)-472(housing)]TJ T* [(mark)30(et.)-442(Garriga)-291(et)-311(al.)-432((2008))-301(quan)30(tify)-322(the)-311(impact)-311(of)-311(aggregate)-300(house)-311(price)-321(sho)-31(c)31(ks)-332(on)-301(default)]TJ 0 -1.21454 TD [(rates)-332(where)-330(there)-332(is)-332(cross-subsidization)-342(of)-322(mortgages)]TJ /F5 1 Tf 22.77509 0 Td (within)Tj /F8 1 Tf 3.44286 0 Td [(but)-332(not)]TJ /F5 1 Tf 3.5332 0 Td (across)Tj /F8 1 Tf 3.27222 0 Td [(mortgage)-321(t)30(yp)-30(es)]TJ ET q 189.36 0 0 -0.48 71.988 196.428 cm /Im1 Do Q BT /F12 1 Tf 6.97385 0 0 6.97385 85.44 188.64 Tm (2)Tj /F7 1 Tf 9.96264 0 0 9.96264 89.88 184.92 Tm [(There)-493(are)-482(other)-495(pap)-24(ers)-482(whic)24(h)-494(are)-481(a)-494(bit)-507(less)-482(closely)-494(related.)-915(Campb)-24(ell)-506(and)-494(Co)-23(cco)-481((2003))-483(study)-495(the)]TJ -1.7947 -1.19245 TD [(micro)-24(economic)-361(determinan)24(ts)-362(of)-374(mortgage)-349(c)24(hoice)-361(but)-386(do)-373(so)-362(in)-373(a)-373(mo)-24(del)-374(where)-361(all)-373(agen)25(ts)-363(are)-361(home-o)24(wners)-350(b)25(y)]TJ 0 -1.2045 TD [(assumption,)-351(and)-361(fo)-24(cus)-350(their)-350(atten)24(tion)-362(on)-349(the)-362(c)25(hoice)-337(b)-24(et)24(w)24(een)-361(adjustable)-350(rate)-349(mortgages)-326(and)-350(standard)-338(FRMs)]TJ 0 -1.19246 TD [(with)-398(no)-373(option)-386(for)-386(default.)-614(Rios-Rull)-374(and)-386(Sanc)25(hez-Marcos)-350((2008))-374(dev)24(elop)-385(a)-373(mo)-24(del)-385(of)-398(housing)-374(c)25(hoice)-373(where)]TJ 0 -1.2045 TD [(agen)25(ts)-278(can)-289(c)24(ho)-24(ose)-277(to)-301(mo)24(v)24(e)-277(to)-289(bigger)-277(houses)-290(o)24(v)24(er)-277(time,)-301(a)-289(feature)-290(from)-289(whic)24(h)-301(w)24(e)-288(abstract)-279(to)-289(k)24(eep)-288(computations)]TJ T* [(manageable.)-409(A)-265(di\013eren)24(t)-277(strand)-266(of)-265(the)-278(housing)-265(literature)-254($see)-278(e.g.)-409(Gerv)60(ais,)-277(2002,)-265(and)-265(Jesk)24(e)-252(and)-277(Krueger,)-254(2005$)]TJ 0 -1.1925 TD [(studies)-278(the)-277(macro)-25(economic)-240(e\013ects)-277(of)-277(v)61(arious)-254(institutional)-279(features)-266(of)-265(the)-277(mortgage)-253(industry)82(,)-277(again)-265(where)-264(there)]TJ 0 -1.2045 TD [(is)-326(no)-337(p)-24(ossibilit)22(y)-325(of)-337(default.)]TJ /F8 1 Tf 11.95517 0 0 11.95517 305.64 67.44 Tm (4)Tj ET endstream endobj 7 0 obj << /Length 11124 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 72 683.16 Tm 0 g [($e.g.)-703(FRM)-411(or)-412(IOM$.)-413(A)-421(k)30(ey)-431(di\013erence)-431(b)-30(et)30(w)31(een)-431(our)-412(pap)-30(er)-412(and)-421(theirs)-423(is)-422(that)-412(w)31(e)-421(consider)-432(a)]TJ 0 -1.21454 TD [(men)30(u)-341(of)-321(di\013eren)30(t)-331(terms)-343(on)-321(con)31(tracts)]TJ /F5 1 Tf 15.91947 0 Td [(b)-30(oth)]TJ /F8 1 Tf 2.59971 0 Td (within)Tj /F5 1 Tf 3.0514 0 Td (and)Tj /F8 1 Tf 2.11791 0 Td [(across)-332(mortgage)-321(t)30(yp)-30(es.)]TJ /F11 1 Tf 7.97011 0 0 7.97011 471.24 673.08 Tm (3)Tj /F8 1 Tf 11.95517 0 0 11.95517 481.32 668.64 Tm [(This)-341(enables)]TJ -34.23791 -1.2045 TD [(us)-271(to)-252(build)-271(a)-261(mo)-30(del)-270(that)-252(is)-271(consisten)29(t)-281(with)-271(the)-261(heterogeneit)30(y)-281(of)-260(foreclosure)-271(rates)-272(and)-261(mortgage)]TJ T* [(terms)-252(across)-251(w)30(ealth)-251(and)-251(income)-250(categories,)-270(whic)31(h)-261(w)30(e)-251(view)-250(as)-251(basic)-251(ingredien)31(ts)-262(of)-241(a)-241(satisfactory)]TJ 0 -1.21454 TD [(mo)-30(del)-351(of)-351(the)-352(US)-351(housing)-361(mark)30(et.)-512(Along)-351(this)-352(dimension)-372(our)-341(pap)-30(er)-352(is)-361(more)-352(closely)-360(related)-362(to)]TJ 0 -1.2045 TD [(Guler)-351((2008))-332(where)-360(in)30(termediaries)-362(o\013er)-351(a)-342(men)31(u)-361(of)-342(FRMs)-342(at)-341(di\013eren)30(t)-362(p)-30(ossible)-362(do)31(wnpa)30(ymen)31(t)]TJ T* [(rates.)-673(He)-411(then)-412(studies)-422(the)-402(impact)-411(of)-402(an)-401(inno)30(v)50(ation)-411(to)-402(the)-412(screening)-421(tec)31(hnology)-411(on)-402(default)]TJ 0 -1.21454 TD (rates.)Tj /F9 1 Tf 17.21544 0 0 17.21544 72 542.04 Tm [(2)-1122(The)-369(en)28(vironmen)27(t)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 515.76 Tm [(W)81(e)-351(study)-363(an)-351(economic)-360(en)31(vironmen)30(t)-372(where)-360(time)-352(is)-352(discrete)-371(and)-351(in\fnite.)-512(Eac)30(h)-352(p)-30(erio)-30(d)-351(a)-351(mass)]TJ 0 -1.2045 TD [(one)-270(of)-261(agen)30(ts)-271(is)-272(b)-30(orn.)-412(Ov)30(er)-271(time,)-281(agen)31(ts)-282(mo)30(v)31(e)-271(sto)-31(c)31(hastically)-292(through)-261(four)-262(stages)-271(of)-261(life:)-411(y)30(oung)]TJ T* [((Y),)-402(middle-aged)-411((M),)-403(old)-401((O))-402(and)-402(dead.)-662(All)-411(agen)31(ts)-402(are)-402(b)-30(orn)-402(y)30(oung.)-672(A)31(t)-402(the)-402(b)-30(eginning)-411(of)]TJ 0 -1.21454 TD [(eac)31(h)-381(p)-31(erio)-30(d,)-371(y)30(oung)-381(agen)31(ts)-372(b)-30(ecome)-381(middle-aged)-370(with)-382(probabilit)30(y)]TJ /F14 1 Tf 28.00462 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 412.92 476.76 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 422.4 472.44 Tm [(,)-381(middle-age)-371(households)]TJ -29.3095 -1.2045 TD [(b)-30(ecome)-400(old)-382(with)-401(probabilit)29(y)]TJ /F14 1 Tf 12.61714 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 228.96 462.36 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 236.04 458.04 Tm [(,)-402(while)-400(old)-392(agen)31(ts)-392(die)-401(with)-392(probabilit)30(y)]TJ /F14 1 Tf 17.06375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 446.16 462.36 Tm (D)Tj /F14 1 Tf 11.95517 0 0 11.95517 453.84 458.04 Tm (:)Tj /F8 1 Tf 0.65244 0 Td [(W)81(e)-402(assume)-401(that)]TJ -32.59176 -1.21454 TD [(p)-30(opulation)-362(size)-361(is)-371(at)-352(its)-362(unique)-371(in)30(v)50(arian)30(t)-362(v)51(alue,)-371(and)-361(that)-363(the)-361(fraction)-352(of)-351(agen)31(ts)-372(of)-352(eac)32(h)-372(t)30(yp)-30(e)]TJ 0 -1.2045 TD [(ob)-30(eys)-341(a)-321(la)30(w)-331(of)-321(large)-321(n)30(um)30(b)-30(ers.)]TJ 1.46548 -1.2045 TD [(Eac)30(h)-391(p)-30(erio)-30(d,)-382(as)-382(long)-371(as)-381(they)-382(are)-381(y)30(oung)-381(or)-372(middle-aged,)-390(agen)30(ts)-392(earn)-371(p)-30(ositiv)29(e)-391(income)-381(de-)]TJ -1.46548 -1.21454 TD [(nominated)-291(in)-281(terms)-292(of)-271(the)-291(unique)-291(consumption)-301(go)-30(o)-30(d.)-412(All)-280(agen)30(ts)-292(b)-30(egin)-280(life)-281(at)-281(the)-281(lo)30(w)30(er)-291(b)-30(ound)]TJ 0 -1.2045 TD [(of)-301(income)-310(supp)-31(ort)]TJ /F16 1 Tf 7.97981 0 Td (f)Tj /F14 1 Tf 0.50187 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 179.16 384 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 185.4 385.8 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 196.44 384 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 205.8 385.8 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 216.84 384 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 224.88 385.8 Tm (g)Tj /F8 1 Tf 0.79296 0 Td [(where)-320(0)]TJ /F14 1 Tf 3.57335 0 Td 0.281 Tc (Tj /F8 1 Tf 1.00375 0 Td [(whic)31(h)-432(w)31(e)-422(assume)-431(ergo)-30(dic.)-693(Agen)31(ts)-432(b)-30(egin)-411(life)-412(at)-411(a)-412(v)51(alue)]TJ /F14 1 Tf -15.4979 -1.21454 TD (y)Tj /F16 1 Tf 0.79296 0 Td 0.282 Tc (2f)Tj /F14 1 Tf 1.4454 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 104.52 355.08 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 110.76 356.88 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 121.8 355.08 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 131.16 356.88 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 142.2 355.08 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 150.12 356.88 Tm (g)Tj /F8 1 Tf 0.83311 0 Td [(dra)30(wn)-331(from)-332(the)-331(unique)-341(in)30(v)50(arian)30(t)-331(distribution)-343(asso)-31(ciated)-331(with)]TJ /F14 1 Tf 26.47892 0 Td <19>Tj /F8 1 Tf 0.59221 0 Td [(.)-442(When)-330(old,)]TJ -34.43866 -1.2045 TD [(agen)31(ts)-332(earn)-331(a)-321(\fxed,)-341(certain)-332(amoun)31(t)-332(of)]TJ /F14 1 Tf 16.59199 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 276.6 346.8 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 287.64 342.48 Tm [(of)-321(income.)]TJ -16.57191 -1.21454 TD [(Un)30(til)-432(they)-421(b)-30(ecome)-431(old,)-441(agen)31(ts)-433(can)-421(sa)30(v)30(e)-431(in)-422(one-p)-30(erio)-30(d)-421(b)-30(onds)-422(that)-423(earn)-421(rate)-422(1)-281(+)]TJ /F14 1 Tf 35.24166 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 516.12 326.16 Tm (t)Tj /F16 1 Tf 11.95517 0 0 11.95517 524.88 327.96 Tm <15>Tj /F8 1 Tf 1.21454 0 Td (0)Tj -39.09606 -1.2045 TD [(at)-362(date)]TJ /F14 1 Tf 3.44286 0 Td (t)Tj /F8 1 Tf 0.7227 0 Td [(with)-361(certain)30(t)29(y)81(.)-562(When)-371(old,)-371(the)-372(agen)31(ts)-372(can)-361(buy)-371(ann)30(uities)-382(that)-362(pa)30(y)-371(rate)]TJ /F11 1 Tf 7.97011 0 0 7.97011 489.48 318.24 Tm (1+)Tj /F15 1 Tf 1.35506 0 Td (r)Tj /F17 1 Tf 5.97758 0 0 5.97758 504.12 317.28 Tm (t)Tj ET q 21.84 0 0 -0.48 487.548 316.788 cm /Im1 Do Q BT /F11 1 Tf 7.97011 0 0 7.97011 487.56 309.48 Tm (1)Tj /F18 1 Tf 0.52697 0 Td <00>Tj /F15 1 Tf 0.82809 0 Td <1A>Tj /F17 1 Tf 5.97758 0 0 5.97758 502.68 311.76 Tm (D)Tj /F8 1 Tf 11.95517 0 0 11.95517 514.92 313.56 Tm [(in)-361(the)]TJ -37.04841 -1.2045 TD [(follo)30(wing)-330(p)-31(erio)-30(d)-321(pro)30(vided)-341(they)-341(are)-321(aliv)30(e,)-341(and)-331(pa)30(y)-331(nothing)-331(otherwise.)]TJ 1.46548 -1.21454 TD [(Agen)31(ts)-342(v)50(alue)-331(b)-30(oth)-331(consumption)-342(and)-331(housing)-331(services.)-472(They)-341(order)-331(non-negativ)30(e)-331(pro)-30(cesses)]TJ /F16 1 Tf -1.46548 -1.2045 TD (f)Tj /F14 1 Tf 0.50187 0 Td (c)Tj /F15 1 Tf 7.97011 0 0 7.97011 83.04 268.44 Tm (t)Tj /F14 1 Tf 11.95517 0 0 11.95517 86.52 270.24 Tm 0.171 Tc (;s)Tj /F15 1 Tf 7.97011 0 0 7.97011 97.32 268.44 Tm 0 Tc (t)Tj /F16 1 Tf 11.95517 0 0 11.95517 100.92 270.24 Tm (g)Tj /F11 1 Tf 7.97011 0 0 7.97011 106.92 275.16 Tm (+)Tj /F18 1 Tf 0.82809 0 Td (1)Tj /F15 1 Tf -0.82809 -0.99371 TD (t)Tj /F11 1 Tf 0.37641 0 Td (=0)Tj /F8 1 Tf 11.95517 0 0 11.95517 126.36 270.24 Tm [(according)-330(to:)]TJ /F14 1 Tf 11.62342 -2.0878 TD (E)Tj /F11 1 Tf 7.97011 0 0 7.97011 273.96 243.48 Tm (0)Tj 0.97866 2.10787 TD (+)Tj /F18 1 Tf 0.82809 0 Td (1)Tj /F19 1 Tf 11.95517 0 0 11.95517 280.68 256.68 Tm (X)Tj /F15 1 Tf 7.97011 0 0 7.97011 282.36 231.48 Tm (t)Tj /F11 1 Tf 0.37641 0 Td (=0)Tj /F14 1 Tf 11.95517 0 0 11.95517 299.88 245.28 Tm (\f)Tj /F15 1 Tf 7.97011 0 0 7.97011 307.2 250.44 Tm (t)Tj /F14 1 Tf 11.95517 0 0 11.95517 310.8 245.28 Tm (U)Tj /F8 1 Tf 0.76285 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (c)Tj /F15 1 Tf 7.97011 0 0 7.97011 329.52 243.48 Tm (t)Tj /F14 1 Tf 11.95517 0 0 11.95517 333.12 245.28 Tm 0.171 Tc (;s)Tj /F15 1 Tf 7.97011 0 0 7.97011 343.92 243.48 Tm 0 Tc (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 347.4 245.28 Tm ($)Tj -23.03606 -2.83057 TD (where)Tj /F14 1 Tf 2.82054 0 Td (U)Tj /F8 1 Tf 1.07401 0 Td [(satis\fes)-342(standard)-313(assumptions.)-453(They)-330(can)-311(ren)30(t)-321(quan)30(tit)29(y)]TJ /F11 1 Tf 7.97011 0 0 7.97011 404.88 218.28 Tm <16>Tj /F15 1 Tf -0.01506 -0.25596 TD (h)Tj ET q 4.92 0 0 -0.48 404.748 214.668 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 404.88 207.36 Tm <11>Tj /F14 1 Tf 11.95517 0 0 11.95517 414.24 211.44 Tm (>)Tj /F8 1 Tf 1.03386 0 Td [(0)-311(of)-311(housing)-322(services)-341(at)]TJ -29.66081 -1.2045 TD (price)Tj /F14 1 Tf 2.43911 0 Td (R)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.04 195.24 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 118.08 197.04 Tm [(at)-372(date)]TJ /F14 1 Tf 3.46294 0 Td (t)Tj /F8 1 Tf 0.35131 0 Td [(.)-582(W)80(e)-371(assume)-391(that)]TJ /F14 1 Tf 8.18056 0 Td <11>Tj /F16 1 Tf 0.87326 0 Td <15>Tj /F8 1 Tf 1.13424 0 Td [(1.)-572(In)-372(the)-381(p)-30(erio)-30(d)-372(when)-380(agen)30(ts)-382(mo)30(v)30(e)-391(from)-371(y)30(outh)-382(to)]TJ -17.85671 -1.2045 TD [(middle-age,)-351(agen)31(ts)-342(can)-351(c)31(ho)-30(ose)-341(instead)-352(to)-342(purc)30(hase)-351(quan)31(tit)29(y)]TJ 25.81645 0.26097 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj /F8 1 Tf 0.90337 0 Td [(of)-331(housing)-342(capital)-351(for)-331(price)]TJ /F14 1 Tf 11.87436 0 Td (q)Tj /F15 1 Tf 7.97011 0 0 7.97011 538.44 180.84 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 541.92 182.64 Tm (,)Tj -39.30685 -1.21454 TD [(an)-341(asset)-342(whic)31(h)-352(w)31(e)-351(refer)-342(to)-331(as)-342(a)-331(house)-351(that)-332(deliv)31(ers)-362(quan)30(tit)29(y)]TJ 25.91682 0.26097 TD <16>Tj /F14 1 Tf 0 -0.26097 TD <6812>Tj /F8 1 Tf 1.37514 0 Td [(of)-341(housing)-342(ev)31(ery)-351(p)-31(erio)-30(d)-341(with)]TJ /F14 1 Tf -27.29196 -1.2045 TD <12>Tj /F16 1 Tf 0.76285 0 Td <15>Tj /F8 1 Tf 1.05394 0 Td (1.)Tj ET q 189.36 0 0 -0.48 71.988 144.348 cm /Im1 Do Q BT /F12 1 Tf 6.97385 0 0 6.97385 85.44 136.56 Tm (3)Tj /F7 1 Tf 9.96264 0 0 9.96264 89.88 132.96 Tm [(E\013ectiv)25(ely)84(,)-433(Garriga)-386(et)-410(al.)-675((2008))-398(apply)-409(the)-422(equilibrium)-410(concept)-409(in)-410(A)25(threy)23(a)-397((2002))-398(while)-421(w)24(e)-397(apply)-410(the)]TJ -1.7947 -1.2045 TD [(equilibrium)-338(concept)-325(in)-337(Chatterjee)-325(et)-338(al.)-445((2007).)]TJ /F8 1 Tf 11.95517 0 0 11.95517 305.64 67.44 Tm (5)Tj ET endstream endobj 8 0 obj << /Length 14243 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 89.52 683.16 Tm 0 g [(Ev)30(ery)-392(p)-30(erio)-30(d,)-371(a)-361(fraction)]TJ /F14 1 Tf 10.73009 0 Td 0.341 Tc <153E>Tj /F8 1 Tf 2.01754 0 Td 0 Tc [(0)-361(of)-362(house-o)31(wners)-392(see)-371(the)-371(quan)30(tit)29(y)-381(of)-362(capital)-361(they)-381(o)30(wn)-371(fall)]TJ -14.2131 -1.21454 TD [(p)-30(ermanen)30(tly)-422(to)]TJ /F11 1 Tf 7.97011 0 0 7.97011 157.32 675.48 Tm <16>Tj /F15 1 Tf -0.01506 -0.25596 TD (h)Tj ET q 4.92 0 0 -0.48 157.188 671.868 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 157.32 664.56 Tm <11>Tj /F14 1 Tf 11.95517 0 0 11.95517 168 668.64 Tm (>)Tj /F8 1 Tf 1.16435 0 Td [(0.)-652(Lik)30(e)-412(apartmen)30(ts,)-432(these)-412(houses)-412(generate)-401(quan)31(tit)29(y)]TJ /F11 1 Tf 7.97011 0 0 7.97011 456.6 675.48 Tm <16>Tj /F15 1 Tf 0 -0.25596 TD (h)Tj ET q 4.92 0 0 -0.48 456.588 671.868 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 456.72 664.56 Tm <11>Tj /F14 1 Tf 11.95517 0 0 11.95517 467.4 668.64 Tm (>)Tj /F8 1 Tf 1.16435 0 Td [(0)-401(of)-392(housing)]TJ -34.23791 -1.2045 TD [(services.)-572(W)80(e)-371(will)-371(in)30(terpret)-372(this)-372(sho)-31(c)31(k)-381(as)-362(an)-361(idiosyncratic)-392(house)-371(price)-371(sho)-31(c)31(k.)-562(Assuming)-382(that)]TJ T* [(follo)30(wing)-320(this)-312(sho)-31(c)31(k)-332(the)-321(house)-321(size)-321(b)-30(ecomes)-330(that)-312(of)-311(ren)30(tal)-322(units)-322(and)-311(yields)-331(the)-321(same)-321(quan)30(tit)29(y)]TJ 0 -1.21454 TD [(of)-311(services)-351(as)-312(ren)30(tal)-331(units)-322(simpli\fes)-342(the)-322(analysis)-341(b)30(y)-321(k)30(eeping)-341(the)-321(size)-331(of)-311(the)-321(housing)-332(c)31(hoice)-330(set)]TJ 0 -1.2045 TD [(small,)-422(namely)]TJ /F16 1 Tf 6.39389 0 Td (f)Tj /F11 1 Tf 7.97011 0 0 7.97011 155.76 617.76 Tm <16>Tj /F15 1 Tf -0.01506 -0.27101 TD (h)Tj ET q 4.92 0 0 -0.48 155.628 614.148 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 155.76 606.84 Tm <11>Tj /F14 1 Tf 11.95517 0 0 11.95517 161.64 610.92 Tm (;)Tj /F8 1 Tf 0.45169 0.26097 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj /F16 1 Tf 0.5621 0 Td (g)Tj /F8 1 Tf 0.50187 0 Td [(.)-642(Since)-411(depreciated)-411(houses)-412(pro)30(vide)-411(no)-402(adv)51(an)30(tage)-401(o)30(v)30(er)-401(ren)30(tal)-402(units,)-432(no)]TJ -9.00364 -1.2045 TD [(agen)31(t)-272(who)-270(b)-30(ecomes)-280(middle-aged)-281(w)31(ould)-281(strictly)-283(prefer)-271(to)-261(purc)30(hase)-291(a)-261(depreciated)-290(house,)-291(and)-271(all)]TJ 0 -1.21454 TD [(agen)31(ts)-322(who)-311(exp)-30(erience)-340(a)-301(house)-321(sho)-30(c)30(k)-331(are)-311(at)-301(least)-322(as)-311(w)30(ell)-321<6F0B>-311(selling)-321(their)-322(house)-321(and)-311(b)-30(ecoming)]TJ 0 -1.2045 TD [(ren)30(ters)-342(as)-332(they)-331(w)31(ould)-342(b)-30(e)-330(if)-322(they)-331(k)30(eep)-350(their)-332(house.)]TJ /F11 1 Tf 7.97011 0 0 7.97011 325.08 571.92 Tm (4)Tj /F8 1 Tf 11.95517 0 0 11.95517 89.52 553.08 Tm [(Owners)-291(of)-271(a)-281(house)-281(of)-271(size)]TJ /F14 1 Tf 10.87061 0 Td (h)Tj /F16 1 Tf 0.84315 0 Td 0.282 Tc (2f)Tj /F11 1 Tf 7.97011 0 0 7.97011 248.16 559.92 Tm 0 Tc <16>Tj /F15 1 Tf -0.01506 -0.25596 TD (h)Tj ET q 4.92 0 0 -0.48 248.028 556.308 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 248.16 549 Tm <11>Tj /F14 1 Tf 11.95517 0 0 11.95517 254.16 553.08 Tm (;)Tj /F8 1 Tf 0.44165 0.27101 TD <16>Tj /F14 1 Tf 0 -0.27101 TD (h)Tj /F16 1 Tf 0.5621 0 Td (g)Tj /F8 1 Tf 0.77289 0 Td [(b)-30(ear)-271(main)30(tenance)-300(costs)]TJ /F14 1 Tf 10.13787 0 Td 0.04 Tc <0E68>Tj /F8 1 Tf 1.31491 0 Td 0 Tc [(in)-281(all)-281(p)-30(erio)-30(ds)-282(where)]TJ /F14 1 Tf 8.57202 0 Td 0.311 Tc <0E3E>Tj /F8 1 Tf 1.78667 0 Td 0 Tc (0.)Tj -38.82505 -1.2045 TD [(Main)30(tenance)-320(costs)-302(are)-301(denominated)-311(in)-301(terms)-312(of)-291(the)-301(consumption)-312(go)-30(o)-30(d.)-421(W)80(e)-300(assume)-312(that)-302(once)]TJ T* [(agen)31(ts)-372(sell)-372(or)-361(foreclose)-371(their)-372(house,)-382(they)-371(are)-361(constrained)-372(to)-361(relying)-372(on)-361(the)-371(ren)30(tal)-372(mark)30(et)-372(for)]TJ 0 -1.21454 TD [(the)-371(remainder)-382(of)-361(their)-372(life.)-572(W)81(e)-371(also)-372(assume)-382(that)-362(in)-371(the)-372(p)-30(erio)-30(d)-371(in)-372(whic)31(h)-381(agen)31(ts)-383(b)-30(ecome)-370(old,)]TJ 0 -1.2045 TD [(they)-331(m)30(ust)-342(sell)-342(their)-331(house)-332(immediately)-350(and)-321(b)-31(ecome)-340(ren)30(ters)-342(for)-321(the)-332(remainder)-341(of)-321(their)-332(life.)]TJ 1.46548 -1.21454 TD [(A)-351(\fnancial)-351(in)30(termediary)-361(holds)-352(household)-361(sa)30(vings.)-512(The)-351(in)30(termediary)-362(can)-350(store)-352(sa)29(vings)-361(at)]TJ -1.46548 -1.2045 TD [(exogenously)-421(giv)31(en)-411(return)-403(1)-271(+)]TJ /F14 1 Tf 13.0086 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 232.8 464.64 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 241.08 466.44 Tm [(at)-392(date)]TJ /F14 1 Tf 3.51312 0 Td (t)Tj /F8 1 Tf 0.35131 0 Td [(.)-652(It)-403(can)-401(also)-401(transform)-403(eac)31(h)-412(unit)-402(of)-391(consumption)]TJ -18.00727 -1.2045 TD [(go)-30(o)-30(d)-281(sa)30(v)30(ed)-321(in)30(to)-291(quan)30(tit)30(y)]TJ /F14 1 Tf 10.82042 0 Td 0.271 Tc (A>)Tj /F8 1 Tf 2.04765 0 Td 0 Tc [(0)-291(of)-291(housing)-301(capital,)-311(and)-291(eac)31(h)-311(unit)-302(of)-291(housing)-301(capital)-301(bac)30(k)-301(in)30(to)]TJ -12.86807 -1.21454 TD [(quan)30(tit)30(y)]TJ /F11 1 Tf 7.97011 0 0 7.97011 120.6 442.32 Tm (1)Tj ET q 6.36 0 0 -0.48 119.508 440.748 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 119.52 433.44 Tm (A)Tj /F8 1 Tf 11.95517 0 0 11.95517 130.56 437.52 Tm [(of)-291(the)-291(consumption)-302(go)-29(o)-30(d.)-412(Housing)-301(capital)-291(can)-290(b)-31(e)-290(ren)30(ted)-301(at)-292(rate)]TJ /F14 1 Tf 27.32207 0 Td (R)Tj /F15 1 Tf 7.97011 0 0 7.97011 466.08 435.72 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 473.04 437.52 Tm [(at)-291(date)]TJ /F14 1 Tf 3.30234 0 Td (t)Tj /F8 1 Tf 0.35131 0 Td [(.)-432(The)]TJ -37.19897 -1.2045 TD [(in)30(termediary)-382(incurs)-362(main)31(tenance)-381(cost)]TJ /F14 1 Tf 16.48157 0 Td <0E>Tj /F8 1 Tf 0.83311 0 Td [(on)-351(eac)31(h)-372(unit)-361(of)-352(housing)-361(capital)-361(ren)30(ted,)-382(measured)-371(in)]TJ -17.31469 -1.2045 TD [(terms)-342(of)-321(the)-332(consumption)-341(go)-30(o)-30(d.)-422(A)31(t)-332(date)]TJ /F14 1 Tf 17.666 0 Td (t)Tj /F8 1 Tf 0.35131 0 Td [(,)-331(eac)31(h)-342(unit)-331(of)-321(consumption)-342(go)-30(o)-30(d)-311(ren)30(ted)-341(th)29(us)-341(earns)]TJ -18.01731 -1.21454 TD [(net)-422(return)]TJ /F14 1 Tf 4.84811 0 Td (A)Tj /F8 1 Tf 0.73274 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (R)Tj /F15 1 Tf 7.97011 0 0 7.97011 152.16 392.4 Tm (t)Tj /F16 1 Tf 11.95517 0 0 11.95517 159.12 394.2 Tm <00>Tj /F14 1 Tf 1.06397 0 Td <0E>Tj /F8 1 Tf 0.47176 0 Td [($.)-693(The)-431(in)30(termediary)-432(can)-411(also)-421(sell)-422(housing)-422(capital)-411(as)-422(houses)-432(to)-402(eligible)]TJ -8.82296 -1.2045 TD (households.)Tj 1.46548 -1.21454 TD [(W)81(e)-331(assume)-342(that)-322(households)-341(that)-322(can)-331(purc)30(hase)-341(a)-321(house)-341(at)-322(a)-321(giv)30(en)-330(date)-332(are)-321(constrained)-341(to)]TJ -1.46548 -1.2045 TD [(\fnance)-300(this)-292(purc)30(hase)-301(with)-301(one)-291(of)-281(t)30(w)30(o)-291(p)-30(ossible)-301(t)29(yp)-30(es)-301(of)-291(mortgage)-281(con)31(tracts.)-433(The)-300(\frst)-293(con)31(tract)]TJ T* [($whic)30(h)-491(w)30(e)-491(design)-492(to)-472(mimic)-492(the)-492(basic)-481(features)-493(of)-471(standard)-483(\fxed-rate)-492(mortgage,)-512(or)-482(FRM$)]TJ 0 -1.21454 TD [(requires)-312(a)-280(do)30(wnpa)30(ymen)31(t)-312(of)-291(size)-301($1)]TJ /F16 1 Tf 14.54434 0 Td <00>Tj /F14 1 Tf 0.91341 0 Td <0B>Tj /F8 1 Tf 0.63236 0 Td ($)Tj 0.39146 0.27101 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD (hq)Tj /F8 1 Tf 1.32495 0 Td (where)Tj /F14 1 Tf 2.79042 0 Td <0B>Tj /F16 1 Tf 0.90337 0 Td (2)Tj /F8 1 Tf 0.94353 0 Td ($0)Tj /F14 1 Tf 0.87326 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td [(1$)-281(and)-291(stipulates)-303(a)-291(yield)]TJ /F14 1 Tf 10.50926 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 487.2 326.28 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 509.52 321.96 Tm 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 520.2 320.16 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 525 321.96 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 536.04 320.16 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 540.72 321.96 Tm ($)Tj -39.20647 -1.2045 TD [(that)-483(dep)-29(ends)-512(on)-482(the)-492(household)-502(w)31(ealth)-502(and)-482(income)-501(c)31(haracteristics)-513($)]TJ /F14 1 Tf 30.1125 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 438.12 305.76 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 442.8 307.56 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 453.84 305.76 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 458.52 307.56 Tm [($)-482(at)-492(the)-492(time)-492(of)]TJ -32.33079 -1.2045 TD [(origination)-251(of)-241(the)-261(loan.)-411(Giv)30(en)-251(the)-261(yield)]TJ /F14 1 Tf 16.66225 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 276.84 297.48 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 299.28 293.16 Tm 0 Tc ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 309.96 291.36 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 314.64 293.16 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 325.68 291.36 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 330.36 293.16 Tm [($)-251(the)-261(constan)30(t)-262(pa)30(ymen)31(ts)]TJ /F14 1 Tf 10.42896 0 Td (m)Tj /F15 1 Tf 7.97011 0 0 7.97011 465.24 297.48 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 487.68 293.16 Tm 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 498.36 291.36 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 503.16 293.16 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 514.2 291.36 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 518.76 293.16 Tm [($)-251(and)]TJ -37.36961 -1.21454 TD [(principal)-401(balance)-391(sc)30(hedule)]TJ /F16 1 Tf 11.69369 0 Td (f)Tj /F14 1 Tf 0.50187 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 222.72 282.96 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.91843 TD 0 Tc <1C>Tj /F8 1 Tf 11.95517 0 0 11.95517 245.28 278.64 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 255.96 276.84 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 260.64 278.64 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 271.68 276.84 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 276.36 278.64 Tm ($)Tj /F16 1 Tf 0.38142 0 Td (g)Tj /F15 1 Tf 7.97011 0 0 7.97011 286.92 282.96 Tm (T)Tj 0 -0.91843 TD <1C>Tj /F11 1 Tf 0.58719 0 Td (=0)Tj /F8 1 Tf 11.95517 0 0 11.95517 307.56 278.64 Tm [(can)-391(b)-30(e)-391(computed)-401(using)-392(standard)-393(calculations,)]TJ -19.70361 -1.2045 TD (where)Tj /F14 1 Tf 2.83057 0 Td (T)Tj /F8 1 Tf 1.03386 0 Td [(is)-332(the)-331(maturit)29(y)-341(of)-321(the)-332(loan.)]TJ -2.39896 -1.21454 TD [(Sp)-30(eci\fcally)81(,)-351(suppressing)-352(the)-332(initial)-321(c)30(haracteristics)-352(for)-322(notational)-321(simplicit)29(y)81(,)]TJ /F14 1 Tf 10.32859 -2.75027 TD (m)Tj /F15 1 Tf 7.97011 0 0 7.97011 223.2 221.76 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 249 216.84 Tm 0 Tc (=)Tj /F14 1 Tf 3.7741 0.67251 TD (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 299.76 229.2 Tm 0.15 Tc [(FR)150(M)]TJ ET q 91.08 0 0 -0.48 262.548 219.948 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 262.56 208.56 Tm 0 Tc (1)Tj /F16 1 Tf 0.71266 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td [($1)-211(+)]TJ /F14 1 Tf 2.06772 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 313.44 212.04 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 335.88 208.56 Tm 0 Tc ($)Tj /F18 1 Tf 7.97011 0 0 7.97011 340.44 212.04 Tm <00>Tj /F15 1 Tf 0.82809 0 Td (T)Tj /F8 1 Tf 11.95517 0 0 11.95517 354.84 216.84 Tm ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <0B>Tj /F8 1 Tf 0.63236 0 Td ($)Tj 0.39146 0.26097 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (hq)Tj /F8 1 Tf -26.75997 -2.76031 TD [(and,)-331(for)-322(all)]TJ /F14 1 Tf 5.02879 0 Td <1C>Tj /F16 1 Tf 0.81304 0 Td 0.292 Tc (2f)Tj /F8 1 Tf 1.45544 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc (;T)Tj /F16 1 Tf 1.3651 0 Td 0 Tc <00>Tj /F8 1 Tf 0.99371 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td (g)Tj /F8 1 Tf 0.50187 0 Td (,)Tj /F14 1 Tf 1.18443 -2.19821 TD (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 224.28 162.6 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.99371 TD 0 Tc <1C>Tj /F11 1 Tf 0.58719 0 Td (+1)Tj /F8 1 Tf 11.95517 0 0 11.95517 250.08 157.56 Tm (=)Tj /F14 1 Tf 1.0439 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 267.48 162.6 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.99371 TD 0 Tc <1C>Tj /F8 1 Tf 11.95517 0 0 11.95517 289.92 157.56 Tm [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 320.4 162.6 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 342.84 157.56 Tm 0 Tc ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (m)Tj /F15 1 Tf 7.97011 0 0 7.97011 372.12 162.6 Tm 0.15 Tc [(FR)150(M)]TJ /F14 1 Tf 11.95517 0 0 11.95517 394.68 157.56 Tm 0 Tc (;)Tj /F8 1 Tf -26.99084 -2.18817 TD (where)Tj /F14 1 Tf 2.83057 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.76 135.72 Tm 0.15 Tc [(FR)150(M)]TJ /F11 1 Tf 0 -0.91843 TD 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 136.56 131.4 Tm 0.281 Tc [(=$)281(1)]TJ /F16 1 Tf 2.12795 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <0B>Tj /F8 1 Tf 0.63236 0 Td ($)Tj 0.39146 0.26097 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (hq)Tj /F8 1 Tf 1.35506 0 Td [(so)-332(that)]TJ /F14 1 Tf 3.32241 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 246.96 135.72 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.91843 TD 0 Tc (T)Tj /F8 1 Tf 11.95517 0 0 11.95517 272.76 131.4 Tm 0.281 Tc (=0)Tj /F14 1 Tf 1.53574 0 Td 0 Tc (:)Tj ET q 189.36 0 0 -0.48 71.988 120.708 cm /Im1 Do Q BT /F12 1 Tf 6.97385 0 0 6.97385 85.44 112.92 Tm (4)Tj /F7 1 Tf 9.96264 0 0 9.96264 89.88 109.32 Tm [(Arbitrage)-290(implies)-289(that)-302(the)-302(presen)24(t)-289(v)60(alue)-289(of)-301(ren)24(ting)-290(housing)-289(services)-278(eac)25(h)-289(p)-24(erio)-24(d)-290(is)-289(the)-302(same)-289(as)-289(purc)24(hasing)]TJ -1.7947 -1.2045 TD [(a)-325(depreciated)-325(house.)-446(Selling)-325(the)-337(depreciated)-325(house,)-326(ho)24(w)25(ev)24(er,)-313(can)-325(relax)-313(an)-337(agen)24(t's)-314(liquidit)23(y)-337(constrain)23(t.)]TJ /F8 1 Tf 11.95517 0 0 11.95517 305.64 67.44 Tm (6)Tj ET endstream endobj 9 0 obj << /Length 11371 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 89.52 683.16 Tm 0 g [(The)-230(second)-231(con)31(tract)-221($in)29(terest-only)-242(mortgage,)-230(or)-211(IOM$)-232(stipulates)-232(an)-211(in)30(terest)-242(rate)]TJ /F14 1 Tf 33.66577 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 497.64 687.48 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 518.04 683.16 Tm 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 528.72 681.36 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 533.52 683.16 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 544.56 681.36 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 549.2401 683.16 Tm ($,)Tj -39.91914 -1.21454 TD [(no)-321(do)30(wn-pa)31(ymen)30(t,)-352(constan)30(t)-331(pa)30(ymen)30(ts)]TJ /F14 1 Tf 16.53176 0 Td (m)Tj /F15 1 Tf 7.97011 0 0 7.97011 279.84 673.08 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 300.36 668.64 Tm 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 311.04 666.84 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 315.72 668.64 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 326.76 666.84 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 331.44 668.64 Tm 0.281 Tc ($=)Tj 1.70637 0.27101 TD 0 Tc <16>Tj /F14 1 Tf -0.01004 -0.27101 TD [(hq)-40(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 369.72 673.08 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 390.12 668.64 Tm 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 400.8 666.84 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 405.6 668.64 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 416.64 666.84 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 421.2 668.64 Tm [($)-322(that)-322(do)-331(not)-321(reduce)-331(the)]TJ -29.20912 -1.2045 TD [(principal)-311(for)-302(the)-301(\frst)]TJ /F14 1 Tf 9.18431 0 Td 0.311 Tc [(k<)40(T)]TJ /F8 1 Tf 2.87072 0 Td 0 Tc [(p)-30(erio)-30(ds,)-312(and)-311(\fxed-pa)31(ymen)30(ts)-332(for)-291(the)-312(follo)31(wing)]TJ /F14 1 Tf 19.53297 0 Td (T)Tj /F16 1 Tf 0.8833 0 Td <00>Tj /F14 1 Tf 0.95356 0 Td (k)Tj /F8 1 Tf 0.84315 0 Td [(p)-30(erio)-30(ds)-312(with)]TJ -34.26802 -1.2045 TD [(a)-291(standard)-302(FRM-lik)29(e)-290(balance)-300(sc)30(hedule)]TJ /F16 1 Tf 16.5418 0 Td (f)Tj /F14 1 Tf 0.50187 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 280.68 644.16 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.91843 TD 0 Tc <1C>Tj /F8 1 Tf 11.95517 0 0 11.95517 301.08 639.84 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 311.76 638.04 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 316.56 639.84 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 327.6 638.04 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 332.28 639.84 Tm ($)Tj /F16 1 Tf 0.38142 0 Td (g)Tj /F15 1 Tf 7.97011 0 0 7.97011 342.84 644.16 Tm (T)Tj 0 -0.93349 TD <1C>Tj /F11 1 Tf 0.57214 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td (k)Tj /F8 1 Tf 11.95517 0 0 11.95517 359.16 639.84 Tm [(.)-422(Notice)-300(that)-292(households)-311(accum)31(ulate)]TJ -24.01974 -1.21454 TD [(no)-321(house)-341(equit)30(y)-341(for)]TJ /F14 1 Tf 8.54191 0 Td (k)Tj /F8 1 Tf 0.87326 0 Td [(p)-30(erio)-30(ds)-332(under)-331(the)-331(second)-341(con)30(tract.)]TJ -7.9497 -1.2045 TD [(In)-332(other)-331(w)30(ords,)]TJ /F14 1 Tf 9.26461 -3.04136 TD (m)Tj /F15 1 Tf 7.97011 0 0 7.97011 210.48 579.48 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.99371 TD 0 Tc <1C>Tj /F8 1 Tf 11.95517 0 0 11.95517 234.24 574.56 Tm (=)Tj /F19 1 Tf 1.0439 1.70637 TD ($)Tj /F8 1 Tf 1.23461 -0.67251 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD [(hq)-40(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 279.36 588.12 Tm 0.075 Tc [(IO)45(M)]TJ /F14 1 Tf 11.95517 0 0 11.95517 363.12 583.6801 Tm 0 Tc [(if)-763<1C>-391(<)-271(k)]TJ /F15 1 Tf 7.97011 0 0 7.97011 290.16 572.52 Tm (r)Tj /F17 1 Tf 5.97758 0 0 5.97758 294.24 575.28 Tm 0.08 Tc [(IO)40(M)]TJ ET q 77.16 0 0 -0.48 262.548 570.948 cm /Im1 Do Q BT /F11 1 Tf 7.97011 0 0 7.97011 262.56 563.28 Tm 0 Tc (1)Tj /F18 1 Tf 0.52697 0 Td <00>Tj /F11 1 Tf 0.82809 0 Td (\(1+)Tj /F15 1 Tf 1.76158 0 Td (r)Tj /F17 1 Tf 5.97758 0 0 5.97758 291.48 565.44 Tm 0.08 Tc [(IO)40(M)]TJ /F11 1 Tf 7.97011 0 0 7.97011 309.12 563.28 Tm 0 Tc ($)Tj /F20 1 Tf 5.97758 0 0 5.97758 312.36 565.56 Tm <00>Tj /F21 1 Tf 0.9636 0 Td ($)Tj /F17 1 Tf 0.4818 0 Td (T)Tj /F20 1 Tf 0.8833 0 Td <00>Tj /F17 1 Tf 0.9636 0 Td (k)Tj /F21 1 Tf 0.68255 0 Td ($)Tj /F8 1 Tf 11.95517 0 0 11.95517 340.92 570.96 Tm <16>Tj /F14 1 Tf -0.01004 -0.26097 TD [(hq)-873(if)-763<1C>]TJ /F16 1 Tf 4.2559 0 Td <15>Tj /F14 1 Tf 1.05394 0 Td (k)Tj /F8 1 Tf -27.79384 -2.06772 TD [(and,)-331(for)-322(all)]TJ /F14 1 Tf 5.02879 0 Td <1C>Tj /F16 1 Tf 0.81304 0 Td 0.292 Tc (2f)Tj /F8 1 Tf 1.45544 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc (;T)Tj /F16 1 Tf 1.3651 0 Td 0 Tc <00>Tj /F8 1 Tf 0.99371 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td (g)Tj /F8 1 Tf 0.50187 0 Td (,)Tj /F14 1 Tf 1.51566 -2.20825 TD (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 228.24 521.64 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.97866 TD 0 Tc <1C>Tj /F11 1 Tf 0.60225 0 Td (+1)Tj /F8 1 Tf 11.95517 0 0 11.95517 252.12 516.72 Tm (=)Tj /F14 1 Tf 1.03386 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 269.4 521.64 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.97866 TD 0 Tc <1C>Tj /F8 1 Tf 11.95517 0 0 11.95517 289.92 516.72 Tm [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 320.4 521.64 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 340.8 516.72 Tm 0 Tc ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (m)Tj /F15 1 Tf 7.97011 0 0 7.97011 370.2 521.64 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.97866 TD 0 Tc <1C>Tj /F14 1 Tf 11.95517 0 0 11.95517 390.6 516.72 Tm (;)Tj /F8 1 Tf -26.64956 -2.20825 TD (where)Tj /F14 1 Tf 2.8105 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.52 494.64 Tm 0.075 Tc [(IO)45(M)]TJ /F11 1 Tf 0 -0.90337 TD 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 134.28 490.32 Tm (=)Tj 1.05394 0.27101 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD (hq)Tj /F8 1 Tf 1.03386 0 Td [(.)-432(Notice)-310(that)-302(for)]TJ /F14 1 Tf 7.32737 0 Td 0.401 Tc [<1C3C>130(k)371(;)90(b)]TJ /F15 1 Tf 7.97011 0 0 7.97011 287.28 494.64 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.90337 TD 0 Tc <1C>Tj /F11 1 Tf 0.58719 0 Td (+1)Tj /F8 1 Tf 11.95517 0 0 11.95517 311.04 490.32 Tm (=)Tj /F14 1 Tf 1.0439 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 328.44 494.64 Tm 0.075 Tc [(IO)45(M)]TJ /F11 1 Tf 0 -0.90337 TD 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 352.56 490.32 Tm [(so)-311(that)-312(the)-312(principal)-311(is)-311(not)-312(paid)-311(do)30(wn)]TJ -23.46767 -1.2045 TD (for)Tj /F14 1 Tf 1.49559 0 Td (k)Tj /F8 1 Tf 0.87326 0 Td [(p)-30(erio)-30(ds)-332(and)-321(hence)-340(the)-331(mortgage)-321(pa)30(ymen)30(ts)-352(are)-331(bac)31(kloaded)-341(and)]TJ /F14 1 Tf 27.01091 0 Td (b)Tj /F15 1 Tf 7.97011 0 0 7.97011 428.16 480.24 Tm 0.075 Tc [(IO)45(M)]TJ 0 -0.91843 TD 0 Tc (T)Tj /F8 1 Tf 11.95517 0 0 11.95517 452.04 475.92 Tm 0.271 Tc (=0)Tj /F14 1 Tf 1.5257 0 Td 0 Tc (:)Tj /F8 1 Tf -31.84899 -1.2045 TD [(Mortgages)-322(are)-311(issued)-332(b)31(y)-322(the)-321(\fnancial)-320(in)30(termediary)80(.)-442(The)-331(in)31(termediary)-332(incurs)-322(service)-341(costs)]TJ -1.46548 -1.21454 TD [(whic)31(h)-311(w)30(e)-311(mo)-30(del)-310(as)-302(a)-291(premium)]TJ /F14 1 Tf 13.13909 0 Td 0.281 Tc <1E3E>Tj /F8 1 Tf 1.89709 0 Td 0 Tc [(0)-301(on)-301(the)-301(opp)-30(ortunit)29(y)-301(cost)-312(of)-291(funds)-312(loaned)-300(to)-301(the)-302(agen)31(t)-301(for)]TJ -15.03617 -1.2045 TD [(housing)-331(purp)-31(oses.)]TJ 1.46548 -1.21454 TD [(The)-330(agen)30(t)-311(can)-321(terminate)-322(the)-321(con)31(tract)-322(at)-312(the)-311(b)-30(eginning)-320(of)-312(an)31(y)-321(p)-31(erio)-30(d,)-321(an)-311(ev)31(en)30(t)-331(whic)30(h)-331(can)]TJ -1.46548 -1.2045 TD [(o)-30(ccur)-431(for)-432(sev)30(eral)-442(p)-30(ossible)-452(reasons.)-753(First,)-464(b)-30(ecause)-441(of)-431(the)-432(p)-30(ossibilit)29(y)-452(of)-421(house)-442(v)51(alue)-442(sho)-30(c)31(ks,)]TJ T* [(terminations)-403(o)-30(ccur)-391(when)-400(the)-392(outstanding)-402(principal)-392(exceeds)-420(the)-392(house)-401(v)50(alue.)-632(W)81(e)-391(will)-401(think)]TJ 0 -1.21454 TD [(of)-411(that)-403(ev)31(en)30(t)-432(as)-411(a)-412(foreclosure.)-702(In)-412(that)-413(ev)31(en)30(t,)-452(the)-421(in)30(termediary)-432(loses)-422(fraction)]TJ /F14 1 Tf 33.95686 0 Td 0.422 Tc <143E>Tj /F8 1 Tf 2.1681 0 Td 0 Tc [(0)-411(of)-402(the)]TJ -36.12496 -1.2045 TD [(principal)-412(pa)31(ymen)30(t)-422(it)-402(collects.)-682(T)81(ermination)-412(also)-402(o)-29(ccurs)-412(when)-411(the)-412(agen)31(t's)-412(income)-411(falls)-402(short)]TJ T* [(of)-401(the)-412(stipulated)-412(pa)30(ymen)30(t)-422(for)-402(the)-411(p)-30(erio)-30(d.)-673(In)-412(that)-402(case,)-431(the)-412(house)-411(is)-412(sold)-412(immediately)81(,)-442(the)]TJ 0 -1.21454 TD [(agen)31(t's)-352(house)-362(equit)30(y)81(,)-372(if)-341(an)30(y)81(,)-362(augmen)31(ts)-352(his)-362(liquid)-351(asset)-362(p)-30(osition,)-352(and)-352(the)-341(agen)31(t)-352(is)-352(constrained)]TJ 0 -1.2045 TD [(to)-342(b)-30(ecome)-350(a)-331(ren)30(ter.)-492(Agen)31(t)-342(ma)30(y)-351(also)-341(c)30(ho)-30(ose)-351(to)-331(sell)-352(their)-352(house)-351(ev)31(en)-351(when)-351(they)-351(can)-341(meet)-351(the)]TJ 0 -1.21454 TD [(pa)30(ymen)31(t)-312(and)-291(ha)30(v)31(e)-301(p)-30(ositiv)29(e)-300(equit)30(y)80(,)-311(for)-292(instance)-301(b)-30(ecause)-300(they)-301(are)-291(b)-30(orro)29(wing)-290(constrained)-302(in)-291(the)]TJ 0 -1.2045 TD [(curren)30(t)-342(p)-30(erio)-30(d.)-431(Finally)80(,)-332(termination)-332(o)-30(ccurs)-331(b)30(y)-341(assumption)-342(when)-341(agen)31(ts)-332(b)-30(ecome)-330(old.)]TJ 1.46548 -1.2045 TD [(The)-330(timing)-312(in)-321(eac)31(h)-321(p)-31(erio)-30(d)-311(is)-321(as)-312(follo)30(ws)-321($see)-321(app)-30(endix)-331(for)-311(\ro)30(w)-321(c)30(hart.$)-432(A)30(t)-311(the)-322(b)-30(eginning)-320(of)]TJ -1.46548 -1.21454 TD [(the)-281(p)-30(erio)-30(d,)-281(agen)30(ts)-281(disco)30(v)30(er)-291(whether)-291(or)-271(not)-272(they)-281(ha)31(v)30(e)-281(aged,)-290(and)-271(receiv)31(e)-291(a)-271(p)-30(erfectly)-291(informativ)30(e)]TJ 0 -1.2045 TD [(signal)-462(ab)-30(out)-452(their)-462(income)-471(dra)30(w)-461(for)-453(the)-471(p)-31(erio)-30(d.)-823(Middle-aged)-471(agen)31(ts)-463(who)-461(o)30(wn)-471(homes)-462(also)]TJ 0 -1.21454 TD [(observ)30(e)-391(the)-372(realization)-381(of)-371(their)-372(dev)51(aluation)-382(sho)-30(c)30(k)-381(at)-372(the)-371(b)-30(eginning)-381(of)-371(the)-372(p)-30(erio)-30(d,)-391(hence)-381(the)]TJ 0 -1.2045 TD [(mark)30(et)-382(v)51(alue)-381(of)-372(their)-381(home.)-582(These)-391(agen)31(ts)-382(then)-382(decide)-390(whether)-392(to)-371(remain)-382(home-o)31(wners,)-402(or,)]TJ T* [(instead,)-312(to)-291(b)-30(ecome)-300(ren)30(ters)-312(in)-291(whic)31(h)-311(case)-301(their)-302(house)-301(is)-301(sold.)-432(Agen)31(ts)-302(who)-301(just)-302(b)-30(ecame)-300(middle-)]TJ 0 -1.21454 TD [(aged)-441(also)-452(mak)31(e)-452(their)-452(home-buying)-461(and)-442(mortgage)-441(c)30(hoice)-461(decisions)-461(at)-442(the)-452(b)-30(eginning)-451(of)-442(the)]TJ 0 -1.2045 TD [(p)-30(erio)-30(d,)-492(after)-452(all)-462(uncertain)30(t)30(y)-472(for)-452(the)-461(p)-31(erio)-30(d)-451(is)-472(resolv)29(ed.)-842(A)30(t)-462(the)-462(end)-461(of)-452(the)-462(p)-30(erio)-30(d,)-492(agen)31(ts)]TJ T* [(receiv)31(e)-351(their)-332(income,)-330(mortgage)-331(pa)30(ymen)31(ts)-343(are)-331(made,)-330(and)-332(consumption)-341(tak)30(es)-342(place.)]TJ 19.54301 -7.58835 TD (7)Tj ET endstream endobj 10 0 obj << /Length 13154 >> stream /GS4 gs BT /F9 1 Tf 17.21544 0 0 17.21544 72 683.16 Tm 0 g [(3)-1122(Equilibrium)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 656.88 Tm [(W)81(e)-331(will)-341(only)-331(study)-352(equilibria)-342(in)-331(whic)31(h)-341(all)-331(prices)-352(are)-331(constan)30(t.F)79(or)-331(simplicit)29(y)81(,)-351(w)30(e)-341(no)30(w)-340(drop)-332(all)]TJ 0 -1.21454 TD [(time)-331(subscripts.)]TJ /F22 1 Tf 14.34624 0 0 14.34624 72 607.8 Tm [(3.1)-1131(Agen)33(t's)-386(problem)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 585.6 Tm [(W)81(e)-392(will)-391(state)-392(the)-391(household)-402(problem)-391(recursiv)30(ely)80(.)-642(In)-392(general,)-411(the)-391(household)-402(v)51(alue)-391(functions)]TJ 0 -1.21454 TD [(will)-331(b)-30(e)-331(written)-332(as)]TJ /F14 1 Tf 7.80917 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 172.2 569.28 Tm [(ag)-30(e)]TJ /F8 1 Tf 11.95517 0 0 11.95517 185.4 571.08 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td [($)-322(where)]TJ /F14 1 Tf 3.5332 0 Td (!)Tj /F16 1 Tf 0.92345 0 Td (2)Tj /F8 1 Tf 0.94352 0 Td (\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 270.72 569.28 Tm [(ag)-30(e)]TJ /F8 1 Tf 11.95517 0 0 11.95517 287.88 571.08 Tm [(is)-332(the)-331(state)-332(facing)-331(an)-321(agen)31(t)-332(of)]TJ /F14 1 Tf 13.03871 0 Td [(ag)-40(e)]TJ /F16 1 Tf 1.75656 0 Td 0.282 Tc (2f)Tj /F14 1 Tf 1.4454 0 Td 0.05 Tc [(Y;)-121(M;)-120(O)]TJ /F16 1 Tf 3.28226 0 Td 0 Tc (g)Tj /F8 1 Tf 0.50187 0 Td (.)Tj /F5 1 Tf -38.08227 -2.59971 TD [(3.1.1)-1125(Old)-382(agen)30(ts)]TJ /F8 1 Tf 0 -1.85694 TD [(F)80(or)-412(old)-421(agen)30(ts,)-462(the)-422(state)-432(space)-431(is)-432(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 260.52 516 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 273 517.8 Tm (=)Tj /F14 1 Tf 1.2045 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 298.56 522.12 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 310.68 517.8 Tm [(with)-422(t)30(ypical)-441(elemen)31(t)]TJ /F14 1 Tf 9.34491 0 Td (!)Tj /F16 1 Tf 1.08405 0 Td <11>Tj /F14 1 Tf 1.21454 0 Td (a)Tj /F16 1 Tf 0.9636 0 Td <15>Tj /F8 1 Tf 1.21454 0 Td [(0.)-723(The)-430(v)50(alue)]TJ -33.78622 -1.2045 TD [(function)-402($that)-402(is,)-422(the)-412(exp)-30(ected)-420(presen)30(t)-412(v)50(alue)-411(of)-392(future)-402(utilit)30(y$)-412(for)-402(an)-392(old)-401(agen)31(t)-412(with)-402(assets)]TJ /F14 1 Tf 0 -1.21454 TD (a)Tj /F16 1 Tf 0.79296 0 Td (2)Tj /F14 1 Tf 0.94352 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 103.92 493.2 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 114.84 488.88 Tm [(solv)30(es)]TJ /F14 1 Tf 6.51434 -1.62607 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 199.56 467.64 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 206.64 469.44 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($)-281(=)-271(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 239.52 461.88 Tm (a)Tj /F20 1 Tf 5.97758 0 0 5.97758 243.96 464.16 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 246.72 461.88 Tm <15>Tj /F11 1 Tf 0.82809 0 Td (0)Tj /F19 1 Tf 11.95517 0 0 11.95517 261.48 486.24 Tm <1A>Tj /F14 1 Tf 0.74278 -1.40525 TD (U)Tj /F19 1 Tf 0.93349 1.40525 TD <12>Tj /F14 1 Tf 0.74278 -1.40525 TD (c;)Tj /F8 1 Tf 0.9636 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD (h)Tj ET q 6.84 0 0 -0.48 301.788 472.668 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 302.04 461.28 Tm <11>Tj /F19 1 Tf 0.65244 2.0878 TD <13>Tj /F8 1 Tf 0.95356 -1.40525 TD (+)Tj /F14 1 Tf 0.98367 0 Td (\f)Tj /F8 1 Tf 0.61229 0 Td ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 371.28 474.36 Tm (D)Tj /F8 1 Tf 11.95517 0 0 11.95517 378.96 469.44 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 390.36 467.64 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 397.56 469.44 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 408.24 474.36 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 411 469.44 Tm ($)Tj /F19 1 Tf 0.38143 1.40525 TD <1B>Tj /F8 1 Tf -28.73736 -3.59342 TD (s.t.)Tj /F14 1 Tf 12.67736 -1.58592 TD (c)Tj /F8 1 Tf 0.70263 0 Td (=)Tj /F14 1 Tf 1.03386 0 Td (a)Tj /F8 1 Tf 0.61229 0.67251 TD [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj ET q 35.04 0 0 -0.48 251.628 427.428 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 252 416.04 Tm (1)Tj /F16 1 Tf 0.7227 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 278.64 419.52 Tm (D)Tj /F8 1 Tf 11.95517 0 0 11.95517 290.52 424.32 Tm (+)Tj /F14 1 Tf 0.98367 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 308.52 429.24 Tm (O)Tj /F16 1 Tf 11.95517 0 0 11.95517 318.24 424.32 Tm <00>Tj /F8 1 Tf 1.10412 0.93349 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 331.308 427.428 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 331.56 416.04 Tm <11>Tj 0.65244 0.69259 TD (R)Tj /F16 1 Tf 0.97364 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 369 429.24 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 375.24 424.32 Tm <15>Tj /F8 1 Tf 1.05394 0 Td (0)Tj /F5 1 Tf -26.4187 -3.06144 TD [(3.1.2)-1125(Mid-aged)-403(agen)30(ts)]TJ /F8 1 Tf 0 -1.85694 TD [(F)80(or)-392(mid-aged)-391(agen)31(ts,)-433(the)-391(state)-402(space)-411(is)-402(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 289.44 363.72 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 303.72 365.52 Tm (=)Tj /F14 1 Tf 1.15431 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 328.68 369.84 Tm 0 Tc (+)Tj /F16 1 Tf 11.95517 0 0 11.95517 339 365.52 Tm 0.271 Tc <0266>Tj /F14 1 Tf 1.54577 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 363.24 363.72 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 369.48 365.52 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 380.52 363.72 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 389.88 365.52 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 400.92 363.72 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 408.96 365.52 Tm 0.261 Tc [<6702>-20(f)]TJ /F8 1 Tf 2.31866 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td 0.261 Tc <6702>Tj /F14 1 Tf 1.80675 0 Td -0.251 Tc (IN)Tj /F16 1 Tf 1.33499 0 Td 0.271 Tc <0266>Tj /F8 1 Tf 1.54577 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td 0.261 Tc <6702>Tj -38.04212 -1.2045 TD 0 Tc (f)Tj /F14 1 Tf 0.50187 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0.01 Tc <6702>Tj /F14 1 Tf 1.29484 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 168 355.44 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 177.6 351.12 Tm [(with)-231(t)30(ypical)-231(elemen)32(t)]TJ /F14 1 Tf 8.74266 0 Td (!)Tj /F8 1 Tf 0.92345 0 Td 0.281 Tc (=$)Tj /F14 1 Tf 1.42533 0 Td 0.171 Tc [(a)171(;y)131(;)1(H)151<3B1C>71<3B1B>]TJ /F8 1 Tf 4.74774 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 389.04 355.44 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 393.72 351.12 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 404.4 349.32 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 409.2 351.12 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 420.24 349.32 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 424.92 351.12 Tm [($\).)-402(Here,)]TJ /F14 1 Tf 3.9347 0 Td (H)Tj /F8 1 Tf 1.16435 0 Td [(=)-271(1)-221(denotes)]TJ -34.61934 -1.21454 TD [(whether)-371(the)-352(agen)31(t)-361(b)-31(egins)-361(the)-361(p)-30(erio)-30(d)-352(as)-351(a)-352(house)-361(o)30(wner,)-371(while)]TJ /F14 1 Tf 26.56926 0 Td (H)Tj /F8 1 Tf 1.2045 0 Td [(=)-331(0)-351(if)-352(they)-361(are)-351(ren)30(ters.)-533(W)81(e)]TJ -27.77376 -1.2045 TD (write)Tj /F14 1 Tf 2.4893 0 Td <1C>Tj /F16 1 Tf 0.82308 0 Td 0.282 Tc (2f)Tj /F8 1 Tf 1.4454 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [(;:)1(::)]TJ /F16 1 Tf 1.57589 0 Td 0 Tc (g)Tj /F8 1 Tf 0.81304 0 Td [(for)-312(the)-331(n)30(um)30(b)-30(er)-331(of)-311(p)-30(erio)-30(ds)-322(the)-321(agen)31(t)-322(has)-322(b)-30(een)-320(mid-aged,)-321(hence)-330(the)-321(age)-321(of)]TJ -8.57202 -1.2045 TD [(their)-272(mortgage)-260(when)-271(they)-281(ha)31(v)30(e)-271(one,)-280(and)]TJ /F14 1 Tf 17.20427 0 Td <1B>Tj /F8 1 Tf 0.86323 0 Td [(=)-281(1)-261(if)-261(the)-271(agen)31(t's)-272(house)-281(has)-261(dev)50(alued.)-431(The)-270(last)-272(t)30(w)30(o)]TJ -18.0675 -1.21454 TD [(argumen)30(ts,)-412($)]TJ /F14 1 Tf 5.49051 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 154.56 297.6 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 159.24 293.28 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 169.92 291.48 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 174.72 293.28 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 185.76 291.48 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 190.44 293.28 Tm ($\))Tj /F16 1 Tf 1.14427 0 Td 0.382 Tc (2f)Tj /F14 1 Tf 1.54577 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0.251 Tc <6702>Tj /F14 1 Tf 1.79671 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 318.6 297.6 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 325.68 293.28 Tm [(,)-402(are)-391(the)-391(agen)30(t's)-392(mortgage)-381(t)30(yp)-31(e)-401(and)-381(yield.)]TJ -21.21927 -1.2045 TD [(The)-320(long)-321(notation)-312(for)]TJ /F14 1 Tf 9.50551 0 Td (r)Tj /F8 1 Tf 0.78293 0 Td [(is)-322(mean)31(t)-332(to)-311(emphasize)-331(that)-321(the)-322(mortgage)-311(terms)-322(are)-321(a)-311(function)-321(of)-311(the)]TJ -10.28844 -1.2045 TD [(agen)31(t's)-372(w)30(ealth-income)-371(p)-30(osition)-372(when)-370(they)-372(b)-30(ecome)-370(mid-aged.)-542(In)-361(order)-362(to)-362(de\fne)-370(the)-372(agen)31(t's')]TJ 0 -1.21454 TD [(v)50(alue)-330(function)]TJ /F14 1 Tf 6.36377 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 154.92 248.16 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 167.76 249.96 Tm 0.271 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 182.64 248.16 Tm 0 Tc (M)Tj /F16 1 Tf 11.95517 0 0 11.95517 195.6 249.96 Tm (7!)Tj /F14 1 Tf 1.27476 0 Td -0.251 Tc (IR)Tj /F8 1 Tf 0.93349 0 Td 0 Tc [(,)-321(,)-331(it)-322(is)-332(useful)-341(to)-322(consider)-341(di\013eren)30(t)-341(cases.)]TJ /F5 1 Tf -11.0814 -2.38892 TD [(Case)-381(1:)]TJ /F14 1 Tf 4.00496 0 Td <1C>Tj /F16 1 Tf 0.81304 0 Td <15>Tj /F8 1 Tf 1.05394 0 Td (1)Tj /F16 1 Tf -5.88197 -3.48301 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-322(the)-331(agen)31(t)-332(en)31(ters)-342(the)-332(p)-30(erio)-30(d)-331(as)-332(a)-321(ren)30(ter)-331($i.e.)]TJ /F14 1 Tf 19.8341 0 Td (H)Tj /F8 1 Tf 1.17439 0 Td [(=)-271(0$:)]TJ /F14 1 Tf -18.72997 -2.84061 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 135.36 144 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 144.84 145.8 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td [($)-803(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 224.4 138.24 Tm (c;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 234.96 140.52 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 243.84 145.8 Tm (U)Tj /F19 1 Tf 0.94352 1.41529 TD <12>Tj /F14 1 Tf 0.73274 -1.41529 TD (c;)Tj /F8 1 Tf 0.97364 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 275.388 149.028 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 275.64 137.64 Tm <11>Tj /F19 1 Tf 0.6424 2.09784 TD <13>Tj /F8 1 Tf 0.95356 -1.41529 TD (+)Tj /F14 1 Tf 0.98367 0 Td 0.06 Tc (\fE)Tj /F15 1 Tf 7.97011 0 0 7.97011 322.44 144 Tm 0 Tc (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 326.88 146.28 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 329.64 144 Tm (j)Tj /F15 1 Tf 0.30113 0 Td (y)Tj /F8 1 Tf 11.95517 0 0 11.95517 338.88 145.8 Tm ([$1)Tj /F16 1 Tf 1.3651 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 373.2 143.04 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 380.4 145.8 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 391.8 144 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 401.28 145.8 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 411.96 150.84 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 414.72 145.8 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 426.24 150.84 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 428.88 145.8 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td 0.211 Tc ($+)Tj /F14 1 Tf 1.57589 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 473.52 143.04 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 480.72 145.8 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 487.56 144 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 494.76 145.8 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 505.44 150.84 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 508.2 145.8 Tm ($])Tj -30.64449 -2.78039 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 188.28 117.48 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 201 112.56 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F8 1 Tf 0.74278 0 Td (+)Tj /F14 1 Tf 0.98367 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.59221 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (R)Tj /F8 1 Tf 0.86323 0.93349 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 306.588 115.788 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 306.84 104.28 Tm <11>Tj /F8 1 Tf -0.10038 -3.08151 TD (8)Tj ET endstream endobj 11 0 obj << /Length 22185 >> stream /GS4 gs BT /F16 1 Tf 11.95517 0 0 11.95517 89.4 683.16 Tm 0 g <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-342(the)-341(agen)31(t)-342(is)-342(a)-331(home-o)31(wner)-351($i.e.)]TJ /F14 1 Tf 14.74509 0 Td (H)Tj /F8 1 Tf 1.18442 0 Td [(=)-291(1$)-341(but)-342(it)-342(is)-342(not)-331(budget)-351(feasible)-351(for)-332(her)-341(to)-332(mak)30(e)]TJ -15.92951 -1.21454 TD [(her)-331(mortgage)-321(pa)30(ymen)30(t)]TJ /F14 1 Tf 9.97727 0 Td (m)Tj /F8 1 Tf 0.85319 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54202 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 264 673.08 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 268.68 668.64 Tm [($,)-332(or:)]TJ /F14 1 Tf -3.5332 -1.88705 TD (y)Tj /F8 1 Tf 0.73274 0 Td (+)Tj /F14 1 Tf 0.98367 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (m)Tj /F8 1 Tf 0.85319 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54203 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 346.08 651 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 350.76 646.08 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td 0.04 Tc <0E68>Tj /F8 1 Tf 1.03386 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F14 1 Tf 0.65244 0 Td (<)Tj /F8 1 Tf 1.0439 0 Td [(0)-8451((3.1))]TJ -26.1778 -1.88705 TD (where)Tj /F14 1 Tf 2.83057 0 Td (h)Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F16 1 Tf 0.65244 0 Td <11>Tj /F8 1 Tf 1.06397 0 Td ($1)Tj /F16 1 Tf 1.08405 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj ET q 6.84 0 0 -0.48 210.588 633.708 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 210.6 623.52 Tm (h)Tj /F8 1 Tf 0.78292 0 Td (+)Tj /F14 1 Tf 0.98367 0 Td <1B>Tj /F11 1 Tf 7.97011 0 0 7.97011 240.12 630.36 Tm <16>Tj /F15 1 Tf -0.01506 -0.27101 TD (h)Tj ET q 4.92 0 0 -0.48 239.988 626.748 cm /Im1 Do Q BT /F15 1 Tf 7.97011 0 0 7.97011 240.12 619.44 Tm <11>Tj /F14 1 Tf 11.95517 0 0 11.95517 246.12 623.52 Tm (;)Tj /F8 1 Tf 0.27101 0 Td [(then)-331(the)-332(v)51(alue)-331(function)-331(solv)30(es)]TJ /F14 1 Tf -12.38627 -2.74023 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 108.12 588.96 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 117.6 590.76 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>81(;)1<1B>]TJ /F8 1 Tf 1.98742 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 196.92 595.6801 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 201.6 590.76 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 212.28 588.96 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 217.08 590.76 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 228.12 588.96 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 232.68 590.76 Tm [($\))-834(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 275.16 583.2 Tm (c;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 285.72 585.48 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 294.6 590.76 Tm (U)Tj /F19 1 Tf 0.94352 1.40525 TD <12>Tj /F14 1 Tf 0.73274 -1.40525 TD (c;)Tj /F8 1 Tf 0.9636 0.94352 TD <16>Tj /F14 1 Tf 0 -0.27101 TD (h)Tj ET q 6.84 0 0 -0.48 326.148 593.988 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 326.4 582.6 Tm <11>Tj /F19 1 Tf 0.6424 2.0878 TD <13>Tj /F8 1 Tf 0.95356 -1.40525 TD (+)Tj /F14 1 Tf 0.98367 0 Td 0.06 Tc (\fE)Tj /F15 1 Tf 7.97011 0 0 7.97011 373.2 588.84 Tm 0 Tc (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 377.64 591.12 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 380.4 588.84 Tm (j)Tj /F15 1 Tf 0.30113 0 Td (y)Tj /F8 1 Tf 11.95517 0 0 11.95517 389.64 590.76 Tm ([$1)Tj /F16 1 Tf 1.3651 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 423.96 587.88 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 431.16 590.76 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 442.56 588.96 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 452.04 590.76 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 462.72 595.6801 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 465.48 590.76 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 477 595.6801 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 479.64 590.76 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td 0.211 Tc ($+)Tj /F14 1 Tf 1.57589 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 524.28 587.88 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 531.48 590.76 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 538.32 588.96 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 545.52 590.76 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 556.2 595.6801 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 558.96 590.76 Tm ($])Tj -30.64449 -2.79042 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98367 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 239.04 562.32 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 251.76 557.4 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F8 1 Tf 0.73274 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td 0.221 Tc [($+m)221(a)221(x)]TJ /F19 1 Tf 3.57335 0.81304 TD 0 Tc (\b)Tj /F8 1 Tf 0.58217 -0.81304 TD ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <14>Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td 0.04 Tc (qh)Tj /F8 1 Tf 1.03386 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54203 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 495.24 562.32 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 500.04 557.4 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F19 1 Tf 0.49184 0.81304 TD (\t)Tj /F16 1 Tf 0.79296 -0.81304 TD <00>Tj /F14 1 Tf 1.00375 0 Td (R)Tj /F8 1 Tf 0.86323 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD (h)Tj ET q 6.84 0 0 -0.48 547.428 560.628 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 547.68 549.2401 Tm <11>Tj /F16 1 Tf -38.33321 -2.07776 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-382(it)-392(is)-392(budget)-391(feasible)-391(for)-382(a)-381(homeo)30(wner)-401($i.e.)]TJ /F14 1 Tf 19.8341 0 Td (H)Tj /F8 1 Tf 1.26472 0 Td [(=)-371(1$)-382(to)-382(mak)31(e)-401(her)-392(mortgage)-381(pa)30(ymen)31(t)]TJ -21.09882 -1.21454 TD [($that)-322(is,)-332((3.1))-322(do)-30(es)-331(not)-332(hold$)-331(but)-322(it)-331(has)-332(negativ)30(e)-340(equit)30(y)-341(in)-332(his)-331(house,)-342(that)-322(is:)]TJ /F14 1 Tf 13.74134 -1.88705 TD 0.04 Tc (qh)Tj /F8 1 Tf 1.03386 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54203 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 346.8 492.24 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 351.48 487.32 Tm ($)Tj /F14 1 Tf 0.66247 0 Td (<)Tj /F8 1 Tf 1.0439 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 11.99481 0 Td ((3.2))Tj -35.12121 -1.88705 TD [(then,)-392(if)-371(the)-372(household)-391(c)31(ho)-30(oses)-382(to)-372(ren)30(t)-381(in)-372(the)-381(next)-382(p)-30(erio)-30(d)-371($so)-372(that)]TJ /F14 1 Tf 28.77751 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 456 469.08 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 462.96 464.76 Tm [(=)-361(0$,)-382(de\fne)-381(the)]TJ -30.25302 -1.2045 TD [(v)50(alue)-330(function)-332(b)30(y)]TJ /F14 1 Tf 0 -2.46922 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.64 425.76 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 118.2 428.64 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 120.96 425.76 Tm (=0)Tj /F15 1 Tf -1.61102 -0.97866 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 132.24 420.84 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.99746 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 211.56 425.76 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 216.36 420.84 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 227.04 419.04 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 231.72 420.84 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 242.76 419.04 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 247.44 420.84 Tm [($\))-834(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 289.8 413.28 Tm (c;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 300.36 415.56 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 309.36 420.84 Tm (U)Tj /F19 1 Tf 0.93349 1.41529 TD <12>Tj /F14 1 Tf 0.73274 -1.41529 TD (c;)Tj /F8 1 Tf 0.97364 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 340.788 424.068 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 341.04 412.68 Tm <11>Tj /F19 1 Tf 0.6424 2.09784 TD <13>Tj /F8 1 Tf 0.9636 -1.41529 TD (+)Tj /F14 1 Tf 0.98367 0 Td 0.05 Tc (\fE)Tj /F15 1 Tf 7.97011 0 0 7.97011 387.84 419.04 Tm 0 Tc (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 392.28 421.32 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 395.04 419.04 Tm (j)Tj /F15 1 Tf 0.30112 0 Td (y)Tj /F8 1 Tf 11.95517 0 0 11.95517 404.4 420.84 Tm ([$1)Tj /F16 1 Tf 1.3651 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 438.72 418.08 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 445.8 420.84 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 457.2 419.04 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 466.68 420.84 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 477.36 425.76 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 480.12 420.84 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 491.64 425.76 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 494.4 420.84 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td 0.201 Tc ($+)Tj /F14 1 Tf 1.56585 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 539.04 418.08 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 546.12 420.84 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 552.96 419.04 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 560.16 420.84 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 570.84 425.76 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 573.6 420.84 Tm ($])Tj -30.64449 -2.79042 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 253.68 392.52 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 266.52 387.48 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F8 1 Tf 0.73274 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (R)Tj /F8 1 Tf 0.86323 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 371.988 390.708 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 372.24 379.32 Tm <11>Tj 0.6424 0.68255 TD (:)Tj /F16 1 Tf -24.30079 -2.76031 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-382(it)-392(is)-392(budget)-391(feasible)-391(for)-382(a)-381(homeo)30(wner)-401($i.e.)]TJ /F14 1 Tf 19.8341 0 Td (H)Tj /F8 1 Tf 1.26472 0 Td [(=)-371(1$)-382(to)-382(mak)31(e)-401(her)-392(mortgage)-381(pa)30(ymen)31(t)]TJ -21.09882 -1.2045 TD [(and)-351(she)-372(has)-361(nonnegativ)30(e)-361(equit)30(y)-381(in)-351(her)-362(house)-361($that)-362(is,)-362((3.2))-352(do)-30(es)-361(not)-352(hold$,)-372(then)-361(if)-352(the)]TJ 0 -1.21454 TD [(household)-341(c)30(ho)-30(oses)-341(to)-322(sell)-331(her)-331(house)-341($)]TJ /F14 1 Tf 15.74884 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 300.24 329.88 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 306.24 325.56 Tm [(=)-281(0$,)-321(de\fne)-341(the)-331(v)50(alue)-331(function)-331(b)30(y)]TJ /F14 1 Tf -17.14405 -2.51941 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.64 300.36 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 118.2 303.24 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 120.96 300.36 Tm (=0)Tj /F15 1 Tf -1.61102 -0.97866 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 132.24 295.44 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.99746 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 211.56 300.36 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 216.36 295.44 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 227.04 293.64 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 231.72 295.44 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 242.76 293.64 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 247.44 295.44 Tm [($\))-834(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 289.8 287.88 Tm (c;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 300.36 290.16 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 309.36 295.44 Tm (U)Tj /F19 1 Tf 0.93349 1.41529 TD <12>Tj /F14 1 Tf 0.73274 -1.41529 TD (c;)Tj /F8 1 Tf 0.97364 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 340.788 298.668 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 341.04 287.28 Tm <11>Tj /F19 1 Tf 0.6424 2.09784 TD <13>Tj /F8 1 Tf 0.9636 -1.41529 TD (+)Tj /F14 1 Tf 0.98367 0 Td 0.05 Tc (\fE)Tj /F15 1 Tf 7.97011 0 0 7.97011 387.84 293.64 Tm 0 Tc (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 392.28 295.92 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 395.04 293.64 Tm (j)Tj /F15 1 Tf 0.30112 0 Td (y)Tj /F8 1 Tf 11.95517 0 0 11.95517 404.4 295.44 Tm ([$1)Tj /F16 1 Tf 1.3651 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 438.72 292.68 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 445.8 295.44 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 457.2 293.64 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 466.68 295.44 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 477.36 300.36 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 480.12 295.44 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 491.64 300.36 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 494.4 295.44 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td 0.201 Tc ($+)Tj /F14 1 Tf 1.56585 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 539.04 292.68 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 546.12 295.44 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 552.96 293.64 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 560.16 295.44 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 570.84 300.36 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 573.6 295.44 Tm ($])Tj -30.64449 -2.78039 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 253.68 267.12 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 266.52 262.2 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F8 1 Tf 0.73274 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td 0.221 Tc ($+)Tj /F14 1 Tf 1.58593 0 Td 0.04 Tc (qh)Tj /F8 1 Tf 1.03386 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54202 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 442.92 267.12 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 447.6 262.2 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (R)Tj /F8 1 Tf 0.86323 0.93349 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 476.988 265.308 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 477.24 253.92 Tm <11>Tj 0.6424 0.69259 TD (:)Tj /F16 1 Tf -33.0836 -2.77035 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-402(the)-412(agen)31(t)-412(is)-412(in)-411(the)-412(same)-411(state)-413(but)-412(c)31(ho)-30(oses)-422(to)-402(k)31(eep)-421(her)-412(house)-411($)]TJ /F14 1 Tf 28.5868 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 453.72 233.4 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 461.4 229.08 Tm [(=)-411(1$,)-422(de\fne)-421(the)]TJ -30.12254 -1.2045 TD [(v)50(alue)-330(function)-332(b)30(y)]TJ /F14 1 Tf 0 -1.88705 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.64 197.04 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 118.2 199.8 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 120.96 197.04 Tm (=1)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 132.24 192.12 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.99746 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 211.56 197.04 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 216.36 192.12 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 227.04 190.32 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 231.72 192.12 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 242.76 190.32 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 247.44 192.12 Tm [($\))-834(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 289.8 184.44 Tm (c;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 300.36 186.72 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 309.36 192.12 Tm (U)Tj /F8 1 Tf 0.93349 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td [(c;)-170(h)]TJ /F8 1 Tf 1.42532 0 Td (\()Tj /F14 1 Tf 0.38143 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td 0.171 Tc ($[)Tj /F14 1 Tf 0.81304 0 Td 0 Tc <1B>Tj /F8 1 Tf 0.82307 0 Td 0.221 Tc [(+$)221(1)]TJ /F16 1 Tf 2.06773 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <12>Tj /F8 1 Tf 0.4818 0 Td (]\))Tj -13.46029 -2.65994 TD (+)Tj /F14 1 Tf 1.59596 0 Td 0.05 Tc (\fE)Tj /F11 1 Tf 7.97011 0 0 7.97011 301.44 158.4 Tm 0 Tc ($)Tj /F15 1 Tf 0.40652 0 Td (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 309.12 160.68 Tm (0)Tj /F15 1 Tf 7.97011 0 0 7.97011 311.88 158.4 Tm <3B1B>Tj /F20 1 Tf 5.97758 0 0 5.97758 319.44 160.68 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 322.08 158.4 Tm ($)Tj /F18 1 Tf 0.40652 0 Td (j)Tj /F11 1 Tf 0.30113 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td 0.03 Tc [(y;)30<1B>]TJ /F11 1 Tf 1.50563 0 Td 0 Tc ($)Tj /F19 1 Tf 11.95517 0 0 11.95517 348.72 177.12 Tm <14>Tj /F8 1 Tf 3.89455 -0.79296 TD ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 426.24 164.76 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 433.44 167.64 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 444.84 165.84 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 454.32 167.64 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 465 171.96 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 467.76 167.64 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 479.28 171.96 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 481.92 167.64 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc <3B1C>Tj /F8 1 Tf 1.19446 0 Td 0.221 Tc (+1)Tj /F14 1 Tf 1.47551 0 Td 0.171 Tc <3B1B>Tj /F18 1 Tf 7.97011 0 0 7.97011 537.36 171.96 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 540.12 167.64 Tm (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td ($)Tj -15.78899 -1.21454 TD (+)Tj /F14 1 Tf 0.76285 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 375.24 150.36 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 382.32 153.12 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 389.16 151.32 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 396.36 153.12 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 407.04 157.44 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 412.44 153.12 Tm [(+)-221(max)]TJ /F19 1 Tf 2.98114 0.81304 TD (\b)Tj /F14 1 Tf 0.58217 -0.81304 TD 0.04 Tc (qh)Tj /F8 1 Tf 1.03386 0 Td 0 Tc (\()Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.76285 0 Td 0.221 Tc [(+1)221(;)]TJ /F14 1 Tf 1.91716 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 556.56 157.44 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 561.2401 153.12 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F19 1 Tf 0.49184 0.81304 TD (\t)Tj /F8 1 Tf 0.58217 -0.81304 TD (\))Tj /F19 1 Tf 0.79296 2.0075 TD <15>Tj /F8 1 Tf -32.30067 -3.57335 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 253.68 139.32 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 266.52 134.4 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F8 1 Tf 0.73274 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (m)Tj /F8 1 Tf 0.85319 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54203 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 405.24 139.32 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 409.92 134.4 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td 0.04 Tc <0E68>Tj /F8 1 Tf 1.03386 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (:)Tj /F8 1 Tf -29.8114 -1.887 TD (where)Tj /F14 1 Tf 2.8808 0 Td (m)Tj /F8 1 Tf 0.8532 0 Td ($)Tj /F14 1 Tf 0.3814 0 Td <1C>Tj /F8 1 Tf 0.542 0 Td (;)Tj /F14 1 Tf 0.4416 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 179.16 116.16 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 183.84 111.84 Tm 0.381 Tc [($)9(=0f)381(o)381(r)]TJ /F14 1 Tf 4.32616 0 Td 0 Tc <1C>Tj /F16 1 Tf 0.90338 0 Td <15>Tj /F14 1 Tf 1.15431 0 Td 0.08 Tc (T:)Tj /F8 1 Tf 1.31491 0 Td 0 Tc [(Notice)-391(that)-382(w)31(e)-391(are)-392(making)-391(the)-381(assumption)-403(that)-382(the)]TJ -14.6046 -1.2145 TD [(age)-320(sho)-31(c)31(k)-342(o)-30(ccurs)-331(b)-30(efore)-331(the)-331(price)-341(sho)-31(c)31(k)-331(since)-341(w)30(e)-341(use)]TJ /F14 1 Tf 22.7048 0 Td (h)Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.3814 0 Td <1B>Tj /F8 1 Tf 0.6023 0 Td [($)-322(instead)-341(of)]TJ /F14 1 Tf 5.1994 0 Td (h)Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.3814 0 Td <1B>Tj /F18 1 Tf 7.97011 0 0 7.97011 471.72 101.64 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 474.48 97.32 Tm ($.)Tj -14.12276 -2.49934 TD (9)Tj ET endstream endobj 12 0 obj << /Length 22768 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 89.52 683.16 Tm 0 g [(W)81(e)-381(let)-382(an)-371(indicator)-382(function)-381(for)-372(in)30(v)30(olun)30(tary)-392(default)-381(b)-30(e)-381(denoted)]TJ /F14 1 Tf 27.93436 0 Td (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 433.56 687.48 Tm (I)Tj /F8 1 Tf 11.95517 0 0 11.95517 438.36 683.16 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td [($)-362(=)-361(1)-371(in)-382(the)-381(ev)30(en)31(t)]TJ /F14 1 Tf -31.66831 -1.21454 TD (H)Tj /F8 1 Tf 1.29484 0 Td [(=)-411(1)-402(and)-401((3.1))-402(where)]TJ /F14 1 Tf 9.36499 0 Td (!)Tj /F8 1 Tf 1.06397 0 Td 0.401 Tc (=$)Tj /F14 1 Tf 1.54578 0 Td 0 Tc [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.99746 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 305.4 673.08 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 310.08 668.64 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 320.76 666.84 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 325.56 668.64 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 336.6 666.84 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 341.28 668.64 Tm [($\),)-422(zero)-401(otherwise.)-693(Similarly)80(,)-432(w)31(e)-411(let)-412(an)]TJ -22.52415 -1.2045 TD [(indicator)-271(function)-261(for)-262(v)31(olun)30(tary)-282(default)-261(b)-30(e)-271(denoted)]TJ /F14 1 Tf 21.75126 0 Td (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 342.12 658.56 Tm (V)Tj /F8 1 Tf 11.95517 0 0 11.95517 349.44 654.2401 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td [($)-271(=)-281(1)-261(in)-261(the)-271(ev)30(en)31(t)-282(that)]TJ /F14 1 Tf 9.72634 0 Td (H)Tj /F8 1 Tf 1.16435 0 Td 0.281 Tc (=1)Tj /F14 1 Tf 1.53574 0 Td 0 Tc (;)Tj /F8 1 Tf 0.53199 0 Td ($3.1$\))Tj -37.18893 -1.2045 TD [(do)-30(es)-331(not)-322(hold)-331(but)-332($3)]TJ /F14 1 Tf 8.79285 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(2$)-321(holds,)-332(and)]TJ /F14 1 Tf 6.07269 -2.14802 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 262.32 619.2 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 269.88 621.96 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 272.64 619.2 Tm (=0)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 283.92 614.16 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F14 1 Tf 0.66248 0 Td 0.271 Tc (>V)Tj /F15 1 Tf 7.97011 0 0 7.97011 325.92 619.2 Tm 0 Tc (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 333.48 621.96 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 336.12 619.2 Tm (=1)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 347.52 614.16 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj -24.06992 -2.13799 TD (where)Tj /F14 1 Tf 2.86069 0 Td (!)Tj /F8 1 Tf 0.97364 0 Td 0.331 Tc (=$)Tj /F14 1 Tf 1.47551 0 Td 0 Tc [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>81(;)1<1B>]TJ /F8 1 Tf 1.98742 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 210.24 592.92 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 214.92 588.6 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 225.6 586.8 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 230.4 588.6 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 241.44 586.8 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 246 588.6 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (;)Tj /F8 1 Tf 0.27101 0 Td [(zero)-361(otherwise.)-542(Finally)80(,)-371(w)30(e)-371(let)-361(an)-351(indicator)-362(function)-361(for)]TJ -15.58824 -1.2045 TD [(a)-381(house)-402(sale)-401(b)-30(e)-391(denoted)]TJ /F14 1 Tf 10.79031 0 Td (S)Tj /F8 1 Tf 0.66247 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.98742 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 288.24 578.52 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 292.92 574.2 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 303.6 572.4 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 308.4 574.2 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 319.44 572.4 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 324.12 574.2 Tm [($\))-382(=)-382(1)-381(in)-391(the)-402(ev)31(en)30(t)-402(that)]TJ /F14 1 Tf 10.95091 0 Td (H)Tj /F8 1 Tf 1.26473 0 Td 0.391 Tc (=1)Tj /F14 1 Tf 1.64615 0 Td 0 Tc (;)Tj /F8 1 Tf 0.65244 0 Td [((3.1))-382(and)]TJ -35.60301 -1.21453 TD [((3.2)do)-322(not)-321(hold,)-331(but:)]TJ /F14 1 Tf 15.13655 -1.2045 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 262.32 550.2 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 269.88 553.08 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 272.64 550.2 Tm (=0)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 283.92 545.28 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F14 1 Tf 0.66248 0 Td 0.271 Tc (>V)Tj /F15 1 Tf 7.97011 0 0 7.97011 325.92 550.2 Tm 0 Tc (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 333.48 553.08 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 336.12 550.2 Tm (=1)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 347.52 545.28 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj -24.06992 -1.71641 TD (where)Tj /F14 1 Tf 2.83057 0 Td (!)Tj /F8 1 Tf 0.92345 0 Td 0.271 Tc (=$)Tj /F14 1 Tf 1.41529 0 Td 0 Tc [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.99746 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 208.68 529.08 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 213.36 524.76 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 224.04 522.96 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 228.72 524.76 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 239.76 522.96 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 244.44 524.76 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (;)Tj /F8 1 Tf 0.59221 0 Td [(zero)-331(otherwise.)-451(With)-332(these)-341(de\fnitions:)]TJ /F14 1 Tf -6.85561 -2.14802 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 185.52 497.28 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 195 499.08 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td 0.271 Tc [($=)-10($)271(1)]TJ /F16 1 Tf 2.79042 0 Td 0 Tc <00>Tj /F14 1 Tf 0.99371 0 Td (S)Tj /F8 1 Tf 0.66248 0 Td (\()Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($\))Tj /F16 1 Tf 0.98368 0 Td <01>Tj /F14 1 Tf 0.50187 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 300 504.12 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 307.56 506.88 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 310.2 504.12 Tm (=1)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 321.48 499.08 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td [($\))-222(+)]TJ /F14 1 Tf 1.96735 0 Td (S)Tj /F8 1 Tf 0.66247 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <01>Tj /F14 1 Tf 0.50187 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 400.08 504.12 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 407.64 506.88 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 410.4 504.12 Tm (=0)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 421.68 499.08 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj -30.2731 -2.13799 TD (where)Tj /F14 1 Tf 2.83057 0 Td (!)Tj /F8 1 Tf 0.92345 0 Td 0.271 Tc (=$)Tj /F14 1 Tf 1.41529 0 Td 0 Tc [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.99746 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 208.68 477.84 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 213.36 473.52 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 224.04 471.72 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 228.72 473.52 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 239.76 471.72 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 244.44 473.52 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (:)Tj /F5 1 Tf -13.72126 -2.38892 TD [(Case)-381(2:)]TJ /F14 1 Tf 4.00496 0 Td <1C>Tj /F8 1 Tf 0.81304 0 Td [(=)-281(0)-321($The)-331(agen)31(t)-332(just)-332(b)-30(ecame)-340(mid-aged$)]TJ /F16 1 Tf -4.82804 -3.40271 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(In)-332(the)-331(agen)31(t)-332(con)31(tin)30(ues)-342(to)-331(ren)30(t,)-332(her)-331(v)50(alue)-331(function)-331(is:)]TJ /F14 1 Tf 0.19071 -2.71012 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 113.04 376.8 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 120.6 379.56 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 123.24 376.8 Tm (=0)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 134.64 371.88 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 145.32 370.08 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 150 371.88 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 161.04 370.08 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 165.72 371.88 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td [($)-813(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 234.36 364.2 Tm (c;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 244.92 366.48 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 253.8 371.88 Tm (U)Tj /F19 1 Tf 0.93349 1.40525 TD <12>Tj /F14 1 Tf 0.74278 -1.40525 TD (c;)Tj /F8 1 Tf 0.9636 0.93349 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 285.228 374.988 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 285.48 363.6 Tm <11>Tj /F19 1 Tf 0.65244 2.09784 TD <13>Tj /F8 1 Tf 0.95356 -1.40525 TD (+)Tj /F14 1 Tf 0.98367 0 Td 0.06 Tc (\fE)Tj /F15 1 Tf 7.97011 0 0 7.97011 332.4 369.96 Tm 0 Tc (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 336.84 372.24 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 339.48 369.96 Tm (j)Tj /F15 1 Tf 0.30112 0 Td (y)Tj /F21 1 Tf 5.97758 0 0 5.97758 346.08 368.88 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 352.68 371.88 Tm ([$1)Tj /F16 1 Tf 1.3651 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 387 369 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 394.2 371.88 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 405.6 370.08 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 415.08 371.88 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 425.76 376.8 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 428.52 371.88 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 440.04 376.8 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 442.68 371.88 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td 0.211 Tc ($+)Tj /F14 1 Tf 1.57589 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 498.48 369 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 505.68 371.88 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 512.52 370.08 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 519.6 371.88 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 530.28 376.8 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 533.16 371.88 Tm ($])Tj -31.89917 -2.79042 TD (s.t.)Tj /F14 1 Tf 1.73649 0 Td (c)Tj /F8 1 Tf 0.65244 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 198.24 343.44 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 210.96 338.52 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F11 1 Tf 7.97011 0 0 7.97011 235.8 336.72 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 243.12 338.52 Tm (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 261 336.72 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 265.8 338.52 Tm [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.59221 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (R)Tj /F8 1 Tf 0.86323 0.93349 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 325.548 341.748 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 325.8 330.24 Tm <11>Tj /F16 1 Tf -19.77387 -2.50937 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-462(a)-462(mortgage)-461(con)30(tract)-472(is)-472(budget)-462(feasible)-481($i.e.)]TJ /F14 1 Tf 21.07875 0 Td (y)Tj /F11 1 Tf 7.97011 0 0 7.97011 359.04 298.44 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 367.44 300.24 Tm (+)Tj /F19 1 Tf 1.08405 0.81304 TD <00>Tj /F14 1 Tf 0.45169 -0.81304 TD (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 391.92 298.44 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 399.36 300.24 Tm <00>Tj /F14 1 Tf 1.00375 0 Td <0B71>Tj ET q 6.84 0 0 -0.48 424.428 310.428 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 424.44 300.24 Tm (h)Tj /F16 1 Tf 0.79296 0 Td <01>Tj /F8 1 Tf 0.49184 0 Td (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 445.68 298.44 Tm (f)Tj /F15 1 Tf 0.52697 0 Td <10>Tj /F11 1 Tf 0.54203 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td 0.15 Tc [(FR)150(M)]TJ /F18 1 Tf 2.75529 0 Td 0 Tc (g)Tj /F19 1 Tf 11.95517 0 0 11.95517 487.44 309.96 Tm <01>Tj /F8 1 Tf 0.62232 -0.81304 TD [(\(1)-321(+)]TJ /F14 1 Tf 2.26847 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.69259 0 Td <00>Tj /F14 1 Tf -36.35582 -1.32495 TD (m)Tj /F8 1 Tf 0.85319 0 Td ($0;)Tj /F14 1 Tf 1.31491 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 144.12 288.72 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 148.8 284.4 Tm ($)Tj /F16 1 Tf 0.62232 0 Td <00>Tj /F14 1 Tf 1.02382 0 Td <0E>Tj ET q 6.84 0 0 -0.48 174.108 294.588 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 174.12 284.4 Tm (h)Tj /F16 1 Tf 0.90337 0 Td <15>Tj /F8 1 Tf 1.10412 0 Td [(0)-361(for)]TJ /F14 1 Tf 2.37889 0 Td <10>Tj /F16 1 Tf 0.84315 0 Td 0.342 Tc (2f)Tj /F14 1 Tf 1.50562 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0 Tc (g)Tj /F5 1 Tf 1.26472 0 Td (and)Tj /F14 1 Tf 2.5696 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 369.96 282.6 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 377.64 284.4 Tm <00>Tj /F14 1 Tf 1.02383 0 Td 0.01 Tc <0B71>Tj ET q 6.84 0 0 -0.48 403.068 294.588 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 403.08 284.4 Tm 0 Tc (h)Tj /F16 1 Tf 0.803 0 Td <01>Tj /F8 1 Tf 0.52195 0 Td (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 424.8 282.48 Tm (f)Tj /F15 1 Tf 0.52697 0 Td <10>Tj /F11 1 Tf 0.54203 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td 0.15 Tc [(FR)150(M)]TJ /F18 1 Tf 2.75529 0 Td 0 Tc (g)Tj /F16 1 Tf 11.95517 0 0 11.95517 470.52 284.4 Tm <15>Tj /F8 1 Tf 1.11416 0 Td [(0\),)-372(then)-361(the)]TJ -31.99955 -1.2045 TD [(v)50(alue)-330(function)-332(of)-321(an)-331(agen)31(t)-322(c)31(ho)-30(osing)-342(con)31(tract)]TJ /F14 1 Tf 19.29207 0 Td <10>Tj /F8 1 Tf 0.82307 0 Td [(is)-332(giv)31(en)-341(b)30(y:)]TJ /F14 1 Tf -20.11515 -2.14802 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 110.64 250.08 Tm <10>Tj -0.31618 -1.12922 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 117.6 244.32 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 128.28 242.52 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 132.96 244.32 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 144 242.52 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 148.68 244.32 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 204.12 249.24 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 208.8 244.32 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 219.48 242.52 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 224.28 244.32 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 235.32 242.52 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 240 244.32 Tm [($\))-834(=)-1385(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 278.28 236.76 Tm (c)Tj /F18 1 Tf 0.46674 0 Td <15>Tj /F11 1 Tf 0.82809 0 Td (0)Tj /F15 1 Tf 0.52697 0 Td (;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 299.64 239.04 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 302.28 236.76 Tm <15>Tj /F11 1 Tf 0.82809 0 Td (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 315.12 244.32 Tm (U)Tj /F19 1 Tf 0.93349 0.81304 TD <00>Tj /F14 1 Tf 0.46172 -0.81304 TD (c;)Tj ET q 6.84 0 0 -0.48 342.108 254.508 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 342.12 244.32 Tm <6812>Tj /F19 1 Tf 1.0439 0.81304 TD <01>Tj /F8 1 Tf -7.98985 -3.5332 TD (+)Tj /F14 1 Tf 1.606 0 Td 0.06 Tc (\fE)Tj /F11 1 Tf 7.97011 0 0 7.97011 294.24 209.88 Tm 0 Tc ($)Tj /F15 1 Tf 0.40652 0 Td (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 301.92 212.16 Tm (0)Tj /F15 1 Tf 7.97011 0 0 7.97011 304.68 209.88 Tm <3B1B>Tj /F20 1 Tf 5.97758 0 0 5.97758 312.12 212.16 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 314.88 209.88 Tm ($)Tj /F18 1 Tf 0.40652 0 Td (j)Tj /F11 1 Tf 0.30113 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td 0.03 Tc (y;)Tj /F11 1 Tf 0.85821 0 Td 0 Tc (0$)Tj /F19 1 Tf 11.95517 0 0 11.95517 340.56 228.6 Tm <14>Tj /F8 1 Tf 1.57589 -0.81304 TD ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 390.48 216 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 397.68 218.88 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 411.6 224.52 Tm <10>Tj -0.31618 -1.11416 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 418.44 218.88 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 429.12 223.2 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 432 218.88 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 443.52 223.2 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 446.16 218.88 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc <3B1C>Tj /F8 1 Tf 1.19446 0 Td 0.221 Tc (+1)Tj /F14 1 Tf 1.47551 0 Td 0.171 Tc <3B1B>Tj /F18 1 Tf 7.97011 0 0 7.97011 501.48 223.2 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 504.36 218.88 Tm (;)Tj /F14 1 Tf 0.44165 0 Td 0.06 Tc [<103B>-110(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 526.44 223.2 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 531.2401 218.88 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 541.92 217.08 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 546.6 218.88 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 557.64 217.08 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 562.32 218.88 Tm ($\))Tj -17.59574 -1.26472 TD (+)Tj /F14 1 Tf 0.76285 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 367.08 201 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 374.16 203.76 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 381 201.96 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 388.2 203.76 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 398.88 208.2 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 404.4 203.76 Tm [(+)-221(max)]TJ /F19 1 Tf 2.9711 0.81304 TD (\b)Tj /F14 1 Tf 0.58217 -0.81304 TD (q)Tj ET q 6.84 0 0 -0.48 452.508 214.068 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 452.52 203.76 Tm (h)Tj /F16 1 Tf 0.78293 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td (\(1;)Tj /F14 1 Tf 1.31491 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 511.44 208.2 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 516.12 203.76 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 526.8 201.96 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 531.48 203.76 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 542.52 201.96 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 547.2 203.76 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F19 1 Tf 0.49184 0.81304 TD (\t)Tj /F8 1 Tf 0.57214 -0.81304 TD (\))Tj /F19 1 Tf 0.803 2.07776 TD <15>Tj /F8 1 Tf -32.13004 -3.66369 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 246.24 189.72 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 259.08 184.8 Tm (=)Tj /F14 1 Tf 1.606 0 Td (y)Tj /F11 1 Tf 7.97011 0 0 7.97011 284.04 183 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 291.36 184.8 Tm (+)Tj /F19 1 Tf 0.98367 0.81304 TD <00>Tj /F14 1 Tf 0.46172 -0.81304 TD (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 314.76 183 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 322.2 184.8 Tm <00>Tj /F14 1 Tf 0.99371 0 Td 0.01 Tc <0B71>Tj ET q 6.84 0 0 -0.48 347.268 194.988 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 347.28 184.8 Tm 0 Tc (h)Tj /F16 1 Tf 0.78292 0 Td <01>Tj /F8 1 Tf 0.50188 0 Td (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 368.52 183 Tm (f)Tj /F15 1 Tf 0.52697 0 Td <10>Tj /F11 1 Tf 0.54203 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td 0.15 Tc [(FR)150(M)]TJ /F18 1 Tf 2.75529 0 Td 0 Tc (g)Tj /F19 1 Tf 11.95517 0 0 11.95517 410.28 194.52 Tm <01>Tj /F8 1 Tf 0.62232 -0.81304 TD [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (m)Tj /F8 1 Tf 0.85319 0 Td ($0;)Tj /F14 1 Tf 1.31491 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 510.12 189.72 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 514.8 184.8 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <0E>Tj ET q 6.84 0 0 -0.48 539.628 194.988 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 539.64 184.8 Tm (h)Tj /F8 1 Tf -27.12132 -1.57589 TD (and)Tj /F14 1 Tf 1.90713 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 244.32 164.16 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 259.08 165.96 Tm <00>Tj /F14 1 Tf 1.606 0 Td 0.01 Tc <0B71>Tj ET q 6.84 0 0 -0.48 291.468 176.148 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 291.48 165.96 Tm 0 Tc (h)Tj /F16 1 Tf 0.78292 0 Td <01>Tj /F8 1 Tf 0.50187 0 Td (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 312.72 164.04 Tm (f)Tj /F15 1 Tf 0.52697 0 Td <10>Tj /F11 1 Tf 0.52697 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td 0.15 Tc [(FR)150(M)]TJ /F18 1 Tf 2.75529 0 Td 0 Tc (g)Tj /F16 1 Tf 11.95517 0 0 11.95517 357.72 165.96 Tm <15>Tj /F8 1 Tf 1.05394 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf -23.97958 -2.54952 TD [(A)-381(newly)-391(mid-aged)-371(agen)31(t)-382(will)-381(con)31(tin)29(ues)-401(to)-372(ren)30(t)-382($that)-372(is,)]TJ /F14 1 Tf 24.40116 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 391.92 139.8 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 394.56 135.48 Tm (\()Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 472.2 139.8 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 476.88 135.48 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 487.56 133.68 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 492.24 135.48 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 503.28 133.68 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 507.96 135.48 Tm [($\))-362(=)-361(0\))]TJ -36.46624 -1.2045 TD (if:)Tj 1.1945 -1.9874 TD [(1.)-492(there)-331(exists)-352(no)-321(con)30(tract)-332($)]TJ /F14 1 Tf 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 247.08 101.64 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 251.76 97.32 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 262.44 95.52 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 267.24 97.32 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 278.28 95.52 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 282.96 97.32 Tm [($\))-322(that)-322(is)-332(budget)-341(feasible;)]TJ 1.65619 -2.49934 TD (10)Tj ET endstream endobj 13 0 obj << /Length 20117 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 86.28 683.16 Tm 0 g [(2.)-492(for)-321(an)30(y)-331(budget)-331(feasible)-341(con)30(tract)-332($)]TJ /F14 1 Tf 15.53805 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 288.96 687.48 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 293.64 683.16 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 304.32 681.36 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 309.12 683.16 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 320.16 681.36 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 324.84 683.16 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (;)Tj /F8 1 Tf 0.59221 0 Td -0.03 Tc [(we)-370(h)-30(ave)]TJ /F14 1 Tf -12.02492 -1.93724 TD 0 Tc (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 206.76 664.92 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 214.32 667.8 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 216.96 664.92 Tm (=0)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 228.24 660 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 238.92 658.2 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 243.72 660 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 254.76 658.2 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 259.44 660 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td ($)Tj /F14 1 Tf 0.6424 0 Td 0.271 Tc (>V)Tj /F15 1 Tf 7.97011 0 0 7.97011 319.92 665.64 Tm 0 Tc <10>Tj -0.33124 -1.11416 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 326.76 660 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.04 Tc [<103B>-130(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 404.28 664.92 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 408.96 660 Tm (\()Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 419.64 658.2 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 424.44 660 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 435.48 658.2 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 440.16 660 Tm ($\))Tj -28.3459 -1.93724 TD [(for)-281(an)30(y)-281($)]TJ /F14 1 Tf 3.63357 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 161.64 641.16 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 166.44 636.84 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 177.12 635.04 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 181.8 636.84 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 192.84 635.04 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 197.52 636.84 Tm [($\))-282(suc)30(h)-301(that)]TJ /F14 1 Tf 5.27972 0 Td (y)Tj /F11 1 Tf 7.97011 0 0 7.97011 266.4 635.04 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 272.76 636.84 Tm (+)Tj /F19 1 Tf 0.89334 0.81304 TD <00>Tj /F14 1 Tf 0.45169 -0.81304 TD (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 294.96 635.04 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 302.4 636.84 Tm <00>Tj /F14 1 Tf 1.00375 0 Td <0B71>Tj ET q 6.84 0 0 -0.48 327.468 647.028 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 327.48 636.84 Tm (h)Tj /F16 1 Tf 0.79296 0 Td <01>Tj /F8 1 Tf 0.49184 0 Td (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 348.72 635.04 Tm (f)Tj /F15 1 Tf 0.52697 0 Td <10>Tj /F11 1 Tf 0.54203 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td 0.15 Tc [(FR)150(M)]TJ /F18 1 Tf 2.75529 0 Td 0 Tc (g)Tj /F19 1 Tf 11.95517 0 0 11.95517 390.48 646.56 Tm <01>Tj /F8 1 Tf 0.63236 -0.81304 TD [($1)-131(+)]TJ /F14 1 Tf 1.89709 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.51191 0 Td <00>Tj /F14 1 Tf 0.90338 0 Td (m)Tj /F8 1 Tf 0.85319 0 Td ($0;)Tj /F14 1 Tf 1.31491 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 486.12 641.16 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 490.8 636.84 Tm ($)Tj /F16 1 Tf 0.51191 0 Td <00>Tj /F14 1 Tf 0.90338 0 Td <0E>Tj ET q 6.84 0 0 -0.48 513.468 647.028 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 513.48 636.84 Tm (h)Tj /F16 1 Tf 0.84315 0 Td <15>Tj /F8 1 Tf 1.05394 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf -37.85141 -1.80675 TD [(The)-330(agen)30(t)-311(c)30(ho)-30(oses)-331(a)-311(feasible)-321(con)30(tract)-321($)]TJ /F14 1 Tf 16.56187 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 304.44 619.56 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 309.12 615.2401 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 319.8 613.44 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 324.6 615.2401 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 335.64 613.44 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 340.32 615.2401 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (;)Tj /F8 1 Tf 0.58218 0 Td [(that)-312(is)-322<0428>]TJ /F14 1 Tf 4.11537 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.04 Tc [<103B>-130(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 478.56 619.56 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 483.24 615.2401 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 493.92 613.44 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 498.72 615.2401 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 509.76 613.44 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 514.32 615.2401 Tm [($\))-282(=)]TJ /F14 1 Tf 2.07776 0 Td <10>Tj /F8 1 Tf -39.07598 -1.2045 TD (and)Tj /F14 1 Tf 1.90712 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 105.48 605.16 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 108.12 600.84 Tm ($)Tj /F14 1 Tf 0.38143 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 185.76 605.16 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 190.44 600.84 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 201.12 599.04 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 205.8 600.84 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 216.84 599.04 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 221.52 600.84 Tm [($\))-282(=)-271(1)]TJ /F14 1 Tf 2.5696 0 Td (;)Tj /F8 1 Tf 0.60225 0 Td (if)Tj /F14 1 Tf -14.2934 -1.93723 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 98.04 583.32 Tm <10>Tj -0.33124 -1.11416 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 104.88 577.68 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.04 Tc [<103B>-130(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 182.4 582.6 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 187.08 577.68 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 197.76 575.88 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 202.56 577.68 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 213.6 575.88 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 218.28 577.68 Tm ($\))Tj /F16 1 Tf 1.03386 0 Td <15>Tj /F8 1 Tf 1.05394 0 Td (max)Tj /F16 1 Tf 1.82682 0 Td (f)Tj /F14 1 Tf 0.50187 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 280.44 582.6 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 288 585.36 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 290.76 582.6 Tm (=0)Tj /F15 1 Tf -1.61102 -0.99371 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 302.04 577.68 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 312.72 575.88 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 317.52 577.68 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 328.56 575.88 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 333.12 577.68 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td 0.171 Tc (;V)Tj /F15 1 Tf 7.97011 0 0 7.97011 383.16 583.32 Tm 0 Tc <10>Tj -0.30113 -1.11416 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 390 577.68 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F16 1 Tf 0.93349 0 Td (n)Tj /F14 1 Tf 0.50187 0 Td 0.04 Tc [<103B>-130(r)]TJ /F18 1 Tf 7.97011 0 0 7.97011 473.52 582.6 Tm 0 Tc (n)Tj /F15 1 Tf 0.52697 0 Td <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 482.52 577.68 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 493.2 575.88 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 497.88 577.68 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 508.92 575.88 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 513.6 577.68 Tm ($\))Tj /F16 1 Tf 0.76285 0 Td (g)Tj /F8 1 Tf -37.70085 -1.93724 TD (where)Tj /F16 1 Tf 2.83057 0 Td (n)Tj /F14 1 Tf 0.50187 0 Td <10>Tj /F8 1 Tf 0.82307 0 Td [(is)-332(de\fned)-340(to)-332(b)-30(e)-321(the)-331(other)-332(t)30(yp)-30(e)-341(of)-321(mortgage.)-431(With)-332(these)-341(de\fnitions:)]TJ /F14 1 Tf -3.12166 -1.93724 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 91.2 529.56 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 100.68 531.36 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td 0.271 Tc [($=)-10($)271(1)]TJ /F16 1 Tf 2.79042 0 Td 0 Tc <00>Tj /F14 1 Tf 0.99371 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 168.96 536.28 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 171.72 531.36 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($\))Tj /F14 1 Tf 0.76285 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 202.56 536.28 Tm (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 210.12 539.16 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 212.76 536.28 Tm (=0)Tj /F15 1 Tf -1.61102 -0.97866 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 224.04 531.36 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td 0.221 Tc ($+)Tj /F14 1 Tf 1.58593 0 Td 0 Tc (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 266.04 536.28 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 268.8 531.36 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F19 1 Tf 0.55206 0.81304 TD <02>Tj /F8 1 Tf 0.41154 -0.81304 TD (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 298.44 529.56 Tm (f)Tj /F11 1 Tf 0.52697 0 Td <0428>Tj /F15 1 Tf 1.11416 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td (\)=)Tj /F15 1 Tf 1.23461 0 Td 0.15 Tc [(FR)150(M)]TJ /F18 1 Tf 2.75529 0 Td 0 Tc (g)Tj /F14 1 Tf 11.95517 0 0 11.95517 353.64 531.36 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 363.12 536.28 Tm 0.15 Tc [(FR)150(M)]TJ -0.33124 -0.97866 TD 0 Tc (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 385.56 531.36 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.221 Tc ($+1)Tj /F18 1 Tf 7.97011 0 0 7.97011 422.64 529.56 Tm 0 Tc (f)Tj /F11 1 Tf 0.52697 0 Td <0428>Tj /F15 1 Tf 1.11416 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td (\)=)Tj /F15 1 Tf 1.23461 0 Td 0.075 Tc [(IO)45(M)]TJ /F18 1 Tf 2.51439 0 Td 0 Tc (g)Tj /F14 1 Tf 11.95517 0 0 11.95517 475.92 531.36 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 485.28 536.28 Tm 0.075 Tc [(IO)45(M)]TJ -0.31618 -0.97866 TD 0 Tc (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 505.8 531.36 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F19 1 Tf 0.38143 0.81304 TD <03>Tj /F14 1 Tf 0.58217 -0.81304 TD (:)Tj /F5 1 Tf -38.27299 -2.55956 TD [(3.1.3)-1125(Y)90(oung)-382(agen)30(ts)]TJ /F8 1 Tf 0 -1.85694 TD [(F)80(or)-281(y)30(oung)-291(agen)31(ts,)-312(the)-291(state)-292(space)-301(is)-301(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 264.12 476.76 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 274.68 478.56 Tm (=)Tj /F14 1 Tf 1.0439 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 298.32 482.88 Tm 0 Tc (+)Tj /F16 1 Tf 11.95517 0 0 11.95517 307.08 478.56 Tm 0.14 Tc <0266>Tj /F14 1 Tf 1.41529 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 329.76 476.76 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 336.12 478.56 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 347.16 476.76 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 356.52 478.56 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 367.56 476.76 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 375.48 478.56 Tm (g)Tj /F8 1 Tf 0.79296 0 Td [(with)-291(t)30(ypical)-301(elemen)31(t)]TJ /F14 1 Tf 8.94341 0 Td (!)Tj /F8 1 Tf 0.92345 0 Td 0.281 Tc (=$)Tj /F14 1 Tf 1.42532 0 Td 0 Tc [(a;)-171(y)]TJ /F8 1 Tf 1.47551 0 Td ($.)Tj -38.9455 -1.21454 TD [(The)-341(v)51(alue)-331(function)]TJ /F14 1 Tf 8.38131 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 179.04 462.24 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 189.6 464.04 Tm 0.281 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 204.6 462.24 Tm 0 Tc (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 211.92 464.04 Tm (\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 220.32 462.24 Tm (Y)Tj /F16 1 Tf 11.95517 0 0 11.95517 231 464.04 Tm (7!)Tj /F14 1 Tf 1.27476 0 Td -0.251 Tc (IR)Tj /F8 1 Tf 1.25469 0 Td 0 Tc [(for)-322(a)-331(y)31(oung)-331(agen)30(t)-331(with)-332(assets)]TJ /F14 1 Tf 12.85804 0 Td (a)Tj /F8 1 Tf 0.84315 0 Td [(and)-321(income)]TJ /F14 1 Tf 5.2195 0 Td (y)Tj /F8 1 Tf 0.83311 0 Td [(solv)30(es)]TJ /F14 1 Tf -32.65199 -2.50937 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 113.88 432.24 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 121.08 434.04 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)]TJ /F8 1 Tf 1.47551 0 Td [($)-823(=)-833(max)]TJ /F15 1 Tf 7.97011 0 0 7.97011 178.68 426.48 Tm (a)Tj /F20 1 Tf 5.97758 0 0 5.97758 183.12 428.76 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 185.88 426.48 Tm <15>Tj /F11 1 Tf 0.82809 0 Td (0)Tj /F19 1 Tf 11.95517 0 0 11.95517 200.52 450.96 Tm <1A>Tj /F14 1 Tf 0.75281 -1.41529 TD (U)Tj /F19 1 Tf 0.93349 1.41529 TD <12>Tj /F14 1 Tf 0.74278 -1.41529 TD (c;)Tj /F8 1 Tf 0.9636 0.94352 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 240.948 437.268 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 241.2 425.88 Tm <11>Tj /F19 1 Tf 0.6424 2.09784 TD <13>Tj /F8 1 Tf 0.9636 -1.41529 TD (+)Tj /F14 1 Tf 0.98367 0 Td 0.05 Tc (\fE)Tj /F15 1 Tf 7.97011 0 0 7.97011 288 432.24 Tm 0 Tc (y)Tj /F20 1 Tf 5.97758 0 0 5.97758 292.44 434.52 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 295.2 432.24 Tm (j)Tj /F15 1 Tf 0.30112 0 Td (y)Tj /F8 1 Tf 11.95517 0 0 11.95517 304.56 434.04 Tm ([$1)Tj /F16 1 Tf 1.3651 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 338.88 431.28 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 348.36 434.04 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 359.76 432.24 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 366.96 434.04 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 377.64 438.96 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 380.52 434.04 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 392.04 438.96 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 394.68 434.04 Tm 0.221 Tc ($+)Tj /F14 1 Tf 1.58592 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 419.64 431.28 Tm (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 429.12 434.04 Tm (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 435.96 432.24 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 445.44 434.04 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 456.12 438.96 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 459 434.04 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 470.52 438.96 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 473.16 434.04 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td ($])Tj /F19 1 Tf 0.63236 1.41529 TD <1B>Tj /F8 1 Tf -34.55911 -4.19567 TD (s.t.)Tj /F14 1 Tf 1.74652 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 144.96 405.72 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 157.68 400.8 Tm (=)Tj /F14 1 Tf 1.59596 0 Td (y)Tj /F8 1 Tf 0.73274 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td (a)Tj /F8 1 Tf 0.51191 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (R)Tj /F8 1 Tf 0.86323 0.93349 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj ET q 6.84 0 0 -0.48 263.268 403.908 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 263.52 392.52 Tm <11>Tj 0.6424 0.69259 TD (:)Tj /F22 1 Tf 14.34624 0 0 14.34624 72 363 Tm [(3.2)-1131(In)33(termediary's)-394(problem)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 340.8 Tm [(All)-341(p)-30(ossible)-352(uses)-352(of)-331(loanable)-330(funds)-352(m)30(ust)-342(earn)-341(the)-342(same)-341(return)-342(for)-332(the)-341(in)30(termediary)80(.)-482(In)-342(other)]TJ 0 -1.2045 TD [(w)30(ords,)-342(the)-331(follo)30(wing)-330(arbitrage)-322(conditions)-341(m)30(ust)-332(hold)-332(at)-321(all)-331(dates:)]TJ /F14 1 Tf 13.20935 -1.93724 TD (r)Tj /F8 1 Tf 0.75281 0 Td (=)Tj /F14 1 Tf 1.03386 0 Td (A)Tj /F8 1 Tf 0.73274 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (R)Tj /F16 1 Tf 0.97364 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <0E>Tj /F8 1 Tf 0.47176 0 Td 0.281 Tc ($=)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (Aq)Tj /F8 1 Tf 1.2045 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F8 1 Tf 0.99371 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf -26.0975 -1.93724 TD [(This)-301(pins)-302(do)30(wn)-290(all)-291(prices)-302(as)-291(a)-291(function)-291(of)-281(returns)-302(to)-292(storage.)-422(Note)-290(that)-282(the)-301(v)50(alue)-291(of)-281(the)-301(house)]TJ 0 -1.2045 TD [(is)-342(m)30(ultiplied)-341(b)30(y)-341($1)-221(+)]TJ /F14 1 Tf 9.09397 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td [($)-322(b)-30(ecause,)-350(b)30(y)-341(con)30(v)31(en)30(tion,)-352(the)-341(purc)30(hase)-341(of)-331(the)-332(house)-341(tak)30(es)-351(place)-331(at)-331(the)]TJ -9.56574 -1.2045 TD [(b)-30(eginning)-331(of)-321(p)-30(erio)-30(d)]TJ /F14 1 Tf 8.65232 0 Td (t)Tj /F8 1 Tf 0.35131 0 Td (.)Tj -7.53816 -1.21454 TD [(The)-270(arbitrage)-262(condition)-260(implies)-272(as)-261(usual)-271(that)-262(the)-261(mark)30(et)-271(v)50(alue)-260(of)-251(eac)31(h)-271(unit)-262(of)-251(houses)-281(is)-261(the)]TJ -1.46548 -1.2045 TD [(presen)30(t)-322(discoun)31(ted)-332(v)50(alue)-310(of)-301(all)-311(future)-312(ren)30(ts)-312(that)-312(unit)-312(w)31(ould)-311(earn)-311(on)-301(the)-311(sp)-31(ot)-311(mark)30(et.)-442(Indeed:)]TJ /F11 1 Tf 7.97011 0 0 7.97011 213.24 204.36 Tm (+)Tj /F18 1 Tf 0.82809 0 Td (1)Tj /F19 1 Tf 11.95517 0 0 11.95517 212.16 200.76 Tm (X)Tj /F15 1 Tf 7.97011 0 0 7.97011 213.84 175.68 Tm (t)Tj /F11 1 Tf 0.37641 0 Td (=1)Tj /F14 1 Tf 11.95517 0 0 11.95517 237.24 197.52 Tm (R)Tj /F16 1 Tf 0.97364 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <0E>Tj ET q 38.64 0 0 -0.48 232.548 192.588 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 232.56 181.2 Tm [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F15 1 Tf 7.97011 0 0 7.97011 267.6 184.68 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 282.24 189.36 Tm (=)Tj /F11 1 Tf 7.97011 0 0 7.97011 302.4 204.36 Tm (+)Tj /F18 1 Tf 0.82809 0 Td (1)Tj /F19 1 Tf 11.95517 0 0 11.95517 301.32 200.76 Tm (X)Tj /F15 1 Tf 7.97011 0 0 7.97011 303 175.68 Tm (t)Tj /F11 1 Tf 0.37641 0 Td (=1)Tj /F14 1 Tf 11.95517 0 0 11.95517 342.6 197.52 Tm (r)Tj ET q 47.4 0 0 -0.48 321.828 192.588 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 321.84 181.2 Tm (A)Tj /F8 1 Tf 0.73274 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F15 1 Tf 7.97011 0 0 7.97011 365.64 184.68 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 282.24 149.52 Tm (=)Tj /F14 1 Tf 3.10159 0.67251 TD (r)Tj ET q 39.24 0 0 -0.48 302.508 152.748 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 302.52 141.24 Tm (A)Tj /F8 1 Tf 0.73274 0 Td [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F11 1 Tf 7.97011 0 0 7.97011 346.08 164.4 Tm (+)Tj /F18 1 Tf 0.8281 0 Td (1)Tj /F19 1 Tf 11.95517 0 0 11.95517 344.88 160.8 Tm (X)Tj /F15 1 Tf 7.97011 0 0 7.97011 346.56 135.72 Tm (t)Tj /F11 1 Tf 0.37641 0 Td (=0)Tj /F8 1 Tf 11.95517 0 0 11.95517 381.72 157.56 Tm (1)Tj ET q 38.64 0 0 -0.48 365.388 152.748 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 365.4 141.24 Tm [(\(1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F15 1 Tf 7.97011 0 0 7.97011 400.44 144.72 Tm (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 282.24 114.72 Tm (=)Tj 1.81679 0.68255 TD (1)Tj ET q 8.88 0 0 -0.48 302.508 117.948 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 302.52 106.56 Tm (A)Tj /F8 1 Tf -1.69634 -0.77289 TD (=)Tj /F14 1 Tf 1.59596 0 Td 0.04 Tc (q:)Tj /F8 1 Tf 0.12045 -2.49934 TD 0 Tc (11)Tj ET endstream endobj 14 0 obj << /Length 19737 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 89.52 683.16 Tm 0 g [(Arbitrage)-362(also)-361(requires)-372(that)-352(for)-352(all)-361(mortgage)-351(issued)-372(at)-352(a)-351(giv)31(en)-371(date,)-372(the)-361(exp)-30(ected)-370(return)]TJ -1.46548 -1.21454 TD [(on)-321(the)-321(mortgage)-321(net)-332(of)-311(exp)-29(ected)-341(foreclosure)-331(costs)-332(co)30(v)31(er)-342(the)-321(opp)-30(ortunit)29(y)-331(cost)-322(of)-321(funds,)-332(whic)31(h)]TJ 0 -1.2045 TD [(b)30(y)-331(assumption)-342(is)-342(the)-331(returns)-333(to)-321(storage)-332(plus)-332(the)-331(servicing)-351(premium)]TJ /F14 1 Tf 29.10875 0 Td <1E>Tj /F8 1 Tf 0.58218 0 Td (.)Tj -28.22545 -1.2045 TD [(T)81(o)-291(mak)30(e)-311(this)-292(precise,)-321(denote)-300(the)-291(v)50(alue)-301(to)-291(the)-291(in)30(termediary)-312(of)-291(a)-281(mortgage)-291(con)31(tract)-302(held)-301(b)31(y)]TJ -1.46548 -1.21454 TD [(a)-321(mid-aged)-331(agen)31(t)-332(in)-331(state)]TJ /F14 1 Tf 11.242 0 Td (!)Tj /F16 1 Tf 0.92345 0 Td (2)Tj /F8 1 Tf 0.94352 0 Td (\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 237.12 623.52 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 250.56 625.32 Tm -0.03 Tc (by)Tj /F14 1 Tf 1.35506 0 Td 0 Tc (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td [($.)-432(Again,)-331(w)31(e)-341(need)-331(to)-331(consider)-331(sev)30(eral)-351(cases.)]TJ /F16 1 Tf -16.92322 -2.28854 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-221(the)-221(agen)31(t)-222(a)-210(homeo)31(wner)-231(whose)-230(mortgage)-221(is)-221(not)-221(paid)-211(o\013,)-241(so)-221(that)]TJ /F14 1 Tf 26.94065 0 Td (!)Tj /F8 1 Tf 0.92345 0 Td 0.271 Tc (=$)Tj /F14 1 Tf 1.41529 0 Td 0 Tc [(a;)-171(y)-40(;)]TJ /F8 1 Tf 1.91716 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc [<3B1C>71(;)1<1B>]TJ /F8 1 Tf 1.98742 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 526.08 602.28 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 530.76 597.96 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 541.44 596.16 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 546.2401 597.96 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 557.28 596.16 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 561.96 597.96 Tm ($\))Tj -38.53396 -1.2045 TD (with)Tj /F14 1 Tf 2.22832 0 Td <1C>Tj /F16 1 Tf 0.81304 0 Td (2)Tj /F8 1 Tf 0.94352 0 Td ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;T)Tj /F16 1 Tf 1.37514 0 Td 0 Tc <00>Tj /F8 1 Tf 0.99371 0 Td [(1],)-331(then:)]TJ /F14 1 Tf -7.227 -2.20825 TD (W)Tj /F8 1 Tf 1.06397 0 Td (\()Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.834 Tc ($=)Tj /F19 1 Tf 2.8105 0.803 TD 0 Tc <00>Tj /F14 1 Tf 0.45169 -0.803 TD (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 175.32 562.08 Tm (I)Tj /F8 1 Tf 11.95517 0 0 11.95517 180.12 557.16 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.221 Tc ($+)Tj /F14 1 Tf 1.58593 0 Td 0 Tc (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 221.4 562.08 Tm (V)Tj /F8 1 Tf 11.95517 0 0 11.95517 228.72 557.16 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F19 1 Tf 0.38143 0.803 TD <01>Tj /F8 1 Tf 0.62232 -0.803 TD (max)Tj /F16 1 Tf 1.82682 0 Td (f)Tj /F8 1 Tf 0.50188 0 Td ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <14>Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td 0.04 Tc (qh)Tj /F8 1 Tf 1.03386 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td 0.171 Tc (;b)Tj /F8 1 Tf 0.85319 0 Td 0 Tc ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54203 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 389.04 562.08 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 393.72 557.16 Tm ($)Tj /F16 1 Tf 0.38142 0 Td (g)Tj /F8 1 Tf 0.7227 0 Td (+)Tj /F14 1 Tf 0.98367 0 Td (S)Tj /F8 1 Tf 0.66248 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.53199 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 481.44 562.08 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 486.12 557.16 Tm ($)Tj -27.29196 -2.18817 TD (+)Tj /F19 1 Tf 0.93349 0.81304 TD <00>Tj /F8 1 Tf 0.45169 -0.81304 TD (1)Tj /F16 1 Tf 0.71266 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 206.88 535.92 Tm (I)Tj /F8 1 Tf 11.95517 0 0 11.95517 211.68 531 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 253.2 535.92 Tm (V)Tj /F8 1 Tf 11.95517 0 0 11.95517 260.52 531 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (S)Tj /F8 1 Tf 0.66248 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td ($)Tj /F19 1 Tf 0.38143 0.81304 TD <01>Tj 0.62232 0.59221 TD <12>Tj /F14 1 Tf 0.83311 -0.73274 TD (m)Tj /F8 1 Tf 0.85319 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1C>Tj /F8 1 Tf 0.54203 0 Td (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 377.52 543.36 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 382.2 539.04 Tm ($)Tj ET q 52.68 0 0 -0.48 334.068 534.228 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 336.84 522.72 Tm 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (r)Tj /F8 1 Tf 0.68255 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td <1E>Tj /F8 1 Tf 1.13424 0.69259 TD (+)Tj /F14 1 Tf 0.98367 0 Td (E)Tj /F15 1 Tf 7.97011 0 0 7.97011 411 529.08 Tm (!)Tj /F20 1 Tf 5.97758 0 0 5.97758 416.52 531.36 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 419.28 529.08 Tm (j)Tj /F15 1 Tf 0.30112 0 Td (!)Tj /F19 1 Tf 11.95517 0 0 11.95517 429.6 547.8 Tm <14>Tj /F14 1 Tf 0.63236 -0.73274 TD (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 460.56 543.36 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 463.32 539.04 Tm 0.171 Tc (;y)Tj /F18 1 Tf 7.97011 0 0 7.97011 474.84 543.36 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 477.48 539.04 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td 0.171 Tc <3B1C>Tj /F8 1 Tf 1.19446 0 Td 0.221 Tc (+1)Tj /F14 1 Tf 1.47551 0 Td 0.171 Tc <3B1B>Tj /F18 1 Tf 7.97011 0 0 7.97011 532.8 543.36 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 535.68 539.04 Tm (;)Tj /F16 1 Tf 0.44165 0 Td <01>Tj /F8 1 Tf 0.28105 0 Td ($)Tj ET q 111.72 0 0 -0.48 437.148 534.228 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 469.32 522.72 Tm 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (r)Tj /F8 1 Tf 0.69259 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td <1E>Tj /F19 1 Tf 3.3726 2.09784 TD -0.01 Tc <1513>Tj /F16 1 Tf -38.52392 -4.54699 TD 0 Tc <0F>Tj /F8 1 Tf 0.99371 0 Td [(If)-392(the)-401(household)-402(just)-392(b)-30(ecame)-401(mid-aged)-401(and)-391(her)-392(budget)-401(set)-402(is)-402(not)-392(empt)30(y)-401(so)-402(that)]TJ /F14 1 Tf 35.34203 0 Td (!)Tj /F8 1 Tf 1.03386 0 Td (=)Tj -36.3759 -1.21453 TD ($)Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 111.96 477.12 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 116.64 478.92 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 127.68 477.12 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 132.36 478.92 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 187.8 483.24 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 192.6 478.92 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 203.28 477.12 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 207.96 478.92 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 219 477.12 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 223.68 478.92 Tm [($\))-322(and)]TJ /F14 1 Tf 2.99117 0 Td (y)Tj /F11 1 Tf 7.97011 0 0 7.97011 265.2 477.12 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 272.52 478.92 Tm (+)Tj /F14 1 Tf 0.98367 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 290.4 477.12 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 295.2 478.92 Tm [($1)-221(+)]TJ /F14 1 Tf 2.07776 0 Td (r)Tj /F8 1 Tf 0.47176 0 Td ($)Tj /F16 1 Tf 0.59221 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (m)Tj /F8 1 Tf 0.85319 0 Td ($0;)Tj /F14 1 Tf 1.31491 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 387.6 483.24 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 392.28 478.92 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <0E>Tj ET q 6.84 0 0 -0.48 416.988 489.108 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 417 478.92 Tm (h)Tj /F16 1 Tf 0.84315 0 Td <15>Tj /F8 1 Tf 1.05394 0 Td (0)Tj /F14 1 Tf -18.25821 -2.83057 TD (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.281 Tc ($=)Tj /F14 1 Tf 1.79671 0.67251 TD 0 Tc (m)Tj /F8 1 Tf 0.85319 0 Td ($0;)Tj /F14 1 Tf 1.31491 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 310.68 457.44 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 315.36 453.12 Tm ($)Tj ET q 52.08 0 0 -0.48 267.828 448.308 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 270.24 436.8 Tm 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (r)Tj /F8 1 Tf 0.69259 0 Td (+)Tj /F14 1 Tf 0.98368 0 Td <1E>Tj /F8 1 Tf 1.10413 0.69259 TD (+)Tj /F14 1 Tf 0.98367 0 Td (E)Tj /F15 1 Tf 7.97011 0 0 7.97011 344.16 443.16 Tm (!)Tj /F20 1 Tf 5.97758 0 0 5.97758 349.8 445.44 Tm (0)Tj /F18 1 Tf 7.97011 0 0 7.97011 352.44 443.16 Tm (j)Tj /F15 1 Tf 0.30113 0 Td (!)Tj /F19 1 Tf 11.95517 0 0 11.95517 362.88 461.88 Tm <14>Tj /F14 1 Tf 1.24465 -0.73274 TD (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F18 1 Tf 7.97011 0 0 7.97011 402.72 457.44 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 405.6 453.12 Tm ($)Tj ET q 47.28 0 0 -0.48 370.308 448.308 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 370.32 436.8 Tm 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (r)Tj /F8 1 Tf 0.69259 0 Td (+)Tj /F14 1 Tf 0.98367 0 Td <1E>Tj /F19 1 Tf 0.68255 2.09784 TD <15>Tj /F16 1 Tf -27.55294 -4.64736 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(In)-332(all)-321(other)-331(cases,)]TJ /F14 1 Tf 7.8694 0 Td (W)Tj /F8 1 Tf 1.06398 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.281 Tc [($=)10(0)]TJ /F14 1 Tf 2.18818 0 Td 0 Tc (:)Tj /F11 1 Tf 7.97011 0 0 7.97011 249.72 410.64 Tm (5)Tj /F8 1 Tf 11.95517 0 0 11.95517 89.52 378.84 Tm [(Then,)-431(the)-401(exp)-30(ected)-421(presen)30(t)-422(discoun)30(ted)-411(v)50(alue)-411(of)-392(a)-401(loan)-391(con)30(tract)-402($)]TJ /F14 1 Tf 28.41616 0 Td 0.08 Tc [<103B>-91(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 446.28 383.16 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 450.96 378.84 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 461.64 377.04 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 466.32 378.84 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 477.36 377.04 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 482.04 378.84 Tm [($\))-402(o\013ered)-401(to)]TJ -34.29813 -1.2045 TD [(a)-452(household)-471(that)-453(just)-462(turned)-463(mid-age)-461(with)-462(c)31(haracteristics)-483($)]TJ /F14 1 Tf 26.35847 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 393.24 362.64 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 397.92 364.44 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 408.96 362.64 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 413.64 364.44 Tm [($)-462(is)-462(denoted)]TJ /F14 1 Tf 5.7816 0 Td (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F11 1 Tf 7.97011 0 0 7.97011 507.72 362.64 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 512.4 364.44 Tm [($)-462(with)]TJ /F14 1 Tf -36.83762 -1.2045 TD (!)Tj /F11 1 Tf 7.97011 0 0 7.97011 79.68 348.24 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 89.28 350.04 Tm 0.401 Tc (=$)Tj /F14 1 Tf 1.54577 0 Td 0 Tc (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 113.88 348.24 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 118.56 350.04 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 129.6 348.24 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 134.28 350.04 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 189.72 354.36 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 194.4 350.04 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 205.08 348.24 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 209.88 350.04 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 220.92 348.24 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 225.48 350.04 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (:)Tj /F8 1 Tf 0.67251 0 Td [(The)-411(zero)-401(pro\ft)-402(condition)-401(on)-402(a)-391(loan)-401(con)30(tract)-402($)]TJ /F14 1 Tf 20.13522 0 Td 0.07 Tc [<103B>-101(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 500.28 354.36 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 504.96 350.04 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 515.64 348.24 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 520.44 350.04 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 531.48 348.24 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 536.16 350.04 Tm ($\))Tj /F14 1 Tf -38.82505 -1.21454 TD (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F11 1 Tf 7.97011 0 0 7.97011 96.96 333.72 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 101.64 335.52 Tm [($)-332(with)]TJ /F14 1 Tf 2.94099 0 Td (!)Tj /F11 1 Tf 7.97011 0 0 7.97011 144.48 333.72 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 152.52 335.52 Tm 0.281 Tc (=$)Tj /F14 1 Tf 1.42532 0 Td 0 Tc (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 175.68 333.72 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 180.48 335.52 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 191.52 333.72 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 196.08 335.52 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 251.52 339.84 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 256.32 335.52 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 267 333.72 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 271.68 335.52 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 282.72 333.72 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 287.4 335.52 Tm ($\))Tj /F14 1 Tf 0.76285 0 Td (:)Tj /F8 1 Tf 0.59221 0 Td [(can)-331(no)31(w)-331(b)-30(e)-331(written)-342(as)]TJ /F14 1 Tf -9.52559 -2.20825 TD (W)Tj /F8 1 Tf 1.06397 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 213.12 307.32 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 217.8 309.12 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 228.84 307.32 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 233.52 309.12 Tm (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0;)Tj /F14 1 Tf 0.93349 0 Td 0.05 Tc [<103B>-120(r)]TJ /F15 1 Tf 7.97011 0 0 7.97011 288.96 314.04 Tm 0 Tc <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 293.64 309.12 Tm (\()Tj /F14 1 Tf 0.38142 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 304.32 307.32 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 309.12 309.12 Tm 0.171 Tc (;y)Tj /F11 1 Tf 7.97011 0 0 7.97011 320.16 307.32 Tm 0 Tc (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 324.72 309.12 Tm ($\))Tj /F16 1 Tf 0.98367 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td <0B>Tj /F15 1 Tf 7.97011 0 0 7.97011 381 314.04 Tm <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 385.8 309.12 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (q)Tj ET q 6.84 0 0 -0.48 395.988 319.308 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 396 309.12 Tm (h)Tj /F8 1 Tf 0.83311 0 Td 0.281 Tc (=0)Tj /F14 1 Tf 1.53574 0 Td 0 Tc (:)Tj /F8 1 Tf 8.10026 0 Td ((3.3))Tj /F22 1 Tf 14.34624 0 0 14.34624 72 274.44 Tm [(3.3)-1131(Distribution)-387(of)-385(agen)33(t)-385(states)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 252.36 Tm [(The)-330(agen)30(t's)-332(problem)-331(yields)-331(optimal)-322(p)-30(olicies)-331(functions)-331(for)-322(a)-311(giv)30(en)-340(set)-322(of)-321(prices.)-452(In)-322(turn,)-322(these)]TJ 0 -1.21454 TD [(p)-30(olicy)-311(functions)-321(imply)-322(in)-311(the)-311(usual)-312(w)31(a)30(y)-321(transition)-312(probabilit)29(y)-321(functions)-322(across)-312(p)-30(ossible)-321(agen)31(t)]TJ 0 -1.2045 TD [(states.)-603(W)80(e)-381(will)-381(study)-392(equilibria)-392(in)-381(whic)31(h)-392(the)-381(distribution)-393(of)-372(agen)31(t)-382(states)-382(is)-382(in)30(v)50(arian)30(t)-392(under)]TJ 0 -1.21454 TD [(those)-332(probabilit)30(y)-341(functions.)-442(This)-342(section)-341(mak)30(es)-341(this)-332(notion)-332(precise.)]TJ ET q 189.36 0 0 -0.48 71.988 198.948 cm /Im1 Do Q BT /F12 1 Tf 6.97385 0 0 6.97385 85.44 191.16 Tm (5)Tj /F7 1 Tf 9.96264 0 0 9.96264 89.88 187.56 Tm [(Sp)-24(eci\fcally)85(,)-337(this)-339(is)-337(the)-338(case)-313(when:)]TJ -0.57816 -1.69834 TD [(1.)-590(the)-301(agen)24(t)-289(just)-315(turned)-302(mid-aged)-289(and)-301(her)-289(budget)-301(set)-302(is)-302(empt)24(y)-301(so)-302(that)]TJ /F23 1 Tf 30.93156 0 Td (!)Tj /F7 1 Tf 0.93951 0 Td 0.265 Tc (=$)Tj /F23 1 Tf 1.43336 0 Td 0 Tc (a)Tj /F12 1 Tf 6.97385 0 0 6.97385 421.2 169.2 Tm (0)Tj /F23 1 Tf 9.96264 0 0 9.96264 425.76 170.64 Tm 0.169 Tc (;y)Tj /F12 1 Tf 6.97385 0 0 6.97385 435.12 169.2 Tm 0 Tc (0)Tj /F23 1 Tf 9.96264 0 0 9.96264 439.56 170.64 Tm (;)Tj /F7 1 Tf 0.44566 0 Td (0)Tj /F23 1 Tf 0.50589 0 Td (;)Tj /F7 1 Tf 0.44566 0 Td (0)Tj /F23 1 Tf 0.50589 0 Td (;)Tj /F7 1 Tf 0.44566 0 Td (0;)Tj /F23 1 Tf 0.95156 0 Td 0.048 Tc [<103B>-120(r)]TJ /F24 1 Tf 6.97385 0 0 6.97385 486.36 174.24 Tm 0 Tc <10>Tj /F7 1 Tf 9.96264 0 0 9.96264 491.04 170.64 Tm (\()Tj /F23 1 Tf 0.38544 0 Td (a)Tj /F12 1 Tf 6.97385 0 0 6.97385 500.16 169.2 Tm (0)Tj /F23 1 Tf 9.96264 0 0 9.96264 504.6 170.64 Tm 0.169 Tc (;y)Tj /F12 1 Tf 6.97385 0 0 6.97385 513.96 169.2 Tm 0 Tc (0)Tj /F7 1 Tf 9.96264 0 0 9.96264 518.4 170.64 Tm [($\))-314(and)]TJ /F23 1 Tf -42.21772 -1.2045 TD (y)Tj /F12 1 Tf 6.97385 0 0 6.97385 102.72 157.2 Tm (0)Tj /F7 1 Tf 9.96264 0 0 9.96264 109.32 158.64 Tm (+)Tj /F23 1 Tf 0.99974 0 Td (a)Tj /F12 1 Tf 6.97385 0 0 6.97385 124.56 157.2 Tm (0)Tj /F7 1 Tf 9.96264 0 0 9.96264 129 158.64 Tm [($1)-217(+)]TJ /F23 1 Tf 2.10787 0 Td (r)Tj /F7 1 Tf 0.46976 0 Td ($)Tj /F2 1 Tf 0.62634 0 Td <00>Tj /F23 1 Tf 0.99973 0 Td (m)Tj /F7 1 Tf 0.87928 0 Td ($0;)Tj /F23 1 Tf 1.337 0 Td 0.072 Tc [<103B>-97(r)]TJ /F24 1 Tf 6.97385 0 0 6.97385 207.12 162.24 Tm 0 Tc <10>Tj /F7 1 Tf 9.96264 0 0 9.96264 211.8 158.64 Tm ($)Tj /F2 1 Tf 0.6143 0 Td <00>Tj /F23 1 Tf 0.99974 0 Td <0E>Tj ET q 5.76 0 0 -0.48 232.668 167.268 cm /Im1 Do Q BT /F23 1 Tf 9.96264 0 0 9.96264 232.68 158.64 Tm 0.265 Tc (h<)Tj /F7 1 Tf 1.90311 0 Td 0 Tc (0)Tj -16.81482 -1.69834 TD [(2.)-590(the)-338(agen)25(t)-314(is)-337(a)-325(ren)23(ter)]TJ /F23 1 Tf 10.55142 0 Td (!)Tj /F7 1 Tf 0.92747 0 Td 0.277 Tc (=$)Tj /F23 1 Tf 1.4454 0 Td 0 Tc [(a;)-169(y)-36(;)]TJ /F7 1 Tf 1.95129 0 Td (0)Tj /F23 1 Tf 0.50589 0 Td 0.169 Tc [<3B1C>61(;)1<1B>]TJ /F7 1 Tf 2.03561 0 Td 0 Tc (;)Tj /F23 1 Tf 0.44567 0 Td 0.072 Tc [<103B>-97(r)]TJ /F24 1 Tf 6.97385 0 0 6.97385 276.24 145.32 Tm 0 Tc <10>Tj /F7 1 Tf 9.96264 0 0 9.96264 280.92 141.72 Tm (\()Tj /F23 1 Tf 0.38544 0 Td (a)Tj /F12 1 Tf 6.97385 0 0 6.97385 290.04 140.28 Tm (0)Tj /F23 1 Tf 9.96264 0 0 9.96264 294.6 141.72 Tm 0.169 Tc (;y)Tj /F12 1 Tf 6.97385 0 0 6.97385 303.96 140.28 Tm 0 Tc (0)Tj /F7 1 Tf 9.96264 0 0 9.96264 308.28 141.72 Tm [($\))-350(with)]TJ /F23 1 Tf 3.39669 0 Td 0.385 Tc <1C3E>Tj /F7 1 Tf 1.87902 0 Td 0 Tc (0)Tj /F23 1 Tf 0.50589 0 Td (;)Tj /F7 1 Tf -28.28166 -1.69834 TD [(3.)-590(the)-338(agen)25(t)-314(has)-325(b)-24(een)-337(mid-aged)-325(for)-326(more)-325(than)]TJ /F23 1 Tf 20.63309 0 Td (T)Tj /F7 1 Tf 1.04791 0 Td [(p)-24(erio)-24(ds.)]TJ /F8 1 Tf 11.95517 0 0 11.95517 302.76 67.44 Tm (12)Tj ET endstream endobj 15 0 obj << /Length 18398 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 89.52 683.16 Tm 0 g [(In)-332(our)-331(en)30(vironmen)31(t,)-352(the)-331(transition)-333(matrix)-332(across)-332(ages)-331(is)-331(giv)30(en)-341(b)30(y:)]TJ /F19 1 Tf 11.30222 -1.11416 TD (2)Tj 0 -1.80675 TD (4)Tj /F8 1 Tf 1.08405 1.01379 TD ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 268.68 657.48 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 278.16 660.36 Tm ($)Tj /F14 1 Tf 2.35881 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 312.36 657.48 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 359.52 660.36 Tm (0)Tj -8.55195 -1.21454 TD 2.469 Tc [(0$)2469(1)]TJ /F16 1 Tf 4.05515 0 Td 0 Tc <00>Tj /F14 1 Tf 0.99371 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 323.76 643.08 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 330.84 645.84 Tm ($)Tj /F14 1 Tf 2.09784 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 361.92 643.08 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 253.32 631.44 Tm <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 259.32 628.56 Tm (D)Tj /F8 1 Tf 11.95517 0 0 11.95517 311.16 631.44 Tm 2.369 Tc (01)Tj /F16 1 Tf 3.57335 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 371.88 628.56 Tm (D)Tj /F19 1 Tf 11.95517 0 0 11.95517 384.6 669.84 Tm (3)Tj 0 -1.80675 TD (5)Tj /F8 1 Tf -26.14769 -3.38264 TD [(since)-331(the)-311(old)-321(are)-311(immediately)-331(replaced)-320(b)30(y)-321(newly)-331(b)-30(orn)-311(y)30(oung)-321(p)-30(eople.)-441(Let)-312($)]TJ /F14 1 Tf 31.57797 0 Td (n)Tj /F15 1 Tf 7.97011 0 0 7.97011 456.48 606 Tm (Y)Tj /F14 1 Tf 11.95517 0 0 11.95517 463.8 607.8 Tm 0.171 Tc (;n)Tj /F15 1 Tf 7.97011 0 0 7.97011 476.04 606 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 485.52 607.8 Tm 0.171 Tc (;n)Tj /F15 1 Tf 7.97011 0 0 7.97011 497.76 606 Tm 0 Tc (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 504.96 607.8 Tm [($)-312(b)-30(e)-310(the)]TJ -36.2153 -1.21454 TD [(corresp)-30(onding)-362(in)30(v)51(arian)30(t)-352(distribution)-363(of)-351(ages.)-512(The)-361(in)31(v)50(arian)30(t)-352(mass)-362(of)-341(agen)31(ts)-363(b)-30(orn)-351(eac)31(h)-362(p)-30(erio)-30(d)]TJ 0 -1.2045 TD [(is)-332(then)-331(giv)30(en)-341(b)31(y)]TJ /F14 1 Tf 17.33476 -1.21454 TD <16>Tj /F11 1 Tf 7.97011 0 0 7.97011 286.2 561.6 Tm (0)Tj /F16 1 Tf 11.95517 0 0 11.95517 294.24 564.36 Tm <11>Tj /F14 1 Tf 1.06397 0 Td (n)Tj /F15 1 Tf 7.97011 0 0 7.97011 313.92 562.56 Tm (O)Tj /F14 1 Tf 11.95517 0 0 11.95517 321 564.36 Tm <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 327.12 561.6 Tm (D)Tj /F14 1 Tf 11.95517 0 0 11.95517 334.8 564.36 Tm (:)Tj /F8 1 Tf -21.98212 -1.65619 TD [(With)-321(this)-322(notation)-312(in)-311(hand,)-321(w)30(e)-331(can)-320(de\fne)-321(in)30(v)50(arian)30(t)-321(distributions)-334(o)31(v)30(er)-331(p)-31(ossible)-321(states)-332(at)-312(eac)31(h)]TJ 0 -1.2045 TD [(demographic)-331(stage.)]TJ /F5 1 Tf 0 -2.57964 TD [(3.3.1)-1125(The)-381(y)29(oung)]TJ /F8 1 Tf 0 -1.8469 TD [(The)-341(in)31(v)50(arian)30(t)-332(distribution)]TJ /F14 1 Tf 11.45279 0 Td <16>Tj /F15 1 Tf 7.97011 0 0 7.97011 216 474.36 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 227.16 477.24 Tm [(on)-331(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 251.88 475.44 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 263.04 477.24 Tm [(solv)30(es,)-351(for)-322(all)]TJ /F14 1 Tf 5.92212 0 Td (y)Tj /F16 1 Tf 0.78293 0 Td 0.282 Tc (2f)Tj /F14 1 Tf 1.4454 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 366.24 475.44 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 372.48 477.24 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 383.52 475.44 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 392.88 477.24 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 403.92 475.44 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 411.96 477.24 Tm (g)Tj /F8 1 Tf 0.82307 0 Td (and)Tj /F14 1 Tf 1.90712 0 Td (A)Tj /F16 1 Tf 1.01379 0 Td <1A>Tj /F14 1 Tf 1.05394 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 480.48 481.56 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 487.44 477.24 Tm (:)Tj /F14 1 Tf -29.24927 -2.65994 TD <16>Tj /F15 1 Tf 7.97011 0 0 7.97011 144.72 442.68 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 152.04 445.44 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(A;)-170(y)]TJ /F8 1 Tf 1.69634 0 Td 0.271 Tc ($=)Tj /F14 1 Tf 1.6863 0 Td 0 Tc <16>Tj /F11 1 Tf 7.97011 0 0 7.97011 204.12 442.68 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 208.8 445.44 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 214.68 443.64 Tm (f)Tj /F11 1 Tf 0.52697 0 Td (0)Tj /F18 1 Tf 0.52697 0 Td (2)Tj /F15 1 Tf 0.70764 0 Td (A;y)Tj /F11 1 Tf 1.65619 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td (y)Tj /F17 1 Tf 5.97758 0 0 5.97758 252.72 442.32 Tm (L)Tj /F18 1 Tf 7.97011 0 0 7.97011 258.36 443.64 Tm (g)Tj /F8 1 Tf 11.95517 0 0 11.95517 265.68 445.44 Tm 0.221 Tc [(+$)221(1)]TJ /F16 1 Tf 2.07776 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 308.52 442.68 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 318 445.44 Tm ($)Tj /F19 1 Tf 0.55206 1.3651 TD (Z)Tj /F15 1 Tf 7.97011 0 0 7.97011 331.2 434.64 Tm (!)Tj /F18 1 Tf 0.69259 0 Td (2)Tj /F11 1 Tf 0.70764 0 Td (\n)Tj /F17 1 Tf 5.97758 0 0 5.97758 348.48 433.32 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 357.36 445.44 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 363.24 443.52 Tm (f)Tj /F15 1 Tf 0.52697 0 Td (a)Tj /F20 1 Tf 5.97758 0 0 5.97758 371.88 446.28 Tm (0)Tj /F17 1 Tf 0 -0.92345 TD (Y)Tj /F11 1 Tf 7.97011 0 0 7.97011 378.36 443.52 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($)Tj /F18 1 Tf 0.40652 0 Td (2)Tj /F15 1 Tf 0.70764 0 Td (A)Tj /F18 1 Tf 0.79798 0 Td (g)Tj /F8 1 Tf 11.95517 0 0 11.95517 407.16 445.44 Tm <0528>Tj /F14 1 Tf 1.11416 0 Td (y)Tj /F16 1 Tf 0.52195 0 Td (j)Tj /F14 1 Tf 0.28105 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td (\))Tj /F14 1 Tf 0.38142 0 Td <6416>Tj /F15 1 Tf 7.97011 0 0 7.97011 455.4 450.36 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 462.72 445.44 Tm ($)Tj /F14 1 Tf 0.38143 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj -33.70593 -2.30862 TD (where)Tj /F14 1 Tf 2.87072 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 112.44 422.16 Tm (0)Tj /F15 1 Tf 0 -0.91843 TD (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 124.08 417.84 Tm 0.361 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 140.04 416.04 Tm 0 Tc (Y)Tj /F16 1 Tf 11.95517 0 0 11.95517 151.56 417.84 Tm (7!)Tj /F14 1 Tf 1.3651 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 179.04 422.16 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 190.56 417.84 Tm [(is)-372(the)-381(optimal)-372(sa)30(ving)-391(p)-30(olicy)-381(for)-362(y)30(oung)-381(agen)31(ts,)-392(and,)-392(abusing)-381(notation)]TJ -9.91705 -1.21454 TD [(somewhat,)-331<0528>]TJ /F14 1 Tf 5.95224 0 Td (y)Tj /F16 1 Tf 0.52195 0 Td (j)Tj /F14 1 Tf 0.28105 0 Td (!)Tj /F8 1 Tf 0.63236 0 Td [(\))-312(is)-321(the)-311(lik)30(eliho)-30(o)-30(d)-321(of)-311(income)-321(dra)30(w)]TJ /F14 1 Tf 14.59452 0 Td (y)Tj /F16 1 Tf 0.79296 0 Td 0.282 Tc (2f)Tj /F14 1 Tf 1.4454 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 367.32 401.52 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 373.44 403.32 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 384.48 401.52 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 393.96 403.32 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 405 401.52 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 412.92 403.32 Tm (g)Tj /F8 1 Tf 0.81304 0 Td [(in)-321(the)-311(next)-322(p)-30(erio)-30(d)-311(giv)30(en)]TJ -29.32957 -1.2045 TD [(curren)30(t)-342(state)]TJ /F14 1 Tf 5.80167 0 Td (!)Tj /F16 1 Tf 0.92345 0 Td (2)Tj /F8 1 Tf 0.94352 0 Td (\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 172.08 387.12 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 179.4 388.92 Tm (.)Tj /F5 1 Tf -8.98356 -2.57964 TD [(3.3.2)-1125(The)-381(mid-aged)]TJ /F8 1 Tf 0 -4.22579 TD [(F)80(or)-301(mid-aged,)-311(recall)-311(that)-302(the)-311(state)-312(space)-321(is)-311(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 301.92 305.76 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 314.76 307.56 Tm (=)Tj /F14 1 Tf 1.0439 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 338.4 312 Tm 0 Tc (+)Tj /F16 1 Tf 11.95517 0 0 11.95517 347.52 307.56 Tm 0.191 Tc <0266>Tj /F14 1 Tf 1.46547 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 370.8 305.76 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 376.92 307.56 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 387.96 305.76 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 397.44 307.56 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 408.48 305.76 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 416.4 307.56 Tm 0.181 Tc [<6702>1(f)]TJ /F8 1 Tf 2.13799 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td 0.171 Tc <6702>Tj /F14 1 Tf 1.63611 0 Td -0.251 Tc (IN)Tj /F16 1 Tf 1.24465 0 Td 0.181 Tc <0266>Tj /F8 1 Tf 1.45544 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td 0.171 Tc <6702>Tj -38.13246 -1.2045 TD 0 Tc (f)Tj /F14 1 Tf 0.50187 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0.221 Tc <6702>Tj /F14 1 Tf 1.71641 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 173.04 297.48 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 183.96 293.16 Tm [(with)-341(t)29(ypical)-330(elemen)31(t)]TJ /F14 1 Tf 9.06386 0 Td (!)Tj /F8 1 Tf 0.92345 0 Td 0.271 Tc (=$)Tj /F14 1 Tf 1.41529 0 Td 0.171 Tc [(a)171(;y)131(;)1(H)151<3B1C>71<3B1B>]TJ /F8 1 Tf 4.74774 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F8 1 Tf 1.41529 0 Td 0 Tc [($.)-432(The)-331(in)31(v)50(arian)30(t)-332(distribution)]TJ /F14 1 Tf -27.37226 -1.2045 TD <16>Tj /F15 1 Tf 7.97011 0 0 7.97011 79.08 275.88 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 92.04 278.76 Tm [(on)-281(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 116.16 276.96 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 129.24 278.76 Tm [(solv)30(es,)-311(for)-282(all)]TJ /F14 1 Tf 5.80167 0 Td (y)Tj /F16 1 Tf 0.79296 0 Td 0.282 Tc (2f)Tj /F14 1 Tf 1.4454 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 231.12 276.96 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 237.36 278.76 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 248.4 276.96 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 257.76 278.76 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 268.8 276.96 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 276.72 278.76 Tm (g)Tj /F8 1 Tf 0.50187 0 Td (,)Tj /F14 1 Tf 0.57214 0 Td (A)Tj /F16 1 Tf 1.01379 0 Td <1A>Tj /F14 1 Tf 1.05394 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 325.44 283.08 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 335.88 278.76 Tm [(and)-291($)]TJ /F14 1 Tf 2.2484 0 Td 0.02 Tc [(H;)-151<1C>-100(;)-150<1B>]TJ /F8 1 Tf 2.84061 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F8 1 Tf 1.41529 0 Td 0 Tc ($)Tj /F16 1 Tf 0.65244 0 Td 0.282 Tc (2f)Tj /F8 1 Tf 1.4454 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td 0.15 Tc <6702>Tj /F14 1 Tf 1.57589 0 Td -0.251 Tc (IN)Tj /F16 1 Tf 1.2045 0 Td 0.15 Tc <0266>Tj /F8 1 Tf 1.42532 0 Td 0 Tc (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td 0.15 Tc <6702>Tj -38.17261 -1.21454 TD 0 Tc (f)Tj /F14 1 Tf 0.50187 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0.211 Tc <6702>Tj /F14 1 Tf 1.71641 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 173.04 268.56 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 180.12 264.24 Tm (:)Tj /F14 1 Tf -8.34116 -3.43282 TD <16>Tj /F15 1 Tf 7.97011 0 0 7.97011 87.36 228.12 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 96.84 223.2 Tm ($\()Tj /F14 1 Tf 0.76285 0 Td 0.17 Tc [(A)170(;y)130(;)-1(H)150(;)-1<1C>70<3B1B>]TJ /F8 1 Tf 4.96856 0 Td 0 Tc (;)Tj /F14 1 Tf 0.44165 0 Td 0.07 Tc [<103B>-101(r)]TJ /F8 1 Tf 1.41529 0 Td 0 Tc [($\))-834(=)]TJ /F14 1 Tf 3.20196 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 231.84 220.32 Tm (M)Tj /F19 1 Tf 11.95517 0 0 11.95517 243.36 239.4 Tm (Z)Tj /F11 1 Tf 7.97011 0 0 7.97011 249.96 212.4 Tm (\n)Tj /F17 1 Tf 5.97758 0 0 5.97758 256.08 211.08 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 264.96 223.2 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 270.84 221.28 Tm (f)Tj /F11 1 Tf 0.52697 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td [(H)-15<3B1C>-121<3B1B>]TJ /F11 1 Tf 2.71013 0 Td ($=$0)Tj /F15 1 Tf 2.1681 0 Td (;)Tj /F11 1 Tf 0.30113 0 Td (0)Tj /F15 1 Tf 0.52697 0 Td (;)Tj /F11 1 Tf 0.30113 0 Td (0$)Tj /F18 1 Tf 0.93349 0 Td (g)Tj /F8 1 Tf 11.95517 0 0 11.95517 338.52 223.2 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 344.4 221.28 Tm (f)Tj /F15 1 Tf 0.52697 0 Td (a)Tj /F20 1 Tf 5.97758 0 0 5.97758 353.04 223.92 Tm (0)Tj /F17 1 Tf 0 -0.92345 TD (Y)Tj /F11 1 Tf 7.97011 0 0 7.97011 359.52 221.28 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($)Tj /F18 1 Tf 0.40652 0 Td (2)Tj /F15 1 Tf 0.70764 0 Td (A)Tj /F18 1 Tf 0.79798 0 Td (g)Tj /F8 1 Tf 11.95517 0 0 11.95517 388.32 223.2 Tm <0528>Tj /F14 1 Tf 1.11416 0 Td (y)Tj /F16 1 Tf 0.52195 0 Td (j)Tj /F14 1 Tf 0.28105 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td (\))Tj /F14 1 Tf 0.38142 0 Td <6416>Tj /F15 1 Tf 7.97011 0 0 7.97011 436.56 220.32 Tm (Y)Tj /F8 1 Tf 11.95517 0 0 11.95517 443.88 223.2 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj -20.86796 -2.71013 TD 0.843 Tc [(+$)843(1)]TJ /F16 1 Tf 2.69005 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F11 1 Tf 7.97011 0 0 7.97011 256.8 187.92 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 261.6 190.8 Tm ($)Tj /F19 1 Tf 0.55206 1.35506 TD (Z)Tj /F11 1 Tf 7.97011 0 0 7.97011 274.8 180 Tm (\n)Tj /F17 1 Tf 5.97758 0 0 5.97758 280.92 178.68 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 291.48 190.8 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 297.36 188.88 Tm (f)Tj /F11 1 Tf 0.52697 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 312.36 191.16 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 315.12 188.88 Tm (\()Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($=)Tj /F15 1 Tf 1.23461 0 Td 0.015 Tc [(H;)15<1C>]TJ /F11 1 Tf 1.77664 0 Td 0 Tc ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.69259 0 Td ($=)Tj /F15 1 Tf 1.23461 0 Td <1C>Tj /F18 1 Tf 0.60225 0 Td <00>Tj /F11 1 Tf 0.82809 0 Td (1)Tj /F15 1 Tf 0.52697 0 Td (;a)Tj /F20 1 Tf 5.97758 0 0 5.97758 389.04 191.52 Tm (0)Tj /F17 1 Tf 0 -0.90337 TD (M)Tj /F11 1 Tf 7.97011 0 0 7.97011 397.08 188.88 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($)Tj /F18 1 Tf 0.40652 0 Td (2)Tj /F15 1 Tf 0.70764 0 Td (A)Tj /F18 1 Tf 0.79798 0 Td (g)Tj /F8 1 Tf 11.95517 0 0 11.95517 426 190.8 Tm <0528>Tj /F14 1 Tf 1.11416 0 Td (y)Tj /F16 1 Tf 0.52195 0 Td (j)Tj /F14 1 Tf 0.28105 0 Td (!)Tj /F8 1 Tf 0.63236 0 Td (\))Tj /F14 1 Tf 0.38143 0 Td (P)Tj /F8 1 Tf 0.77289 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <1B>Tj /F16 1 Tf 0.58218 0 Td (j)Tj /F14 1 Tf 0.28105 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td <6416>Tj /F15 1 Tf 7.97011 0 0 7.97011 510.6 187.92 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 520.08 190.8 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj /F16 1 Tf -27.25181 -2.19821 TD <02>Tj /F19 1 Tf 1.61604 0.81304 TD (\b)Tj /F8 1 Tf 0.58217 -0.81304 TD (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 238.68 162.24 Tm (f)Tj /F15 1 Tf 0.52697 0 Td <1C>Tj /F11 1 Tf 0.58719 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.69259 0 Td ($=0)Tj /F15 1 Tf 1.76158 0 Td (;)Tj /F11 1 Tf 0.30113 0 Td <0428>Tj /F15 1 Tf 1.11416 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td (\)=)Tj /F15 1 Tf 1.23461 0 Td 0.075 Tc [<103B>75(r)]TJ /F17 1 Tf 5.97758 0 0 5.97758 307.92 164.52 Tm 0 Tc <10>Tj /F11 1 Tf 7.97011 0 0 7.97011 312.12 162.24 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (a)Tj /F11 1 Tf 0.55708 0 Td (\()Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.7227 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (;y)Tj /F11 1 Tf 0.85821 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($\)=)Tj /F15 1 Tf 1.64113 0 Td (r)Tj /F18 1 Tf 0.51191 0 Td (g)Tj /F8 1 Tf 11.95517 0 0 11.95517 372.36 164.52 Tm 0.221 Tc (+1)Tj /F18 1 Tf 7.97011 0 0 7.97011 390 162.6 Tm 0 Tc (f)Tj /F15 1 Tf 0.52697 0 Td <1C>Tj /F11 1 Tf 0.58719 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (>)Tj /F11 1 Tf 0.82809 0 Td (0)Tj /F15 1 Tf 0.52697 0 Td <3B10>Tj /F11 1 Tf 0.84315 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td <10>Tj /F11 1 Tf 0.52697 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (;r)Tj /F11 1 Tf 0.81304 0 Td (=)Tj /F15 1 Tf 0.82809 0 Td (r)Tj /F11 1 Tf 0.51191 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.69259 0 Td ($)Tj /F18 1 Tf 0.40652 0 Td (g)Tj /F19 1 Tf 11.95517 0 0 11.95517 485.4 174.24 Tm (\t)Tj /F8 1 Tf -34.57919 -2.8105 TD (where)Tj /F14 1 Tf 2.8908 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 112.68 144.96 Tm (0)Tj /F15 1 Tf 0 -0.91843 TD (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 126.72 140.64 Tm 0.391 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 143.04 138.84 Tm 0 Tc (M)Tj /F16 1 Tf 11.95517 0 0 11.95517 157.08 140.64 Tm (7!)Tj /F14 1 Tf 1.38518 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 184.8 144.96 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 196.44 140.64 Tm [(is)-402(the)-391(optimal)-392(sa)30(ving)-392(p)-30(olicy)-401(for)-381(mid-aged)-391(agen)30(ts,)]TJ /F14 1 Tf 21.69104 0 Td <1C>Tj /F8 1 Tf 0.53199 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td [($)-382(extracts)-402(the)]TJ -33.66577 -1.2045 TD [(con)31(tract)-403(age)-390(argumen)30(t)-402(of)]TJ /F14 1 Tf 11.34237 0 Td (!)Tj /F8 1 Tf 0.65244 0 Td (,)Tj /F14 1 Tf 0.68255 0 Td <10>Tj /F8 1 Tf 0.50187 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td [($)-402(extracts)-402(the)-402(con)31(tract)-402(t)29(yp)-30(e)-411(argumen)31(t)-402(of)]TJ /F14 1 Tf 18.1478 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td (,)Tj /F14 1 Tf 0.68255 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 480.24 130.56 Tm <10>Tj /F8 1 Tf 11.95517 0 0 11.95517 485.04 126.24 Tm ($)Tj /F14 1 Tf 0.38142 0 Td [(a;)-171(y)]TJ /F8 1 Tf 1.47551 0 Td [($)-382(is)-402(the)]TJ -36.406 -1.2045 TD [(in)30(termediary's)-462(pricing)-452(p)-30(olicies)-441(for)-442(mortgages)-432(of)-442(t)30(yp)-30(e)]TJ /F14 1 Tf 23.4275 0 Td <10>Tj /F16 1 Tf 0.9736 0 Td 0.472 Tc (2f)Tj /F14 1 Tf 1.6361 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0 Tc (g)Tj /F8 1 Tf 0.9435 0 Td [(for)-432(agen)31(ts)-443(whose)]TJ -32.2806 -1.2145 TD [(initial)-332(w)31(ealth-income)-341(p)-30(osition)-332(is)-331($)]TJ /F14 1 Tf 14.3737 0 Td [(a;)-171(y)]TJ /F8 1 Tf 1.4755 0 Td [($,)-312(and)]TJ /F14 1 Tf 2.8707 0 Td (r)Tj /F8 1 Tf 0.4718 0 Td ($)Tj /F14 1 Tf 0.3814 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td [($)-322(is)-341(the)-332(con)31(tract)-332(rate)-321(argumen)30(t)-332(of)]TJ /F14 1 Tf 14.725 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td (.)Tj -16.28082 -2.49934 TD (13)Tj ET endstream endobj 16 0 obj << /Length 13454 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 89.52 683.16 Tm 0 g [(The)-361(\frst)-362(term)-362(corresp)-31(onds)-361(to)-352(agen)31(ts)-362(who)-351(go)-351(from)-352(b)-30(eing)-351(y)31(oung)-362(to)-351(b)-30(eing)-351(mid-aged,)-361(while)]TJ -1.46548 -1.21454 TD [(the)-351(second)-361(in)30(tegral)-352(corresp)-30(onds)-372(to)-341(agen)30(ts)-352(who)-361(w)31(ere)-361(mid-aged)-351(in)-351(the)-352(previous)-361(p)-31(erio)-30(d)-351(and)-351(do)]TJ 0 -1.2045 TD [(not)-352(get)-341(old.)-502(The)-360(indicator)-352(functions)-362(re\rect)-361(the)-351(fact)-351(that)-342(agen)31(ts)-363(mak)31(e)-361(their)-352(mortgage)-341(c)30(hoice)]TJ T* [(in)-331(\frst)-333(p)-30(erio)-30(d)-321(but)-332(cannot)-331(revisit)-342(that)-322(c)31(hoice)-341(in)-331(subsequen)30(t)-362(p)-30(erio)-30(ds.)]TJ /F5 1 Tf 0 -2.60975 TD [(3.3.3)-1125(The)-381(old)]TJ /F8 1 Tf 0 -1.85694 TD [(The)-341(in)31(v)50(arian)30(t)-332(distribution)]TJ /F14 1 Tf 11.45279 0 Td <16>Tj /F15 1 Tf 7.97011 0 0 7.97011 216 590.88 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 227.04 586.44 Tm [(on)-331(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 251.76 584.64 Tm (O)Tj /F16 1 Tf 11.95517 0 0 11.95517 262.2 586.44 Tm <11>Tj /F14 1 Tf 1.06398 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 286.08 590.88 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 297 586.44 Tm [(solv)30(es,)-341(for)-332(all)]TJ /F14 1 Tf 5.91209 0 Td (A)Tj /F16 1 Tf 1.01379 0 Td <1A>Tj /F14 1 Tf 1.05394 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 403.56 590.88 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 410.64 586.44 Tm (:)Tj /F14 1 Tf -28.28567 -3.62354 TD <16>Tj /F11 1 Tf 7.97011 0 0 7.97011 79.56 548.04 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 84.24 543.12 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (A)Tj /F8 1 Tf 0.73274 0 Td 0.281 Tc [($=$)281(1)]TJ /F16 1 Tf 2.79042 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 148.92 540.2401 Tm (D)Tj /F8 1 Tf 11.95517 0 0 11.95517 156.6 543.12 Tm ($)Tj /F19 1 Tf 0.55206 1.35506 TD (Z)Tj /F11 1 Tf 7.97011 0 0 7.97011 169.8 532.32 Tm (\n)Tj /F17 1 Tf 5.97758 0 0 5.97758 175.92 531 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 184.68 543.12 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 190.56 541.2 Tm (f)Tj /F15 1 Tf 0.52697 0 Td (a)Tj /F20 1 Tf 5.97758 0 0 5.97758 199.2 543.84 Tm (0)Tj /F17 1 Tf 0 -0.92345 TD (O)Tj /F11 1 Tf 7.97011 0 0 7.97011 205.56 541.2 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($)Tj /F18 1 Tf 0.40652 0 Td (2)Tj /F15 1 Tf 0.70764 0 Td (A)Tj /F18 1 Tf 0.79798 0 Td (g)Tj /F14 1 Tf 11.95517 0 0 11.95517 234.48 543.12 Tm <6416>Tj /F15 1 Tf 7.97011 0 0 7.97011 247.56 548.04 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 254.76 543.12 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.221 Tc ($+)Tj /F14 1 Tf 1.58593 0 Td 0 Tc <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 291.96 540.2401 Tm (O)Tj /F19 1 Tf 11.95517 0 0 11.95517 301.2 559.32 Tm (Z)Tj /F11 1 Tf 7.97011 0 0 7.97011 307.8 532.32 Tm (\n)Tj /F17 1 Tf 5.97758 0 0 5.97758 313.92 531 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 324.48 543.12 Tm (1)Tj /F18 1 Tf 7.97011 0 0 7.97011 330.36 541.2 Tm (f)Tj /F15 1 Tf 0.52697 0 Td (a)Tj /F20 1 Tf 5.97758 0 0 5.97758 339 543.84 Tm (0)Tj /F17 1 Tf 0 -0.92345 TD (M)Tj /F11 1 Tf 7.97011 0 0 7.97011 347.16 541.2 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (s)Tj /F11 1 Tf 0.49686 0 Td ($+max)Tj /F18 1 Tf 3.22204 0 Td (f)Tj /F15 1 Tf 0.52697 0 Td (H)Tj /F20 1 Tf 5.97758 0 0 5.97758 391.8 543.36 Tm (0)Tj /F11 1 Tf 7.97011 0 0 7.97011 394.44 541.2 Tm ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.70764 0 Td ($[)Tj /F15 1 Tf 0.70764 0 Td 0.03 Tc (qh)Tj /F11 1 Tf 1.12922 0 Td 0 Tc ($)Tj /F15 1 Tf 0.40652 0 Td (!)Tj /F11 1 Tf 0.69259 0 Td ($)Tj /F18 1 Tf 0.40652 0 Td <00>Tj /F15 1 Tf 0.82809 0 Td (b)Tj /F11 1 Tf 0.45169 0 Td ($)Tj /F15 1 Tf 0.40652 0 Td <1C>Tj /F11 1 Tf 0.60225 0 Td (+1)Tj /F15 1 Tf 1.35506 0 Td [<3B10>-75(;r)]TJ /F11 1 Tf 1.65619 0 Td ($])Tj /F15 1 Tf 0.69259 0 Td (;)Tj /F11 1 Tf 0.30113 0 Td (0)Tj /F18 1 Tf 0.52697 0 Td (g2)Tj /F15 1 Tf 1.23461 0 Td (A)Tj /F18 1 Tf 0.79798 0 Td (g)Tj /F14 1 Tf 11.95517 0 0 11.95517 505.32 543.12 Tm <6416>Tj /F15 1 Tf 7.97011 0 0 7.97011 518.4 548.04 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 527.88 543.12 Tm ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td ($)Tj -39.15628 -2.77035 TD [(where,)-341(for)]TJ /F14 1 Tf 4.59717 0 Td (!)Tj /F16 1 Tf 0.92345 0 Td (2)Tj /F8 1 Tf 0.94353 0 Td (\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 157.68 508.2 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 167.16 510 Tm (,)Tj /F14 1 Tf 7.09651 -1.78667 TD (h)Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (!)Tj /F8 1 Tf 0.6424 0 Td 0.281 Tc ($=)Tj /F14 1 Tf 1.69634 0 Td 0 Tc <1B>Tj /F8 1 Tf 0.70263 0.94353 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD (h)Tj ET q 6.84 0 0 -0.48 299.508 491.868 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 299.76 480.48 Tm <11>Tj /F8 1 Tf 0.86323 0.68255 TD 0.221 Tc [(+$)221(1)]TJ /F16 1 Tf 2.07776 0 Td 0 Tc <00>Tj /F14 1 Tf 1.00375 0 Td <1B>Tj /F8 1 Tf 0.59221 0 Td ($)Tj 0.39146 0.26098 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj /F8 1 Tf -23.96955 -2.2484 TD (while)Tj /F14 1 Tf 2.58967 0 Td (b)Tj /F8 1 Tf 0.41154 0 Td ($)Tj /F14 1 Tf 0.38143 0 Td <1C>Tj /F8 1 Tf 0.78293 0 Td 0.241 Tc (+1)Tj /F14 1 Tf 1.49559 0 Td 0.171 Tc [<3B10>101(;)1(r)]TJ /F8 1 Tf 1.85694 0 Td 0 Tc [($)-352(is)-362(the)-361(principal)-371(balance)-361(on)-361(a)-361(mortgage)-351(of)-351(t)29(yp)-30(e)]TJ /F14 1 Tf 21.09882 0 Td <10>Tj /F8 1 Tf 0.86322 0 Td [(with)-361(yield)]TJ /F14 1 Tf 4.6574 0 Td (r)Tj /F8 1 Tf 0.82307 0 Td (after)Tj /F14 1 Tf 2.34877 0 Td <1C>Tj /F8 1 Tf 0.78293 0 Td 0.241 Tc (+1)Tj -38.09231 -1.2045 TD 0 Tc [(p)-30(erio)-30(ds.)]TJ /F22 1 Tf 14.34624 0 0 14.34624 72 412.68 Tm [(3.4)-1131(Steady)-385(state)-385(equilibrium)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 390.6 Tm [(Equipp)-31(ed)-351(with)-331(this)-342(notation,)-332(w)31(e)-341(ma)30(y)-341(no)30(w)-331(de\fne)-350(an)-321(equilibrium.)-472(A)-331(steady-state)-353(equilibrium)]TJ 0 -1.21454 TD [(is)-312(a)-301(pair)]TJ /F14 1 Tf 3.75402 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 122.52 380.4 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 148.2 376.08 Tm 0 Tc (:)Tj /F14 1 Tf 0.55206 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 165.96 380.4 Tm 0 Tc (+)Tj /F16 1 Tf 11.95517 0 0 11.95517 175.2 376.08 Tm 0.191 Tc <0266>Tj /F14 1 Tf 1.46547 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 198.48 374.28 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 204.6 376.08 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 215.64 374.28 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 225 376.08 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 236.04 374.28 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 244.08 376.08 Tm 0.271 Tc [(g7)271(!)]TJ /F14 1 Tf 2.05769 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 279.84 380.4 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 290.52 376.08 Tm (and)Tj /F14 1 Tf 1.88705 0 Td (r)Tj /F15 1 Tf 7.97011 0 0 7.97011 318.72 380.4 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 342.36 376.08 Tm 0 Tc (:)Tj /F14 1 Tf 0.55206 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 360.12 380.4 Tm 0 Tc (+)Tj /F16 1 Tf 11.95517 0 0 11.95517 369.36 376.08 Tm 0.181 Tc <0266>Tj /F14 1 Tf 1.45544 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 392.52 374.28 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 398.76 376.08 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 409.8 374.28 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 419.16 376.08 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 430.2 374.28 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 438.24 376.08 Tm 0.271 Tc [(g7)271(!)]TJ /F14 1 Tf 2.05769 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 474 380.4 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 484.68 376.08 Tm [(of)-301(mortgage)]TJ -34.51896 -1.2045 TD [(pricing)-371(functions,)-382(agen)31(t)-362(v)50(alue)-361(functions)]TJ /F14 1 Tf 17.32472 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 285.96 359.88 Tm [(ag)-30(e)]TJ /F8 1 Tf 11.95517 0 0 11.95517 303.24 361.68 Tm 0.341 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 318.96 359.88 Tm 0 Tc [(ag)-30(e)]TJ /F16 1 Tf 11.95517 0 0 11.95517 336.24 361.68 Tm (7!)Tj /F14 1 Tf 1.34502 0 Td -0.251 Tc (IR)Tj /F8 1 Tf 1.2848 0 Td 0 Tc (for)Tj /F14 1 Tf 1.53574 0 Td [(ag)-40(e)]TJ /F16 1 Tf 1.80675 0 Td 0.342 Tc (2f)Tj /F14 1 Tf 1.50562 0 Td 0.05 Tc [(Y;)-121(M;)-120(O)]TJ /F16 1 Tf 3.28226 0 Td 0 Tc (g)Tj /F8 1 Tf 0.50187 0 Td [(,)-361(sa)29(ving)-371(p)-30(olicy)]TJ -33.36465 -1.2045 TD (functions)Tj /F14 1 Tf 4.26594 0 Td (a)Tj /F18 1 Tf 7.97011 0 0 7.97011 129.12 351.6 Tm (0)Tj /F15 1 Tf 0 -0.91843 TD [(ag)-30(e)]TJ /F8 1 Tf 11.95517 0 0 11.95517 146.52 347.28 Tm 0.351 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 162.36 345.48 Tm 0 Tc [(ag)-30(e)]TJ /F16 1 Tf 11.95517 0 0 11.95517 179.88 347.28 Tm (7!)Tj /F14 1 Tf 1.34502 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 207.12 351.6 Tm 0 Tc (+)Tj /F8 1 Tf 11.95517 0 0 11.95517 214.2 347.28 Tm [(,)-381(a)-372(mortgage)-361(c)31(hoice)-381(p)-30(olicy)-381(function)-371<04>-352(:)-351(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 428.64 345.48 Tm (Y)Tj /F16 1 Tf 11.95517 0 0 11.95517 440.16 347.28 Tm [(7!)-341(f)]TJ /F14 1 Tf 1.8469 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0 Tc (g)Tj /F8 1 Tf 0.50187 0 Td 0.381 Tc (,a)Tj -38.44362 -1.21454 TD 0 Tc [(housing)-321(p)-31(olicy)-310(function)]TJ /F14 1 Tf 10.26836 0 Td (H)Tj /F18 1 Tf 7.97011 0 0 7.97011 205.44 337.08 Tm (0)Tj /F8 1 Tf 11.95517 0 0 11.95517 211.44 332.76 Tm 0.281 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 226.44 330.96 Tm 0 Tc (Y)Tj /F16 1 Tf 11.95517 0 0 11.95517 237.12 332.76 Tm [(7!)-271(f)]TJ /F8 1 Tf 1.77664 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td (g)Tj /F8 1 Tf 0.50187 0 Td [(,)-301(in)30(v)30(olun)30(tary)-331(and)-312(v)31(olun)30(tary)-332(default)-311(p)-30(olicy)-321(functions)]TJ /F14 1 Tf -17.51544 -1.2045 TD (D)Tj /F15 1 Tf 7.97011 0 0 7.97011 82.08 322.68 Tm (I)Tj /F14 1 Tf 11.95517 0 0 11.95517 86.88 318.36 Tm 0.171 Tc (;D)Tj /F15 1 Tf 7.97011 0 0 7.97011 102.24 322.68 Tm 0 Tc (V)Tj /F8 1 Tf 11.95517 0 0 11.95517 112.8 318.36 Tm 0.271 Tc (:\n)Tj /F15 1 Tf 7.97011 0 0 7.97011 127.68 316.56 Tm 0 Tc (Y)Tj /F16 1 Tf 11.95517 0 0 11.95517 138.36 318.36 Tm [(7!)-281(f)]TJ /F8 1 Tf 1.78667 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F16 1 Tf 0.49184 0 Td (g)Tj /F8 1 Tf 0.50187 0 Td [(,)-311(and)-331(distributions)]TJ /F14 1 Tf 8.21067 0 Td <16>Tj /F15 1 Tf 7.97011 0 0 7.97011 288 315.48 Tm [(ag)-30(e)]TJ /F8 1 Tf 11.95517 0 0 11.95517 305.04 318.36 Tm [(of)-331(agen)31(t)-322(states)-342(on)-322(\n)]TJ /F15 1 Tf 7.97011 0 0 7.97011 407.88 316.56 Tm [(ag)-30(e)]TJ /F8 1 Tf 11.95517 0 0 11.95517 425.16 318.36 Tm [(suc)30(h)-341(that:)]TJ -28.3459 -2.02757 TD [(1.)-492(Agen)31(t)-331(p)-31(olicies)-340(are)-321(optimal)-332(giv)30(en)-340(pricing)-332(functions.)]TJ 0 -2.03761 TD [(2.)-492(The)-230(in)30(termediary)-251(exp)-30(ects)-241(to)-221(mak)31(e)-241(zero)-220(pro\ft)-232(on)-221(all)-230(mortgages.)-402(In)-231(other)-221(w)30(ords,)-262(condition)]TJ 1.25469 -1.2045 TD [((3.3))-322(holds)-331(for)-322(all)-331($)]TJ /F14 1 Tf 8.14041 0 Td [(a;)-171(y)]TJ /F8 1 Tf 1.47551 0 Td ($)Tj /F16 1 Tf 0.6424 0 Td (2)Tj /F14 1 Tf 0.94353 0 Td -0.251 Tc (IR)Tj /F11 1 Tf 7.97011 0 0 7.97011 246.36 259.68 Tm 0 Tc (+)Tj /F16 1 Tf 11.95517 0 0 11.95517 256.08 255.36 Tm 0.231 Tc <0266>Tj /F14 1 Tf 1.50562 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 279.84 253.56 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 285.96 255.36 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 297 253.56 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 306.48 255.36 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 317.52 253.56 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 325.44 255.36 Tm (g)Tj /F8 1 Tf 0.83311 0 Td [(and)-321(for)]TJ /F14 1 Tf 3.39267 0 Td <10>Tj /F16 1 Tf 0.78293 0 Td 0.282 Tc (2f)Tj /F14 1 Tf 1.4454 0 Td 0.141 Tc [(FR)131(M)92(;)-30(I)61(O)111(M)]TJ /F16 1 Tf 5.2998 0 Td 0 Tc (g)Tj /F8 1 Tf 0.50187 0 Td (.)Tj -32.26052 -2.03761 TD [(3.)-492(The)-330(distribution)-343(of)-321(states)-343(is)-331(in)30(v)50(arian)30(t)-332(giv)31(en)-341(pricing)-331(functions)-332(and)-331(agen)30(t)-331(p)-30(olicies.)]TJ 0.27101 -2.01754 TD [(The)-230(next)-231(section)-231(sim)30(ulates)-241(this)-222(econom)31(y)-231(under)-231(v)51(arious)-222(calibrations.)-412(W)81(e)-221(will)-230(b)-30(e)-221(particularly)]TJ -1.46548 -1.21454 TD [(in)30(terested)-282(in)-271(the)-271(fraction)-261(of)-261(agen)31(ts)-272(who)-270(c)30(ho)-30(ose)-271(to)-261(terminate)-282(their)-261(mortgages)-271(early)80(.)-421(As)-272(w)31(e)-271(ha)31(v)30(e)]TJ 0 -1.2045 TD [(discussed,)-352(this)-342(ma)30(y)-331(o)-30(ccur)-331(for)-321(v)30(olun)30(tary)-342(or)-321(in)30(v)30(olun)30(tary)-352(reasons.)]TJ /F9 1 Tf 17.21544 0 0 17.21544 72 138.12 Tm [(4)-1122(P)28(arameterization)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 111.84 Tm [(The)-280(b)-30(enc)30(hmark)-301(v)30(ersion)-291(of)-271(the)-271(mo)-30(del)-281(only)-281(mak)31(es)-292(standard)-282(FRM)-271(con)31(tracts)-293(a)31(v)50(ailable)-281(to)-271(agen)31(ts.)]TJ 0 -1.2145 TD [(W)81(e)-301(c)30(ho)-30(ose)-311(parameters)-312(so)-301(that)-302(this)-302(b)-30(enc)31(hmark)-321(mo)-30(del)-301(matc)30(hes)-321(the)-301(relev)50(an)30(t)-311(features)-302(of)-301(the)-301(US)]TJ 19.30211 -2.49934 TD (14)Tj ET endstream endobj 17 0 obj << /Length 11252 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 72 683.16 Tm 0 g [(housing)-392(mark)30(et)-391(b)-30(efore)-391(2000.)-592(W)81(e)-392(will)-391(then)-391(in)30(tro)-31(duce)-391(the)-391(option)-382(to)-381(\fnance)-391(house)-391(purc)30(hases)]TJ 0 -1.21454 TD [(with)-412(an)-401(IOM)-402(instead)-422(of)-391(an)-402(FRM,)-412(and)-401(ask)-412(whether)-411(the)-412(mo)-30(del)-401(can)-411(replicate)-411(the)-412(pic)31(k-up)-412(in)]TJ 0 -1.2045 TD [(o)30(wnership)-341(and)-331(foreclosure)-342(rates)-331(that)-322(has)-332(tak)30(en)-341(place)-330(in)-332(the)-331(US)-331(since)-341(2000.)]TJ 1.46548 -1.2045 TD [(W)81(e)-351(will)-351(think)-352(of)-331(a)-341(mo)-30(del)-341(p)-30(erio)-30(d)-352(as)-341(represen)30(ting)-362(1)-341(y)30(ear.)-492(Then,)-350(w)30(e)-361(set)-341(demographic)-351(para-)]TJ -1.46548 -1.21454 TD [(meters)-352(to)-341($)]TJ /F14 1 Tf 4.76781 0 Td <1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 135 629.64 Tm (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 144.48 625.32 Tm 0.171 Tc <3B1A>Tj /F11 1 Tf 7.97011 0 0 7.97011 155.76 629.64 Tm 0 Tc (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 160.44 625.32 Tm 0.171 Tc <3B1A>Tj /F15 1 Tf 7.97011 0 0 7.97011 171.72 629.64 Tm 0 Tc (D)Tj /F8 1 Tf 11.95517 0 0 11.95517 179.4 625.32 Tm 0.302 Tc [($=)1($)302(0)]TJ /F14 1 Tf 2.61979 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27101 0 Td (06)Tj /F14 1 Tf 0.98368 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (03)Tj /F14 1 Tf 0.98368 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(06$)-311(so)-342(that,)-342(on)-341(a)30(v)31(erage,)-351(agen)31(ts)-352(are)-342(y)31(oung)-341(for)-342(16)-331(y)30(ears,)]TJ -16.25071 -1.2045 TD [(middle-aged)-331(for)-321(33)-321(y)30(ears,)-341(and)-331(retired)-332(for)-322(16)-331(y)30(ears.)]TJ 1.46548 -1.2045 TD [(The)-290(lab)-30(or)-272(income)-280(pro)-30(cess)-291(tak)30(es)-292(v)51(alues)-291(in)]TJ /F16 1 Tf 17.48532 0 Td (f)Tj /F8 1 Tf 0.50187 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 314.88 594.72 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 321.12 596.52 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 332.16 594.72 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 341.52 596.52 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 352.56 594.72 Tm 0 Tc (H)Tj /F8 1 Tf 11.95517 0 0 11.95517 360.6 596.52 Tm ($)Tj /F16 1 Tf 0.38142 0 Td (g)Tj /F8 1 Tf 0.77289 0 Td (=)Tj /F16 1 Tf 1.0439 0 Td (f)Tj /F8 1 Tf 0.50187 0 Td ($0)Tj /F14 1 Tf 0.87326 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (2823)Tj /F14 1 Tf 1.96735 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (3)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(5428$,)-251(while)]TJ /F14 1 Tf 5.3801 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 525.72 594.72 Tm (O)Tj /F8 1 Tf 11.95517 0 0 11.95517 536.16 596.52 Tm (=)Tj -38.82505 -1.21454 TD (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(25.)-562(The)-380(income)-381(transition)-373(probabilit)30(y)-382(matrix)-372(for)-362(y)31(oung)-381(and)-372(middle-aged)-380(agen)30(ts,)-392(whic)31(h)-382(is)]TJ -0.76285 -1.2045 TD [(de\fned)-341(o)31(v)30(er)]TJ /F16 1 Tf 5.47044 0 Td (f)Tj /F14 1 Tf 0.50187 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 149.16 565.8 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 155.28 567.6 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 166.32 565.8 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 175.68 567.6 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 186.72 565.8 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 194.76 567.6 Tm 0.221 Tc [<6702>-9(f)]TJ /F14 1 Tf 2.22833 0 Td 0 Tc (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 227.16 565.8 Tm (L)Tj /F14 1 Tf 11.95517 0 0 11.95517 233.28 567.6 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 244.32 565.8 Tm 0 Tc (M)Tj /F14 1 Tf 11.95517 0 0 11.95517 253.68 567.6 Tm 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 264.72 565.8 Tm 0 Tc (H)Tj /F16 1 Tf 11.95517 0 0 11.95517 272.76 567.6 Tm (g)Tj /F8 1 Tf 0.50187 0 Td [(,)-321(is)-332(giv)30(en)-340(b)30(y:)]TJ /F19 1 Tf -3.50309 -1.38517 TD (2)Tj 0 -1.80675 TD (4)Tj /F8 1 Tf 1.08405 1.01379 TD (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(9980)-822(0)]TJ /F14 1 Tf 3.28226 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(0020)-1937(0)]TJ -4.31612 -1.21454 TD (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(0007)-822(0)]TJ /F14 1 Tf 3.28226 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(9986)-822(0)]TJ /F14 1 Tf 3.28226 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0007)Tj -6.75524 -1.2045 TD 1.947 Tc (00)Tj /F14 1 Tf 2.93095 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27101 0 Td [(0020)-822(0)]TJ /F14 1 Tf 3.28226 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (9980)Tj /F19 1 Tf 2.37889 3.212 TD (3)Tj 0 -1.80675 TD (5)Tj /F8 1 Tf -25.12386 -3.54324 TD [(This)-392(implies)-391(a)-381(v)50(ariance)-381(of)-371(log)-381(income)-381(among)-381(activ)30(e)-391(agen)31(ts)-382(of)-382(0)]TJ /F14 1 Tf 27.41241 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(4)-371(and)-382(an)-381(auto)-30(correlation)-372(of)]TJ -27.68342 -1.21454 TD (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(95)-421(whic)31(h)-432(is)-432(consisten)30(t)-442(with)-432(the)-432(evidence)-440(on)-421(US)-432(lab)-30(or)-412(earnings)-431(discussed)-453(for)-422(instance)-441(b)30(y)]TJ -0.76285 -1.2045 TD [(Krueger)-331(and)-331(P)29(erri)-331((2005).)]TJ 1.46548 -1.2045 TD [(W)81(e)-311(let)]TJ /F14 1 Tf 3.0514 0 Td (r)Tj /F8 1 Tf 0.75281 0 Td 0.271 Tc (=0)Tj /F14 1 Tf 1.5257 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27101 0 Td [(04)-301(and)-301(c)31(ho)-30(ose)-311(the)-302(main)31(tenance)-321(cost)-311($)]TJ /F14 1 Tf 15.93955 0 Td <0E>Tj /F8 1 Tf 0.47176 0 Td [($)-302(to)-291(matc)30(h)-311(the)-311(estimated)-312(gross)-312(rate)-301(of)]TJ -23.47771 -1.21454 TD [(depreciation)-341(of)-321(housing)-331(capital,)-331(whic)30(h)-341(is)-331(2)]TJ /F14 1 Tf 18.01731 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(5%)-331(ann)30(ually)-331(according)-330(to)-322(Haring)-331(et)-331(al.,)-321(2007.)]TJ -16.82285 -1.2045 TD [(W)81(e)-341(then)-342(normalize)-340(the)-332(initial)-341(house)-342(size)]TJ 17.52547 0.26098 TD <16>Tj /F14 1 Tf -0.01004 -0.26097 TD (h)Tj /F8 1 Tf 0.89334 0 Td [(and)-341(\fx)]TJ /F14 1 Tf 3.30234 0 Td (A)Tj /F8 1 Tf 1.07401 0 Td ($hence)Tj /F14 1 Tf 3.10159 0 Td (q)Tj /F8 1 Tf 0.47176 0 Td [(,)-331(giv)30(en)]TJ /F14 1 Tf 3.17185 0 Td (r)Tj /F8 1 Tf 0.79296 0 Td (and)Tj /F14 1 Tf 1.91716 0 Td <0E>Tj /F8 1 Tf 0.47176 0 Td [($)-332(so)-331(that)-332(the)]TJ -34.17768 -1.21454 TD [(ratio)-402(of)-412(house)-411(price)]TJ 8.9133 0.27101 TD <16>Tj /F14 1 Tf -0.01004 -0.27101 TD (hq)Tj /F8 1 Tf 1.4454 0 Td [(to)-402(income)-420(among)-412(home)-411(buy)31(ers)-433(is)-412(roughly)-411(2)]TJ /F14 1 Tf 19.00099 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(5,)-431(a)-402(n)30(um)30(b)-30(er)-421(consisten)29(t)]TJ -29.62066 -1.2045 TD [(with)-331(pre-2000)-321(evidence)-350(a)30(v)51(ailable)-331(from)-322(the)-331(American)-340(Housing)-332(Surv)30(ey)-341((AHS).)]TJ 1.46548 -1.2045 TD [(As)-331(for)-322(preferences,)-351(w)31(e)-341(initially)-332(sp)-30(ecify)81(,)-342(for)-321(all)-331($)]TJ /F14 1 Tf 19.98466 0 Td [(c;)-170(h)]TJ /F8 1 Tf 1.42533 0 Td ($)Tj /F14 1 Tf 0.65244 0 Td (>)Tj /F8 1 Tf 1.0439 0 Td ($0)Tj /F14 1 Tf 0.87326 0 Td (;)Tj /F8 1 Tf 0.44165 0 Td (0$,)Tj /F14 1 Tf -10.79031 -2.20825 TD (U)Tj /F8 1 Tf 0.76285 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td [(c;)-170(s)]TJ /F8 1 Tf 1.32495 0 Td [($)-281(=)-271(log)]TJ /F14 1 Tf 3.1317 0 Td (c)Tj /F8 1 Tf 0.6424 0 Td [(+)-221(log)]TJ /F14 1 Tf 2.41904 0 Td (s;)Tj /F8 1 Tf -23.75876 -2.20825 TD [(although)-412(w)31(e)-431(will)-422(also)-411(study)-433(the)-411(impact)-422(of)-411(v)50(arious)-422(degrees)-431(of)-412(substitutabilit)28(y)-432(b)-30(et)30(w)31(een)-441(con-)]TJ 0 -1.21454 TD [(sumption)-452(and)-432(housing)-442(services.)-793(W)81(e)-442(select)]TJ /F14 1 Tf 18.99095 0 Td <12>Tj /F8 1 Tf 0.92345 0 Td [(so)-432(that)-442(the)-442(o)30(v)31(erall)-442(home-o)30(wnership)-461(rate)-432(is)]TJ /F11 1 Tf 7.97011 0 0 7.97011 539.76 308.88 Tm (2)Tj ET q 4.32 0 0 -0.48 539.748 307.428 cm /Im1 Do Q BT /F11 1 Tf 7.97011 0 0 7.97011 539.76 300.12 Tm (3)Tj /F8 1 Tf 11.95517 0 0 11.95517 72 289.8 Tm [(among)-301(middle-aged)-320(agen)31(ts,)-322(whic)30(h)-321(is)-311(consisten)29(t)-331(with)-312(the)-311(pre-2000)-301(evidence)-329(a)30(v)50(ailable)-310(from)-302(the)]TJ 0 -1.21454 TD [(Census)-351(Bureau.)]TJ 1.46548 -1.2045 TD [(W)81(e)-392(select)]TJ /F14 1 Tf 4.47672 0 Td (\f)Tj /F8 1 Tf 0.99371 0 Td [(so)-392(that)-382(the)-391(a)30(v)30(erage)-401(non-housing)-392(assets)-402(to)-382(income)-390(ratio)-382(is)-402(ab)-30(out)-382(2)]TJ /F14 1 Tf 28.60688 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(25.)-602(This)]TJ -35.8138 -1.2045 TD [(is)-432(the)-432(a)31(v)30(erage)-441(ratio)-422(of)-422(non-housing)-432(assets)-443(to)-421(income)-431(among)-431(households)-442(whose)-441(head)-432(age)-420(is)]TJ 0 -1.21454 TD [(b)-30(et)30(w)30(een)-350(35)-321(and)-321(70)-321(in)-331(the)-332(1998)-320(Surv)30(ey)-341(of)-321(Consumer)-352(Finance)-330((SCF).)]TJ 1.46548 -1.2045 TD [(The)-451(stipulations)-453(of)-432(FRM)-432(con)31(tracts)-453(are)-441(set)-443(to)-431(mimic)-452(the)-442(features)-452(of)-431(common)-441(standard)]TJ -1.46548 -1.2045 TD [(\fxed-rate)-301(mortgages)-302(in)-291(the)-301(US.)-301(The)-300(do)30(wn-pa)30(ymen)31(t)-322(ratio)]TJ /F14 1 Tf 24.45135 0 Td <0B>Tj /F8 1 Tf 0.92345 0 Td [(is)-302(20%)-290(while)-311(the)-301(maturit)29(y)]TJ /F14 1 Tf 11.27211 0 Td (T)Tj /F8 1 Tf 1.00375 0 Td [(is)-302(15)]TJ -37.65066 -1.21454 TD [(y)30(ears.)-462(The)]TJ /F14 1 Tf 4.91837 0 Td 0.08 Tc [(IO)50(M)]TJ /F8 1 Tf 2.66997 0 Td 0 Tc [(w)30(e)-350(in)30(tro)-31(duce)-341(in)-331(our)-332(main)-331(exp)-29(erimen)30(t)-362(has)]TJ /F14 1 Tf 17.99724 0 Td (k)Tj /F8 1 Tf 0.83311 0 Td [(=)-281(3)-331(and)]TJ /F14 1 Tf 3.7741 0 Td (T)Tj /F8 1 Tf 0.99371 0 Td [(=)-291(10)-331(so)-331(that)-332(agen)31(ts)]TJ -31.18651 -1.2045 TD [(mak)30(e)-331(no)-311(pa)31(ymen)30(t)-341(for)-312(3)-311(y)30(ears,)-331(and)-321(mak)30(e)-331(\fxed)-321(pa)30(ymen)31(ts)-342(for)-312(the)-321(remaining)-331(7)-311(con)31(tract)-322(p)-30(erio)-30(ds)]TJ 0 -1.21454 TD [(unless)-342(the)-331(con)31(tract)-332(is)-332(terminated)-342(b)-30(efore)-331(maturit)29(y)81(.)]TJ 1.46548 -1.2045 TD [(W)81(e)-241(set)]TJ /F14 1 Tf 3.03132 0 Td <14>Tj /F8 1 Tf 0.803 0 Td (and)Tj /F14 1 Tf 1.81679 0 Td <11>Tj /F8 1 Tf 0.75281 0 Td [(join)30(tly)-241(to)-231(matc)30(h)-241(estimates)-262(of)-231(the)-241(loss)-241(incidence)-260(rate)-231(for)-231(lenders)-251(on)-231(foreclosed)]TJ -7.8694 -1.2045 TD [(prop)-30(erties)-402(and)-382(estimates)-412(of)-381(the)-392(price)-401(discoun)30(t)-402(on)-381(these)-402(prop)-30(erties)-402(relativ)30(e)-402(to)-381(other,)-412(similar)]TJ 0 -1.2145 TD [(prop)-30(erties.)-493(The)-350(loss)-352(sev)30(erit)29(y)-371(rate)-341(is)-352(the)-352(presen)30(t)-361(v)50(alue)-341(all)-341(losses)-362(on)-341(a)-341(giv)30(en)-351(loan)-341(as)-351(a)-342(fraction)]TJ 0 -1.2045 TD [(of)-321(the)-331(default)-322(date)-331(balance.)-440(As)-332(Ha)31(yre)-342(and)-321(Saraf)-321((2008))-311(explain,)-341(these)-342(losses)-342(are)-321(caused)-340(b)-31(oth)]TJ 19.30211 -2.8908 TD (15)Tj ET endstream endobj 18 0 obj << /Length 4948 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 72 683.16 Tm 0 g [(b)30(y)-391(transaction)-393(and)-381(time)-391(costs)-393(asso)-30(ciated)-391(with)-392(the)-391(foreclosing)-392(pro)-30(cess,)-412(and)-381(b)30(y)-391(the)-392(fact)-381(that)]TJ 0 -1.21454 TD [(foreclosed)-421(prop)-31(erties)-432(tend)-411(to)-412(sell)-432(at)-412(a)-401(discoun)30(t)-432(relativ)30(e)-431(to)-412(other,)-432(similar)-422(prop)-31(erties.)-713(Using)]TJ 0 -1.2045 TD [(a)-381(data)-382(set)-392(of)-371(a)-381(dataset)-392(of)-382(90,000)-370(\frst-lien)-393(liquidated)-391(loans,)-402(they)-391(estimate)-402(that)-383(loss)-392(sev)30(erit)30(y)]TJ T* [(rates)-312(range)-301(from)-291(around)-312(35%)-290(among)-301(recen)31(t)-322(mortgages)-301(to)-302(as)-301(m)30(uc)30(h)-321(as)-301(60%)-301(among)-301(older)-301(loans.)]TJ 0 -1.21454 TD [(They)-330(also)-322(estimate)-331(that)-322(foreclosed)-331(prop)-30(erties)-332(sell)-332(a)-321(discoun)31(t)-332(relativ)30(e)-331(to)-321(their)-322(appraised)-332(v)51(alue)]TJ 0 -1.2045 TD [(that)-372(ranges)-382(from)-371(10%)-372(among)-371(prop)-30(erties)-382(with)-381(appraisal)-372(v)50(alues)-391(o)30(v)30(er)-381($180,000)-361(to)-371(45%)-371(among)]TJ T* [(prop)-30(erties)-453(with)-451(appraisal)-453(v)51(alues)-452(near)-451($20,000.)-772(Other)-452(studies)-463(of)-442(foreclosure)-451(discoun)30(ts)-463($see)]TJ 0 -1.21454 TD [(P)30(ennington-Cross,)-473(2004,)-441(for)-422(a)-421(review$)-442(t)30(ypically)-441(\fnd)-432(discoun)31(t)-432(rates)-433(near)-431(one)-421(quarter,)-463(with)]TJ 0 -1.2045 TD [(some)-271(exceptions.)-441(Based)-271(on)-260(these)-272(studies)-282(w)31(e)-281(select)]TJ /F14 1 Tf 21.25942 0 Td <14>Tj /F8 1 Tf 0.83311 0 Td (and)Tj /F14 1 Tf 1.83686 0 Td <11>Tj /F8 1 Tf 0.78293 0 Td [(so)-261(that)-262(1\))-261(houses)-282(that)-261(sell)-271(follo)30(wing)]TJ -24.71232 -1.21453 TD [(a)-391(default)-392(in)-401(our)-392(mo)-30(del)-391($whether)-412(v)30(olun)30(tary)-402(or)-391(in)30(v)30(olun)30(tary$)-412(sell)-402(at)-392(25%)-391(discoun)30(t)-402(on)-401(a)30(v)30(erage)]TJ 0 -1.2045 TD [(relativ)30(e)-341(to)-321(other)-332(houses,)-342(and)-331(2\))-321(in)-332(the)-331(ev)31(en)30(t)-341(of)-322(default)-331(and)-331(on)-321(a)30(v)30(erage,)]TJ 14.74509 -2.0878 TD (min)Tj /F16 1 Tf 1.62607 0 Td (f)Tj /F8 1 Tf 0.50188 0 Td ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td <14>Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td 0.04 Tc [(qh)40(;)-131(d)]TJ /F8 1 Tf 1.98742 0 Td 0 Tc (\))Tj ET q 90.12 0 0 -0.48 248.268 508.908 cm /Im1 Do Q BT /F14 1 Tf 11.95517 0 0 11.95517 290.16 497.52 Tm (d)Tj /F8 1 Tf 4.40646 0.68255 TD 0.271 Tc (=0)Tj /F14 1 Tf 1.5257 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27101 0 Td (5)Tj -24.45135 -2.45919 TD (where)Tj /F14 1 Tf 2.78039 0 Td (d)Tj /F8 1 Tf 0.79296 0 Td [(is)-292(the)-281(outstanding)-292(principal)-291(at)-281(the)-291(time)-281(of)-281(default)-291(and)]TJ /F14 1 Tf 23.1264 0 Td 0.04 Tc (qh)Tj /F8 1 Tf 1.31491 0 Td 0 Tc [(is)-292(the)-281(house)-291(v)51(alue.)-431(In)-282(other)]TJ -28.01466 -1.21454 TD [(w)30(ords,)-372(on)-341(a)31(v)30(erage,)-371(the)-351(in)30(termediary)-372(reco)31(v)30(ers)-372(50%)-351(of)-341(the)-362(outstanding)-352(principal)-361(it)-352(is)-352(o)31(w)30(ed)-371(on)]TJ 0 -1.2045 TD [(defaulted)-331(loans.)]TJ 1.46548 -1.21454 TD [(W)81(e)-381(assume)-392(that)-382(agen)30(ts)-382(exp)-30(erience)-400(a)-371(house)-382(v)51(alue)-381(sho)-31(c)31(k)-391(with)-382(probabilit)29(y)]TJ /F14 1 Tf 31.5579 0 Td <15>Tj /F8 1 Tf 0.93349 0 Td 0.361 Tc (=0)Tj /F14 1 Tf 1.61604 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27102 0 Td [(03.)-572(This)]TJ -35.84391 -1.2045 TD [(yields)-331(a)-311(default)-311(rate)-322(of)-301(1)]TJ /F14 1 Tf 10.40889 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(25%)-311(whic)31(h)-331(is)-322(near)-311(the)-321(a)30(v)30(erage)-320(foreclosure)-321(rate)-312(among)-311(all)-311(mortgages)]TJ -10.6799 -1.2045 TD [(in)-331(during)-332(the)-331(1990s)-321(in)-331(the)-332(Mortgage)-321(Bank)31(ers)-342(Asso)-31(ciation's)-341(National)-321(Delinquency)-350(surv)29(ey)81(.)]TJ 1.46548 -1.21454 TD [(Finally)80(,)-421(w)30(e)-411(select)-411(the)-402(mortgage)-391(service)-421(premium)-402($)]TJ /F14 1 Tf 21.83156 0 Td <1E>Tj /F8 1 Tf 0.58217 0 Td [($)-402(so)-392(that)-402(the)-401(a)30(v)30(erage)-401(yield)-411(on)-401(FRM)]TJ -23.87921 -1.2045 TD [(con)31(tracts)-423(in)-422(the)-421(b)-30(enc)30(hmark)-431(econom)31(y)-432(is)-412(roughly)-421(7.5%.)-703(This)-421(w)30(as)-432(the)-411(a)30(v)30(erage)-431(con)31(tract)-423(rate)]TJ T* [(on)-361(con)30(v)31(en)30(tional,)-402(\fxed)-371(rate)-371(mortgages)-362(b)-30(et)30(w)31(een)-391(1990)-351(and)-371(2000)-351(according)-370(to)-362(F)80(ederal)-371(Housing)]TJ 0 -1.21454 TD [(Finance)-331(Board)-321(data.)]TJ 1.46548 -1.2045 TD [(T)81(able)-341(1)-321(summarizes)-352(our)-321(b)-31(enc)31(hmark)-341(parameterization.)]TJ 17.83664 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3.4529 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0000)Tj /F16 1 Tf 2.22832 0 Td <14>Tj /F14 1 Tf 1.06398 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 406.92 602.52 Tm (0)Tj ET q 218.04001 0 0 -0.48 199.668 600.108 cm /Im1 Do Q q 218.04001 0 0 -0.48 199.668 598.068 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 229.2 540 Tm [(T)81(able)-331(3:)-432(Steady)-331(state)-332(statistics)]TJ ET q 386.52002 0 0 -0.48 115.428 523.788 cm /Im1 Do Q q 386.52002 0 0 -0.48 115.428 521.748 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 252.24 511.2 Tm [(Data)-1345(Benc)31(h.)-1024(IOM)-331((1))-995(FRM)-321((2))-995(IOM)-331((2))]TJ ET q 386.52002 0 0 -0.48 115.428 506.988 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 121.32 496.32 Tm [(Home-o)31(wnership)-352(rate)-1797(66.00)-1625(60.12)-1997(63.02)-2479(55.83)-2468(58.48)]TJ 0 -1.2045 TD [(Default)-331(rate)-5401(1.2-4.8)-1565(1.06)-2499(1.18)-2960(1.43)-2971(1.58)]TJ T* [(Av)30(erage)-340(L)80(TY)-5631(2.5)-2358(2.26)-2499(2.41)-2960(2.15)-2971(2.28)]TJ 0 -1.21454 TD [(Av)30(erage)-340(L)80(TV)-5380(0.85)-2117(0.80)-2499(0.83)-2960(0.80)-2971(0.83)]TJ 0 -1.2045 TD [(Av)30(erage)-340(Asset/income)-1566(2.23)-2117(2.69)-2499(2.64)-2960(3.03)-2971(2.98)]TJ 0 -1.21454 TD [(Reco)31(v)31(ery)-352(rate)-5240(0.50)-1876(54.02)-1997(51.07)-2479(53.27)-2468(50.48)]TJ 0 -1.2045 TD [(F)80(oreclosure)-341(discoun)30(t)-2199(75.00)-1625(74.51)-1997(73.97)-2479(76.28)-2468(75.95)]TJ ET q 386.52002 0 0 -0.48 115.428 405.468 cm /Im1 Do Q q 386.52002 0 0 -0.48 115.428 403.428 cm /Im1 Do Q BT /F9 1 Tf 17.21544 0 0 17.21544 72 358.08 Tm [(5)-1122(Results)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 331.8 Tm [(The)-240(b)-30(enc)31(hmark)-252(econom)32(y)-251(deliv)30(ers)-251(a)-231(n)30(um)30(b)-30(er)-251(of)-231(in)30(tuitiv)30(ely)-251(app)-30(ealing)-240(predictions.)-422(The)-240(top)-231(panel)]TJ 0 -1.2045 TD [(of)-291(\fgure)-301(2)-291(sho)30(ws)-311(the)-302(FRM)-291(rates)-302(agen)31(ts)-302(at)-292(v)51(arious)-302(asset-income)-311(p)-30(ositions)-302(can)-301(obtain)-291(from)-292(the)]TJ T* [(in)30(termediary)-482(when)-481(they)-472(b)-30(ecome)-470(middle-aged.)-863(The)-471(\fgure)-462(sho)30(ws,)-522(\frst,)-503(that)-462(agen)30(ts)-472(whose)]TJ 0 -1.21454 TD [(income)-451(and)-441(assets)-463(are)-442(lo)31(w)-442(do)-441(not)-442(get)-442(a)-441(mortgage)-442(in)-441(equilibrium.)-804(This)-451(o)-30(ccurs)-452(for)-442(sev)30(eral)]TJ 0 -1.2045 TD [(reasons.)-713(First,)-444(asset)-432(and)-411(income)-431(p)-30(o)-30(or)-402(agen)31(ts)-423(cannot)-421(meet)-431(the)-412(do)30(wn-pa)31(ymen)30(t)-442(requiremen)31(t)]TJ 0 -1.21454 TD [(and/or)-401(mortgage)-402(pa)30(ymen)31(ts.)-683(Second,)-431(these)-422(agen)31(ts)-412(are)-402(more)-401(lik)30(ely)-421(to)-402(default,)-432(hence)-410(receiv)31(e)]TJ 0 -1.2045 TD [(less)-342(fa)30(v)31(orable)-331(b)-31(orro)30(wing)-331(terms.)]TJ 1.46548 -1.2045 TD [(In)-322(some)-311(cases)-331(in)-311(fact,)-311(there)-311(is)-322(no)-311(yield)-321(suc)30(h)-321(that)-312(the)-311(in)30(termediary)-332(w)31(ould)-321(exp)-30(ects)-321(to)-312(break)]TJ -1.46548 -1.21454 TD [(ev)31(en)-452(on)-441(the)-442(mortgage,)-462(ev)31(en)-451(when)-451(the)-442(agen)31(ts)-443(ha)31(v)30(e)-452(the)-441(means)-442(to)-442(\fnance)-441(the)-441(initial)-442(do)30(wn-)]TJ 0 -1.2045 TD [(pa)30(ymen)31(t.)-683(Among)-401(agen)31(ts)-413(who)-411(do)-401(receiv)31(e)-421(a)-402(mortgage)-391(o\013er,)-432(yields)-411(fall)-402(b)-30(oth)-402(with)-411(assets)-413(and)]TJ T* [(income.)-872(Giv)30(en)-482(the)-471(monotonicit)30(y)-482(of)-462(rates)-482(and)-472(mortgage)-461(a)30(v)50(ailabilit)30(y)-482(in)-472(asset)-472(and)-472(income,)]TJ 0 -1.21454 TD [(o)30(wnership)-321(rates)-302(are)-301(also)-291(monotonic)-311(in)-301(assets)-312(and)-301(income,)-311(as)-301(table)-301(2)-301(sho)30(ws.)-442(Ov)30(erall)-301($see)-311(table)]TJ 0 -1.2045 TD [(3$,)-321(home)-331(o)30(wnership-rates)-352(are)-332(near)-321(60%.)]TJ 1.46548 -1.21454 TD [(Once)-451(IOMs)-452(are)-432(in)30(tro)-31(duced)-461($an)-432(exp)-29(erimen)30(t)-462(w)31(e)-452(call)-441(IOM\(1$\),)-473(agen)31(ts)-453(face)-441(t)30(w)30(o)-441(p)-30(oten)30(tial)]TJ -1.46548 -1.2045 TD [(pa)30(ymen)31(t)-292(sc)30(hedules.)-451(Since)-290(prices)-292(do)-281(not)-271(c)31(hange)-291(b)30(y)-281(assumption,)-302(the)-281(FRM)-282(pa)31(ymen)30(t)-291(sc)30(hedule)-301(as)]TJ T* [(a)-281(function)-291(of)-281(agen)31(t's)-302(initial)-292(asset-income)-301(p)-30(osition)-282(is)-291(unc)30(hanged.)-441(The)-300(new)-291(men)31(u)-301(of)-281(IOM)-292(yields)]TJ 0 -1.2145 TD [(is)-302(sho)30(wn)-321(in)-301(the)-301(b)-30(ottom)-302(panel)-300(of)-301(\fgure)-302(2.)-431(Sev)31(eral)-311(facts)-302(are)-301(immediately)-321(apparen)31(t.)-432(First,)-313(IOM)]TJ 19.30211 -2.78039 TD (18)Tj ET endstream endobj 21 0 obj << /Length 24316 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 189.72 546.84 Tm 0 g [(Figure)-322(2:)-441(Equilibrium)-342(yield)-341(sc)30(hedules,)-361(IOM(1))]TJ ET q 78.48 239.72 460.75 290.2 re W n 1 g 78.48 239.6701 460.8 290.25 re f 138.38 419.3201 307.6 88.85 re f 1 j 0.3 w 1 G 138.38 419.3201 m 138.38 508.1701 l 445.98 508.1701 l 445.98 419.3201 l 138.38 419.3201 l S 0 G 138.38 508.1701 m 445.98 508.1701 l S 138.38 419.3201 m 445.98 419.3201 l S 445.98 419.3201 m 445.98 508.1701 l S 138.38 419.3201 m 138.38 508.1701 l S 138.38 419.3201 m 445.98 419.3201 l S 138.38 419.3201 m 138.38 508.1701 l S 138.38 419.3201 m 138.38 422.42 l S 138.38 508.1701 m 138.38 505.1201 l S BT /F13 1 Tf 6 0 0 6 136.73 412.0701 Tm 0 g (0)Tj ET 169.13 419.3201 m 169.13 422.42 l S 169.13 508.1701 m 169.13 505.1201 l S BT /F13 1 Tf 6 0 0 6 164.98 412.0701 Tm (0.5)Tj ET 199.88 419.3201 m 199.88 422.42 l S 199.88 508.1701 m 199.88 505.1201 l S BT /F13 1 Tf 6 0 0 6 198.23 412.0701 Tm (1)Tj ET 230.63 419.3201 m 230.63 422.42 l S 230.63 508.1701 m 230.63 505.1201 l S BT /F13 1 Tf 6 0 0 6 226.48 412.0701 Tm (1.5)Tj ET 261.38 419.3201 m 261.38 422.42 l S 261.38 508.1701 m 261.38 505.1201 l S BT /F13 1 Tf 6 0 0 6 259.73 412.0701 Tm (2)Tj ET 292.18 419.3201 m 292.18 422.42 l S 292.18 508.1701 m 292.18 505.1201 l S BT /F13 1 Tf 6 0 0 6 288.03 412.0701 Tm (2.5)Tj ET 322.93 419.3201 m 322.93 422.42 l S 322.93 508.1701 m 322.93 505.1201 l S BT /F13 1 Tf 6 0 0 6 321.28 412.0701 Tm (3)Tj ET 353.68 419.3201 m 353.68 422.42 l S 353.68 508.1701 m 353.68 505.1201 l S BT /F13 1 Tf 6 0 0 6 349.53 412.0701 Tm (3.5)Tj ET 384.43 419.3201 m 384.43 422.42 l S 384.43 508.1701 m 384.43 505.1201 l S BT /F13 1 Tf 6 0 0 6 382.78 412.0701 Tm (4)Tj ET 415.18 419.3201 m 415.18 422.42 l S 415.18 508.1701 m 415.18 505.1201 l S BT /F13 1 Tf 6 0 0 6 411.0301 412.0701 Tm (4.5)Tj ET 445.98 419.3201 m 445.98 422.42 l S 445.98 508.1701 m 445.98 505.1201 l S BT /F13 1 Tf 6 0 0 6 444.33 412.0701 Tm (5)Tj ET 138.38 419.3201 m 141.43 419.3201 l S 445.98 419.3201 m 442.88 419.3201 l S BT /F13 1 Tf 6 0 0 6 121.63 417.1201 Tm (0.066)Tj ET 138.38 437.1201 m 141.43 437.1201 l S 445.98 437.1201 m 442.88 437.1201 l S BT /F13 1 Tf 6 0 0 6 121.63 434.9201 Tm (0.068)Tj ET 138.38 454.8701 m 141.43 454.8701 l S 445.98 454.8701 m 442.88 454.8701 l S BT /F13 1 Tf 6 0 0 6 124.98 452.6701 Tm (0.07)Tj ET 138.38 472.6701 m 141.43 472.6701 l S 445.98 472.6701 m 442.88 472.6701 l S BT /F13 1 Tf 6 0 0 6 121.63 470.4701 Tm (0.072)Tj ET 138.38 490.4201 m 141.43 490.4201 l S 445.98 490.4201 m 442.88 490.4201 l S BT /F13 1 Tf 6 0 0 6 121.63 488.2201 Tm (0.074)Tj ET 138.38 508.1701 m 141.43 508.1701 l S 445.98 508.1701 m 442.88 508.1701 l S BT /F13 1 Tf 6 0 0 6 121.63 505.9701 Tm (0.076)Tj ET 138.38 508.1701 m 445.98 508.1701 l S 138.38 419.3201 m 445.98 419.3201 l S 445.98 419.3201 m 445.98 508.1701 l S 138.38 419.3201 m 138.38 508.1701 l S q 138.38 419.2701 307.65 88.9 re W n 1 0 0 RG 252.38 493.5201 m 264.48 493.5201 l 276.58 487.92 l 288.68 487.92 l 300.78 487.92 l 312.88 481.9701 l 324.98 481.9701 l 337.08 461.2701 l 349.1799 461.2701 l 361.2799 449.6201 l 373.3799 449.6201 l 385.4799 442.5201 l 397.5799 433.0201 l 409.6799 433.0201 l 421.7799 433.0201 l 433.8799 433.0201 l 445.9799 433.0201 l S 1.2 w 0 0 1 RG 216.08 433.4701 m 228.18 433.0701 l 240.28 433.0701 l 252.38 433.0701 l 264.48 433.0701 l 276.58 433.0701 l 288.68 433.0701 l 300.78 433.0701 l 312.88 433.0201 l 324.98 433.0201 l 337.08 433.0201 l 349.1799 433.0201 l 361.2799 433.0201 l 373.3799 433.0201 l 385.4799 433.0201 l 397.5799 433.0201 l 409.6799 433.0201 l 421.7799 433.0201 l 433.8799 433.0201 l 445.9799 433.0201 l S 0.3 w 0 G 216.08 433.0201 m 228.18 433.0201 l 240.28 433.0201 l 252.38 433.0201 l 264.48 433.0201 l 276.58 433.0201 l 288.68 433.0201 l 300.78 433.0201 l 312.88 433.0201 l 324.98 433.0201 l 337.08 433.0201 l 349.1799 433.0201 l 361.2799 433.0201 l 373.3799 433.0201 l 385.4799 433.0201 l 397.5799 433.0201 l 409.6799 433.0201 l 421.7799 433.0201 l 433.8799 433.0201 l 445.9799 433.0201 l S Q q 212.43 429.3201 237.25 7.35 re W n 216.68 433.0201 m 216.68 432.6887 216.4114 432.4201 216.08 432.4201 c 215.7486 432.4201 215.48 432.6887 215.48 433.0201 c 215.48 433.3514 215.7486 433.6201 216.08 433.6201 c 216.4114 433.6201 216.68 433.3514 216.68 433.0201 c f 228.78 433.0201 m 228.78 432.6887 228.5114 432.4201 228.18 432.4201 c 227.8486 432.4201 227.58 432.6887 227.58 433.0201 c 227.58 433.3514 227.8486 433.6201 228.18 433.6201 c 228.5114 433.6201 228.78 433.3514 228.78 433.0201 c f 240.88 433.0201 m 240.88 432.6887 240.6114 432.4201 240.28 432.4201 c 239.9487 432.4201 239.68 432.6887 239.68 433.0201 c 239.68 433.3514 239.9487 433.6201 240.28 433.6201 c 240.6114 433.6201 240.88 433.3514 240.88 433.0201 c f 252.98 433.0201 m 252.98 432.6887 252.7114 432.4201 252.38 432.4201 c 252.0486 432.4201 251.78 432.6887 251.78 433.0201 c 251.78 433.3514 252.0486 433.6201 252.38 433.6201 c 252.7114 433.6201 252.98 433.3514 252.98 433.0201 c f 265.08 433.0201 m 265.08 432.6887 264.8114 432.4201 264.48 432.4201 c 264.1486 432.4201 263.88 432.6887 263.88 433.0201 c 263.88 433.3514 264.1486 433.6201 264.48 433.6201 c 264.8114 433.6201 265.08 433.3514 265.08 433.0201 c f 277.18 433.0201 m 277.18 432.6887 276.9114 432.4201 276.58 432.4201 c 276.2487 432.4201 275.98 432.6887 275.98 433.0201 c 275.98 433.3514 276.2487 433.6201 276.58 433.6201 c 276.9114 433.6201 277.18 433.3514 277.18 433.0201 c f 289.28 433.0201 m 289.28 432.6887 289.0114 432.4201 288.68 432.4201 c 288.3486 432.4201 288.08 432.6887 288.08 433.0201 c 288.08 433.3514 288.3486 433.6201 288.68 433.6201 c 289.0114 433.6201 289.28 433.3514 289.28 433.0201 c f 301.38 433.0201 m 301.38 432.6887 301.1114 432.4201 300.78 432.4201 c 300.4487 432.4201 300.18 432.6887 300.18 433.0201 c 300.18 433.3514 300.4487 433.6201 300.78 433.6201 c 301.1114 433.6201 301.38 433.3514 301.38 433.0201 c f 313.48 433.0201 m 313.48 432.6887 313.2114 432.4201 312.88 432.4201 c 312.5486 432.4201 312.28 432.6887 312.28 433.0201 c 312.28 433.3514 312.5486 433.6201 312.88 433.6201 c 313.2114 433.6201 313.48 433.3514 313.48 433.0201 c f 325.58 433.0201 m 325.58 432.6887 325.3114 432.4201 324.98 432.4201 c 324.6487 432.4201 324.38 432.6887 324.38 433.0201 c 324.38 433.3514 324.6487 433.6201 324.98 433.6201 c 325.3114 433.6201 325.58 433.3514 325.58 433.0201 c f 337.68 433.0201 m 337.68 432.6887 337.4114 432.4201 337.08 432.4201 c 336.7487 432.4201 336.48 432.6887 336.48 433.0201 c 336.48 433.3514 336.7487 433.6201 337.08 433.6201 c 337.4114 433.6201 337.68 433.3514 337.68 433.0201 c f 349.78 433.0201 m 349.78 432.6887 349.5114 432.4201 349.18 432.4201 c 348.8487 432.4201 348.58 432.6887 348.58 433.0201 c 348.58 433.3514 348.8487 433.6201 349.18 433.6201 c 349.5114 433.6201 349.78 433.3514 349.78 433.0201 c f 361.88 433.0201 m 361.88 432.6887 361.6114 432.4201 361.28 432.4201 c 360.9486 432.4201 360.68 432.6887 360.68 433.0201 c 360.68 433.3514 360.9486 433.6201 361.28 433.6201 c 361.6114 433.6201 361.88 433.3514 361.88 433.0201 c f 373.98 433.0201 m 373.98 432.6887 373.7114 432.4201 373.38 432.4201 c 373.0487 432.4201 372.78 432.6887 372.78 433.0201 c 372.78 433.3514 373.0487 433.6201 373.38 433.6201 c 373.7114 433.6201 373.98 433.3514 373.98 433.0201 c f 386.08 433.0201 m 386.08 432.6887 385.8114 432.4201 385.48 432.4201 c 385.1487 432.4201 384.88 432.6887 384.88 433.0201 c 384.88 433.3514 385.1487 433.6201 385.48 433.6201 c 385.8114 433.6201 386.08 433.3514 386.08 433.0201 c f 398.18 433.0201 m 398.18 432.6887 397.9114 432.4201 397.58 432.4201 c 397.2487 432.4201 396.98 432.6887 396.98 433.0201 c 396.98 433.3514 397.2487 433.6201 397.58 433.6201 c 397.9114 433.6201 398.18 433.3514 398.18 433.0201 c f 410.2801 433.0201 m 410.2801 432.6887 410.0114 432.4201 409.6801 432.4201 c 409.3487 432.4201 409.08 432.6887 409.08 433.0201 c 409.08 433.3514 409.3487 433.6201 409.6801 433.6201 c 410.0114 433.6201 410.2801 433.3514 410.2801 433.0201 c f 422.38 433.0201 m 422.38 432.6887 422.1114 432.4201 421.78 432.4201 c 421.4487 432.4201 421.18 432.6887 421.18 433.0201 c 421.18 433.3514 421.4487 433.6201 421.78 433.6201 c 422.1114 433.6201 422.38 433.3514 422.38 433.0201 c f 434.48 433.0201 m 434.48 432.6887 434.2114 432.4201 433.88 432.4201 c 433.5486 432.4201 433.28 432.6887 433.28 433.0201 c 433.28 433.3514 433.5486 433.6201 433.88 433.6201 c 434.2114 433.6201 434.48 433.3514 434.48 433.0201 c f 446.58 433.0201 m 446.58 432.6887 446.3114 432.4201 445.98 432.4201 c 445.6487 432.4201 445.38 432.6887 445.38 433.0201 c 445.38 433.3514 445.6487 433.6201 445.98 433.6201 c 446.3114 433.6201 446.58 433.3514 446.58 433.0201 c f Q q 138.38 419.2701 307.65 88.9 re W n Q BT /F13 1 Tf 6 0 0 6 269.68 404.9201 Tm (Initial Assets $a)Tj 4.8 0 0 4.8 310.33 401.9201 Tm (0)Tj 6 0 0 6 312.98 404.9201 Tm ($)Tj 0 6 -6 0 117.53 420.4701 Tm (FRM mortgage interest rate r)Tj 0 4.8 -4.8 0 114.53 497.6701 Tm (FRM)Tj ET 1 g 451.98 476.0701 41.45 32.1 re f 1 G 451.98 476.0701 m 451.98 508.1701 l 493.4301 508.1701 l 493.4301 476.0701 l 451.98 476.0701 l S 0 G 451.98 508.1701 m 493.4301 508.1701 l S 451.98 476.0701 m 493.4301 476.0701 l S 493.4301 476.0701 m 493.4301 508.1701 l S 451.98 476.0701 m 451.98 508.1701 l S 451.98 476.0701 m 493.4301 476.0701 l S 451.98 476.0701 m 451.98 508.1701 l S 451.98 508.1701 m 493.4301 508.1701 l S 451.98 476.0701 m 493.4301 476.0701 l S 493.4301 476.0701 m 493.4301 508.1701 l S 451.98 476.0701 m 451.98 508.1701 l S BT /F13 1 Tf 6 0 0 6 474.9301 501.4201 Tm 0 g (y)Tj 4.8 0 0 4.8 477.9301 498.4201 Tm (0)Tj 6 0 0 6 480.58 501.4201 Tm (=y)Tj 4.8 0 0 4.8 487.08 498.4201 Tm (L)Tj ET q 451.98 476.0201 41.5 32.15 re W n 1 0 0 RG 455.48 502.2201 m 473.13 502.2201 l S Q BT /F13 1 Tf 6 0 0 6 474.9301 491.3201 Tm (y)Tj 4.8 0 0 4.8 477.9301 488.3201 Tm (0)Tj 6 0 0 6 480.58 491.3201 Tm (=y)Tj 4.8 0 0 4.8 487.08 488.3201 Tm (M)Tj ET q 451.98 476.0201 41.5 32.15 re W n 1.2 w 0 0 1 RG 455.48 492.1201 m 473.13 492.1201 l S Q BT /F13 1 Tf 6 0 0 6 474.9301 481.2701 Tm (y)Tj 4.8 0 0 4.8 477.9301 478.2701 Tm (0)Tj 6 0 0 6 480.58 481.2701 Tm (=y)Tj 4.8 0 0 4.8 487.08 478.2701 Tm (H)Tj ET q 451.98 476.0201 41.5 32.15 re W n 455.48 482.0701 m 473.13 482.0701 l S q 460.63 478.3701 7.35 7.35 re W n 464.88 482.0701 m 464.88 481.7387 464.6114 481.4701 464.2801 481.4701 c 463.9487 481.4701 463.6801 481.7387 463.6801 482.0701 c 463.6801 482.4015 463.9487 482.6701 464.2801 482.6701 c 464.6114 482.6701 464.88 482.4015 464.88 482.0701 c f Q Q 1 g 138.38 276.7201 307.6 93.95 re f 1 G 138.38 276.7201 m 138.38 370.6701 l 445.98 370.6701 l 445.98 276.7201 l 138.38 276.7201 l S 0 G 138.38 370.67 m 445.98 370.67 l S 138.38 276.7201 m 445.98 276.7201 l S 445.98 276.7201 m 445.98 370.67 l S 138.38 276.7201 m 138.38 370.67 l S 138.38 276.7201 m 445.98 276.7201 l S 138.38 276.7201 m 138.38 370.67 l S 138.38 276.7201 m 138.38 279.8201 l S 138.38 370.67 m 138.38 367.6201 l S BT /F13 1 Tf 6 0 0 6 136.73 269.4701 Tm 0 g (0)Tj ET 169.13 276.7201 m 169.13 279.8201 l S 169.13 370.67 m 169.13 367.6201 l S BT /F13 1 Tf 6 0 0 6 164.98 269.4701 Tm (0.5)Tj ET 199.88 276.7201 m 199.88 279.8201 l S 199.88 370.67 m 199.88 367.6201 l S BT /F13 1 Tf 6 0 0 6 198.23 269.4701 Tm (1)Tj ET 230.63 276.7201 m 230.63 279.8201 l S 230.63 370.67 m 230.63 367.6201 l S BT /F13 1 Tf 6 0 0 6 226.48 269.4701 Tm (1.5)Tj ET 261.38 276.7201 m 261.38 279.8201 l S 261.38 370.67 m 261.38 367.6201 l S BT /F13 1 Tf 6 0 0 6 259.73 269.4701 Tm (2)Tj ET 292.18 276.7201 m 292.18 279.8201 l S 292.18 370.67 m 292.18 367.6201 l S BT /F13 1 Tf 6 0 0 6 288.03 269.4701 Tm (2.5)Tj ET 322.93 276.7201 m 322.93 279.8201 l S 322.93 370.67 m 322.93 367.6201 l S BT /F13 1 Tf 6 0 0 6 321.28 269.4701 Tm (3)Tj ET 353.68 276.7201 m 353.68 279.8201 l S 353.68 370.67 m 353.68 367.6201 l S BT /F13 1 Tf 6 0 0 6 349.53 269.4701 Tm (3.5)Tj ET 384.43 276.7201 m 384.43 279.8201 l S 384.43 370.67 m 384.43 367.6201 l S BT /F13 1 Tf 6 0 0 6 382.78 269.4701 Tm (4)Tj ET 415.18 276.7201 m 415.18 279.8201 l S 415.18 370.67 m 415.18 367.6201 l S BT /F13 1 Tf 6 0 0 6 411.0301 269.4701 Tm (4.5)Tj ET 445.98 276.7201 m 445.98 279.8201 l S 445.98 370.67 m 445.98 367.6201 l S BT /F13 1 Tf 6 0 0 6 444.33 269.4701 Tm (5)Tj ET 138.38 276.7201 m 141.43 276.7201 l S 445.98 276.7201 m 442.88 276.7201 l S BT /F13 1 Tf 6 0 0 6 121.63 274.5201 Tm (0.074)Tj ET 138.38 290.1701 m 141.43 290.1701 l S 445.98 290.1701 m 442.88 290.1701 l S BT /F13 1 Tf 6 0 0 6 121.63 287.9701 Tm (0.075)Tj ET 138.38 303.5701 m 141.43 303.5701 l S 445.98 303.5701 m 442.88 303.5701 l S BT /F13 1 Tf 6 0 0 6 121.63 301.3701 Tm (0.076)Tj ET 138.38 317.0201 m 141.43 317.0201 l S 445.98 317.0201 m 442.88 317.0201 l S BT /F13 1 Tf 6 0 0 6 121.63 314.8201 Tm 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7.97011 347.04 601.2 Tm (0)Tj /F14 1 Tf 11.95517 0 0 11.95517 355.2 603 Tm (<)Tj /F8 1 Tf 1.03386 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(0000)-993(1)]TJ /F14 1 Tf 3.4529 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0000)Tj /F16 1 Tf 2.23836 0 Td <14>Tj /F14 1 Tf 1.05394 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 466.68 601.2 Tm (0)Tj ET q 337.56003 0 0 -0.48 139.788 598.668 cm /Im1 Do Q q 337.56003 0 0 -0.48 139.788 596.748 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 72 551.4 Tm [(rates)-332(exceed)-350(FRM)-321(rates)-332(at)-332(all)-321(p)-30(ossible)-342(asset-income)-341(p)-30(ositions)-342(since)-341(they)-332(en)31(tail)-342(a)-321(greater)-331(risk)]TJ 0 -1.2045 TD [(of)-321(default)-331(b)-31(ecause)-340(home)-331(equit)30(y)-341(is)-331(m)30(uc)30(h)-341(slo)30(w)30(er)-341(to)-322(rise.)-452(The)-330(lik)30(eliho)-30(o)-30(d)-331(that)-332(an)-321(agen)31(t)-332(will)-331(\fnd)]TJ T* [(herself)-412(with)-401(negativ)30(e)-401(equit)30(y)-411(on)-402(her)-401(home)-401(is)-392(higher)-402(when)-410(she)-402(holds)-402(an)-401(IOM)-402(than)-392(when)-411(she)]TJ 0 -1.21454 TD [(holds)-332(an)-331(FRM.)]TJ 1.46548 -1.2045 TD [(Despite)-381(the)-382(default)-371(premium,)-402(a)-371(signi\fcan)30(t)-392(n)30(um)30(b)-30(er)-381(of)-372(agen)31(ts)-382(do)-371(opt)-372(for)-372(IOM)-372(when)-390(they)]TJ -1.46548 -1.21454 TD [(b)-30(ecome)-430(a)30(v)50(ailable.)-732(This)-432(is)-432(the)-431(case)-432(for)-411(man)30(y)-442(agen)31(ts)-432(who)-422(are)-421(not)-422(o\013ered)-431(an)-422(FRM)-422(b)-30(ecause)]TJ 0 -1.2045 TD [(they)-311(cannot)-301(meet)-311(the)-301(do)30(wn-pa)31(ymen)30(t)-322(and/or)-301(cannot)-301(mak)31(e)-311(the)-301(\frst)-313(pa)31(ymen)30(t.)-442(The)-310(presence)-321(of)]TJ T* [(IOMs,)-272(in)-241(other)-241(w)30(ords,)-271(enables)-251(some)-251(agen)31(ts)-252(at)-231(the)-251(b)-30(ottom)-231(of)-241(the)-241(asset)-252(and)-241(income)-250(distributions)]TJ 0 -1.21454 TD [(to)-321(b)-31(ecome)-340(home-o)31(wners)-341(instead)-332(of)-331(ren)30(ting.)]TJ 1.46548 -1.2045 TD [(In)-352(addition,)-351(some)-361(agen)30(ts)-352(who)-351(w)31(ere)-361(able)-341(to)-341(obtain)-352(a)-341(mortgage)-341(in)-351(the)-352(FRM-only)-342(econom)32(y)]TJ -1.46548 -1.21454 TD [(switc)30(h)-432(to)-421(IOMs)-423(to)-422(tak)30(e)-421(adv)50(an)31(tage)-422(of)-411(the)-432(bac)31(k-loaded)-421(pa)30(ymen)30(ts.)-743(This)-422(option,)-442(once)-430(again,)]TJ 0 -1.2045 TD [(is)-372(particularly)-382(attractiv)29(e)-381(for)-361(agen)30(ts)-382(whose)-381(curren)30(t)-382(income)-380(and)-372(assets)-382(are)-371(lo)30(w.)-572(Asset)-382(and/or)]TJ T* [(income)-240(ric)30(h)-241(agen)31(ts,)-262(for)-221(their)-232(part,)-251(tend)-241(to)-231(opt)-221(for)-232(lo)31(w)30(er-yields)-251(FRMs)-232(since)-250(large)-231(early)-231(pa)31(ymen)30(ts)]TJ 0 -1.21454 TD [(do)-301(not)-311(a\013ect)-301(their)-312(curren)30(t)-321(consumption)-322(m)30(uc)31(h.)-442(This)-321(con)30(tract)-312(selection)-320(pattern)-302(is)-312(displa)30(y)30(ed)-331(in)]TJ 0 -1.2045 TD [(table)-331(4.)]TJ 1.46548 -1.2045 TD [(The)-330(in)30(tro)-31(duction)-321(of)-322(IOMs)-322(has)-321(sev)30(eral)-341(consequences)-350(on)-321(equilibrium)-342(statistics)-333($see)-331(the)-322(sec-)]TJ -1.46548 -1.21454 TD [(ond)-401(column)-411(of)-392(table)-411(3.$)-653(Home-o)31(wnership)-422(rates)-402(rise)-412(as)-402(more)-401(agen)30(ts)-412(are)-401(able)-401(to)-402(\fnance)-411(the)]TJ 0 -1.2045 TD [(house)-391(purc)30(hase.)-613(Giv)31(en)-391(the)-392(bac)31(k-loaded)-391(nature)-382(of)-381(IOMs,)-403(a)30(v)31(erage)-391(loan-to-v)50(alue)-371(and)-381(loan-to-)]TJ 0 -1.21454 TD [(income)-381(ratios)-372(rise,)-392(as)-382(do)-371(default)-371(rates.)-583(These)-391(patterns)-383(are)-371(qualitativ)30(ely)-391(consisten)30(t)-392(with)-382(the)]TJ 0 -1.2045 TD [(recen)31(t)-342(US)-331(evidence)-350(displa)30(y)30(ed)-351(in)-321(\fgure)-331(1.)]TJ 1.46548 -1.2045 TD [(In)-472(this)-483(exp)-29(erimen)30(t,)-522(IOMs)-483(turn)-473(out)-462(to)-462(b)-30(e)-471(selected)-492(b)31(y)-482(roughly)-472(12%)-461(of)-462(agen)31(ts)-483(whic)31(h)-482(is)]TJ -1.46548 -1.21454 TD [(a)-462(reasonable)-481(fraction)-472(giv)30(en)-471(the)-482(evidence)-490(a)30(v)50(ailable)-471(from)-462(the)-482(MBA's)-472(Mortgage)-472(Origination)]TJ 0 -1.2045 TD [(Surv)30(ey)81(.)-452(F)80(or)-312(these)-331(agen)31(ts,)-332(the)-322(default)-321(risk)-322(and)-321(the)-321(asso)-31(ciated)-331(premium)-331(are)-321(to)-30(o)-301(small)-332(to)-311(o\013set)]TJ 0 -1.21454 TD [(the)-331(fron)29(t-loaded)-321(nature)-331(of)-322(FRM)-331(pa)30(ymen)31(ts.)]TJ 1.46548 -1.2045 TD [(Raising)-441(the)-442(probabilit)29(y)-451(of)-432(a)-441(house)-442(dev)51(aluation)-442(sho)-30(c)30(k)-452($an)-441(exp)-30(erimen)30(t)-462(w)31(e)-442(call)-441(IOM\(2$\),)]TJ -1.46548 -1.2045 TD [(whic)31(h)-392(causes)-381(a)-371(drop)-372(in)-381(a)30(v)30(erage)-381(house)-381(prices)-382(in)-381(our)-362(mo)-30(del,)-391(leads)-381(the)-382(prop)-30(ortion)-362(of)-371(IOMs)-383(to)]TJ 0 -1.21454 TD [(decline)-320(as)-312(default)-311(premiums)-332(b)-30(ecome)-310(higher.)-441(F)80(urthermore,)-312(the)-312(e\013ect)-320(of)-301(the)-311(dev)50(aluation)-311(sho)-30(c)30(k)]TJ 0 -1.2045 TD [(is)-392(magni\fed)-391(when)-391(mortgages)-381(with)-392(bac)31(k-loaded)-391(pa)30(ymen)31(ts)-403(are)-391(a)30(v)51(ailable.)-602(Figure)-382(3)-381(sho)30(ws)-402(the)]TJ T* [(impact)-311(on)-291(the)-311(yield)-311(sc)30(hedule)-320(of)-302(a)-290(30%)-301(increase)-321(in)-301(the)-301(lik)30(eliho)-30(o)-30(d)-311(of)-301(a)-291(dev)51(aluation)-312(sho)-30(c)31(k,)-312(while)]TJ 0 -1.21454 TD [(table)-351(5)-351(sho)29(ws)-361(the)-351(e\013ect)-361(on)-341(mortgage)-351(selection)-361(patterns.)-513(Yields)-362(rise)-361(on)-342(b)-30(oth)-351(mortgage)-341(t)29(yp)-30(es)]TJ 0 -1.2045 TD [(at)-402(all)-411(asset-income)-432(p)-30(ositions)-413(since)-421(the)-411(lik)30(eliho)-30(o)-30(d)-421(of)-402(default)-411(has)-422(risen.)-693(The)-421(asso)-31(ciated)-411(pa)30(y-)]TJ 0 -1.2145 TD [(men)30(ts)-322(b)-30(ecome)-310(prohibitiv)30(e)-321(particularly)-322(for)-291(asset)-322(and)-301(income)-321(p)-30(o)-30(or)-291(agen)31(ts.)-443(The)-310(asset)-312(threshold)]TJ 19.30211 -3.02129 TD (20)Tj ET endstream endobj 23 0 obj << /Length 24795 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 189.72 676.2 Tm 0 g [(Figure)-322(3:)-441(Equilibrium)-342(yield)-341(sc)30(hedules,)-361(IOM(2))]TJ ET q 158.28 378.9301 300.6 280.35 re W n 1 g 158.28 378.8801 300.65 280.4 re f 197.38 542.6301 232.95 95.6 re f 1 j 0.3 w 1 G 197.38 542.6301 m 197.38 638.23 l 430.33 638.23 l 430.33 542.6301 l 197.38 542.6301 l S 0 G 197.38 638.2301 m 430.33 638.2301 l S 197.38 542.6301 m 430.33 542.6301 l S 430.33 542.6301 m 430.33 638.2301 l S 197.38 542.6301 m 197.38 638.2301 l S 197.38 542.6301 m 430.33 542.6301 l S 197.38 542.6301 m 197.38 638.2301 l S 197.38 542.6301 m 197.38 544.9801 l S 197.38 638.2301 m 197.38 635.9301 l S BT /F13 1 Tf 6 0 0 6 195.73 535.3801 Tm 0 g (0)Tj ET 220.63 542.6301 m 220.63 544.9801 l S 220.63 638.2301 m 220.63 635.9301 l S BT /F13 1 Tf 6 0 0 6 216.48 535.3801 Tm (0.5)Tj ET 243.93 542.6301 m 243.93 544.9801 l S 243.93 638.2301 m 243.93 635.9301 l S BT /F13 1 Tf 6 0 0 6 242.28 535.3801 Tm (1)Tj ET 267.23 542.6301 m 267.23 544.9801 l S 267.23 638.2301 m 267.23 635.9301 l S BT /F13 1 Tf 6 0 0 6 263.08 535.3801 Tm (1.5)Tj ET 290.53 542.6301 m 290.53 544.9801 l S 290.53 638.2301 m 290.53 635.9301 l S BT /F13 1 Tf 6 0 0 6 288.88 535.3801 Tm (2)Tj ET 313.83 542.6301 m 313.83 544.9801 l S 313.83 638.2301 m 313.83 635.9301 l S BT /F13 1 Tf 6 0 0 6 309.68 535.3801 Tm (2.5)Tj ET 337.13 542.6301 m 337.13 544.9801 l S 337.13 638.2301 m 337.13 635.9301 l S BT /F13 1 Tf 6 0 0 6 335.48 535.3801 Tm (3)Tj ET 360.43 542.6301 m 360.43 544.9801 l S 360.43 638.2301 m 360.43 635.9301 l S BT /F13 1 Tf 6 0 0 6 356.28 535.3801 Tm (3.5)Tj ET 383.73 542.6301 m 383.73 544.9801 l S 383.73 638.2301 m 383.73 635.9301 l S BT /F13 1 Tf 6 0 0 6 382.08 535.3801 Tm (4)Tj ET 407.03 542.6301 m 407.03 544.9801 l S 407.03 638.2301 m 407.03 635.9301 l S BT /F13 1 Tf 6 0 0 6 402.88 535.3801 Tm (4.5)Tj ET 430.33 542.6301 m 430.33 544.9801 l S 430.33 638.2301 m 430.33 635.9301 l S BT /F13 1 Tf 6 0 0 6 428.68 535.3801 Tm (5)Tj ET 197.38 542.6301 m 199.68 542.6301 l S 430.33 542.6301 m 427.98 542.6301 l S BT /F13 1 Tf 6 0 0 6 183.98 540.4301 Tm (0.07)Tj ET 197.38 558.5801 m 199.68 558.5801 l S 430.33 558.5801 m 427.98 558.5801 l S BT /F13 1 Tf 6 0 0 6 180.63 556.3801 Tm (0.072)Tj ET 197.38 574.5301 m 199.68 574.5301 l S 430.33 574.5301 m 427.98 574.5301 l S BT /F13 1 Tf 6 0 0 6 180.63 572.3301 Tm (0.074)Tj ET 197.38 590.4301 m 199.68 590.4301 l S 430.33 590.4301 m 427.98 590.4301 l S BT /F13 1 Tf 6 0 0 6 180.63 588.23 Tm (0.076)Tj ET 197.38 606.3801 m 199.68 606.3801 l S 430.33 606.3801 m 427.98 606.3801 l S BT /F13 1 Tf 6 0 0 6 180.63 604.1801 Tm (0.078)Tj ET 197.38 622.3301 m 199.68 622.3301 l S 430.33 622.3301 m 427.98 622.3301 l S BT /F13 1 Tf 6 0 0 6 183.98 620.1301 Tm (0.08)Tj ET 197.38 638.2301 m 199.68 638.2301 l S 430.33 638.2301 m 427.98 638.2301 l S BT /F13 1 Tf 6 0 0 6 180.63 636.0301 Tm (0.082)Tj ET 197.38 638.2301 m 430.33 638.2301 l S 197.38 542.6301 m 430.33 542.6301 l S 430.33 542.6301 m 430.33 638.2301 l S 197.38 542.6301 m 197.38 638.2301 l S q 197.38 542.5801 233 95.65 re W n 1 0 0 RG 283.68 622.3301 m 292.88 622.3301 l 302.03 622.3301 l 311.18 614.3801 l 320.33 614.3801 l 329.53 606.3801 l 338.68 606.3801 l 347.83 582.4802 l 356.98 582.4802 l 366.1801 582.4802 l 375.33 566.5302 l 384.48 566.5302 l 393.63 558.5801 l 402.83 558.5801 l 411.98 550.6302 l 421.1301 550.6302 l 430.3301 550.6302 l S 1.2 w 0 0 1 RG 256.23 550.6301 m 265.38 550.6301 l 274.53 550.6301 l 283.68 550.6301 l 292.88 550.6301 l 302.03 550.6301 l 311.18 550.6301 l 320.33 550.6301 l 329.53 550.6301 l 338.68 550.6301 l 347.83 550.6301 l 356.98 550.6301 l 366.1801 550.6301 l 375.33 550.6301 l 384.48 550.6301 l 393.63 550.6301 l 402.83 550.6301 l 411.98 550.6301 l 421.1301 550.6301 l 430.3301 550.6301 l S 0.3 w 0 G 256.23 550.6301 m 265.38 550.6301 l 274.53 550.6301 l 283.68 550.6301 l 292.88 550.6301 l 302.03 550.6301 l 311.18 550.6301 l 320.33 550.6301 l 329.53 550.6301 l 338.68 550.6301 l 347.83 550.6301 l 356.98 550.6301 l 366.1801 550.6301 l 375.33 550.6301 l 384.48 550.6301 l 393.63 550.6301 l 402.83 550.6301 l 411.98 550.6301 l 421.1301 550.6301 l 430.3301 550.6301 l S Q q 252.58 546.9301 181.45 7.35 re W n 254.43 550.6301 m 258.03 550.6301 l S 256.23 552.4301 m 256.23 548.8301 l S 263.58 550.6301 m 267.18 550.6301 l S 265.38 552.4301 m 265.38 548.8301 l S 272.73 550.6301 m 276.33 550.6301 l S 274.53 552.4301 m 274.53 548.8301 l S 281.88 550.6301 m 285.48 550.6301 l S 283.68 552.4301 m 283.68 548.8301 l S 291.08 550.6301 m 294.68 550.6301 l S 292.88 552.4301 m 292.88 548.8301 l S 300.23 550.6301 m 303.83 550.6301 l S 302.03 552.4301 m 302.03 548.8301 l S 309.38 550.6301 m 312.98 550.6301 l S 311.18 552.4301 m 311.18 548.8301 l S 318.53 550.6301 m 322.13 550.6301 l S 320.33 552.4301 m 320.33 548.8301 l S 327.73 550.6301 m 331.33 550.6301 l S 329.53 552.4301 m 329.53 548.8301 l S 336.88 550.6301 m 340.48 550.6301 l S 338.68 552.4301 m 338.68 548.8301 l S 346.03 550.6301 m 349.63 550.6301 l S 347.83 552.4301 m 347.83 548.8301 l S 355.18 550.6301 m 358.78 550.6301 l S 356.98 552.4301 m 356.98 548.8301 l S 364.38 550.6301 m 367.98 550.6301 l S 366.18 552.4301 m 366.18 548.8301 l S 373.53 550.6301 m 377.13 550.6301 l S 375.33 552.4301 m 375.33 548.8301 l S 382.68 550.6301 m 386.28 550.6301 l S 384.48 552.4301 m 384.48 548.8301 l S 391.83 550.6301 m 395.43 550.6301 l S 393.63 552.4301 m 393.63 548.8301 l S 401.03 550.6301 m 404.63 550.6301 l S 402.83 552.4301 m 402.83 548.8301 l S 410.18 550.6301 m 413.78 550.6301 l S 411.98 552.4301 m 411.98 548.8301 l S 419.33 550.6301 m 422.93 550.6301 l S 421.13 552.4301 m 421.13 548.8301 l S 428.53 550.6301 m 432.13 550.6301 l S 430.33 552.4301 m 430.33 548.8301 l S 254.98 551.8801 m 257.48 549.3801 l S 257.48 551.8801 m 254.98 549.3801 l S 264.13 551.8801 m 266.63 549.3801 l S 266.63 551.8801 m 264.13 549.3801 l S 273.28 551.8801 m 275.78 549.3801 l S 275.78 551.8801 m 273.28 549.3801 l S 282.43 551.8801 m 284.93 549.3801 l S 284.93 551.8801 m 282.43 549.3801 l S 291.63 551.8801 m 294.13 549.3801 l S 294.13 551.8801 m 291.63 549.3801 l S 300.78 551.8801 m 303.28 549.3801 l S 303.28 551.8801 m 300.78 549.3801 l S 309.93 551.8801 m 312.43 549.3801 l S 312.43 551.8801 m 309.93 549.3801 l S 319.08 551.8801 m 321.58 549.3801 l S 321.58 551.8801 m 319.08 549.3801 l S 328.28 551.8801 m 330.78 549.3801 l S 330.78 551.8801 m 328.28 549.3801 l S 337.43 551.8801 m 339.93 549.3801 l S 339.93 551.8801 m 337.43 549.3801 l S 346.58 551.8801 m 349.08 549.3801 l S 349.08 551.8801 m 346.58 549.3801 l S 355.73 551.8801 m 358.23 549.3801 l S 358.23 551.8801 m 355.73 549.3801 l S 364.93 551.8801 m 367.43 549.3801 l S 367.43 551.8801 m 364.93 549.3801 l S 374.08 551.8801 m 376.58 549.3801 l S 376.58 551.8801 m 374.08 549.3801 l S 383.23 551.8801 m 385.73 549.3801 l S 385.73 551.8801 m 383.23 549.3801 l S 392.38 551.8801 m 394.88 549.3801 l S 394.88 551.8801 m 392.38 549.3801 l S 401.58 551.8801 m 404.08 549.3801 l S 404.08 551.8801 m 401.58 549.3801 l S 410.73 551.8801 m 413.23 549.3801 l S 413.23 551.8801 m 410.73 549.3801 l S 419.88 551.8801 m 422.38 549.3801 l S 422.38 551.8801 m 419.88 549.3801 l S 429.08 551.8801 m 431.58 549.3801 l S 431.58 551.8801 m 429.08 549.3801 l S Q q 197.38 542.5801 233 95.65 re W n Q BT /F13 1 Tf 6 0 0 6 291.33 528.23 Tm (Initial Assets $a)Tj 4.8 0 0 4.8 331.98 525.23 Tm (0)Tj 6 0 0 6 334.63 528.23 Tm ($)Tj 0 6 -6 0 176.53 547.1301 Tm (FRM mortgage interest rate r)Tj 0 4.8 -4.8 0 173.53 624.3301 Tm (FRM)Tj ET 1 g 385.98 603.1301 41.4 32.1 re f 1 G 385.98 603.1301 m 385.98 635.2301 l 427.38 635.2301 l 427.38 603.1301 l 385.98 603.1301 l S 0 G 385.98 635.2301 m 427.38 635.2301 l S 385.98 603.1301 m 427.38 603.1301 l S 427.38 603.1301 m 427.38 635.2301 l S 385.98 603.1301 m 385.98 635.2301 l S 385.98 603.1301 m 427.38 603.1301 l S 385.98 603.1301 m 385.98 635.2301 l S 385.98 635.2301 m 427.38 635.2301 l S 385.98 603.1301 m 427.38 603.1301 l S 427.38 603.1301 m 427.38 635.2301 l S 385.98 603.1301 m 385.98 635.2301 l S BT /F13 1 Tf 6 0 0 6 408.93 628.4801 Tm 0 g (y)Tj 4.8 0 0 4.8 411.93 625.4801 Tm (0)Tj 6 0 0 6 414.58 628.4801 Tm (=y)Tj 4.8 0 0 4.8 421.08 625.4801 Tm (L)Tj ET q 385.98 603.0801 41.45 32.15 re W n 1 0 0 RG 389.48 629.2801 m 407.08 629.2801 l S Q BT /F13 1 Tf 6 0 0 6 408.93 618.4301 Tm (y)Tj 4.8 0 0 4.8 411.93 615.4301 Tm (0)Tj 6 0 0 6 414.58 618.4301 Tm (=y)Tj 4.8 0 0 4.8 421.08 615.4301 Tm (M)Tj ET q 385.98 603.0801 41.45 32.15 re W n 1.2 w 0 0 1 RG 389.48 619.1801 m 407.08 619.1801 l S Q BT /F13 1 Tf 6 0 0 6 408.93 608.3301 Tm (y)Tj 4.8 0 0 4.8 411.93 605.3301 Tm (0)Tj 6 0 0 6 414.58 608.3301 Tm (=y)Tj 4.8 0 0 4.8 421.08 605.3301 Tm (H)Tj ET q 385.98 603.0801 41.45 32.15 re W n 389.48 609.1301 m 407.08 609.1301 l S q 394.63 605.4301 7.35 7.35 re W n 396.48 609.1301 m 400.08 609.1301 l S 398.28 610.9301 m 398.28 607.3301 l S 397.03 610.3801 m 399.53 607.8801 l S 399.53 610.3801 m 397.03 607.8801 l S Q Q 1 g 197.38 409.8301 232.95 95.65 re f 1 G 197.38 409.8301 m 197.38 505.4801 l 430.33 505.4801 l 430.33 409.8301 l 197.38 409.8301 l S 0 G 197.38 505.4801 m 430.33 505.4801 l S 197.38 409.8301 m 430.33 409.8301 l S 430.33 409.8301 m 430.33 505.4801 l S 197.38 409.8301 m 197.38 505.4801 l S 197.38 409.8301 m 430.33 409.8301 l S 197.38 409.8301 m 197.38 505.4801 l S 197.38 409.8301 m 197.38 412.1301 l S 197.38 505.4801 m 197.38 503.1301 l S BT /F13 1 Tf 6 0 0 6 195.73 402.5301 Tm 0 g (0)Tj ET 220.63 409.8301 m 220.63 412.1301 l S 220.63 505.4801 m 220.63 503.1301 l S BT /F13 1 Tf 6 0 0 6 216.48 402.5301 Tm (0.5)Tj ET 243.93 409.8301 m 243.93 412.1301 l S 243.93 505.4801 m 243.93 503.1301 l S BT /F13 1 Tf 6 0 0 6 242.28 402.5301 Tm (1)Tj ET 267.23 409.8301 m 267.23 412.1301 l S 267.23 505.4801 m 267.23 503.1301 l S BT /F13 1 Tf 6 0 0 6 263.08 402.5301 Tm (1.5)Tj ET 290.53 409.8301 m 290.53 412.1301 l S 290.53 505.4801 m 290.53 503.1301 l S BT /F13 1 Tf 6 0 0 6 288.88 402.5301 Tm (2)Tj ET 313.83 409.8301 m 313.83 412.1301 l S 313.83 505.4801 m 313.83 503.1301 l S BT /F13 1 Tf 6 0 0 6 309.68 402.5301 Tm (2.5)Tj ET 337.13 409.8301 m 337.13 412.1301 l S 337.13 505.4801 m 337.13 503.1301 l S BT /F13 1 Tf 6 0 0 6 335.48 402.5301 Tm (3)Tj ET 360.43 409.8301 m 360.43 412.1301 l S 360.43 505.4801 m 360.43 503.1301 l S BT /F13 1 Tf 6 0 0 6 356.28 402.5301 Tm (3.5)Tj ET 383.73 409.8301 m 383.73 412.1301 l S 383.73 505.4801 m 383.73 503.1301 l S BT /F13 1 Tf 6 0 0 6 382.08 402.5301 Tm (4)Tj ET 407.03 409.8301 m 407.03 412.1301 l S 407.03 505.4801 m 407.03 503.1301 l S BT /F13 1 Tf 6 0 0 6 402.88 402.5301 Tm (4.5)Tj ET 430.33 409.8301 m 430.33 412.1301 l S 430.33 505.4801 m 430.33 503.1301 l S BT /F13 1 Tf 6 0 0 6 428.68 402.5301 Tm (5)Tj ET 197.38 409.8301 m 199.68 409.8301 l S 430.33 409.8301 m 427.98 409.8301 l S BT /F13 1 Tf 6 0 0 6 183.98 407.6301 Tm (0.08)Tj ET 197.38 428.9301 m 199.68 428.9301 l S 430.33 428.9301 m 427.98 428.9301 l S BT /F13 1 Tf 6 0 0 6 180.63 426.7301 Tm (0.085)Tj ET 197.38 448.0801 m 199.68 448.0801 l S 430.33 448.0801 m 427.98 448.0801 l S BT /F13 1 Tf 6 0 0 6 183.98 445.8801 Tm (0.09)Tj ET 197.38 467.1801 m 199.68 467.1801 l S 430.33 467.1801 m 427.98 467.1801 l S BT /F13 1 Tf 6 0 0 6 180.63 464.9801 Tm (0.095)Tj ET 197.38 486.3301 m 199.68 486.3301 l S 430.33 486.3301 m 427.98 486.3301 l S BT /F13 1 Tf 6 0 0 6 187.33 484.1301 Tm (0.1)Tj ET 197.38 505.4801 m 199.68 505.4801 l S 430.33 505.4801 m 427.98 505.4801 l S BT /F13 1 Tf 6 0 0 6 180.63 503.2801 Tm (0.105)Tj ET 197.38 505.4801 m 430.33 505.4801 l S 197.38 409.8301 m 430.33 409.8301 l S 430.33 409.8301 m 430.33 505.4801 l S 197.38 409.8301 m 197.38 505.4801 l S q 197.38 409.73 233 95.75 re W n 1 0 0 RG 224.33 474.83 m 226.78 474.83 l 229.23 474.83 l 231.68 474.83 l 234.13 474.83 l 236.58 474.83 l 239.03 474.83 l 241.48 474.83 l 243.93 474.83 l 256.23 474.83 l 265.38 474.83 l 274.53 474.83 l 283.68 474.83 l 292.88 474.83 l 302.03 474.83 l 311.18 474.83 l 320.33 474.83 l 329.53 474.83 l 338.68 474.83 l 347.83 474.83 l 356.98 474.83 l 366.18 463.38 l 375.33 455.73 l 384.48 455.73 l 393.63 455.73 l 402.83 455.73 l 411.98 451.8801 l 421.13 451.8801 l 430.33 451.8801 l S 1.2 w 0 0 1 RG 197.38 413.6301 m 199.83 413.6301 l 202.28 413.6301 l 204.73 413.6301 l 207.18 413.6301 l 209.63 413.6301 l 212.08 413.6301 l 214.53 413.6301 l 216.98 413.6301 l 219.43 413.6301 l 221.88 413.6301 l 224.33 413.6301 l 226.78 413.6301 l 229.2299 413.6301 l 231.6799 413.6301 l 234.1299 413.6301 l 236.5799 413.6301 l 239.0299 413.6301 l 241.4799 413.6301 l 243.9299 413.6301 l 256.2299 413.6301 l 265.3799 413.6301 l 274.5299 413.6301 l 283.6799 413.6301 l 292.8799 413.6301 l 302.0299 413.6301 l 311.1799 413.6301 l 320.3299 413.6301 l 329.5299 413.6301 l 338.6799 413.6301 l 347.83 413.6301 l 356.98 413.6301 l 366.18 413.6301 l 375.33 413.6301 l 384.4799 413.6301 l 393.6299 413.6301 l 402.83 413.6301 l 411.98 413.6301 l 421.13 413.6301 l 430.33 413.6301 l S 0.3 w 0 G 197.38 413.6301 m 199.83 413.6301 l 202.28 413.6301 l 204.73 413.6301 l 207.18 413.6301 l 209.63 413.6301 l 212.08 413.6301 l 214.53 413.6301 l 216.98 413.6301 l 219.43 413.6301 l 221.88 413.6301 l 224.33 413.6301 l 226.78 413.6301 l 229.2299 413.6301 l 231.6799 413.6301 l 234.1299 413.6301 l 236.5799 413.6301 l 239.0299 413.6301 l 241.4799 413.6301 l 243.9299 413.6301 l 256.2299 413.6301 l 265.3799 413.6301 l 274.5299 413.6301 l 283.6799 413.6301 l 292.8799 413.6301 l 302.0299 413.6301 l 311.1799 413.6301 l 320.3299 413.6301 l 329.5299 413.6301 l 338.6799 413.6301 l 347.83 413.6301 l 356.98 413.6301 l 366.18 413.6301 l 375.33 413.6301 l 384.4799 413.6301 l 393.6299 413.6301 l 402.83 413.6301 l 411.98 413.6301 l 421.13 413.6301 l 430.33 413.6301 l S Q q 193.73 409.9301 240.3 7.35 re W n 195.58 413.6301 m 199.18 413.6301 l S 197.38 415.4301 m 197.38 411.83 l S 198.03 413.6301 m 201.63 413.6301 l S 199.83 415.4301 m 199.83 411.83 l S 200.48 413.6301 m 204.08 413.6301 l S 202.28 415.4301 m 202.28 411.83 l S 202.93 413.6301 m 206.53 413.6301 l S 204.73 415.4301 m 204.73 411.83 l S 205.38 413.6301 m 208.98 413.6301 l S 207.18 415.4301 m 207.18 411.83 l S 207.83 413.6301 m 211.43 413.6301 l S 209.63 415.4301 m 209.63 411.83 l S 210.28 413.6301 m 213.88 413.6301 l S 212.08 415.4301 m 212.08 411.83 l S 212.73 413.6301 m 216.33 413.6301 l S 214.53 415.4301 m 214.53 411.83 l S 215.18 413.6301 m 218.78 413.6301 l S 216.98 415.4301 m 216.98 411.83 l S 217.63 413.6301 m 221.23 413.6301 l S 219.43 415.4301 m 219.43 411.83 l S 220.08 413.6301 m 223.68 413.6301 l S 221.88 415.4301 m 221.88 411.83 l S 222.53 413.6301 m 226.13 413.6301 l S 224.33 415.4301 m 224.33 411.83 l S 224.98 413.6301 m 228.58 413.6301 l S 226.78 415.4301 m 226.78 411.83 l S 227.43 413.6301 m 231.03 413.6301 l S 229.23 415.4301 m 229.23 411.83 l S 229.88 413.6301 m 233.48 413.6301 l S 231.68 415.4301 m 231.68 411.83 l S 232.33 413.6301 m 235.93 413.6301 l S 234.13 415.4301 m 234.13 411.83 l S 234.78 413.6301 m 238.38 413.6301 l S 236.58 415.4301 m 236.58 411.83 l S 237.23 413.6301 m 240.83 413.6301 l S 239.03 415.4301 m 239.03 411.83 l S 239.68 413.6301 m 243.28 413.6301 l S 241.48 415.4301 m 241.48 411.83 l S 242.13 413.6301 m 245.73 413.6301 l S 243.93 415.4301 m 243.93 411.83 l S 254.43 413.6301 m 258.03 413.6301 l S 256.23 415.4301 m 256.23 411.83 l S 263.58 413.6301 m 267.18 413.6301 l S 265.38 415.4301 m 265.38 411.83 l S 272.73 413.6301 m 276.33 413.6301 l S 274.53 415.4301 m 274.53 411.83 l S 281.88 413.6301 m 285.48 413.6301 l S 283.68 415.4301 m 283.68 411.83 l S 291.08 413.6301 m 294.68 413.6301 l S 292.88 415.4301 m 292.88 411.83 l S 300.23 413.6301 m 303.83 413.6301 l S 302.03 415.4301 m 302.03 411.83 l S 309.38 413.6301 m 312.98 413.6301 l S 311.18 415.4301 m 311.18 411.83 l S 318.53 413.6301 m 322.13 413.6301 l S 320.33 415.4301 m 320.33 411.83 l S 327.73 413.6301 m 331.33 413.6301 l S 329.53 415.4301 m 329.53 411.83 l S 336.88 413.6301 m 340.48 413.6301 l S 338.68 415.4301 m 338.68 411.83 l S 346.03 413.6301 m 349.63 413.6301 l S 347.83 415.4301 m 347.83 411.83 l S 355.18 413.6301 m 358.78 413.6301 l S 356.98 415.4301 m 356.98 411.83 l S 364.38 413.6301 m 367.98 413.6301 l S 366.18 415.4301 m 366.18 411.83 l S 373.53 413.6301 m 377.13 413.6301 l S 375.33 415.4301 m 375.33 411.83 l S 382.68 413.6301 m 386.28 413.6301 l S 384.48 415.4301 m 384.48 411.83 l S 391.83 413.6301 m 395.43 413.6301 l S 393.63 415.4301 m 393.63 411.83 l S 401.03 413.6301 m 404.63 413.6301 l S 402.83 415.4301 m 402.83 411.83 l S 410.18 413.6301 m 413.78 413.6301 l S 411.98 415.4301 m 411.98 411.83 l S 419.33 413.6301 m 422.93 413.6301 l S 421.13 415.4301 m 421.13 411.83 l S 428.53 413.6301 m 432.13 413.6301 l S 430.33 415.4301 m 430.33 411.83 l S 196.13 414.8801 m 198.63 412.3801 l S 198.63 414.8801 m 196.13 412.3801 l S 198.58 414.8801 m 201.08 412.3801 l S 201.08 414.8801 m 198.58 412.3801 l S 201.03 414.8801 m 203.53 412.3801 l S 203.53 414.8801 m 201.03 412.3801 l S 203.48 414.8801 m 205.98 412.3801 l S 205.98 414.8801 m 203.48 412.3801 l S 205.93 414.8801 m 208.43 412.3801 l S 208.43 414.8801 m 205.93 412.3801 l S 208.38 414.8801 m 210.88 412.3801 l S 210.88 414.8801 m 208.38 412.3801 l S 210.83 414.8801 m 213.33 412.3801 l S 213.33 414.8801 m 210.83 412.3801 l S 213.28 414.8801 m 215.78 412.3801 l S 215.78 414.8801 m 213.28 412.3801 l S 215.73 414.8801 m 218.23 412.3801 l S 218.23 414.8801 m 215.73 412.3801 l S 218.18 414.8801 m 220.68 412.3801 l S 220.68 414.8801 m 218.18 412.3801 l S 220.63 414.8801 m 223.13 412.3801 l S 223.13 414.8801 m 220.63 412.3801 l S 223.08 414.8801 m 225.58 412.3801 l S 225.58 414.8801 m 223.08 412.3801 l S 225.53 414.8801 m 228.03 412.3801 l S 228.03 414.8801 m 225.53 412.3801 l S 227.98 414.8801 m 230.48 412.3801 l S 230.48 414.8801 m 227.98 412.3801 l S 230.43 414.8801 m 232.93 412.3801 l S 232.93 414.8801 m 230.43 412.3801 l S 232.88 414.8801 m 235.38 412.3801 l S 235.38 414.8801 m 232.88 412.3801 l S 235.33 414.8801 m 237.83 412.3801 l S 237.83 414.8801 m 235.33 412.3801 l S 237.78 414.8801 m 240.28 412.3801 l S 240.28 414.8801 m 237.78 412.3801 l S 240.23 414.8801 m 242.73 412.3801 l S 242.73 414.8801 m 240.23 412.3801 l S 242.68 414.8801 m 245.18 412.3801 l S 245.18 414.8801 m 242.68 412.3801 l S 254.98 414.8801 m 257.48 412.3801 l S 257.48 414.8801 m 254.98 412.3801 l S 264.13 414.8801 m 266.63 412.3801 l S 266.63 414.8801 m 264.13 412.3801 l S 273.28 414.8801 m 275.78 412.3801 l S 275.78 414.8801 m 273.28 412.3801 l S 282.43 414.8801 m 284.93 412.3801 l S 284.93 414.8801 m 282.43 412.3801 l S 291.63 414.8801 m 294.13 412.3801 l S 294.13 414.8801 m 291.63 412.3801 l S 300.78 414.8801 m 303.28 412.3801 l S 303.28 414.8801 m 300.78 412.3801 l S 309.93 414.8801 m 312.43 412.3801 l S 312.43 414.8801 m 309.93 412.3801 l S 319.08 414.8801 m 321.58 412.3801 l S 321.58 414.8801 m 319.08 412.3801 l S 328.28 414.8801 m 330.78 412.3801 l S 330.78 414.8801 m 328.28 412.3801 l S 337.43 414.8801 m 339.93 412.3801 l S 339.93 414.8801 m 337.43 412.3801 l S 346.58 414.8801 m 349.08 412.3801 l S 349.08 414.8801 m 346.58 412.3801 l S 355.73 414.8801 m 358.23 412.3801 l S 358.23 414.8801 m 355.73 412.3801 l S 364.93 414.8801 m 367.43 412.3801 l S 367.43 414.8801 m 364.93 412.3801 l S 374.08 414.8801 m 376.58 412.3801 l S 376.58 414.8801 m 374.08 412.3801 l S 383.23 414.8801 m 385.73 412.3801 l S 385.73 414.8801 m 383.23 412.3801 l S 392.38 414.8801 m 394.88 412.3801 l S 394.88 414.8801 m 392.38 412.3801 l S 401.58 414.8801 m 404.08 412.3801 l S 404.08 414.8801 m 401.58 412.3801 l S 410.73 414.8801 m 413.23 412.3801 l S 413.23 414.8801 m 410.73 412.3801 l S 419.88 414.8801 m 422.38 412.3801 l S 422.38 414.8801 m 419.88 412.3801 l S 429.08 414.8801 m 431.58 412.3801 l S 431.58 414.8801 m 429.08 412.3801 l S Q q 197.38 409.73 233 95.75 re W n Q BT /F13 1 Tf 6 0 0 6 291.33 395.3801 Tm (Initial Assets $a)Tj 4.8 0 0 4.8 331.98 392.3801 Tm (0)Tj 6 0 0 6 334.63 395.3801 Tm ($)Tj 0 6 -6 0 176.53 415.8301 Tm (IOM mortgage interest rate r)Tj 0 4.8 -4.8 0 173.53 491.33 Tm (IOM)Tj ET 1 g 385.98 470.3801 41.4 32.1 re f 1 G 385.98 470.3801 m 385.98 502.4801 l 427.38 502.4801 l 427.38 470.3801 l 385.98 470.3801 l S 0 G 385.98 502.4801 m 427.38 502.4801 l S 385.98 470.3801 m 427.38 470.3801 l S 427.38 470.3801 m 427.38 502.4801 l S 385.98 470.3801 m 385.98 502.4801 l S 385.98 470.3801 m 427.38 470.3801 l S 385.98 470.3801 m 385.98 502.4801 l S 385.98 502.4801 m 427.38 502.4801 l S 385.98 470.3801 m 427.38 470.3801 l S 427.38 470.3801 m 427.38 502.4801 l S 385.98 470.3801 m 385.98 502.4801 l S BT /F13 1 Tf 6 0 0 6 408.93 495.7301 Tm 0 g (y)Tj 4.8 0 0 4.8 411.93 492.7301 Tm (0)Tj 6 0 0 6 414.58 495.7301 Tm (=y)Tj 4.8 0 0 4.8 421.08 492.7301 Tm (L)Tj ET q 385.98 470.33 41.45 32.15 re W n 1 0 0 RG 389.48 496.5301 m 407.08 496.5301 l S Q BT /F13 1 Tf 6 0 0 6 408.93 485.6801 Tm (y)Tj 4.8 0 0 4.8 411.93 482.6801 Tm (0)Tj 6 0 0 6 414.58 485.6801 Tm (=y)Tj 4.8 0 0 4.8 421.08 482.6801 Tm (M)Tj ET q 385.98 470.33 41.45 32.15 re W n 1.2 w 0 0 1 RG 389.48 486.4301 m 407.08 486.4301 l S Q BT /F13 1 Tf 6 0 0 6 408.93 475.58 Tm (y)Tj 4.8 0 0 4.8 411.93 472.58 Tm (0)Tj 6 0 0 6 414.58 475.58 Tm (=y)Tj 4.8 0 0 4.8 421.08 472.58 Tm (H)Tj ET q 385.98 470.33 41.45 32.15 re W n 389.48 476.3801 m 407.08 476.3801 l S q 394.63 472.6801 7.35 7.35 re W n 396.48 476.3801 m 400.08 476.3801 l S 398.28 478.1801 m 398.28 474.5801 l S 397.03 477.6301 m 399.53 475.1301 l S 399.53 477.6301 m 397.03 475.1301 l S Q Q Q q BT /F8 1 Tf 11.95517 0 0 11.95517 72 333.6 Tm [(past)-392(whic)31(h)-402(lo)30(w-income)-400(agen)31(ts)-393(c)31(ho)-30(ose)-401(to)-382(o)30(wn)-401(rather)-382(than)-392(ren)30(t)-402(rises)-402(from)-382(0)]TJ /F14 1 Tf 32.37094 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(68)-381(to)-382(0)]TJ /F14 1 Tf 3.11163 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(90.)-622(The)]TJ -36.02459 -1.2045 TD [(distribution)-363(of)-341(agen)31(ts)-363(across)-362(asset-income)-361(lev)31(els)-372(is)-362(suc)30(h)-361(that)-352(this)-352(c)30(hange)-360(induces)-372(a)-341(complete)]TJ 0 -1.21454 TD [(rev)30(ersal)-392(of)-371(the)-371(mortgage)-372(c)31(hoice)-391(distribution.)-584(The)-380(fraction)-372(of)-371(agen)30(ts)-382(who)-371(opt)-381(for)-362(IOMs)-382(falls)]TJ 0 -1.2045 TD [(from)-322(12)-320(to)-332(11%.)]TJ 1.46548 -1.21454 TD [(Figure)-261(4)-251(plots)-252(the)-261(endogenous)-270(distribution)-263(of)-251(assets)-272(among)-250(agen)31(ts)-262(that)-252(just)-262(turned)-261(middle-)]TJ -1.46548 -1.2045 TD [(aged.)-411(In)-261(the)-251(b)-30(enc)31(hmark)-272(exp)-29(erimen)30(t,)-292(the)-261(upp)-30(er)-261(panel)-250(sho)30(ws)-271(that,)-272(quite)-261(in)30(tuitiv)29(ely)81(,)-291(lo)30(w-income)]TJ T* [(agen)31(ts)-443(tend)-441(to)-432(ha)30(v)30(e)-441(lo)30(w)-441(assets,)-483(and)-432(vice-v)31(ersa.)-783(The)-441(lo)30(w)31(er)-442(panel)-441(sho)30(ws)-452(the)-432(c)31(hange)-451(in)-432(the)]TJ 0 -1.21454 TD [(distribution)-403(when)-401(IOMs)-402(are)-392(in)30(tro)-30(duced,)-421(i.e.)-632(in)-392(exp)-30(erimen)31(t)-412(IOM(1).)-634(Because)-400(IOMs)-402(do)-392(not)]TJ 0 -1.2045 TD [(require)-251(a)-231(do)31(wnpa)30(ymen)31(t,)-272(the)-241(\fgure)-241(mak)31(es)-251(apparen)30(t)-241(that)-232(agen)31(ts)-242(en)31(ter)-242(mid-age)-230(with)-241(less)-251(sa)29(vings.)]TJ 1.46548 -1.2045 TD [(Figure)-301(5)-301(plots)-302(the)-301(distribution)-313(of)-291(con)30(tract)-302(c)31(hoice)-310(b)30(y)-311(asset)-312(and)-301(income)-300(lev)30(el.)-441(In)-312(the)-301(b)-30(enc)31(h-)]TJ -1.46548 -1.21454 TD [(mark)-341(exp)-30(erimen)30(t,)-352(the)-341(upp)-30(er)-331(panel)-341(sho)30(ws)-352(that)-332(agen)31(ts)-342(with)-331(lo)30(w)-341(income)-340(and)-331(lo)30(w)-341(assets)-353(do)-331(not)]TJ 0 -1.2045 TD [(tak)30(e)-401(a)-391(mortgage.)-633(The)-400(lo)30(w)30(er)-401(panel)-401(sho)30(ws)-412(that)-392(when)-401(IOMs)-402(are)-392(in)30(tro)-30(duced,)-421(agen)30(ts)-402(with)-401(lo)30(w)]TJ 0 -1.21454 TD [(income)-340(and)-321(lo)30(w)-331(assets)-343(no)31(w)-341(select)-341(in)30(to)-332(IOMs.)]TJ 1.46548 -1.2045 TD [(The)-250(impact)-231(on)-241(steady)-241(state)-242(statistics)-253(is)-241(also)-231(noticeable)-240($see)-251(the)-231(last)-241(column)-241(of)-231(table)-230(3.$)-412(The)]TJ -1.46548 -1.2045 TD [(home-o)31(wnership)-412(rate)-392(falls)-392(do)30(wn)-401(to)-391(under)-402(60%.)-622(The)-401(loan-to-v)50(alue)-381(and)-391(loan-to-income)-391(ratio)]TJ 0 -1.2145 TD [(also)-271(fall)-271(as)-281(fron)29(t-loaded)-271(mortgages)-271(b)-30(ecome)-280(somewhat)-281(more)-281(imp)-30(ortan)30(t.)-422(The)-281(default)-271(frequency)81(,)]TJ 0 -1.2045 TD [(ho)30(w)31(ev)30(er,)-421(jumps)-402(up)-392(b)30(y)-391(almost)-392(50%)-381(despite)-402(the)-392(lo)31(w)30(er)-401(fraction)-382(of)-381(IOMs.)-624(The)-390(direct)-402(e\013ect)-391(of)]TJ 19.30211 -2.93095 TD (21)Tj ET Q endstream endobj 24 0 obj << /Length 37870 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 168.96 546.84 Tm 0 g [(Figure)-332(4:)-431(Distribution)-333(of)-321(assets)-342(up)-30(on)-332(en)31(tering)-332(mid-age)]TJ ET q 158.28 240.44 300.6 290.2 re W n 1 g 158.28 240.3901 300.65 290.25 re f 197.33 409.8901 183.25 99 re f 1 j 0.3 w 1 G 197.33 409.8901 m 197.33 508.8901 l 380.58 508.8901 l 380.58 409.8901 l 197.33 409.8901 l S 0 G 197.33 508.8901 m 380.58 508.8901 l S 197.33 409.8901 m 380.58 409.8901 l S 380.58 409.8901 m 380.58 508.8901 l S 197.33 409.8901 m 197.33 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422.2901 l S 380.58 422.2901 m 378.73 422.2901 l S BT /F13 1 Tf 6 0 0 6 192.33 420.0901 Tm (1)Tj ET 197.33 434.6401 m 199.18 434.6401 l S 380.58 434.6401 m 378.73 434.6401 l S BT /F13 1 Tf 6 0 0 6 192.33 432.4401 Tm (2)Tj ET 197.33 447.0401 m 199.18 447.0401 l S 380.58 447.0401 m 378.73 447.0401 l S BT /F13 1 Tf 6 0 0 6 192.33 444.8401 Tm (3)Tj ET 197.33 459.3901 m 199.18 459.3901 l S 380.58 459.3901 m 378.73 459.3901 l S BT /F13 1 Tf 6 0 0 6 192.33 457.1901 Tm (4)Tj ET 197.33 471.7901 m 199.18 471.7901 l S 380.58 471.7901 m 378.73 471.7901 l S BT /F13 1 Tf 6 0 0 6 192.33 469.5901 Tm (5)Tj ET 197.33 484.1401 m 199.18 484.1401 l S 380.58 484.1401 m 378.73 484.1401 l S BT /F13 1 Tf 6 0 0 6 192.33 481.9401 Tm (6)Tj ET 197.33 496.5401 m 199.18 496.5401 l S 380.58 496.5401 m 378.73 496.5401 l S BT /F13 1 Tf 6 0 0 6 192.33 494.3401 Tm (7)Tj ET 197.33 508.8901 m 199.18 508.8901 l S 380.58 508.8901 m 378.73 508.8901 l S BT /F13 1 Tf 6 0 0 6 192.33 506.6901 Tm (8)Tj 0.83333 0.81667 TD (x 10)Tj 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409.8901 l S 210.88 409.8901 2.85 0.05 re f 210.88 409.8901 m 210.88 409.9401 l 213.73 409.9401 l 213.73 409.8901 l 210.88 409.8901 l S 212.78 409.8901 2.8 0.05 re f 212.78 409.8901 m 212.78 409.9401 l 215.58 409.9401 l 215.58 409.8901 l 212.78 409.8901 l S 214.63 409.8901 2.85 0.05 re f 214.63 409.8901 m 214.63 409.9401 l 217.48 409.9401 l 217.48 409.8901 l 214.63 409.8901 l S 216.53 409.8901 2.85 0.05 re f 216.53 409.8901 m 216.53 409.9401 l 219.38 409.9401 l 219.38 409.8901 l 216.53 409.8901 l S 218.43 409.8901 m 218.43 409.8901 l 221.28 409.8901 l f* 218.43 409.8901 m 218.43 409.8901 l 221.28 409.8901 l 218.43 409.8901 l S 220.33 409.8901 m 220.33 409.8901 l 223.18 409.8901 l f* 220.33 409.8901 m 220.33 409.8901 l 223.18 409.8901 l 220.33 409.8901 l S 222.23 409.8901 2.8 0.05 re f 222.23 409.8901 m 222.23 409.9401 l 225.03 409.9401 l 225.03 409.8901 l 222.23 409.8901 l S 224.13 409.8901 m 224.13 409.8901 l 226.93 409.8901 l f* 224.13 409.8901 m 224.13 409.8901 l 226.93 409.8901 l 224.13 409.8901 l S 225.98 409.8901 m 225.98 409.8901 l 228.83 409.8901 l f* 225.98 409.8901 m 225.98 409.8901 l 228.83 409.8901 l 225.98 409.8901 l S 227.88 409.8901 m 227.88 409.8901 l 230.73 409.8901 l f* 227.88 409.8901 m 227.88 409.8901 l 230.73 409.8901 l 227.88 409.8901 l S 229.78 409.8901 m 229.78 409.8901 l 232.63 409.8901 l f* 229.78 409.8901 m 229.78 409.8901 l 232.63 409.8901 l 229.78 409.8901 l S 231.68 409.8901 m 231.68 409.8901 l 234.53 409.8901 l f* 231.68 409.8901 m 231.68 409.8901 l 234.53 409.8901 l 231.68 409.8901 l S 233.58 409.8901 2.8 0.15 re f 233.58 409.8901 m 233.58 410.0401 l 236.38 410.0401 l 236.38 409.8901 l 233.58 409.8901 l S 235.43 409.8901 2.85 0.05 re f 235.43 409.8901 m 235.43 409.9401 l 238.28 409.9401 l 238.28 409.8901 l 235.43 409.8901 l S 244.88 409.8901 2.85 0.05 re f 244.88 409.8901 m 244.88 409.9401 l 247.73 409.9401 l 247.73 409.8901 l 244.88 409.8901 l S 251.98 409.8901 2.8 1.05 re f 251.98 409.8901 m 251.98 410.9401 l 254.78 410.9401 l 254.78 409.8901 l 251.98 409.8901 l S 259.03 409.8901 2.85 0.05 re f 259.03 409.8901 m 259.03 409.9401 l 261.88 409.9401 l 261.88 409.8901 l 259.03 409.8901 l S 266.08 409.8901 2.85 0.05 re f 266.08 409.8901 m 266.08 409.9401 l 268.93 409.9401 l 268.93 409.8901 l 266.08 409.8901 l S 273.18 409.8901 2.8 0.05 re f 273.18 409.8901 m 273.18 409.9401 l 275.98 409.9401 l 275.98 409.8901 l 273.18 409.8901 l S 280.23 409.8901 2.85 0.05 re f 280.23 409.8901 m 280.23 409.9401 l 283.08 409.9401 l 283.08 409.8901 l 280.23 409.8901 l S 287.28 409.8901 2.85 0.05 re f 287.28 409.8901 m 287.28 409.9401 l 290.13 409.9401 l 290.13 409.8901 l 287.28 409.8901 l S 294.38 409.8901 2.8 0.05 re f 294.38 409.8901 m 294.38 409.9401 l 297.18 409.9401 l 297.18 409.8901 l 294.38 409.8901 l S 301.43 409.8901 2.85 0.05 re f 301.43 409.8901 m 301.43 409.9401 l 304.28 409.9401 l 304.28 409.8901 l 301.43 409.8901 l S 308.48 409.8901 m 308.48 409.8901 l 311.33 409.8901 l f* 308.48 409.8901 m 308.48 409.8901 l 311.33 409.8901 l 308.48 409.8901 l S 315.53 409.8901 m 315.53 409.8901 l 318.38 409.8901 l f* 315.53 409.8901 m 315.53 409.8901 l 318.38 409.8901 l 315.53 409.8901 l S 322.63 409.8901 m 322.63 409.8901 l 325.43 409.8901 l f* 322.63 409.8901 m 322.63 409.8901 l 325.43 409.8901 l 322.63 409.8901 l S 329.68 409.8901 m 329.68 409.8901 l 332.53 409.8901 l f* 329.68 409.8901 m 329.68 409.8901 l 332.53 409.8901 l 329.68 409.8901 l S 336.73 409.8901 m 336.73 409.8901 l 339.58 409.8901 l f* 336.73 409.8901 m 336.73 409.8901 l 339.58 409.8901 l 336.73 409.8901 l S 343.83 409.8901 m 343.83 409.8901 l 346.63 409.8901 l f* 343.83 409.8901 m 343.83 409.8901 l 346.63 409.8901 l 343.83 409.8901 l S 350.88 409.8901 m 350.88 409.8901 l 353.73 409.8901 l f* 350.88 409.8901 m 350.88 409.8901 l 353.73 409.8901 l 350.88 409.8901 l S 357.93 409.8901 m 357.93 409.8901 l 360.78 409.8901 l f* 357.93 409.8901 m 357.93 409.8901 l 360.78 409.8901 l 357.93 409.8901 l S 365.03 409.8901 m 365.03 409.8901 l 367.83 409.8901 l f* 365.03 409.8901 m 365.03 409.8901 l 367.83 409.8901 l 365.03 409.8901 l S 372.08 409.8901 m 372.08 409.8901 l 374.93 409.8901 l f* 372.08 409.8901 m 372.08 409.8901 l 374.93 409.8901 l 372.08 409.8901 l S 379.13 409.8901 m 379.13 409.8901 l 381.98 409.8901 l f* 379.13 409.8901 m 379.13 409.8901 l 381.98 409.8901 l 379.13 409.8901 l S 197.33 409.8901 m 380.58 409.8901 l S 0.563 1 0.437 rg 199.53 446.8401 2.85 0.1 re f 199.53 446.8401 m 199.53 446.9401 l 202.38 446.9401 l 202.38 446.8401 l 199.53 446.8401 l S 201.43 409.8901 m 201.43 409.8901 l 204.28 409.8901 l f* 201.43 409.8901 m 201.43 409.8901 l 204.28 409.8901 l 201.43 409.8901 l S 203.33 409.8901 m 203.33 409.8901 l 206.13 409.8901 l f* 203.33 409.8901 m 203.33 409.8901 l 206.13 409.8901 l 203.33 409.8901 l S 205.18 409.8901 m 205.18 409.8901 l 208.03 409.8901 l f* 205.18 409.8901 m 205.18 409.8901 l 208.03 409.8901 l 205.18 409.8901 l S 207.08 409.8901 m 207.08 409.8901 l 209.93 409.8901 l f* 207.08 409.8901 m 207.08 409.8901 l 209.93 409.8901 l 207.08 409.8901 l S 208.98 409.9901 m 208.98 409.9901 l 211.83 409.9901 l f* 208.98 409.9901 m 208.98 409.9901 l 211.83 409.9901 l 208.98 409.9901 l S 210.88 409.9401 m 210.88 409.9401 l 213.73 409.9401 l f* 210.88 409.9401 m 210.88 409.9401 l 213.73 409.9401 l 210.88 409.9401 l S 212.78 409.9401 m 212.78 409.9401 l 215.58 409.9401 l f* 212.78 409.9401 m 212.78 409.9401 l 215.58 409.9401 l 212.78 409.9401 l S 214.63 409.9401 m 214.63 409.9401 l 217.48 409.9401 l f* 214.63 409.9401 m 214.63 409.9401 l 217.48 409.9401 l 214.63 409.9401 l S 216.53 409.9401 2.85 6.6 re f 216.53 409.9401 m 216.53 416.5401 l 219.38 416.5401 l 219.38 409.9401 l 216.53 409.9401 l S 218.43 409.8901 m 218.43 409.8901 l 221.28 409.8901 l f* 218.43 409.8901 m 218.43 409.8901 l 221.28 409.8901 l 218.43 409.8901 l S 220.33 409.8901 m 220.33 409.8901 l 223.18 409.8901 l f* 220.33 409.8901 m 220.33 409.8901 l 223.18 409.8901 l 220.33 409.8901 l S 222.23 409.9401 m 222.23 409.9401 l 225.03 409.9401 l f* 222.23 409.9401 m 222.23 409.9401 l 225.03 409.9401 l 222.23 409.9401 l S 224.13 409.8901 m 224.13 409.8901 l 226.93 409.8901 l f* 224.13 409.8901 m 224.13 409.8901 l 226.93 409.8901 l 224.13 409.8901 l S 225.98 409.8901 m 225.98 409.8901 l 228.83 409.8901 l f* 225.98 409.8901 m 225.98 409.8901 l 228.83 409.8901 l 225.98 409.8901 l S 227.88 409.8901 m 227.88 409.8901 l 230.73 409.8901 l f* 227.88 409.8901 m 227.88 409.8901 l 230.73 409.8901 l 227.88 409.8901 l S 229.78 409.8901 m 229.78 409.8901 l 232.63 409.8901 l f* 229.78 409.8901 m 229.78 409.8901 l 232.63 409.8901 l 229.78 409.8901 l S 231.68 409.8901 m 231.68 409.8901 l 234.53 409.8901 l f* 231.68 409.8901 m 231.68 409.8901 l 234.53 409.8901 l 231.68 409.8901 l S 233.58 410.0401 m 233.58 410.0401 l 236.38 410.0401 l f* 233.58 410.0401 m 233.58 410.0401 l 236.38 410.0401 l 233.58 410.0401 l S 235.43 409.9401 2.85 6.2 re f 235.43 409.9401 m 235.43 416.1401 l 238.28 416.1401 l 238.28 409.9401 l 235.43 409.9401 l S 244.88 409.9401 2.85 5.8 re f 244.88 409.9401 m 244.88 415.7401 l 247.73 415.7401 l 247.73 409.9401 l 244.88 409.9401 l S 251.98 410.94 2.8 90.2 re f 251.98 410.9401 m 251.98 501.14 l 254.78 501.14 l 254.78 410.94 l 251.98 410.94 l S 259.03 409.9401 2.85 0.05 re f 259.03 409.9401 m 259.03 409.9901 l 261.88 409.9901 l 261.88 409.9401 l 259.03 409.9401 l S 266.08 409.9401 2.85 0.05 re f 266.08 409.9401 m 266.08 409.9901 l 268.93 409.9901 l 268.93 409.9401 l 266.08 409.9401 l S 273.18 409.9401 2.8 0.05 re f 273.18 409.9401 m 273.18 409.9901 l 275.98 409.9901 l 275.98 409.9401 l 273.18 409.9401 l S 280.23 409.9401 m 280.23 409.9401 l 283.08 409.9401 l f* 280.23 409.9401 m 280.23 409.9401 l 283.08 409.9401 l 280.23 409.9401 l S 287.28 409.9401 2.85 0.05 re f 287.28 409.9401 m 287.28 409.9901 l 290.13 409.9901 l 290.13 409.9401 l 287.28 409.9401 l S 294.38 409.9401 m 294.38 409.9401 l 297.18 409.9401 l f* 294.38 409.9401 m 294.38 409.9401 l 297.18 409.9401 l 294.38 409.9401 l S 301.43 409.9401 2.85 0.05 re f 301.43 409.9401 m 301.43 409.9901 l 304.28 409.9901 l 304.28 409.9401 l 301.43 409.9401 l S 308.48 409.8901 m 308.48 409.8901 l 311.33 409.8901 l f* 308.48 409.8901 m 308.48 409.8901 l 311.33 409.8901 l 308.48 409.8901 l S 315.53 409.8901 2.85 0.1 re f 315.53 409.8901 m 315.53 409.9901 l 318.38 409.9901 l 318.38 409.8901 l 315.53 409.8901 l S 322.63 409.8901 m 322.63 409.8901 l 325.43 409.8901 l f* 322.63 409.8901 m 322.63 409.8901 l 325.43 409.8901 l 322.63 409.8901 l S 329.68 409.8901 m 329.68 409.8901 l 332.53 409.8901 l f* 329.68 409.8901 m 329.68 409.8901 l 332.53 409.8901 l 329.68 409.8901 l S 336.73 409.8901 m 336.73 409.8901 l 339.58 409.8901 l f* 336.73 409.8901 m 336.73 409.8901 l 339.58 409.8901 l 336.73 409.8901 l S 343.83 409.8901 m 343.83 409.8901 l 346.63 409.8901 l f* 343.83 409.8901 m 343.83 409.8901 l 346.63 409.8901 l 343.83 409.8901 l S 350.88 409.8901 m 350.88 409.8901 l 353.73 409.8901 l f* 350.88 409.8901 m 350.88 409.8901 l 353.73 409.8901 l 350.88 409.8901 l S 357.93 409.8901 m 357.93 409.8901 l 360.78 409.8901 l f* 357.93 409.8901 m 357.93 409.8901 l 360.78 409.8901 l 357.93 409.8901 l S 365.03 409.8901 m 365.03 409.8901 l 367.83 409.8901 l f* 365.03 409.8901 m 365.03 409.8901 l 367.83 409.8901 l 365.03 409.8901 l S 372.08 409.8901 m 372.08 409.8901 l 374.93 409.8901 l f* 372.08 409.8901 m 372.08 409.8901 l 374.93 409.8901 l 372.08 409.8901 l S 379.13 409.8901 m 379.13 409.8901 l 381.98 409.8901 l f* 379.13 409.8901 m 379.13 409.8901 l 381.98 409.8901 l 379.13 409.8901 l S 0.5 0 0 rg 199.53 446.9401 m 199.53 446.9401 l 202.38 446.9401 l f* 199.53 446.9401 m 199.53 446.9401 l 202.38 446.9401 l 199.53 446.9401 l S 201.43 409.8901 m 201.43 409.8901 l 204.28 409.8901 l f* 201.43 409.8901 m 201.43 409.8901 l 204.28 409.8901 l 201.43 409.8901 l S 203.33 409.8901 m 203.33 409.8901 l 206.13 409.8901 l f* 203.33 409.8901 m 203.33 409.8901 l 206.13 409.8901 l 203.33 409.8901 l S 205.18 409.8901 m 205.18 409.8901 l 208.03 409.8901 l f* 205.18 409.8901 m 205.18 409.8901 l 208.03 409.8901 l 205.18 409.8901 l S 207.08 409.8901 m 207.08 409.8901 l 209.93 409.8901 l f* 207.08 409.8901 m 207.08 409.8901 l 209.93 409.8901 l 207.08 409.8901 l S 208.98 409.9901 m 208.98 409.9901 l 211.83 409.9901 l f* 208.98 409.9901 m 208.98 409.9901 l 211.83 409.9901 l 208.98 409.9901 l S 210.88 409.9401 m 210.88 409.9401 l 213.73 409.9401 l f* 210.88 409.9401 m 210.88 409.9401 l 213.73 409.9401 l 210.88 409.9401 l S 212.78 409.9401 m 212.78 409.9401 l 215.58 409.9401 l f* 212.78 409.9401 m 212.78 409.9401 l 215.58 409.9401 l 212.78 409.9401 l S 214.63 409.9401 m 214.63 409.9401 l 217.48 409.9401 l f* 214.63 409.9401 m 214.63 409.9401 l 217.48 409.9401 l 214.63 409.9401 l S 216.53 416.5401 m 216.53 416.5401 l 219.38 416.5401 l f* 216.53 416.5401 m 216.53 416.5401 l 219.38 416.5401 l 216.53 416.5401 l S 218.43 409.8901 m 218.43 409.8901 l 221.28 409.8901 l f* 218.43 409.8901 m 218.43 409.8901 l 221.28 409.8901 l 218.43 409.8901 l S 220.33 409.8901 m 220.33 409.8901 l 223.18 409.8901 l f* 220.33 409.8901 m 220.33 409.8901 l 223.18 409.8901 l 220.33 409.8901 l S 222.23 409.9401 m 222.23 409.9401 l 225.03 409.9401 l f* 222.23 409.9401 m 222.23 409.9401 l 225.03 409.9401 l 222.23 409.9401 l S 224.13 409.8901 m 224.13 409.8901 l 226.93 409.8901 l f* 224.13 409.8901 m 224.13 409.8901 l 226.93 409.8901 l 224.13 409.8901 l S 225.98 409.8901 m 225.98 409.8901 l 228.83 409.8901 l f* 225.98 409.8901 m 225.98 409.8901 l 228.83 409.8901 l 225.98 409.8901 l S 227.88 409.8901 m 227.88 409.8901 l 230.73 409.8901 l f* 227.88 409.8901 m 227.88 409.8901 l 230.73 409.8901 l 227.88 409.8901 l S 229.78 409.8901 m 229.78 409.8901 l 232.63 409.8901 l f* 229.78 409.8901 m 229.78 409.8901 l 232.63 409.8901 l 229.78 409.8901 l S 231.68 409.8901 m 231.68 409.8901 l 234.53 409.8901 l f* 231.68 409.8901 m 231.68 409.8901 l 234.53 409.8901 l 231.68 409.8901 l S 233.58 410.0401 m 233.58 410.0401 l 236.38 410.0401 l f* 233.58 410.0401 m 233.58 410.0401 l 236.38 410.0401 l 233.58 410.0401 l S 235.43 416.1401 2.85 2.3 re f 235.43 416.1401 m 235.43 418.4401 l 238.28 418.4401 l 238.28 416.1401 l 235.43 416.1401 l S 244.88 415.7401 m 244.88 415.7401 l 247.73 415.7401 l f* 244.88 415.7401 m 244.88 415.7401 l 247.73 415.7401 l 244.88 415.7401 l S 251.98 501.14 2.8 0.05 re f 251.98 501.14 m 251.98 501.19 l 254.78 501.19 l 254.78 501.14 l 251.98 501.14 l S 259.03 409.9901 m 259.03 409.9901 l 261.88 409.9901 l f* 259.03 409.9901 m 259.03 409.9901 l 261.88 409.9901 l 259.03 409.9901 l S 266.08 409.9901 m 266.08 409.9901 l 268.93 409.9901 l f* 266.08 409.9901 m 266.08 409.9901 l 268.93 409.9901 l 266.08 409.9901 l S 273.18 409.9901 2.8 2.15 re f 273.18 409.9901 m 273.18 412.1401 l 275.98 412.1401 l 275.98 409.9901 l 273.18 409.9901 l S 280.23 409.9401 2.85 0.05 re f 280.23 409.9401 m 280.23 409.9901 l 283.08 409.9901 l 283.08 409.9401 l 280.23 409.9401 l S 287.28 409.9901 m 287.28 409.9901 l 290.13 409.9901 l f* 287.28 409.9901 m 287.28 409.9901 l 290.13 409.9901 l 287.28 409.9901 l S 294.38 409.9401 m 294.38 409.9401 l 297.18 409.9401 l f* 294.38 409.9401 m 294.38 409.9401 l 297.18 409.9401 l 294.38 409.9401 l S 301.43 409.9901 m 301.43 409.9901 l 304.28 409.9901 l f* 301.43 409.9901 m 301.43 409.9901 l 304.28 409.9901 l 301.43 409.9901 l S 308.48 409.8901 m 308.48 409.8901 l 311.33 409.8901 l f* 308.48 409.8901 m 308.48 409.8901 l 311.33 409.8901 l 308.48 409.8901 l S 315.53 409.9901 2.85 33.6 re f 315.53 409.9901 m 315.53 443.5901 l 318.38 443.5901 l 318.38 409.9901 l 315.53 409.9901 l S 322.63 409.8901 m 322.63 409.8901 l 325.43 409.8901 l f* 322.63 409.8901 m 322.63 409.8901 l 325.43 409.8901 l 322.63 409.8901 l S 329.68 409.8901 m 329.68 409.8901 l 332.53 409.8901 l f* 329.68 409.8901 m 329.68 409.8901 l 332.53 409.8901 l 329.68 409.8901 l S 336.73 409.8901 m 336.73 409.8901 l 339.58 409.8901 l f* 336.73 409.8901 m 336.73 409.8901 l 339.58 409.8901 l 336.73 409.8901 l S 343.83 409.8901 m 343.83 409.8901 l 346.63 409.8901 l f* 343.83 409.8901 m 343.83 409.8901 l 346.63 409.8901 l 343.83 409.8901 l S 350.88 409.8901 m 350.88 409.8901 l 353.73 409.8901 l f* 350.88 409.8901 m 350.88 409.8901 l 353.73 409.8901 l 350.88 409.8901 l S 357.93 409.8901 m 357.93 409.8901 l 360.78 409.8901 l f* 357.93 409.8901 m 357.93 409.8901 l 360.78 409.8901 l 357.93 409.8901 l S 365.03 409.8901 m 365.03 409.8901 l 367.83 409.8901 l f* 365.03 409.8901 m 365.03 409.8901 l 367.83 409.8901 l 365.03 409.8901 l S 372.08 409.8901 m 372.08 409.8901 l 374.93 409.8901 l f* 372.08 409.8901 m 372.08 409.8901 l 374.93 409.8901 l 372.08 409.8901 l S 379.13 409.8901 m 379.13 409.8901 l 381.98 409.8901 l f* 379.13 409.8901 m 379.13 409.8901 l 381.98 409.8901 l 379.13 409.8901 l S Q BT /F13 1 Tf 6 0 0 6 266.78 395.4901 Tm (Initial assets $a)Tj 4.8 0 0 4.8 306.78 392.4901 Tm (0)Tj 6 0 0 6 309.43 395.4901 Tm ($)Tj -5.95 19.69167 TD (Benchmark)Tj ET 1 g 386.58 476.7901 41.4 32.1 re f 1 G 386.58 476.7901 m 386.58 508.8901 l 427.98 508.8901 l 427.98 476.7901 l 386.58 476.7901 l S 0 G 386.58 508.8901 m 427.98 508.8901 l S 386.58 476.7901 m 427.98 476.7901 l S 427.98 476.7901 m 427.98 508.8901 l S 386.58 476.7901 m 386.58 508.8901 l S 386.58 476.7901 m 427.98 476.7901 l S 386.58 476.7901 m 386.58 508.8901 l S 386.58 508.8901 m 427.98 508.8901 l S 386.58 476.7901 m 427.98 476.7901 l S 427.98 476.7901 m 427.98 508.8901 l S 386.58 476.7901 m 386.58 508.8901 l S BT /F13 1 Tf 6 0 0 6 409.53 502.1401 Tm 0 g (y)Tj 4.8 0 0 4.8 412.53 499.1401 Tm (0)Tj 6 0 0 6 415.18 502.1401 Tm (=y)Tj 4.8 0 0 4.8 421.68 499.1401 Tm (L)Tj ET q 386.58 476.7401 41.45 32.15 re W n 0 0 0.563 rg 390.08 499.1401 17.6 7.55 re f 390.08 499.1401 m 390.08 506.6901 l 407.68 506.6901 l 407.68 499.1401 l 390.08 499.1401 l S Q BT /F13 1 Tf 6 0 0 6 409.53 492.0401 Tm (y)Tj 4.8 0 0 4.8 412.53 489.0401 Tm (0)Tj 6 0 0 6 415.18 492.0401 Tm (=y)Tj 4.8 0 0 4.8 421.68 489.0401 Tm (M)Tj ET q 386.58 476.7401 41.45 32.15 re W n 0.563 1 0.437 rg 390.08 489.0901 m 390.08 496.64 l 407.68 496.64 l 407.68 489.0901 l 390.08 489.0901 l f* 390.08 489.0901 m 390.08 496.64 l 407.68 496.64 l 407.68 489.0901 l 390.08 489.0901 l S Q BT /F13 1 Tf 6 0 0 6 409.53 481.9901 Tm (y)Tj 4.8 0 0 4.8 412.53 478.9901 Tm (0)Tj 6 0 0 6 415.18 481.9901 Tm (=y)Tj 4.8 0 0 4.8 421.68 478.9901 Tm (H)Tj ET q 386.58 476.7401 41.45 32.15 re W n 0.5 0 0 rg 390.08 479.0401 17.6 7.55 re f 390.08 479.0401 m 390.08 486.5901 l 407.68 486.5901 l 407.68 479.0401 l 390.08 479.0401 l S Q 1 g 197.33 272.3401 183.5 99.05 re f 1 G 197.33 272.3401 m 197.33 371.3901 l 380.83 371.3901 l 380.83 272.3401 l 197.33 272.3401 l S 0 G 197.33 371.39 m 380.83 371.39 l S 197.33 272.3401 m 380.83 272.3401 l S 380.83 272.3401 m 380.83 371.39 l S 197.33 272.3401 m 197.33 371.39 l S 197.33 272.3401 m 380.83 272.3401 l S 197.33 272.3401 m 197.33 371.39 l S 200.93 272.3401 m 200.93 274.1901 l S 200.93 371.39 m 200.93 369.5901 l S BT /F13 1 Tf 6 0 0 6 199.28 265.0901 Tm 0 g (0)Tj ET 236.93 272.3401 m 236.93 274.1901 l S 236.93 371.39 m 236.93 369.5901 l S BT /F13 1 Tf 6 0 0 6 235.28 265.0901 Tm (1)Tj ET 272.88 272.3401 m 272.88 274.1901 l S 272.88 371.39 m 272.88 369.5901 l S BT /F13 1 Tf 6 0 0 6 271.23 265.0901 Tm (2)Tj ET 308.88 272.3401 m 308.88 274.1901 l S 308.88 371.39 m 308.88 369.5901 l S BT /F13 1 Tf 6 0 0 6 307.23 265.0901 Tm (3)Tj ET 344.83 272.3401 m 344.83 274.1901 l S 344.83 371.39 m 344.83 369.5901 l S BT /F13 1 Tf 6 0 0 6 343.18 265.0901 Tm (4)Tj ET 380.83 272.3401 m 380.83 274.1901 l S 380.83 371.39 m 380.83 369.5901 l S BT /F13 1 Tf 6 0 0 6 379.18 265.0901 Tm (5)Tj ET 197.33 272.3401 m 199.18 272.3401 l S 380.83 272.3401 m 378.98 272.3401 l S BT /F13 1 Tf 6 0 0 6 188.83 270.14 Tm (-1)Tj ET 197.33 297.14 m 199.18 297.14 l S 380.83 297.14 m 378.98 297.14 l S BT /F13 1 Tf 6 0 0 6 183.83 294.9401 Tm (-0.5)Tj ET 197.33 321.89 m 199.18 321.89 l S 380.83 321.89 m 378.98 321.89 l S BT /F13 1 Tf 6 0 0 6 192.33 319.6901 Tm (0)Tj ET 197.33 346.64 m 199.18 346.64 l S 380.83 346.64 m 378.98 346.64 l S BT /F13 1 Tf 6 0 0 6 187.33 344.4401 Tm (0.5)Tj ET 197.33 371.39 m 199.18 371.39 l S 380.83 371.39 m 378.98 371.39 l S BT /F13 1 Tf 6 0 0 6 192.33 369.1901 Tm (1)Tj 0.83333 0.81666 TD (x 10)Tj 4 0 0 4 208.63 377.7901 Tm (-3)Tj ET 197.33 371.39 m 380.83 371.39 l S 197.33 272.3401 m 380.83 272.3401 l S 380.83 272.3401 m 380.83 371.39 l S 197.33 272.3401 m 197.33 371.39 l S BT /F13 1 Tf 6 0 0 6 223.68 376.1401 Tm (Changes in distribution after mortgage innovation)Tj ET q 197.33 272.2901 183.55 99.1 re W n 0 0 0.563 rg 199.53 321.89 m 199.53 321.89 l 202.38 321.89 l f* 199.53 321.89 m 199.53 321.89 l 202.38 321.89 l 199.53 321.89 l S 201.43 321.89 m 201.43 321.89 l 204.28 321.89 l f* 201.43 321.89 m 201.43 321.89 l 204.28 321.89 l 201.43 321.89 l S 203.33 321.89 m 203.33 321.89 l 206.18 321.89 l f* 203.33 321.89 m 203.33 321.89 l 206.18 321.89 l 203.33 321.89 l S 205.23 321.89 m 205.23 321.89 l 208.03 321.89 l f* 205.23 321.89 m 205.23 321.89 l 208.03 321.89 l 205.23 321.89 l S 207.08 321.89 m 207.08 321.89 l 209.93 321.89 l f* 207.08 321.89 m 207.08 321.89 l 209.93 321.89 l 207.08 321.89 l S 208.98 321.89 2.85 0.05 re f 208.98 321.89 m 208.98 321.9401 l 211.83 321.9401 l 211.83 321.89 l 208.98 321.89 l S 210.88 321.89 m 210.88 321.89 l 213.73 321.89 l f* 210.88 321.89 m 210.88 321.89 l 213.73 321.89 l 210.88 321.89 l S 212.78 321.89 m 212.78 321.89 l 215.63 321.89 l f* 212.78 321.89 m 212.78 321.89 l 215.63 321.89 l 212.78 321.89 l S 214.68 321.89 m 214.68 321.89 l 217.53 321.89 l f* 214.68 321.89 m 214.68 321.89 l 217.53 321.89 l 214.68 321.89 l S 216.58 321.89 m 216.58 321.89 l 219.43 321.89 l f* 216.58 321.89 m 216.58 321.89 l 219.43 321.89 l 216.58 321.89 l S 218.48 321.89 m 218.48 321.89 l 221.28 321.89 l f* 218.48 321.89 m 218.48 321.89 l 221.28 321.89 l 218.48 321.89 l S 220.38 321.89 m 220.38 321.89 l 223.18 321.89 l f* 220.38 321.89 m 220.38 321.89 l 223.18 321.89 l 220.38 321.89 l S 222.23 321.89 2.85 0.3 re f 222.23 321.89 m 222.23 322.1901 l 225.08 322.1901 l 225.08 321.89 l 222.23 321.89 l S 224.13 321.89 m 224.13 321.89 l 226.98 321.89 l f* 224.13 321.89 m 224.13 321.89 l 226.98 321.89 l 224.13 321.89 l S 226.03 321.89 m 226.03 321.89 l 228.88 321.89 l f* 226.03 321.89 m 226.03 321.89 l 228.88 321.89 l 226.03 321.89 l S 227.93 321.89 m 227.93 321.89 l 230.78 321.89 l f* 227.93 321.89 m 227.93 321.89 l 230.78 321.89 l 227.93 321.89 l S 229.83 321.89 m 229.83 321.89 l 232.68 321.89 l f* 229.83 321.89 m 229.83 321.89 l 232.68 321.89 l 229.83 321.89 l S 231.73 321.89 m 231.73 321.89 l 234.58 321.89 l f* 231.73 321.89 m 231.73 321.89 l 234.58 321.89 l 231.73 321.89 l S 233.63 321.89 m 233.63 321.89 l 236.43 321.89 l f* 233.63 321.89 m 233.63 321.89 l 236.43 321.89 l 233.63 321.89 l S 235.48 321.89 m 235.48 321.89 l 238.33 321.89 l f* 235.48 321.89 m 235.48 321.89 l 238.33 321.89 l 235.48 321.89 l S 244.98 321.89 m 244.98 321.89 l 247.83 321.89 l f* 244.98 321.89 m 244.98 321.89 l 247.83 321.89 l 244.98 321.89 l S 252.03 321.6401 2.85 0.25 re f 252.03 321.89 m 252.03 321.6401 l 254.88 321.6401 l 254.88 321.89 l 252.03 321.89 l S 259.13 321.89 m 259.13 321.89 l 261.98 321.89 l f* 259.13 321.89 m 259.13 321.89 l 261.98 321.89 l 259.13 321.89 l S 266.18 321.89 m 266.18 321.89 l 269.03 321.89 l f* 266.18 321.89 m 266.18 321.89 l 269.03 321.89 l 266.18 321.89 l S 273.28 321.89 m 273.28 321.89 l 276.13 321.89 l f* 273.28 321.89 m 273.28 321.89 l 276.13 321.89 l 273.28 321.89 l S 280.33 321.89 m 280.33 321.89 l 283.18 321.89 l f* 280.33 321.89 m 280.33 321.89 l 283.18 321.89 l 280.33 321.89 l S 287.43 321.89 m 287.43 321.89 l 290.28 321.89 l f* 287.43 321.89 m 287.43 321.89 l 290.28 321.89 l 287.43 321.89 l S 294.48 321.89 m 294.48 321.89 l 297.33 321.89 l f* 294.48 321.89 m 294.48 321.89 l 297.33 321.89 l 294.48 321.89 l S 301.58 321.89 m 301.58 321.89 l 304.38 321.89 l f* 301.58 321.89 m 301.58 321.89 l 304.38 321.89 l 301.58 321.89 l S 308.63 321.89 m 308.63 321.89 l 311.48 321.89 l f* 308.63 321.89 m 308.63 321.89 l 311.48 321.89 l 308.63 321.89 l S 315.73 321.89 m 315.73 321.89 l 318.53 321.89 l f* 315.73 321.89 m 315.73 321.89 l 318.53 321.89 l 315.73 321.89 l S 322.78 321.89 m 322.78 321.89 l 325.63 321.89 l f* 322.78 321.89 m 322.78 321.89 l 325.63 321.89 l 322.78 321.89 l S 329.88 321.89 m 329.88 321.89 l 332.68 321.89 l f* 329.88 321.89 m 329.88 321.89 l 332.68 321.89 l 329.88 321.89 l S 336.93 321.89 m 336.93 321.89 l 339.78 321.89 l f* 336.93 321.89 m 336.93 321.89 l 339.78 321.89 l 336.93 321.89 l S 344.03 321.89 m 344.03 321.89 l 346.83 321.89 l f* 344.03 321.89 m 344.03 321.89 l 346.83 321.89 l 344.03 321.89 l S 351.08 321.89 m 351.08 321.89 l 353.93 321.89 l f* 351.08 321.89 m 351.08 321.89 l 353.93 321.89 l 351.08 321.89 l S 358.18 321.89 m 358.18 321.89 l 360.98 321.89 l f* 358.18 321.89 m 358.18 321.89 l 360.98 321.89 l 358.18 321.89 l S 365.23 321.89 m 365.23 321.89 l 368.08 321.89 l f* 365.23 321.89 m 365.23 321.89 l 368.08 321.89 l 365.23 321.89 l S 372.33 321.89 m 372.33 321.89 l 375.13 321.89 l f* 372.33 321.89 m 372.33 321.89 l 375.13 321.89 l 372.33 321.89 l S 379.38 321.89 m 379.38 321.89 l 382.23 321.89 l f* 379.38 321.89 m 379.38 321.89 l 382.23 321.89 l 379.38 321.89 l S 197.33 321.89 m 380.83 321.89 l S 0.563 1 0.437 rg 199.53 321.89 m 199.53 321.89 l 202.38 321.89 l f* 199.53 321.89 m 199.53 321.89 l 202.38 321.89 l 199.53 321.89 l S 201.43 321.89 m 201.43 321.89 l 204.28 321.89 l f* 201.43 321.89 m 201.43 321.89 l 204.28 321.89 l 201.43 321.89 l S 203.33 321.89 m 203.33 321.89 l 206.18 321.89 l f* 203.33 321.89 m 203.33 321.89 l 206.18 321.89 l 203.33 321.89 l S 205.23 321.89 m 205.23 321.89 l 208.03 321.89 l f* 205.23 321.89 m 205.23 321.89 l 208.03 321.89 l 205.23 321.89 l S 207.08 321.89 m 207.08 321.89 l 209.93 321.89 l f* 207.08 321.89 m 207.08 321.89 l 209.93 321.89 l 207.08 321.89 l S 208.98 321.9401 m 208.98 321.9401 l 211.83 321.9401 l f* 208.98 321.9401 m 208.98 321.9401 l 211.83 321.9401 l 208.98 321.9401 l S 210.88 321.89 m 210.88 321.89 l 213.73 321.89 l f* 210.88 321.89 m 210.88 321.89 l 213.73 321.89 l 210.88 321.89 l S 212.78 321.89 2.85 26.5 re f 212.78 321.89 m 212.78 348.39 l 215.63 348.39 l 215.63 321.89 l 212.78 321.89 l S 214.68 321.89 m 214.68 321.89 l 217.53 321.89 l f* 214.68 321.89 m 214.68 321.89 l 217.53 321.89 l 214.68 321.89 l S 216.58 295.3901 2.85 26.5 re f 216.58 321.89 m 216.58 295.3901 l 219.43 295.3901 l 219.43 321.89 l 216.58 321.89 l S 218.48 321.89 m 218.48 321.89 l 221.28 321.89 l f* 218.48 321.89 m 218.48 321.89 l 221.28 321.89 l 218.48 321.89 l S 220.38 321.89 m 220.38 321.89 l 223.18 321.89 l f* 220.38 321.89 m 220.38 321.89 l 223.18 321.89 l 220.38 321.89 l S 222.23 322.1901 2.85 24.85 re f 222.23 322.1901 m 222.23 347.04 l 225.08 347.04 l 225.08 322.1901 l 222.23 322.1901 l S 224.13 321.89 m 224.13 321.89 l 226.98 321.89 l f* 224.13 321.89 m 224.13 321.89 l 226.98 321.89 l 224.13 321.89 l S 226.03 321.89 m 226.03 321.89 l 228.88 321.89 l f* 226.03 321.89 m 226.03 321.89 l 228.88 321.89 l 226.03 321.89 l S 227.93 321.89 m 227.93 321.89 l 230.78 321.89 l f* 227.93 321.89 m 227.93 321.89 l 230.78 321.89 l 227.93 321.89 l S 229.83 321.89 m 229.83 321.89 l 232.68 321.89 l f* 229.83 321.89 m 229.83 321.89 l 232.68 321.89 l 229.83 321.89 l S 231.73 321.89 m 231.73 321.89 l 234.58 321.89 l f* 231.73 321.89 m 231.73 321.89 l 234.58 321.89 l 231.73 321.89 l S 233.63 321.89 2.8 23.35 re f 233.63 321.89 m 233.63 345.2401 l 236.43 345.2401 l 236.43 321.89 l 233.63 321.89 l S 235.48 296.9901 2.85 24.9 re f 235.48 321.89 m 235.48 296.9901 l 238.33 296.9901 l 238.33 321.89 l 235.48 321.89 l S 244.98 320.4401 2.85 1.45 re f 244.98 321.89 m 244.98 320.4401 l 247.83 320.4401 l 247.83 321.89 l 244.98 321.89 l S 252.03 299.7401 2.85 21.9 re f 252.03 321.6401 m 252.03 299.7401 l 254.88 299.7401 l 254.88 321.6401 l 252.03 321.6401 l S 259.13 321.89 m 259.13 321.89 l 261.98 321.89 l f* 259.13 321.89 m 259.13 321.89 l 261.98 321.89 l 259.13 321.89 l S 266.18 321.89 m 266.18 321.89 l 269.03 321.89 l f* 266.18 321.89 m 266.18 321.89 l 269.03 321.89 l 266.18 321.89 l S 273.28 321.89 m 273.28 321.89 l 276.13 321.89 l f* 273.28 321.89 m 273.28 321.89 l 276.13 321.89 l 273.28 321.89 l S 280.33 321.89 m 280.33 321.89 l 283.18 321.89 l f* 280.33 321.89 m 280.33 321.89 l 283.18 321.89 l 280.33 321.89 l S 287.43 321.89 m 287.43 321.89 l 290.28 321.89 l f* 287.43 321.89 m 287.43 321.89 l 290.28 321.89 l 287.43 321.89 l S 294.48 321.89 m 294.48 321.89 l 297.33 321.89 l f* 294.48 321.89 m 294.48 321.89 l 297.33 321.89 l 294.48 321.89 l S 301.58 321.89 m 301.58 321.89 l 304.38 321.89 l f* 301.58 321.89 m 301.58 321.89 l 304.38 321.89 l 301.58 321.89 l S 308.63 321.89 m 308.63 321.89 l 311.48 321.89 l f* 308.63 321.89 m 308.63 321.89 l 311.48 321.89 l 308.63 321.89 l S 315.73 321.89 m 315.73 321.89 l 318.53 321.89 l f* 315.73 321.89 m 315.73 321.89 l 318.53 321.89 l 315.73 321.89 l S 322.78 321.89 m 322.78 321.89 l 325.63 321.89 l f* 322.78 321.89 m 322.78 321.89 l 325.63 321.89 l 322.78 321.89 l S 329.88 321.89 m 329.88 321.89 l 332.68 321.89 l f* 329.88 321.89 m 329.88 321.89 l 332.68 321.89 l 329.88 321.89 l S 336.93 321.89 m 336.93 321.89 l 339.78 321.89 l f* 336.93 321.89 m 336.93 321.89 l 339.78 321.89 l 336.93 321.89 l S 344.03 321.89 m 344.03 321.89 l 346.83 321.89 l f* 344.03 321.89 m 344.03 321.89 l 346.83 321.89 l 344.03 321.89 l S 351.08 321.89 m 351.08 321.89 l 353.93 321.89 l f* 351.08 321.89 m 351.08 321.89 l 353.93 321.89 l 351.08 321.89 l S 358.18 321.89 m 358.18 321.89 l 360.98 321.89 l f* 358.18 321.89 m 358.18 321.89 l 360.98 321.89 l 358.18 321.89 l S 365.23 321.89 m 365.23 321.89 l 368.08 321.89 l f* 365.23 321.89 m 365.23 321.89 l 368.08 321.89 l 365.23 321.89 l S 372.33 321.89 m 372.33 321.89 l 375.13 321.89 l f* 372.33 321.89 m 372.33 321.89 l 375.13 321.89 l 372.33 321.89 l S 379.38 321.89 m 379.38 321.89 l 382.23 321.89 l f* 379.38 321.89 m 379.38 321.89 l 382.23 321.89 l 379.38 321.89 l S 0.5 0 0 rg 199.53 321.89 m 199.53 321.89 l 202.38 321.89 l f* 199.53 321.89 m 199.53 321.89 l 202.38 321.89 l 199.53 321.89 l S 201.43 321.89 m 201.43 321.89 l 204.28 321.89 l f* 201.43 321.89 m 201.43 321.89 l 204.28 321.89 l 201.43 321.89 l S 203.33 321.89 m 203.33 321.89 l 206.18 321.89 l f* 203.33 321.89 m 203.33 321.89 l 206.18 321.89 l 203.33 321.89 l S 205.23 321.89 m 205.23 321.89 l 208.03 321.89 l f* 205.23 321.89 m 205.23 321.89 l 208.03 321.89 l 205.23 321.89 l S 207.08 321.89 m 207.08 321.89 l 209.93 321.89 l f* 207.08 321.89 m 207.08 321.89 l 209.93 321.89 l 207.08 321.89 l S 208.98 321.9401 m 208.98 321.9401 l 211.83 321.9401 l f* 208.98 321.9401 m 208.98 321.9401 l 211.83 321.9401 l 208.98 321.9401 l S 210.88 321.89 m 210.88 321.89 l 213.73 321.89 l f* 210.88 321.89 m 210.88 321.89 l 213.73 321.89 l 210.88 321.89 l S 212.78 348.3901 m 212.78 348.3901 l 215.63 348.3901 l f* 212.78 348.3901 m 212.78 348.3901 l 215.63 348.3901 l 212.78 348.3901 l S 214.68 321.89 m 214.68 321.89 l 217.53 321.89 l f* 214.68 321.89 m 214.68 321.89 l 217.53 321.89 l 214.68 321.89 l S 216.58 295.3901 m 216.58 295.3901 l 219.43 295.3901 l f* 216.58 295.3901 m 216.58 295.3901 l 219.43 295.3901 l 216.58 295.3901 l S 218.48 321.89 m 218.48 321.89 l 221.28 321.89 l f* 218.48 321.89 m 218.48 321.89 l 221.28 321.89 l 218.48 321.89 l S 220.38 321.89 m 220.38 321.89 l 223.18 321.89 l f* 220.38 321.89 m 220.38 321.89 l 223.18 321.89 l 220.38 321.89 l S 222.23 347.0401 m 222.23 347.0401 l 225.08 347.0401 l f* 222.23 347.0401 m 222.23 347.0401 l 225.08 347.0401 l 222.23 347.0401 l S 224.13 321.89 m 224.13 321.89 l 226.98 321.89 l f* 224.13 321.89 m 224.13 321.89 l 226.98 321.89 l 224.13 321.89 l S 226.03 321.89 m 226.03 321.89 l 228.88 321.89 l f* 226.03 321.89 m 226.03 321.89 l 228.88 321.89 l 226.03 321.89 l S 227.93 321.89 m 227.93 321.89 l 230.78 321.89 l f* 227.93 321.89 m 227.93 321.89 l 230.78 321.89 l 227.93 321.89 l S 229.83 321.89 m 229.83 321.89 l 232.68 321.89 l f* 229.83 321.89 m 229.83 321.89 l 232.68 321.89 l 229.83 321.89 l S 231.73 321.89 m 231.73 321.89 l 234.58 321.89 l f* 231.73 321.89 m 231.73 321.89 l 234.58 321.89 l 231.73 321.89 l S 233.63 345.2401 2.8 9.15 re f 233.63 345.2401 m 233.63 354.3901 l 236.43 354.3901 l 236.43 345.2401 l 233.63 345.2401 l S 235.48 287.8401 2.85 9.15 re f 235.48 296.9901 m 235.48 287.8401 l 238.33 287.8401 l 238.33 296.9901 l 235.48 296.9901 l S 244.98 320.4401 m 244.98 320.4401 l 247.83 320.4401 l f* 244.98 320.4401 m 244.98 320.4401 l 247.83 320.4401 l 244.98 320.4401 l S 252.03 299.7401 m 252.03 299.7401 l 254.88 299.7401 l f* 252.03 299.7401 m 252.03 299.7401 l 254.88 299.7401 l 252.03 299.7401 l S 259.13 321.89 m 259.13 321.89 l 261.98 321.89 l f* 259.13 321.89 m 259.13 321.89 l 261.98 321.89 l 259.13 321.89 l S 266.18 321.89 m 266.18 321.89 l 269.03 321.89 l f* 266.18 321.89 m 266.18 321.89 l 269.03 321.89 l 266.18 321.89 l S 273.28 321.89 m 273.28 321.89 l 276.13 321.89 l f* 273.28 321.89 m 273.28 321.89 l 276.13 321.89 l 273.28 321.89 l S 280.33 321.84 2.85 0.05 re f 280.33 321.89 m 280.33 321.84 l 283.18 321.84 l 283.18 321.89 l 280.33 321.89 l S 287.43 321.89 m 287.43 321.89 l 290.28 321.89 l f* 287.43 321.89 m 287.43 321.89 l 290.28 321.89 l 287.43 321.89 l S 294.48 321.89 m 294.48 321.89 l 297.33 321.89 l f* 294.48 321.89 m 294.48 321.89 l 297.33 321.89 l 294.48 321.89 l S 301.58 321.89 m 301.58 321.89 l 304.38 321.89 l f* 301.58 321.89 m 301.58 321.89 l 304.38 321.89 l 301.58 321.89 l S 308.63 321.89 m 308.63 321.89 l 311.48 321.89 l f* 308.63 321.89 m 308.63 321.89 l 311.48 321.89 l 308.63 321.89 l S 315.73 321.89 m 315.73 321.89 l 318.53 321.89 l f* 315.73 321.89 m 315.73 321.89 l 318.53 321.89 l 315.73 321.89 l S 322.78 321.89 m 322.78 321.89 l 325.63 321.89 l f* 322.78 321.89 m 322.78 321.89 l 325.63 321.89 l 322.78 321.89 l S 329.88 321.89 m 329.88 321.89 l 332.68 321.89 l f* 329.88 321.89 m 329.88 321.89 l 332.68 321.89 l 329.88 321.89 l S 336.93 321.89 m 336.93 321.89 l 339.78 321.89 l f* 336.93 321.89 m 336.93 321.89 l 339.78 321.89 l 336.93 321.89 l S 344.03 321.89 m 344.03 321.89 l 346.83 321.89 l f* 344.03 321.89 m 344.03 321.89 l 346.83 321.89 l 344.03 321.89 l S 351.08 321.89 m 351.08 321.89 l 353.93 321.89 l f* 351.08 321.89 m 351.08 321.89 l 353.93 321.89 l 351.08 321.89 l S 358.18 321.89 m 358.18 321.89 l 360.98 321.89 l f* 358.18 321.89 m 358.18 321.89 l 360.98 321.89 l 358.18 321.89 l S 365.23 321.89 m 365.23 321.89 l 368.08 321.89 l f* 365.23 321.89 m 365.23 321.89 l 368.08 321.89 l 365.23 321.89 l S 372.33 321.89 m 372.33 321.89 l 375.13 321.89 l f* 372.33 321.89 m 372.33 321.89 l 375.13 321.89 l 372.33 321.89 l S 379.38 321.89 m 379.38 321.89 l 382.23 321.89 l f* 379.38 321.89 m 379.38 321.89 l 382.23 321.89 l 379.38 321.89 l S Q BT /F13 1 Tf 6 0 0 6 266.93 257.9401 Tm (Initial assets $a)Tj 4.8 0 0 4.8 306.93 254.9401 Tm (0)Tj 6 0 0 6 309.58 257.9401 Tm ($)Tj ET 1 g 386.83 339.29 41.4 32.1 re f 1 G 386.83 339.29 m 386.83 371.39 l 428.23 371.39 l 428.23 339.29 l 386.83 339.29 l S 0 G 386.83 371.39 m 428.23 371.39 l S 386.83 339.29 m 428.23 339.29 l S 428.23 339.29 m 428.23 371.39 l S 386.83 339.29 m 386.83 371.39 l S 386.83 339.29 m 428.23 339.29 l S 386.83 339.29 m 386.83 371.39 l S 386.83 371.39 m 428.23 371.39 l S 386.83 339.29 m 428.23 339.29 l S 428.23 339.29 m 428.23 371.39 l S 386.83 339.29 m 386.83 371.39 l S BT /F13 1 Tf 6 0 0 6 409.78 364.64 Tm 0 g (y)Tj 4.8 0 0 4.8 412.78 361.64 Tm (0)Tj 6 0 0 6 415.43 364.64 Tm (=y)Tj 4.8 0 0 4.8 421.93 361.64 Tm (L)Tj ET q 386.83 339.2401 41.45 32.15 re W n 0 0 0.563 rg 390.33 361.64 17.6 7.55 re f 390.33 361.64 m 390.33 369.1901 l 407.93 369.1901 l 407.93 361.64 l 390.33 361.64 l S Q BT /F13 1 Tf 6 0 0 6 409.78 354.5401 Tm (y)Tj 4.8 0 0 4.8 412.78 351.5401 Tm (0)Tj 6 0 0 6 415.43 354.5401 Tm (=y)Tj 4.8 0 0 4.8 421.93 351.5401 Tm (M)Tj ET q 386.83 339.2401 41.45 32.15 re W n 0.563 1 0.437 rg 390.33 351.5901 17.6 7.55 re f 390.33 351.5901 m 390.33 359.1401 l 407.93 359.1401 l 407.93 351.5901 l 390.33 351.5901 l S Q BT /F13 1 Tf 6 0 0 6 409.78 344.4901 Tm (y)Tj 4.8 0 0 4.8 412.78 341.4901 Tm (0)Tj 6 0 0 6 415.43 344.4901 Tm (=y)Tj 4.8 0 0 4.8 421.93 341.4901 Tm (H)Tj ET q 386.83 339.2401 41.45 32.15 re W n 0.5 0 0 rg 390.33 341.54 17.6 7.55 re f 390.33 341.54 m 390.33 349.0901 l 407.93 349.0901 l 407.93 341.54 l 390.33 341.54 l S Q Q q BT /F8 1 Tf 11.95517 0 0 11.95517 302.76 67.44 Tm (22)Tj ET Q endstream endobj 25 0 obj << /Length 42192 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 137.76 546.84 Tm 0 g [(Figure)-332(5:)-431(Distribution)-333(of)-321(con)31(tract)-332(c)30(hoice)-340(b)30(y)-341(asset)-332(and)-331(income)-331(lev)31(el)]TJ ET q 158.28 240.44 300.6 290.2 re W n 1 g 158.28 240.3901 300.65 290.25 re f 197.38 409.8901 168.35 99 re f 1 j 0.3 w 1 G 197.38 409.8901 m 197.38 508.8901 l 365.73 508.8901 l 365.73 409.8901 l 197.38 409.8901 l S 0 G 197.38 508.8901 m 365.73 508.8901 l S 197.38 409.8901 m 365.73 409.8901 l S 365.73 409.8901 m 365.73 508.8901 l S 197.38 409.8901 m 197.38 508.8901 l S 197.38 409.8901 m 365.73 409.8901 l S 197.38 409.8901 m 197.38 508.8901 l S 197.38 409.8901 m 197.38 411.5901 l S 197.38 508.8901 m 197.38 507.2401 l S BT /F13 1 Tf 6 0 0 6 195.73 402.6401 Tm 0 g (0)Tj ET 231.03 409.8901 m 231.03 411.5901 l S 231.03 508.8901 m 231.03 507.2401 l S BT /F13 1 Tf 6 0 0 6 229.38 402.6401 Tm (1)Tj ET 264.68 409.8901 m 264.68 411.5901 l S 264.68 508.8901 m 264.68 507.2401 l S BT /F13 1 Tf 6 0 0 6 263.03 402.6401 Tm (2)Tj ET 298.38 409.8901 m 298.38 411.5901 l S 298.38 508.8901 m 298.38 507.2401 l S BT /F13 1 Tf 6 0 0 6 296.73 402.6401 Tm (3)Tj ET 332.03 409.8901 m 332.03 411.5901 l S 332.03 508.8901 m 332.03 507.2401 l S BT /F13 1 Tf 6 0 0 6 330.38 402.6401 Tm (4)Tj ET 365.73 409.8901 m 365.73 411.5901 l S 365.73 508.8901 m 365.73 507.2401 l S BT /F13 1 Tf 6 0 0 6 364.08 402.6401 Tm (5)Tj ET 197.38 409.8901 m 199.03 409.8901 l S 365.73 409.8901 m 364.03 409.8901 l S BT /F13 1 Tf 6 0 0 6 192.33 407.6901 Tm (0)Tj ET 197.38 422.2901 m 199.03 422.2901 l S 365.73 422.2901 m 364.03 422.2901 l S BT /F13 1 Tf 6 0 0 6 192.33 420.0901 Tm (1)Tj ET 197.38 434.6401 m 199.03 434.6401 l S 365.73 434.6401 m 364.03 434.6401 l S BT /F13 1 Tf 6 0 0 6 192.33 432.4401 Tm (2)Tj ET 197.38 447.0401 m 199.03 447.0401 l S 365.73 447.0401 m 364.03 447.0401 l S BT /F13 1 Tf 6 0 0 6 192.33 444.8401 Tm (3)Tj ET 197.38 459.3901 m 199.03 459.3901 l S 365.73 459.3901 m 364.03 459.3901 l S BT /F13 1 Tf 6 0 0 6 192.33 457.1901 Tm (4)Tj ET 197.38 471.7901 m 199.03 471.7901 l S 365.73 471.7901 m 364.03 471.7901 l S BT /F13 1 Tf 6 0 0 6 192.33 469.5901 Tm (5)Tj ET 197.38 484.1401 m 199.03 484.1401 l S 365.73 484.1401 m 364.03 484.1401 l S BT /F13 1 Tf 6 0 0 6 192.33 481.9401 Tm (6)Tj ET 197.38 496.5401 m 199.03 496.5401 l S 365.73 496.5401 m 364.03 496.5401 l S BT /F13 1 Tf 6 0 0 6 192.33 494.3401 Tm (7)Tj ET 197.38 508.8901 m 199.03 508.8901 l S 365.73 508.8901 m 364.03 508.8901 l S BT /F13 1 Tf 6 0 0 6 192.33 506.6901 Tm (8)Tj 0.84167 0.81667 TD (x 10)Tj 4 0 0 4 208.68 515.2901 Tm (-3)Tj ET 197.38 508.8901 m 365.73 508.8901 l S 197.38 409.8901 m 365.73 409.8901 l S 365.73 409.8901 m 365.73 508.8901 l S 197.38 409.8901 m 197.38 508.8901 l S q 197.38 409.8401 168.4 99.05 re W n 0.039 0.141 0.416 rg 196.03 409.8901 m 196.03 409.8901 l 198.68 409.8901 l f* 197.78 409.8901 m 197.78 409.8901 l 200.48 409.8901 l f* 199.58 409.8901 m 199.58 409.8901 l 202.23 409.8901 l f* 201.33 409.8901 m 201.33 409.8901 l 203.98 409.8901 l f* 203.13 409.8901 m 203.13 409.8901 l 205.78 409.8901 l f* 204.88 409.8901 m 204.88 409.8901 l 207.53 409.8901 l f* 206.68 409.8901 m 206.68 409.8901 l 209.33 409.8901 l f* 208.43 409.8901 m 208.43 409.8901 l 211.08 409.8901 l f* 210.18 409.8901 m 210.18 409.8901 l 212.88 409.8901 l f* 211.98 409.8901 m 211.98 409.8901 l 214.63 409.8901 l f* 213.73 409.8901 m 213.73 409.8901 l 216.43 409.8901 l f* 215.53 409.8901 m 215.53 409.8901 l 218.18 409.8901 l f* 217.28 409.8901 m 217.28 409.8901 l 219.93 409.8901 l f* 219.08 409.8901 m 219.08 409.8901 l 221.73 409.8901 l f* 220.83 409.8901 m 220.83 409.8901 l 223.48 409.8901 l f* 222.63 409.8901 m 222.63 409.8901 l 225.28 409.8901 l f* 224.38 409.8901 m 224.38 409.8901 l 227.03 409.8901 l f* 226.13 409.8901 m 226.13 409.8901 l 228.83 409.8901 l f* 227.93 409.8901 m 227.93 409.8901 l 230.58 409.8901 l f* 229.68 409.8901 m 229.68 409.8901 l 232.33 409.8901 l f* 238.58 409.8901 m 238.58 409.8901 l 241.23 409.8901 l f* 245.18 409.8901 m 245.18 409.8901 l 247.83 409.8901 l f* 251.78 409.8901 m 251.78 409.8901 l 254.48 409.8901 l f* 258.43 409.8901 2.65 0.05 re f 265.03 409.8901 2.65 0.05 re f 271.68 409.8901 2.65 0.05 re f 278.28 409.8901 2.65 0.05 re f 284.93 409.8901 2.65 0.05 re f 291.53 409.8901 2.65 0.05 re f 298.18 409.8901 m 298.18 409.8901 l 300.83 409.8901 l f* 304.78 409.8901 m 304.78 409.8901 l 307.43 409.8901 l f* 311.38 409.8901 m 311.38 409.8901 l 314.08 409.8901 l f* 318.03 409.8901 m 318.03 409.8901 l 320.68 409.8901 l f* 324.63 409.8901 m 324.63 409.8901 l 327.28 409.8901 l f* 331.28 409.8901 m 331.28 409.8901 l 333.93 409.8901 l f* 337.88 409.8901 m 337.88 409.8901 l 340.53 409.8901 l f* 344.53 409.8901 m 344.53 409.8901 l 347.18 409.8901 l f* 351.13 409.8901 m 351.13 409.8901 l 353.78 409.8901 l f* 357.73 409.8901 m 357.73 409.8901 l 360.43 409.8901 l f* 364.38 409.8901 m 364.38 409.8901 l 367.03 409.8901 l f* 197.38 409.8901 m 365.73 409.8901 l S 0 0 1 rg 196.03 409.8901 m 196.03 409.8901 l 198.68 409.8901 l f* 197.78 409.8901 m 197.78 409.8901 l 200.48 409.8901 l f* 199.58 409.8901 m 199.58 409.8901 l 202.23 409.8901 l f* 201.33 409.8901 m 201.33 409.8901 l 203.98 409.8901 l f* 203.13 409.8901 m 203.13 409.8901 l 205.78 409.8901 l f* 204.88 409.8901 m 204.88 409.8901 l 207.53 409.8901 l f* 206.68 409.8901 m 206.68 409.8901 l 209.33 409.8901 l f* 208.43 409.8901 m 208.43 409.8901 l 211.08 409.8901 l f* 210.18 409.8901 m 210.18 409.8901 l 212.88 409.8901 l f* 211.98 409.8901 m 211.98 409.8901 l 214.63 409.8901 l f* 213.73 409.8901 m 213.73 409.8901 l 216.43 409.8901 l f* 215.53 409.8901 m 215.53 409.8901 l 218.18 409.8901 l f* 217.28 409.8901 m 217.28 409.8901 l 219.93 409.8901 l f* 219.08 409.8901 m 219.08 409.8901 l 221.73 409.8901 l f* 220.83 409.8901 m 220.83 409.8901 l 223.48 409.8901 l f* 222.63 409.8901 m 222.63 409.8901 l 225.28 409.8901 l f* 224.38 409.8901 m 224.38 409.8901 l 227.03 409.8901 l f* 226.13 409.8901 m 226.13 409.8901 l 228.83 409.8901 l f* 227.93 409.8901 m 227.93 409.8901 l 230.58 409.8901 l f* 229.68 409.8901 2.65 6.25 re f 238.58 409.8901 2.65 5.85 re f 245.18 409.89 2.65 90.2 re f 251.78 409.8901 2.7 0.1 re f 258.43 409.9401 2.65 0.05 re f 265.03 409.9401 2.65 0.05 re f 271.68 409.9401 m 271.68 409.9401 l 274.33 409.9401 l f* 278.28 409.9401 2.65 0.05 re f 284.93 409.9401 m 284.93 409.9401 l 287.58 409.9401 l f* 291.53 409.9401 2.65 0.05 re f 298.18 409.8901 m 298.18 409.8901 l 300.83 409.8901 l f* 304.78 409.8901 2.65 0.1 re f 311.38 409.8901 m 311.38 409.8901 l 314.08 409.8901 l f* 318.03 409.8901 m 318.03 409.8901 l 320.68 409.8901 l f* 324.63 409.8901 m 324.63 409.8901 l 327.28 409.8901 l f* 331.28 409.8901 m 331.28 409.8901 l 333.93 409.8901 l f* 337.88 409.8901 m 337.88 409.8901 l 340.53 409.8901 l f* 344.53 409.8901 m 344.53 409.8901 l 347.18 409.8901 l f* 351.13 409.8901 m 351.13 409.8901 l 353.78 409.8901 l f* 357.73 409.8901 m 357.73 409.8901 l 360.43 409.8901 l f* 364.38 409.8901 m 364.38 409.8901 l 367.03 409.8901 l f* 0 0.749 0.749 rg 196.03 409.8901 m 196.03 409.8901 l 198.68 409.8901 l f* 197.78 409.8901 m 197.78 409.8901 l 200.48 409.8901 l f* 199.58 409.8901 m 199.58 409.8901 l 202.23 409.8901 l f* 201.33 409.8901 m 201.33 409.8901 l 203.98 409.8901 l f* 203.13 409.8901 m 203.13 409.8901 l 205.78 409.8901 l f* 204.88 409.8901 m 204.88 409.8901 l 207.53 409.8901 l f* 206.68 409.8901 m 206.68 409.8901 l 209.33 409.8901 l f* 208.43 409.8901 m 208.43 409.8901 l 211.08 409.8901 l f* 210.18 409.8901 m 210.18 409.8901 l 212.88 409.8901 l f* 211.98 409.8901 m 211.98 409.8901 l 214.63 409.8901 l f* 213.73 409.8901 m 213.73 409.8901 l 216.43 409.8901 l f* 215.53 409.8901 m 215.53 409.8901 l 218.18 409.8901 l f* 217.28 409.8901 m 217.28 409.8901 l 219.93 409.8901 l f* 219.08 409.8901 m 219.08 409.8901 l 221.73 409.8901 l f* 220.83 409.8901 m 220.83 409.8901 l 223.48 409.8901 l f* 222.63 409.8901 m 222.63 409.8901 l 225.28 409.8901 l f* 224.38 409.8901 m 224.38 409.8901 l 227.03 409.8901 l f* 226.13 409.8901 m 226.13 409.8901 l 228.83 409.8901 l f* 227.93 409.8901 m 227.93 409.8901 l 230.58 409.8901 l f* 229.68 416.1401 2.65 2.3 re f 238.58 415.7401 m 238.58 415.7401 l 241.23 415.7401 l f* 245.18 500.0901 2.65 0.05 re f 251.78 409.9901 m 251.78 409.9901 l 254.48 409.9901 l f* 258.43 409.9901 m 258.43 409.9901 l 261.08 409.9901 l f* 265.03 409.9901 2.65 2.15 re f 271.68 409.9401 2.65 0.05 re f 278.28 409.9901 m 278.28 409.9901 l 280.93 409.9901 l f* 284.93 409.9401 m 284.93 409.9401 l 287.58 409.9401 l f* 291.53 409.9901 m 291.53 409.9901 l 294.18 409.9901 l f* 298.18 409.8901 m 298.18 409.8901 l 300.83 409.8901 l f* 304.78 409.9901 2.65 33.6 re f 311.38 409.8901 m 311.38 409.8901 l 314.08 409.8901 l f* 318.03 409.8901 m 318.03 409.8901 l 320.68 409.8901 l f* 324.63 409.8901 m 324.63 409.8901 l 327.28 409.8901 l f* 331.28 409.8901 m 331.28 409.8901 l 333.93 409.8901 l f* 337.88 409.8901 m 337.88 409.8901 l 340.53 409.8901 l f* 344.53 409.8901 m 344.53 409.8901 l 347.18 409.8901 l f* 351.13 409.8901 m 351.13 409.8901 l 353.78 409.8901 l f* 357.73 409.8901 m 357.73 409.8901 l 360.43 409.8901 l f* 364.38 409.8901 m 364.38 409.8901 l 367.03 409.8901 l f* Q BT /F13 1 Tf 6 0 0 6 259.38 395.4901 Tm (Initial assets $a)Tj 4.8 0 0 4.8 299.38 392.4901 Tm (0)Tj 6 0 0 6 302.03 395.4901 Tm ($)Tj /F25 1 Tf 0 6 -6 0 185.53 449.0401 Tm (m)Tj /F13 1 Tf 0.575 0 TD ($a)Tj 0 4.8 -4.8 0 188.53 457.7901 Tm (0)Tj 0 6 -6 0 185.53 460.4401 Tm (,y)Tj 0 4.8 -4.8 0 188.53 465.0901 Tm (0)Tj 0 6 -6 0 185.53 467.7401 Tm ($)Tj ET 1 g 197.38 272.3401 169.05 99.05 re f 1 G 197.38 272.3401 m 197.38 371.3901 l 366.43 371.3901 l 366.43 272.3401 l 197.38 272.3401 l S 0 G 197.38 371.39 m 366.43 371.39 l S 197.38 272.3401 m 366.43 272.3401 l S 366.43 272.3401 m 366.43 371.39 l S 197.38 272.3401 m 197.38 371.39 l S 197.38 272.3401 m 366.43 272.3401 l S 197.38 272.3401 m 197.38 371.39 l S 197.38 272.3401 m 197.38 274.04 l S 197.38 371.39 m 197.38 369.7401 l S BT /F13 1 Tf 6 0 0 6 195.73 265.0901 Tm 0 g (0)Tj ET 231.18 272.3401 m 231.18 274.04 l S 231.18 371.39 m 231.18 369.7401 l S BT /F13 1 Tf 6 0 0 6 229.53 265.0901 Tm (1)Tj ET 264.98 272.3401 m 264.98 274.04 l S 264.98 371.39 m 264.98 369.7401 l S BT /F13 1 Tf 6 0 0 6 263.33 265.0901 Tm (2)Tj ET 298.78 272.3401 m 298.78 274.04 l S 298.78 371.39 m 298.78 369.7401 l S BT /F13 1 Tf 6 0 0 6 297.13 265.0901 Tm (3)Tj ET 332.58 272.3401 m 332.58 274.04 l S 332.58 371.39 m 332.58 369.7401 l S BT /F13 1 Tf 6 0 0 6 330.93 265.0901 Tm (4)Tj ET 366.43 272.3401 m 366.43 274.04 l S 366.43 371.39 m 366.43 369.7401 l S BT /F13 1 Tf 6 0 0 6 364.78 265.0901 Tm (5)Tj ET 197.38 272.3401 m 199.03 272.3401 l S 366.43 272.3401 m 364.73 272.3401 l S BT /F13 1 Tf 6 0 0 6 192.33 270.14 Tm (0)Tj ET 197.38 286.4901 m 199.03 286.4901 l S 366.43 286.4901 m 364.73 286.4901 l S BT /F13 1 Tf 6 0 0 6 192.33 284.2901 Tm (1)Tj ET 197.38 300.6401 m 199.03 300.6401 l S 366.43 300.6401 m 364.73 300.6401 l S BT /F13 1 Tf 6 0 0 6 192.33 298.4401 Tm (2)Tj ET 197.38 314.7901 m 199.03 314.7901 l S 366.43 314.7901 m 364.73 314.7901 l S BT /F13 1 Tf 6 0 0 6 192.33 312.5901 Tm (3)Tj ET 197.38 328.9401 m 199.03 328.9401 l S 366.43 328.9401 m 364.73 328.9401 l S BT /F13 1 Tf 6 0 0 6 192.33 326.7401 Tm (4)Tj ET 197.38 343.0901 m 199.03 343.0901 l S 366.43 343.0901 m 364.73 343.0901 l S BT /F13 1 Tf 6 0 0 6 192.33 340.8901 Tm (5)Tj ET 197.38 357.2401 m 199.03 357.2401 l S 366.43 357.2401 m 364.73 357.2401 l S BT /F13 1 Tf 6 0 0 6 192.33 355.04 Tm (6)Tj ET 197.38 371.39 m 199.03 371.39 l S 366.43 371.39 m 364.73 371.39 l S BT /F13 1 Tf 6 0 0 6 192.33 369.1901 Tm (7)Tj 0.84167 0.81666 TD (x 10)Tj 4 0 0 4 208.68 377.7901 Tm (-3)Tj ET 197.38 371.39 m 366.43 371.39 l S 197.38 272.3401 m 366.43 272.3401 l S 366.43 272.3401 m 366.43 371.39 l S 197.38 272.3401 m 197.38 371.39 l S q 197.38 272.2901 169.1 99.1 re W n 0.039 0.141 0.416 rg 196.03 272.3401 m 196.03 272.3401 l 198.68 272.3401 l f* 0.039 0.141 0.416 RG 196.03 272.3401 m 196.03 272.3401 l 198.68 272.3401 l 196.03 272.3401 l S 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l f* 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l 197.78 272.3401 l S 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l f* 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l 199.58 272.3401 l S 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l f* 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l 201.38 272.3401 l S 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l f* 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l 203.13 272.3401 l S 204.93 272.3401 m 204.93 272.3401 l 207.58 272.3401 l f* 204.93 272.3401 m 204.93 272.3401 l 207.58 272.3401 l 204.93 272.3401 l S 206.68 272.3401 m 206.68 272.3401 l 209.38 272.3401 l f* 206.68 272.3401 m 206.68 272.3401 l 209.38 272.3401 l 206.68 272.3401 l S 208.48 272.3401 m 208.48 272.3401 l 211.13 272.3401 l f* 208.48 272.3401 m 208.48 272.3401 l 211.13 272.3401 l 208.48 272.3401 l S 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l f* 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l 210.28 272.3401 l S 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l f* 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l 212.03 272.3401 l S 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l f* 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l 213.83 272.3401 l S 215.58 272.3401 m 215.58 272.3401 l 218.28 272.3401 l f* 215.58 272.3401 m 215.58 272.3401 l 218.28 272.3401 l 215.58 272.3401 l S 217.38 272.3401 m 217.38 272.3401 l 220.03 272.3401 l f* 217.38 272.3401 m 217.38 272.3401 l 220.03 272.3401 l 217.38 272.3401 l S 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l f* 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l 219.13 272.3401 l S 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l f* 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l 220.93 272.3401 l S 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l f* 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l 222.73 272.3401 l S 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l f* 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l 224.48 272.3401 l S 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l f* 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l 226.28 272.3401 l S 228.03 272.3401 m 228.03 272.3401 l 230.73 272.3401 l f* 228.03 272.3401 m 228.03 272.3401 l 230.73 272.3401 l 228.03 272.3401 l S 229.83 272.3401 m 229.83 272.3401 l 232.48 272.3401 l f* 229.83 272.3401 m 229.83 272.3401 l 232.48 272.3401 l 229.83 272.3401 l S 238.73 272.3401 m 238.73 272.3401 l 241.38 272.3401 l f* 238.73 272.3401 m 238.73 272.3401 l 241.38 272.3401 l 238.73 272.3401 l S 245.38 272.3401 m 245.38 272.3401 l 248.03 272.3401 l f* 245.38 272.3401 m 245.38 272.3401 l 248.03 272.3401 l 245.38 272.3401 l S 252.03 272.3401 m 252.03 272.3401 l 254.68 272.3401 l f* 252.03 272.3401 m 252.03 272.3401 l 254.68 272.3401 l 252.03 272.3401 l S 258.68 272.3401 m 258.68 272.3401 l 261.33 272.3401 l f* 258.68 272.3401 m 258.68 272.3401 l 261.33 272.3401 l 258.68 272.3401 l S 265.33 272.3401 m 265.33 272.3401 l 267.98 272.3401 l f* 265.33 272.3401 m 265.33 272.3401 l 267.98 272.3401 l 265.33 272.3401 l S 271.98 272.3401 m 271.98 272.3401 l 274.63 272.3401 l f* 271.98 272.3401 m 271.98 272.3401 l 274.63 272.3401 l 271.98 272.3401 l S 278.63 272.3401 m 278.63 272.3401 l 281.28 272.3401 l f* 278.63 272.3401 m 278.63 272.3401 l 281.28 272.3401 l 278.63 272.3401 l S 285.28 272.3401 m 285.28 272.3401 l 287.93 272.3401 l f* 285.28 272.3401 m 285.28 272.3401 l 287.93 272.3401 l 285.28 272.3401 l S 291.93 272.3401 m 291.93 272.3401 l 294.58 272.3401 l f* 291.93 272.3401 m 291.93 272.3401 l 294.58 272.3401 l 291.93 272.3401 l S 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l f* 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l 298.58 272.3401 l S 305.23 272.3401 m 305.23 272.3401 l 307.88 272.3401 l f* 305.23 272.3401 m 305.23 272.3401 l 307.88 272.3401 l 305.23 272.3401 l S 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l f* 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l 311.88 272.3401 l S 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l f* 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l 318.53 272.3401 l S 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l f* 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l 325.18 272.3401 l S 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l f* 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l 331.83 272.3401 l S 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l f* 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l 338.48 272.3401 l S 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l f* 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l 345.13 272.3401 l S 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l f* 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l 351.78 272.3401 l S 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l f* 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l 358.43 272.3401 l S 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l f* 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l 365.08 272.3401 l S 0 G 197.38 272.3401 m 366.43 272.3401 l S 0 0 1 rg 196.03 272.3401 m 196.03 272.3401 l 198.68 272.3401 l f* 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l f* 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l f* 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l f* 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l f* 204.93 272.3401 m 204.93 272.3401 l 207.58 272.3401 l f* 206.68 272.3401 m 206.68 272.3401 l 209.38 272.3401 l f* 208.48 272.3401 m 208.48 272.3401 l 211.13 272.3401 l f* 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l f* 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l f* 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l f* 215.58 272.3401 m 215.58 272.3401 l 218.28 272.3401 l f* 217.38 272.3401 m 217.38 272.3401 l 220.03 272.3401 l f* 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l f* 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l f* 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l f* 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l f* 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l f* 228.03 272.3401 m 228.03 272.3401 l 230.73 272.3401 l f* 229.83 272.3401 2.65 0.05 re f 238.73 272.3401 2.65 6.3 re f 245.38 272.3401 2.65 96.9 re f 252.03 272.3401 2.65 0.1 re f 258.68 272.3401 2.65 0.1 re f 265.33 272.3401 2.65 0.1 re f 271.98 272.3401 2.65 0.05 re f 278.63 272.3401 2.65 0.1 re f 285.28 272.3401 2.65 0.05 re f 291.93 272.3401 2.65 0.1 re f 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l f* 305.23 272.3401 2.65 0.1 re f 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l f* 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l f* 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l f* 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l f* 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l f* 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l f* 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l f* 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l f* 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l f* 0 0.749 0.749 rg 196.03 272.3401 m 196.03 272.3401 l 198.68 272.3401 l f* 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l f* 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l f* 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l f* 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l f* 204.93 272.3401 m 204.93 272.3401 l 207.58 272.3401 l f* 206.68 272.3401 m 206.68 272.3401 l 209.38 272.3401 l f* 208.48 272.3401 m 208.48 272.3401 l 211.13 272.3401 l f* 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l f* 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l f* 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l f* 215.58 272.3401 m 215.58 272.3401 l 218.28 272.3401 l f* 217.38 272.3401 m 217.38 272.3401 l 220.03 272.3401 l f* 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l f* 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l f* 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l f* 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l f* 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l f* 228.03 272.3401 m 228.03 272.3401 l 230.73 272.3401 l f* 229.83 272.39 m 229.83 272.39 l 232.48 272.39 l f* 238.73 278.6401 m 238.73 278.6401 l 241.38 278.6401 l f* 245.38 369.2401 2.65 0.05 re f 252.03 272.4401 m 252.03 272.4401 l 254.68 272.4401 l f* 258.68 272.4401 m 258.68 272.4401 l 261.33 272.4401 l f* 265.33 272.4401 2.65 2.45 re f 271.98 272.39 2.65 0.05 re f 278.63 272.4401 m 278.63 272.4401 l 281.28 272.4401 l f* 285.28 272.39 m 285.28 272.39 l 287.93 272.39 l f* 291.93 272.4401 m 291.93 272.4401 l 294.58 272.4401 l f* 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l f* 305.23 272.4401 2.65 38.4 re f 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l f* 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l f* 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l f* 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l f* 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l f* 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l f* 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l f* 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l f* 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l f* 0.6 0.2 0 rg 196.03 272.3401 m 196.03 272.3401 l 198.68 272.3401 l f* 0.937 1 0.063 RG 196.03 272.3401 m 198.68 272.3401 l S 198.68 272.3401 m 196.03 272.3401 l S 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l f* 197.78 272.3401 m 200.48 272.3401 l S 200.48 272.3401 m 197.78 272.3401 l S 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l f* 199.58 272.3401 m 202.23 272.3401 l S 202.23 272.3401 m 199.58 272.3401 l S 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l f* 201.38 272.3401 m 204.03 272.3401 l S 204.03 272.3401 m 201.38 272.3401 l S 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l f* 203.13 272.3401 m 205.83 272.3401 l S 205.83 272.3401 m 203.13 272.3401 l S 204.93 272.3401 m 204.93 272.3401 l 207.58 272.3401 l f* 204.93 272.3401 m 207.58 272.3401 l S 207.58 272.3401 m 204.93 272.3401 l S 206.68 272.3401 m 206.68 272.3401 l 209.38 272.3401 l f* 206.68 272.3401 m 209.38 272.3401 l S 209.38 272.3401 m 206.68 272.3401 l S 208.48 272.3401 m 208.48 272.3401 l 211.13 272.3401 l f* 208.48 272.3401 m 211.13 272.3401 l S 211.13 272.3401 m 208.48 272.3401 l S 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l f* 210.28 272.3401 m 212.93 272.3401 l S 212.93 272.3401 m 210.28 272.3401 l S 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l f* 212.03 272.3401 m 214.68 272.3401 l S 214.68 272.3401 m 212.03 272.3401 l S 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l f* 213.83 272.3401 m 216.48 272.3401 l S 216.48 272.3401 m 213.83 272.3401 l S 215.58 272.3401 m 215.58 272.3401 l 218.28 272.3401 l f* 215.58 272.3401 m 218.28 272.3401 l S 218.28 272.3401 m 215.58 272.3401 l S 217.38 272.3401 m 217.38 272.3401 l 220.03 272.3401 l f* 217.38 272.3401 m 220.03 272.3401 l S 220.03 272.3401 m 217.38 272.3401 l S 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l f* 219.13 272.3401 m 221.83 272.3401 l S 221.83 272.3401 m 219.13 272.3401 l S 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l f* 220.93 272.3401 m 223.58 272.3401 l S 223.58 272.3401 m 220.93 272.3401 l S 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l f* 222.73 272.3401 m 225.38 272.3401 l S 225.38 272.3401 m 222.73 272.3401 l S 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l f* 224.48 272.3401 m 227.18 272.3401 l S 227.18 272.3401 m 224.48 272.3401 l S 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l f* 226.28 272.3401 m 228.93 272.3401 l S 228.93 272.3401 m 226.28 272.3401 l S 228.03 272.3401 m 228.03 272.3401 l 230.73 272.3401 l f* 228.03 272.3401 m 230.73 272.3401 l S 230.73 272.3401 m 228.03 272.3401 l S 229.83 272.39 m 229.83 272.39 l 232.48 272.39 l f* 229.83 272.39 m 232.48 272.39 l S 232.48 272.39 m 229.83 272.39 l S 238.73 278.6401 m 238.73 278.6401 l 241.38 278.6401 l f* 238.73 278.6401 m 241.38 278.6401 l S 241.38 278.6401 m 238.73 278.6401 l S 245.38 369.29 2.65 1.1 re f 245.38 369.29 m 245.38 370.3901 l S 245.38 370.3901 m 248.03 370.3901 l S 248.03 370.3901 m 248.03 369.29 l S 248.03 369.29 m 245.38 369.29 l S 252.03 272.4401 m 252.03 272.4401 l 254.68 272.4401 l f* 252.03 272.4401 m 254.68 272.4401 l S 254.68 272.4401 m 252.03 272.4401 l S 258.68 272.4401 m 258.68 272.4401 l 261.33 272.4401 l f* 258.68 272.4401 m 261.33 272.4401 l S 261.33 272.4401 m 258.68 272.4401 l S 265.33 274.8901 m 265.33 274.8901 l 267.98 274.8901 l f* 265.33 274.8901 m 267.98 274.8901 l S 267.98 274.8901 m 265.33 274.8901 l S 271.98 272.4401 m 271.98 272.4401 l 274.63 272.4401 l f* 271.98 272.4401 m 274.63 272.4401 l S 274.63 272.4401 m 271.98 272.4401 l S 278.63 272.4401 m 278.63 272.4401 l 281.28 272.4401 l f* 278.63 272.4401 m 281.28 272.4401 l S 281.28 272.4401 m 278.63 272.4401 l S 285.28 272.39 m 285.28 272.39 l 287.93 272.39 l f* 285.28 272.39 m 287.93 272.39 l S 287.93 272.39 m 285.28 272.39 l S 291.93 272.4401 m 291.93 272.4401 l 294.58 272.4401 l f* 291.93 272.4401 m 294.58 272.4401 l S 294.58 272.4401 m 291.93 272.4401 l S 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l f* 298.58 272.3401 m 301.23 272.3401 l S 301.23 272.3401 m 298.58 272.3401 l S 305.23 310.8401 m 305.23 310.8401 l 307.88 310.8401 l f* 305.23 310.8401 m 307.88 310.8401 l S 307.88 310.8401 m 305.23 310.8401 l S 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l f* 311.88 272.3401 m 314.53 272.3401 l S 314.53 272.3401 m 311.88 272.3401 l S 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l f* 318.53 272.3401 m 321.18 272.3401 l S 321.18 272.3401 m 318.53 272.3401 l S 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l f* 325.18 272.3401 m 327.83 272.3401 l S 327.83 272.3401 m 325.18 272.3401 l S 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l f* 331.83 272.3401 m 334.48 272.3401 l S 334.48 272.3401 m 331.83 272.3401 l S 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l f* 338.48 272.3401 m 341.13 272.3401 l S 341.13 272.3401 m 338.48 272.3401 l S 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l f* 345.13 272.3401 m 347.78 272.3401 l S 347.78 272.3401 m 345.13 272.3401 l S 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l f* 351.78 272.3401 m 354.43 272.3401 l S 354.43 272.3401 m 351.78 272.3401 l S 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l f* 358.43 272.3401 m 361.08 272.3401 l S 361.08 272.3401 m 358.43 272.3401 l S 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l f* 365.08 272.3401 m 367.73 272.3401 l S 367.73 272.3401 m 365.08 272.3401 l S 0.847 0.161 0 rg 196.03 272.3401 2.65 0.1 re f 1 0.25 0 RG 196.03 272.4401 m 198.68 272.4401 l S 198.68 272.4401 m 198.68 272.3401 l S 198.68 272.3401 m 196.03 272.3401 l S 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l f* 197.78 272.3401 m 200.48 272.3401 l S 200.48 272.3401 m 197.78 272.3401 l S 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l f* 199.58 272.3401 m 202.23 272.3401 l S 202.23 272.3401 m 199.58 272.3401 l S 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l f* 201.38 272.3401 m 204.03 272.3401 l S 204.03 272.3401 m 201.38 272.3401 l S 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l f* 203.13 272.3401 m 205.83 272.3401 l S 205.83 272.3401 m 203.13 272.3401 l S 204.93 272.3401 2.65 0.05 re f 204.93 272.3401 m 204.93 272.39 l S 204.93 272.39 m 207.58 272.39 l S 207.58 272.39 m 207.58 272.3401 l S 207.58 272.3401 m 204.93 272.3401 l S 206.68 272.3401 2.7 0.05 re f 206.68 272.3401 m 206.68 272.39 l S 206.68 272.39 m 209.38 272.39 l S 209.38 272.39 m 209.38 272.3401 l S 209.38 272.3401 m 206.68 272.3401 l S 208.48 272.3401 2.65 7.6 re f 208.48 272.3401 m 208.48 279.9401 l S 208.48 279.9401 m 211.13 279.9401 l S 211.13 279.9401 m 211.13 272.3401 l S 211.13 272.3401 m 208.48 272.3401 l S 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l f* 210.28 272.3401 m 212.93 272.3401 l S 212.93 272.3401 m 210.28 272.3401 l S 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l f* 212.03 272.3401 m 214.68 272.3401 l S 214.68 272.3401 m 212.03 272.3401 l S 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l f* 213.83 272.3401 m 216.48 272.3401 l S 216.48 272.3401 m 213.83 272.3401 l S 215.58 272.3401 2.7 0.05 re f 215.58 272.3401 m 215.58 272.39 l S 215.58 272.39 m 218.28 272.39 l S 218.28 272.39 m 218.28 272.3401 l S 218.28 272.3401 m 215.58 272.3401 l S 217.38 272.3401 2.65 7.15 re f 217.38 272.3401 m 217.38 279.4901 l S 217.38 279.4901 m 220.03 279.4901 l S 220.03 279.4901 m 220.03 272.3401 l S 220.03 272.3401 m 217.38 272.3401 l S 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l f* 219.13 272.3401 m 221.83 272.3401 l S 221.83 272.3401 m 219.13 272.3401 l S 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l f* 220.93 272.3401 m 223.58 272.3401 l S 223.58 272.3401 m 220.93 272.3401 l S 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l f* 222.73 272.3401 m 225.38 272.3401 l S 225.38 272.3401 m 222.73 272.3401 l S 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l f* 224.48 272.3401 m 227.18 272.3401 l S 227.18 272.3401 m 224.48 272.3401 l S 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l f* 226.28 272.3401 m 228.93 272.3401 l S 228.93 272.3401 m 226.28 272.3401 l S 228.03 272.3401 2.7 6.7 re f 228.03 272.3401 m 228.03 279.0401 l S 228.03 279.0401 m 230.73 279.0401 l S 230.73 279.0401 m 230.73 272.3401 l S 230.73 272.3401 m 228.03 272.3401 l S 229.83 272.39 m 229.83 272.39 l 232.48 272.39 l f* 229.83 272.39 m 232.48 272.39 l S 232.48 272.39 m 229.83 272.39 l S 238.73 278.6401 m 238.73 278.6401 l 241.38 278.6401 l f* 238.73 278.6401 m 241.38 278.6401 l S 241.38 278.6401 m 238.73 278.6401 l S 245.38 370.3901 m 245.38 370.3901 l 248.03 370.3901 l f* 245.38 370.3901 m 248.03 370.3901 l S 248.03 370.3901 m 245.38 370.3901 l S 252.03 272.4401 m 252.03 272.4401 l 254.68 272.4401 l f* 252.03 272.4401 m 254.68 272.4401 l S 254.68 272.4401 m 252.03 272.4401 l S 258.68 272.4401 m 258.68 272.4401 l 261.33 272.4401 l f* 258.68 272.4401 m 261.33 272.4401 l S 261.33 272.4401 m 258.68 272.4401 l S 265.33 274.8901 m 265.33 274.8901 l 267.98 274.8901 l f* 265.33 274.8901 m 267.98 274.8901 l S 267.98 274.8901 m 265.33 274.8901 l S 271.98 272.4401 m 271.98 272.4401 l 274.63 272.4401 l f* 271.98 272.4401 m 274.63 272.4401 l S 274.63 272.4401 m 271.98 272.4401 l S 278.63 272.4401 m 278.63 272.4401 l 281.28 272.4401 l f* 278.63 272.4401 m 281.28 272.4401 l S 281.28 272.4401 m 278.63 272.4401 l S 285.28 272.39 m 285.28 272.39 l 287.93 272.39 l f* 285.28 272.39 m 287.93 272.39 l S 287.93 272.39 m 285.28 272.39 l S 291.93 272.4401 m 291.93 272.4401 l 294.58 272.4401 l f* 291.93 272.4401 m 294.58 272.4401 l S 294.58 272.4401 m 291.93 272.4401 l S 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l f* 298.58 272.3401 m 301.23 272.3401 l S 301.23 272.3401 m 298.58 272.3401 l S 305.23 310.8401 m 305.23 310.8401 l 307.88 310.8401 l f* 305.23 310.8401 m 307.88 310.8401 l S 307.88 310.8401 m 305.23 310.8401 l S 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l f* 311.88 272.3401 m 314.53 272.3401 l S 314.53 272.3401 m 311.88 272.3401 l S 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l f* 318.53 272.3401 m 321.18 272.3401 l S 321.18 272.3401 m 318.53 272.3401 l S 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l f* 325.18 272.3401 m 327.83 272.3401 l S 327.83 272.3401 m 325.18 272.3401 l S 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l f* 331.83 272.3401 m 334.48 272.3401 l S 334.48 272.3401 m 331.83 272.3401 l S 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l f* 338.48 272.3401 m 341.13 272.3401 l S 341.13 272.3401 m 338.48 272.3401 l S 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l f* 345.13 272.3401 m 347.78 272.3401 l S 347.78 272.3401 m 345.13 272.3401 l S 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l f* 351.78 272.3401 m 354.43 272.3401 l S 354.43 272.3401 m 351.78 272.3401 l S 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l f* 358.43 272.3401 m 361.08 272.3401 l S 361.08 272.3401 m 358.43 272.3401 l S 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l f* 365.08 272.3401 m 367.73 272.3401 l S 367.73 272.3401 m 365.08 272.3401 l S 1 0.6 0.784 rg 196.03 272.4401 m 196.03 272.4401 l 198.68 272.4401 l f* 0.5 0 0 RG 196.03 272.4401 m 198.68 272.4401 l S 198.68 272.4401 m 196.03 272.4401 l S 197.78 272.3401 m 197.78 272.3401 l 200.48 272.3401 l f* 197.78 272.3401 m 200.48 272.3401 l S 200.48 272.3401 m 197.78 272.3401 l S 199.58 272.3401 m 199.58 272.3401 l 202.23 272.3401 l f* 199.58 272.3401 m 202.23 272.3401 l S 202.23 272.3401 m 199.58 272.3401 l S 201.38 272.3401 m 201.38 272.3401 l 204.03 272.3401 l f* 201.38 272.3401 m 204.03 272.3401 l S 204.03 272.3401 m 201.38 272.3401 l S 203.13 272.3401 m 203.13 272.3401 l 205.83 272.3401 l f* 203.13 272.3401 m 205.83 272.3401 l S 205.83 272.3401 m 203.13 272.3401 l S 204.93 272.39 m 204.93 272.39 l 207.58 272.39 l f* 204.93 272.39 m 207.58 272.39 l S 207.58 272.39 m 204.93 272.39 l S 206.68 272.39 m 206.68 272.39 l 209.38 272.39 l f* 206.68 272.39 m 209.38 272.39 l S 209.38 272.39 m 206.68 272.39 l S 208.48 279.9401 m 208.48 279.9401 l 211.13 279.9401 l f* 208.48 279.9401 m 211.13 279.9401 l S 211.13 279.9401 m 208.48 279.9401 l S 210.28 272.3401 m 210.28 272.3401 l 212.93 272.3401 l f* 210.28 272.3401 m 212.93 272.3401 l S 212.93 272.3401 m 210.28 272.3401 l S 212.03 272.3401 m 212.03 272.3401 l 214.68 272.3401 l f* 212.03 272.3401 m 214.68 272.3401 l S 214.68 272.3401 m 212.03 272.3401 l S 213.83 272.3401 m 213.83 272.3401 l 216.48 272.3401 l f* 213.83 272.3401 m 216.48 272.3401 l S 216.48 272.3401 m 213.83 272.3401 l S 215.58 272.39 m 215.58 272.39 l 218.28 272.39 l f* 215.58 272.39 m 218.28 272.39 l S 218.28 272.39 m 215.58 272.39 l S 217.38 279.4901 m 217.38 279.4901 l 220.03 279.4901 l f* 217.38 279.4901 m 220.03 279.4901 l S 220.03 279.4901 m 217.38 279.4901 l S 219.13 272.3401 m 219.13 272.3401 l 221.83 272.3401 l f* 219.13 272.3401 m 221.83 272.3401 l S 221.83 272.3401 m 219.13 272.3401 l S 220.93 272.3401 m 220.93 272.3401 l 223.58 272.3401 l f* 220.93 272.3401 m 223.58 272.3401 l S 223.58 272.3401 m 220.93 272.3401 l S 222.73 272.3401 m 222.73 272.3401 l 225.38 272.3401 l f* 222.73 272.3401 m 225.38 272.3401 l S 225.38 272.3401 m 222.73 272.3401 l S 224.48 272.3401 m 224.48 272.3401 l 227.18 272.3401 l f* 224.48 272.3401 m 227.18 272.3401 l S 227.18 272.3401 m 224.48 272.3401 l S 226.28 272.3401 m 226.28 272.3401 l 228.93 272.3401 l f* 226.28 272.3401 m 228.93 272.3401 l S 228.93 272.3401 m 226.28 272.3401 l S 228.03 279.0401 2.7 2.6 re f 228.03 279.0401 m 228.03 281.6401 l S 228.03 281.6401 m 230.73 281.6401 l S 230.73 281.6401 m 230.73 279.0401 l S 230.73 279.0401 m 228.03 279.0401 l S 229.83 272.39 m 229.83 272.39 l 232.48 272.39 l f* 229.83 272.39 m 232.48 272.39 l S 232.48 272.39 m 229.83 272.39 l S 238.73 278.6401 m 238.73 278.6401 l 241.38 278.6401 l f* 238.73 278.6401 m 241.38 278.6401 l S 241.38 278.6401 m 238.73 278.6401 l S 245.38 370.3901 m 245.38 370.3901 l 248.03 370.3901 l f* 245.38 370.3901 m 248.03 370.3901 l S 248.03 370.3901 m 245.38 370.3901 l S 252.03 272.4401 m 252.03 272.4401 l 254.68 272.4401 l f* 252.03 272.4401 m 254.68 272.4401 l S 254.68 272.4401 m 252.03 272.4401 l S 258.68 272.4401 m 258.68 272.4401 l 261.33 272.4401 l f* 258.68 272.4401 m 261.33 272.4401 l S 261.33 272.4401 m 258.68 272.4401 l S 265.33 274.8901 m 265.33 274.8901 l 267.98 274.8901 l f* 265.33 274.8901 m 267.98 274.8901 l S 267.98 274.8901 m 265.33 274.8901 l S 271.98 272.4401 m 271.98 272.4401 l 274.63 272.4401 l f* 271.98 272.4401 m 274.63 272.4401 l S 274.63 272.4401 m 271.98 272.4401 l S 278.63 272.4401 m 278.63 272.4401 l 281.28 272.4401 l f* 278.63 272.4401 m 281.28 272.4401 l S 281.28 272.4401 m 278.63 272.4401 l S 285.28 272.39 m 285.28 272.39 l 287.93 272.39 l f* 285.28 272.39 m 287.93 272.39 l S 287.93 272.39 m 285.28 272.39 l S 291.93 272.4401 m 291.93 272.4401 l 294.58 272.4401 l f* 291.93 272.4401 m 294.58 272.4401 l S 294.58 272.4401 m 291.93 272.4401 l S 298.58 272.3401 m 298.58 272.3401 l 301.23 272.3401 l f* 298.58 272.3401 m 301.23 272.3401 l S 301.23 272.3401 m 298.58 272.3401 l S 305.23 310.8401 m 305.23 310.8401 l 307.88 310.8401 l f* 305.23 310.8401 m 307.88 310.8401 l S 307.88 310.8401 m 305.23 310.8401 l S 311.88 272.3401 m 311.88 272.3401 l 314.53 272.3401 l f* 311.88 272.3401 m 314.53 272.3401 l S 314.53 272.3401 m 311.88 272.3401 l S 318.53 272.3401 m 318.53 272.3401 l 321.18 272.3401 l f* 318.53 272.3401 m 321.18 272.3401 l S 321.18 272.3401 m 318.53 272.3401 l S 325.18 272.3401 m 325.18 272.3401 l 327.83 272.3401 l f* 325.18 272.3401 m 327.83 272.3401 l S 327.83 272.3401 m 325.18 272.3401 l S 331.83 272.3401 m 331.83 272.3401 l 334.48 272.3401 l f* 331.83 272.3401 m 334.48 272.3401 l S 334.48 272.3401 m 331.83 272.3401 l S 338.48 272.3401 m 338.48 272.3401 l 341.13 272.3401 l f* 338.48 272.3401 m 341.13 272.3401 l S 341.13 272.3401 m 338.48 272.3401 l S 345.13 272.3401 m 345.13 272.3401 l 347.78 272.3401 l f* 345.13 272.3401 m 347.78 272.3401 l S 347.78 272.3401 m 345.13 272.3401 l S 351.78 272.3401 m 351.78 272.3401 l 354.43 272.3401 l f* 351.78 272.3401 m 354.43 272.3401 l S 354.43 272.3401 m 351.78 272.3401 l S 358.43 272.3401 m 358.43 272.3401 l 361.08 272.3401 l f* 358.43 272.3401 m 361.08 272.3401 l S 361.08 272.3401 m 358.43 272.3401 l S 365.08 272.3401 m 365.08 272.3401 l 367.73 272.3401 l f* 365.08 272.3401 m 367.73 272.3401 l S 367.73 272.3401 m 365.08 272.3401 l S Q BT /F13 1 Tf 6 0 0 6 259.73 257.9401 Tm (Initial assets $a)Tj 4.8 0 0 4.8 299.73 254.9401 Tm (0)Tj 6 0 0 6 302.38 257.9401 Tm ($)Tj /F25 1 Tf 0 6 -6 0 185.53 311.54 Tm (m)Tj /F13 1 Tf 0.575 0 TD ($a)Tj 0 4.8 -4.8 0 188.53 320.2901 Tm (0)Tj 0 6 -6 0 185.53 322.9401 Tm (,y)Tj 0 4.8 -4.8 0 188.53 327.5901 Tm (0)Tj 0 6 -6 0 185.53 330.2401 Tm ($)Tj ET 1 g 372.43 309.29 55.95 62.1 re f 1 G 372.43 309.29 m 372.43 371.39 l 428.38 371.39 l 428.38 309.29 l 372.43 309.29 l S 0 G 372.43 371.39 m 428.38 371.39 l S 372.43 309.29 m 428.38 309.29 l S 428.38 309.29 m 428.38 371.39 l S 372.43 309.29 m 372.43 371.39 l S 372.43 309.29 m 428.38 309.29 l S 372.43 309.29 m 372.43 371.39 l S 372.43 371.39 m 428.38 371.39 l S 372.43 309.29 m 428.38 309.29 l S 428.38 309.29 m 428.38 371.39 l S 372.43 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[(0000)-993(1)]TJ /F14 1 Tf 3.4529 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0000)Tj /F16 1 Tf 2.23836 0 Td <14>Tj /F14 1 Tf 1.05394 0 Td (a)Tj /F11 1 Tf 7.97011 0 0 7.97011 466.68 601.2 Tm (0)Tj ET q 337.56003 0 0 -0.48 139.788 598.668 cm /Im1 Do Q q 337.56003 0 0 -0.48 139.788 596.748 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 72 551.4 Tm [(the)-281(increased)-281(frequency)-300(of)-261(dev)51(aluation)-281(sho)-31(c)31(ks)-292(dominates)-281(the)-281(mortgage)-261(selection)-291(e\013ect.)-431(A)31(t)-272(the)]TJ 0 -1.2045 TD [(same)-331(time,)-342(a)31(v)30(erage)-331(house)-341(prices)-341(fall)-321(as)-332(more)-331(dev)51(alued)-331(houses)-342(are)-331(sold.)]TJ 1.46548 -1.2045 TD [(In)-281(fact,)-291(the)-282(presence)-290(of)-271(IOMs)-292(magni\fes)-281(the)-281(impact)-291(of)-271(the)-281(v)50(alue)-280(sho)-31(c)31(k)-281(probabilit)29(y)-291(increase.)]TJ -1.46548 -1.21454 TD [(In)-311(the)-312(econom)31(y)-331(with)-311(FRM)-312(only)81(,)-311(the)-311(same)-322(sho)-30(c)31(k)-322(only)-311(causes)-331(default)-311(rates)-312(to)-311(rise)-312(b)30(y)-321(34%)-301($see)]TJ 0 -1.2045 TD [(the)-331(FRM(2))-323(column)-330(of)-332(table)-321(3.$)]TJ 1.46548 -1.21454 TD [(T)81(able)-351(6)-331(pro)30(vides)-352(a)-331(breakdo)31(wn)-361(of)-332(default)-331(frequencies)-371(b)30(y)-341(con)31(tract)-342(t)30(yp)-30(e)-351(across)-342(exp)-30(erimen)31(ts)]TJ -1.46548 -1.2045 TD [(analogous)-341(to)-331(the)-352(last)-342(panel)-341(of)-341(\fgure)-341(1.)-472(It)-342(sho)30(ws)-361(that)-332(default)-352(rates)-342(are)-341(m)30(uc)31(h)-351(higher)-352(for)-331(IOM)]TJ T* [(con)31(tracts)-403(than)-392(for)-382(FRM)-381(con)30(tracts.)-633(T)80(able)-401(7)-381(sho)30(ws)-412(the)-391(con)30(tributions)-403(of)-391(eac)31(h)-392(mortgage)-391(t)30(yp)-30(e)]TJ 0 -1.21454 TD [(to)-342(o)31(v)30(erall)-351(default)-352(rates.)-492(These)-361(t)30(w)30(o)-351(tables)-352(sho)30(w)-351(that)-342(default)-351(frequencies)-371(on)-341(IOMs)-352(are)-341(almost)]TJ 0 -1.2045 TD [(double)-331(those)-341(for)-322(FRMs)-322($2%)-332(vs.)-442(1%)-331(for)-321(v)30(olun)30(tary)-342(defaults$.)]TJ 1.46548 -1.21454 TD [(F)80(urthermore,)-352(IOMs)-353(accoun)32(t)-352(for)-342(nearly)-351(25%)-341(of)-331(the)-351(o)30(v)30(erall)-351(default)-342(rates)-352(ev)31(en)-351(though)-351(they)]TJ -1.46548 -1.2045 TD [(only)-391(represen)30(t)-402(12%)-381(of)-382(all)-391(mortgages.)-603(After)-391(raising)-392(the)-382(lik)30(eliho)-29(o)-30(d)-402(of)-371(a)-391(house)-392(v)50(alue)-391(sho)-30(c)31(k)-392(in)]TJ T* [(the)-311(IOM(2))-303(exp)-29(erimen)30(t,)-331(IOMs)-313(accoun)32(t)-312(for)-291(23%)-301(of)-301(the)-312(o)31(v)30(erall)-311(default)-301(rates,)-322(ev)30(en)-311(though)-311(they)]TJ 0 -1.21454 TD [(only)-331(represen)30(t)-352(11%)-321(of)-321(all)-331(mortgages.)]TJ 9.82671 -2.8908 TD [(T)81(able)-331(6:)-442(Default)-321(frequencies)-350(b)30(y)-331(mortgage)-321(t)29(yp)-30(e)]TJ ET q 201.60001 0 0 -0.48 207.828 312.948 cm /Im1 Do Q q 201.60001 0 0 -0.48 207.828 310.908 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 284.52 300.36 Tm [(v)30(olun)30(tary)-1014(in)30(v)30(olun)31(tary)]TJ ET q 201.60001 0 0 -0.48 207.828 296.028 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 213.84 285.48 Tm (Benchmark)Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.04)-3724(0.02)]TJ ET q 201.60001 0 0 -0.48 207.828 266.748 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 213.84 256.2 Tm (IOM(1))Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.04)-3724(0.02)]TJ 0 -1.21454 TD [(IOM)-5069(1.90)-3724(0.01)]TJ ET q 201.60001 0 0 -0.48 207.828 223.068 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 213.84 212.4 Tm (IOM(2))Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.42)-3724(0.01)]TJ T* [(IOM)-5069(2.56)-3724(0.01)]TJ ET q 201.60001 0 0 -0.48 207.828 179.268 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 213.84 168.72 Tm (FRM(2))Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.42)-3724(0.01)]TJ ET q 201.60001 0 0 -0.48 207.828 149.988 cm /Im1 Do Q q 201.60001 0 0 -0.48 207.828 148.068 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 302.76 67.44 Tm (24)Tj ET endstream endobj 27 0 obj << /Length 9117 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 211.68 676.8 Tm 0 g [(T)81(able)-331(7:)-432(Share)-331(of)-331(o)30(v)31(erall)-332(default)-331(rates)]TJ ET q 237.60001 0 0 -0.48 189.828 662.988 cm /Im1 Do Q q 237.60001 0 0 -0.48 189.828 660.948 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 266.4 650.4 Tm [(v)30(olun)30(tary)-1024(in)30(v)30(olun)30(tary)-1014(total)]TJ ET q 237.60001 0 0 -0.48 189.828 646.068 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 195.84 635.52 Tm (Benchmark)Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.04)-3724(0.02)]TJ /F5 1 Tf 16.863 0 Td (1.06)Tj ET q 237.60001 0 0 -0.48 189.828 616.788 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 195.84 606.2401 Tm (IOM(1))Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(0.89)-3724(0.01)-2699(0.90)]TJ 0 -1.21454 TD [(IOM)-5069(0.27)-3724(0.00)-2699(0.27)]TJ 0 -1.2045 TD [(T)81(otal)-4818(1.16)-3724(0.01)]TJ /F5 1 Tf 16.863 0 Td (1.18)Tj ET q 237.60001 0 0 -0.48 189.828 558.588 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 195.84 548.04 Tm (IOM(2))Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.22)-3724(0.00)-2699(1.22)]TJ 0 -1.21454 TD [(IOM)-5069(0.36)-3724(0.00)-2699(0.36)]TJ 0 -1.2045 TD [(T)81(otal)-4818(1.58)-3724(0.00)]TJ /F5 1 Tf 16.863 0 Td (1.58)Tj ET q 237.60001 0 0 -0.48 189.828 500.508 cm /Im1 Do Q BT /F10 1 Tf 11.95517 0 0 11.95517 195.84 489.84 Tm (FRM(2))Tj /F8 1 Tf 0 -1.2045 TD [(FRM)-4818(1.42)-3724(0.01)]TJ /F5 1 Tf 16.863 0 Td (1.43)Tj ET q 237.60001 0 0 -0.48 189.828 471.228 cm /Im1 Do Q q 237.60001 0 0 -0.48 189.828 469.188 cm /Im1 Do Q BT /F9 1 Tf 17.21544 0 0 17.21544 72 423.84 Tm [(6)-1122(The)-369(w)28(elfare)-368(consequences)-349(of)-376(mortgage)-368(inno)28(v)63(ation)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 397.56 Tm [(Mortgage)-271(inno)30(v)50(ation)-281(induces)-291(an)-271(increase)-290(in)-271(default)-281(rates)-272(hence)-290(an)-271(increase)-291(in)-271(the)-281(dead-w)31(eigh)31(t)]TJ 0 -1.2045 TD [(loss)-292(asso)-30(ciated)-291(with)-291(foreclosure.)-432(Y)81(et,)-291(in)-291(our)-282(mo)-30(del,)-291(it)-281(raises)-302(the)-281(w)30(elfare)-290(of)-281(all)-281(agen)31(ts)-292(b)30(y)-291(giving)]TJ T* [(them)-412(an)-401(alternativ)30(e)-422(mortgage)-391(c)31(hoice)-421(without)-412(a\013ecting)-411(an)30(y)-411(of)-392(the)-411(other)-402(opp)-30(ortunities)-423(they)]TJ 0 -1.21454 TD [(face,)-330(including)-341(the)-332(price)-331(of)-321(houses)-341(and)-331(the)-332(returns)-332(to)-332(sa)30(ving.)]TJ 1.46548 -1.2045 TD [(T)81(o)-382(calculate)-390(consumption)-402(equiv)51(alen)31(t)-402(w)30(elfare)-391(gains,)-392(consider)-401(agen)31(ts)-383(b)-30(orn)-381(with)-392(income)]TJ /F14 1 Tf 37.35957 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 541.92 338.04 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 72 325.32 Tm (where)Tj /F14 1 Tf 2.90084 0 Td (i)Tj /F16 1 Tf 0.74278 0 Td 0.412 Tc (2f)Tj /F14 1 Tf 1.57589 0 Td 0 Tc [(L;)-171(M)-50(;)-170(H)]TJ /F16 1 Tf 3.43283 0 Td (g)Tj /F8 1 Tf 0.50187 0 Td [(.)-652(Then)-411(let)]TJ /F14 1 Tf 5.03882 0 Td (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 247.8 323.52 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 255.96 325.32 Tm [(b)-30(e)-411(the)-402(additional)-401(fraction)-402(of)-402(their)-402(lifetime)-411(consumption)]TJ -15.38749 -1.2045 TD [(whic)31(h)-291(agen)31(ts)-292(b)-31(orn)-281(in)-281(the)-281(econom)31(y)-301(with)-291(FRMs)-282(w)30(ould)-291(need)-290(to)-271(receiv)31(e)-301(to)-281(ha)30(v)30(e)-291(the)-291(same)-281(w)31(elfare)]TJ T* [(as)-331(agen)30(ts)-332(b)-30(orn)-321(with)-342(the)-331(same)-331(income)-341(in)-321(an)-331(econom)31(y)-341(with)-331(b)-30(oth)-322(mortgages.)-442(Then:)]TJ /F14 1 Tf 5.73141 -3.03132 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 150 265.2 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 170.4 260.28 Tm 0 Tc ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 191.88 258.48 Tm 0 Tc (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 195.12 260.28 Tm 0.834 Tc ($=)Tj /F14 1 Tf 2.8105 0 Td 0 Tc (E)Tj /F11 1 Tf 7.97011 0 0 7.97011 237.36 258.48 Tm (0)Tj /F19 1 Tf 11.95517 0 0 11.95517 244.08 280.68 Tm (")Tj /F18 1 Tf 7.97011 0 0 7.97011 255.48 275.16 Tm (1)Tj /F19 1 Tf 11.95517 0 0 11.95517 251.04 271.68 Tm (X)Tj /F15 1 Tf 7.97011 0 0 7.97011 252.84 246.48 Tm (t)Tj /F11 1 Tf 0.37641 0 Td (=0)Tj /F14 1 Tf 11.95517 0 0 11.95517 270.36 260.28 Tm (\f)Tj /F15 1 Tf 7.97011 0 0 7.97011 277.68 265.44 Tm (t)Tj /F14 1 Tf 11.95517 0 0 11.95517 281.16 260.28 Tm (u)Tj /F8 1 Tf 0.5621 0 Td ($)Tj /F14 1 Tf 0.38142 0 Td (c)Tj /F15 1 Tf 7.97011 0 0 7.97011 297.48 265.2 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.99371 TD 0 Tc (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 319.92 260.28 Tm [(\(1)-211(+)]TJ /F14 1 Tf 2.06772 0 Td (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 350.76 258.48 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 354.12 260.28 Tm ($)Tj /F14 1 Tf 0.38143 0 Td 0.171 Tc (;s)Tj /F15 1 Tf 7.97011 0 0 7.97011 369.48 265.2 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.99371 TD 0 Tc (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 391.92 260.28 Tm (\))Tj /F19 1 Tf 0.38143 1.70637 TD (#)Tj /F8 1 Tf -15.62839 -5.03882 TD (=)Tj /F14 1 Tf 1.59596 0 Td (E)Tj /F11 1 Tf 7.97011 0 0 7.97011 237.36 218.64 Tm (0)Tj /F19 1 Tf 11.95517 0 0 11.95517 244.08 240.84 Tm (")Tj /F18 1 Tf 7.97011 0 0 7.97011 255.48 235.32 Tm (1)Tj /F19 1 Tf 11.95517 0 0 11.95517 251.04 231.84 Tm (X)Tj /F15 1 Tf 7.97011 0 0 7.97011 252.84 206.64 Tm (t)Tj /F11 1 Tf 0.37641 0 Td (=0)Tj /F14 1 Tf 11.95517 0 0 11.95517 270.36 220.44 Tm (\f)Tj /F15 1 Tf 7.97011 0 0 7.97011 277.68 225.6 Tm (t)Tj /F19 1 Tf 11.95517 0 0 11.95517 283.2 230.16 Tm (\b)Tj /F8 1 Tf 0.58217 -0.81304 TD (ln$)Tj /F14 1 Tf 1.19446 0 Td (c)Tj /F15 1 Tf 7.97011 0 0 7.97011 309.48 225.36 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.99371 TD 0 Tc (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 331.92 220.44 Tm 0.221 Tc [($+l)221(n)221($)221(1+)]TJ /F14 1 Tf 4.47673 0 Td 0 Tc (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 391.56 218.64 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 394.92 220.44 Tm 0.221 Tc [($+l)221(n)211($)]TJ /F14 1 Tf 2.79042 0 Td 0 Tc (s)Tj /F15 1 Tf 7.97011 0 0 7.97011 433.8 225.36 Tm 0.15 Tc [(FR)150(M)]TJ 0 -0.99371 TD 0 Tc (t)Tj /F8 1 Tf 11.95517 0 0 11.95517 456.24 220.44 Tm ($)Tj /F19 1 Tf 0.38143 0.81304 TD (\t)Tj 0.58217 0.89334 TD (#)Tj /F8 1 Tf -21.59066 -4.71762 TD (=)Tj /F14 1 Tf 1.59596 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 238.2 189.36 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 260.64 184.44 Tm 0 Tc ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 282.12 182.64 Tm 0 Tc (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 285.36 184.44 Tm 0.221 Tc ($+)Tj 1.6863 0.67251 TD 0 Tc [(ln$1)-221(+)]TJ /F14 1 Tf 2.8908 0 Td (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 346.2 190.68 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 349.56 192.48 Tm ($)Tj ET q 48.72 0 0 -0.48 305.508 187.668 cm /Im1 Do Q BT /F8 1 Tf 11.95517 0 0 11.95517 311.4 176.28 Tm ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (\f)Tj /F8 1 Tf 0.61229 0 Td ($)Tj -22.7249 -2.02757 TD [(But)-331(then)]TJ 0 -2.20825 TD ($1)Tj /F16 1 Tf 1.09409 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (\f)Tj /F8 1 Tf 0.61229 0 Td ($)Tj /F19 1 Tf 0.55206 0.803 TD <02>Tj /F14 1 Tf 0.41154 -0.803 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 125.28 130.56 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 145.68 125.64 Tm 0 Tc ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 167.16 123.84 Tm 0 Tc (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 170.4 125.64 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 198.96 130.56 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 221.4 125.64 Tm 0 Tc ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 242.88 123.84 Tm 0 Tc (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 246.24 125.64 Tm ($)Tj /F19 1 Tf 0.38143 0.803 TD <03>Tj /F8 1 Tf 1.66622 -0.803 TD [(=)-1244(ln$1)-222(+)]TJ /F14 1 Tf 4.8983 0 Td (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 335.4 123.84 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 338.76 125.64 Tm ($)Tj -6.11284 -1.55581 TD (=)Tj /F16 1 Tf 0.59221 0 Td (\))Tj /F8 1 Tf 1.83686 0 Td 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 321.12 105.24 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 327.72 107.04 Tm [(=)-281(exp)-9($\(1)]TJ /F16 1 Tf 4.015 0 Td <00>Tj /F14 1 Tf 0.99371 0 Td (\f)Tj /F8 1 Tf 0.61229 0 Td ($)Tj /F19 1 Tf 0.55206 0.81304 TD <02>Tj /F14 1 Tf 0.41154 -0.81304 TD (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 415.92 111.96 Tm 0.075 Tc [(IO)45(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 436.32 107.04 Tm 0 Tc ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 457.8 105.24 Tm 0 Tc (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 461.04 107.04 Tm ($)Tj /F16 1 Tf 0.60225 0 Td <00>Tj /F14 1 Tf 1.00375 0 Td (V)Tj /F15 1 Tf 7.97011 0 0 7.97011 489.6 111.96 Tm 0.15 Tc [(FR)150(M)]TJ /F8 1 Tf 11.95517 0 0 11.95517 512.04 107.04 Tm 0 Tc ($0)Tj /F14 1 Tf 0.87326 0 Td 0.171 Tc (;y)Tj /F15 1 Tf 7.97011 0 0 7.97011 533.52 105.24 Tm 0 Tc (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 536.76 107.04 Tm ($)Tj /F19 1 Tf 0.38143 0.81304 TD <03>Tj /F8 1 Tf 0.42157 -0.81304 TD (\))Tj -20.37612 -3.31237 TD (25)Tj ET endstream endobj 28 0 obj << /Length 7952 >> stream /GS4 gs BT /F8 1 Tf 11.95517 0 0 11.95517 72 683.16 Tm 0 g [(The)-310(a)30(v)30(erage)-310(consumption)-312(equiv)51(alen)30(t)-321(gain)-301(is)-302(then)-311(giv)31(en)-311(b)30(y:)]TJ /F19 1 Tf 25.35472 0.75281 TD (P)Tj /F15 1 Tf 7.97011 0 0 7.97011 387.72 679.6801 Tm (i)Tj /F14 1 Tf 11.95517 0 0 11.95517 393.12 683.16 Tm (f)Tj /F15 1 Tf 7.97011 0 0 7.97011 398.88 681.36 Tm (i)Tj /F14 1 Tf 11.95517 0 0 11.95517 402.24 683.16 Tm (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 408.36 681.36 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 415.32 683.16 Tm (where)Tj /F14 1 Tf 2.80046 0 Td (f)Tj /F15 1 Tf 7.97011 0 0 7.97011 454.56 681.36 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 461.52 683.16 Tm [(is)-312(the)-301(fraction)-301(of)]TJ -32.58172 -1.21454 TD [(agen)31(ts)-332(b)-30(orn)-332(with)-331(income)]TJ /F14 1 Tf 10.88065 0 Td (y)Tj /F15 1 Tf 7.97011 0 0 7.97011 207.84 666.84 Tm (i)Tj /F8 1 Tf 11.95517 0 0 11.95517 211.2 668.64 Tm [(.)-442(W)81(e)-331(calculate)-330(that:)]TJ -5.34999 -2.20825 TD 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 173.64 640.44 Tm (L)Tj /F8 1 Tf 11.95517 0 0 11.95517 189.84 642.2401 Tm [(=)-833(exp)-180($)9(\(1)]TJ /F16 1 Tf 4.72766 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(96$)-171([)10($)]TJ /F16 1 Tf 2.17814 0 Td <00>Tj /F8 1 Tf 0.77289 0 Td (25)Tj /F14 1 Tf 0.98367 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0302$)Tj /F16 1 Tf 2.55956 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td ($)Tj /F16 1 Tf 0.38142 0 Td <00>Tj /F8 1 Tf 0.77289 0 Td (25)Tj /F14 1 Tf 0.98368 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(0366$])10(\))-281(=)-271(1)]TJ /F14 1 Tf 4.79793 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0003)Tj -25.57555 -1.45544 TD 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 170.4 623.04 Tm (M)Tj /F8 1 Tf 11.95517 0 0 11.95517 189.84 624.84 Tm [(=)-833(exp)-180($)9(\(1)]TJ /F16 1 Tf 4.72766 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(96$)-171([)10($)]TJ /F16 1 Tf 2.17814 0 Td <00>Tj /F8 1 Tf 0.77289 0 Td (4)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (3119$)Tj /F16 1 Tf 2.55956 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td ($)Tj /F16 1 Tf 0.38143 0 Td <00>Tj /F8 1 Tf 0.77289 0 Td (4)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(6671$]\))-271(=)-281(1)]TJ /F14 1 Tf 4.80796 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0143)Tj -24.48146 -1.45543 TD 0.221 Tc (1+)Tj /F14 1 Tf 1.69634 0 Td 0 Tc (k)Tj /F15 1 Tf 7.97011 0 0 7.97011 171.84 605.64 Tm (H)Tj /F8 1 Tf 11.95517 0 0 11.95517 189.84 607.44 Tm [(=)-833(exp)-180($)9(\(1)]TJ /F16 1 Tf 4.72766 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td (0)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(96$)-171([)10(9)]TJ /F14 1 Tf 2.28855 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (4550)Tj /F16 1 Tf 2.17814 0 Td <00>Tj /F8 1 Tf 1.00375 0 Td (9)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(4547])11(\))-272(=)-281(1)]TJ /F14 1 Tf 4.4165 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0000)Tj -27.5429 -3.66369 TD [(so)-301(that)]TJ /F16 1 Tf 3.26219 0 Td (\))Tj /F14 1 Tf 1.2848 0 Td (ce)Tj /F8 1 Tf 1.14427 0 Td 0.281 Tc [(=$)281(0)]TJ /F14 1 Tf 1.91716 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27101 0 Td (2056)Tj /F16 1 Tf 2.12795 0 Td <01>Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(0003)-160(+)-160(0)]TJ /F14 1 Tf 3.54324 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (5888)Tj /F16 1 Tf 2.12795 0 Td <01>Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td [(0143)-160(+)-160(0)]TJ /F14 1 Tf 3.54324 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (2056)Tj /F16 1 Tf 2.12795 0 Td <01>Tj /F8 1 Tf 0.44165 0 Td (1)Tj /F14 1 Tf 0.49184 0 Td (:)Tj /F8 1 Tf 0.27101 0 Td (0000$)Tj /F16 1 Tf 2.50937 0 Td <00>Tj /F8 1 Tf 0.93349 0 Td 0.231 Tc [(1=)-50(0)]TJ /F14 1 Tf 2.25844 0 Td 0 Tc (:)Tj /F8 1 Tf 0.27101 0 Td [(0085,)-290(whic)30(h)-311(is)-301(near)]TJ -31.4776 -1.21454 TD (1%.)Tj 1.46548 -1.2045 TD [(Wh)30(y)-431(are)-412(gains)-411(so)-422(lo)30(w)-411(among)-411(agen)31(ts)-423(who)-421(are)-411(b)-30(orn)-412(p)-30(o)-30(or?)-683(The)-421(presence)-441(of)-401(IOMs)-423(raises)]TJ -1.46548 -1.21453 TD [(w)30(elfare)-260(b)-30(ecause)-270(agen)30(ts)-261(kno)30(w)-271(that)-251(they)-261(ma)30(y)-261(ev)31(en)30(tually)-281(tak)30(e)-261(adv)51(an)30(tage)-261(of)-251(that)-251(option.)-412(Because)]TJ 0 -1.2045 TD [(income)-330(sho)-31(c)31(ks)-342(are)-331(v)30(ery)-331(p)-30(ersisten)29(t,)-352(agen)31(ts)-332(b)-30(orn)-322(p)-30(o)-30(or)-311(kno)30(w)-341(that)-322(they)-331(are)-321(lik)30(ely)-341(to)-321(b)-30(e)-331(p)-30(o)-30(or)-312(for)]TJ T* [(a)-341(while)-361(and)-351(to)-352(ha)31(v)30(e)-361(accum)31(ulated)-361(little)-352(assets)-363(b)30(y)-361(the)-351(time)-362(the)-351(housing)-352(option)-351(presen)30(ts)-372(itself.)]TJ 0 -1.21454 TD [(They)-280(are)-271(quite)-271(lik)30(ely)81(,)-301(therefore,)-281(to)-272(remain)-271(ren)30(ters)-282(their)-271(en)30(tire)-281(life)-271(ev)31(en)-281(when)-280(IOMs)-272(are)-271(o\013ered.)]TJ 0 -1.2045 TD [(Indeed,)-301(recall)-280(that)-282(agen)31(ts)-282(at)-281(the)-282(v)31(ery)-291(b)-31(ottom)-271(of)-281(the)-281(asset)-282(and)-281(income)-290(distribution)-293(do)-271(not)-281(tak)30(e)]TJ 0 -1.21454 TD [(on)-411(mortgages)-412(in)-422(all)-411(economies.)-712(Lik)30(ewise,)-461(the)-422(ric)30(her)-421(agen)31(ts)-423(kno)30(w)-431(that)-412(they)-422(will)-421(lik)30(ely)-431(\fnd)]TJ 0 -1.2045 TD [(themselv)30(es)-371(at)-342(the)-351(top)-332(of)-341(the)-351(income)-351(and)-341(asset)-352(distributions)-353(when)-361(they)-351(b)-31(ecome)-350(middle-aged,)]TJ T* [(hence)-320(are)-311(quite)-311(lik)30(ely)-331(to)-301(opt)-302(for)-301(FRMs)-312(ev)30(en)-320(when)-321(IOMs)-322(are)-301(a)30(v)50(ailable.)-441(It)-301(should)-322(b)-30(e)-311(exp)-30(ected,)]TJ 0 -1.21454 TD [(therefore,)-341(that)-322(gains)-342(are)-331(particularly)-332(large)-331(for)-331(agen)31(ts)-332(b)-31(orn)-331(in)-331(the)-342(middle-income)-340(distribution)]TJ 0 -1.2045 TD [(whic)31(h,)-341(the)-332(ab)-30(o)31(v)30(e)-341(calculations)-331(sho)30(w,)-341(is)-332(exactly)-340(what)-332(happ)-30(ens.)]TJ /F9 1 Tf 17.21544 0 0 17.21544 72 350.28 Tm [(7)-1122(Summary)]TJ /F8 1 Tf 11.95517 0 0 11.95517 72 324 Tm [(In)-332(our)-321(mo)-30(del:)]TJ /F16 1 Tf 1.45544 -2.03761 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(default)-251(frequencies)-270(on)-251(IOMs)-252(are)-251(almost)-251(double)-251(those)-261(for)-241(FRMs)-252($2%)-241(vs.)-422(1%)-251(for)-241(v)30(olun)30(tary)]TJ 0 -1.21454 TD (defaults$;)Tj /F16 1 Tf -0.99371 -2.03761 TD <0F>Tj /F8 1 Tf 0.99371 0 Td [(in)30(tro)-31(ducing)-330(IOMs)-323(causes)-341(default)-321(rates)-332(to)-311(rise)-332(b)30(y)-331(11%.)-432(IOMs)-332(accoun)31(t)-331(for)-312(nearly)-331(25%)-321(of)]TJ 0 -1.2045 TD [(the)-331(o)30(v)30(erall)-331(default)-331(rates;)]TJ /F16 1 Tf -0.99371 -2.04765 TD <0F>Tj /F8 1 Tf 0.99371 0 Td 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