Equity Extraction and Mortgage Default

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Equity Extraction and Mortgage Default Steven Laufer 2013-30 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Equity Extraction and Mortgage Default ∗ Steven Laufer FederalReserveBoard March 21, 2013 Abstract Using a property-level data set of houses in Los Angeles County, I estimate that 30% of the recent surge in mortgage defaults is attributable to early home-buyers who would not have defaulted had they not borrowed against the rising value of their homes during the boom. I develop and estimate a structural model capable of explaining the patterns of both equity extraction and default observed among this group of homeowners. In the model, most of these defaults are attributable to the high loan-to-value ratios generated by thisadditionalborrowingcombinedwiththeexpectationthathousepriceswouldcontinue to decline. Only 30% are the result of income shocks and liquidity constraints. I use this model to analyze a policy that limits the maximum size of cash-out refinances to 80% of the current house value. I find that this restriction would reduce house prices by 14% and defaults by 28%. Despite the reduced borrowing opportunities, the welfare gain from this policyfornewhomeownersisequivalentto3.2%ofconsumptionbecauseoftheirabilityto purchasehousesatlowerprices. JELCodes: D14,G21,G33,E20,R20. ∗Steven.M.Laufer@frb.gov. This paper is a revised version of the first chapter of my NYU Ph.D. dissertation. I thank Andrew Caplin, Chris Flinn and Stijn Van Nieuwerburgh for their help as well as their general encouragement. IhavealsobenefitedfromconversationswithManolisGalenianos,AhuGemici,AntonioGuarino,John Leahy, Chris Mayer, Jesse Perla, Kevin Thom, Chris Tonetti, Joe Tracy, Ha˚kon Tretvoll, Gianluca Violante, Paul Willen, Matt Wiswall, Karen Pence, as well as seminar participants at the NYU Applied Microeconomics Workshop,theUniversityofMichigan,theFederalHousingFinanceAgency,theUSCensusBureau,theFederalReserve Board, CornerstoneResearch, OhioStateUniversity, YeshivaUniversity, JohnsHopkinsUniversityandtheConsumerFinancialProtectionBureau. SpecialthankstotheeconomistsattheFederalReserveBankofNewYorkfor their hospitality and for much helpful feedback. Finally, I wish to thank to Gunnar Blix and Marco Scoffier for theirhelpwiththedata. Allremainingerrorsaremyown. Theviewsexpressedinthispaperaresolelythoseof theauthorandnotnecessarilythoseoftheFederalReserveBoardortheFederalReserveSystem. 1

1 Introduction Whenhousepricespeakedandbegantodeclinesharplyin2006,mortgagedelinquenciessurged, withthefractionofhousesinsomestageoftheforeclosureprocessreaching4%in2010,almost eight times its historical average.1 Focusing on a sample of homeowners from Los Angeles County,California,Ishowthatnearly40%ofthesedefaultinghomeownerswereearlierhomebuyers who had purchased their homes before 2004. House price growth prior to the peak had been so strong that even after a 30% decline, prices still remained higher than they had been when these owners had first purchased their houses. For more than 90% of these defaulting homeowners, their original mortgage balances would have been less than the current value of their homes, leaving them with positive equity in their homes and little financial motivation to default. However, through cash-out refinances, second mortgages and home equity lines of credit, these homeowners had extracted much of the equity created by the rising value of their homes. As a result, their loan-to-value (LTV) ratios were on average more than 50 percentage points higher than they would have been without this additional borrowing and the majority had mortgage balances that exceeded the value of their homes. The goal of this paper is to develop a model that jointly explains the equity extraction of these early home-buyers and their subsequentdecisiontodefault. Iusethismodeltoevaluatepoliciesthatwouldlimittheability orincentivesofexistinghomeownerstoengageinadditionalborrowingandestimatetheeffect ofsuchpoliciesonhouseprices,defaultratesandhomeowners’welfare. Inordertostudytheconnectionbetweenequityextractionanddefault,Iuseauniquepanel data set from CoreLogic covering single family homes in Los Angeles County, California, from 2000 through 2009.2 This data differs from other commonly used mortgage data, such as the Lender Processing Services data or the CoreLogic Loan Performance data, in that the unit of analysis is the property rather than the individual mortgage and it is possible to link together all the mortgages held by a homeowner over the period spanned by the data. This allows me to compute the combined LTV ratio of all liens against a property and to observe when the homeownerwithdrawsequity. Examiningthisdataset,Ifindthattheimpactofequityextractionondefaultdiffersdepending on which cohort of home buyers we consider, with earlier purchasers having had more opportunity to extract equity during the boom. Figure 1 breaks down each quarter’s defaulters from my Los Angeles data by the year of purchase. While most defaulters during the recent surge were owners who had purchased their homes within several years of the 2006 peak in house prices, a significant and increasing number of defaulters were from earlier cohorts of purchasers. By2009,morethan40%ofthehomeownersdefaultingeachquarterhadpurchased 1LPSMortgageMoniter,February2011. LPSAppliedAnalytics 2AsubsetofthisdatawaspreviouslyusedbyAragonetal. (2010)tostudytheriskinessofmortgagesheldby theFHA. 2

theirhomesin2003orearlier. Atthepointwherehomeownersfromthisgroupdefaulted,over 40%oftheiroutstandingmortgagedebtwasattributabletoequityextractionsubsequenttopurchase. The importance of equity withdrawals declines for later cohorts, becoming insignificant forbuyerspurchasingafterthe2006peak(SeeFigure2). Inthispaper,Ithereforefocusonthese earliercohortsofbuyers. InFigure3,IplotthedistributionofestimatedLTVratiosatthetimeofdefaultfordefaulting homeownerswhopurchasedtheirhomesbetween2000and2003andcomparetheseLTVratios towhattheywouldhavebeenhadthesehomeownersnottakenoutadditionalmortgagedebt.3 Whentheseownersdefaulted,IestimatethattheiraverageLTVratiowasjustover1.0,aquarter had LTV ratios over 1.4 and 10% had LTV ratios over 1.7. Without any equity extraction, the majority of these homeowners would have had LTV ratios under 0.6 and less than 10% would have had ratios that exceeded unity. Insofar as high LTV ratios were an important factor in these default outcomes, equity extraction is a key part of the story. There is also a significant difference in the rate of equity extraction between homeowners who ultimately defaulted and those who did not. In Figure 4, I compare the equity extraction rates of owners from each cohortwhodidanddidnotdefaultduringtheobservationperiod. Earlybuyerswhoremained in their homes throughout the sample period extracted equity at a rate of approximately once every three years. Among homeowners from this group who defaulted by 2009, the rate of equityextractionwas70%higher.4 Explaining this joint behavior of equity extraction and default decisions is made more difficult by limitations of the data. Many of the state variables that we expect to be important factors in these decisions, such as income, assets, the current house value, and expectations about future house prices, are all absent from my mortgage data, as they are from most other mortgagedatasets. Tofillinthesegaps,Iconstructadynamicmodelofhomeownerswhoface both income and house price shocks and make decisions each period regarding savings, their mortgage balance, whether to sell their house and whether to default. The model is closest to those of Yao and Zhang (2008) and Campbell and Cocco (2011) with several important additions that allow me to capture important features of the data. First, in addition to permanent and transitory components, the income process includes a large discrete shock that I associate with unemployment and simulate to match evolving unemployment rates in the data. I find that these unemployment shocks are an important but not dominant driver of defaults. In the simulations, defaulters are five times more likely to be unemployed than the general populationofhomeownersbutonly17%ofdefaultersareunemployedatthetimeofdefault.5 Second, 3TheestimationoftheseLTVratiosisexplainedbelow,whenIdescribethedata. 4Othermeasuresofequityextraction,includingtherateofnewjuniormortgages,cash-outrefinances,andthe dollaramountofequityextracted,allfollowthesamepattern. Forhouseholdswhopurchasedafter2006,greater equityextractionisassociatedwithlowerdefaultrates,perhapsbecausetighteninglendingstandardsprevented riskierborrowersfromtakingonadditionaldebt. 5This is consistent with the empirical findings of Herkenhoff and Ohanian (2012), who document that in the 3

themodel’streatmentofhousepricesisnovelinthatitcapturesthepredictabilityofshort-term house price growth, as first documented by Case and Shiller (1989). Beyond the large movements in realized house prices, I find that changing expectations about future price growth is responsible for 20% of equity extraction when prices were rising during the boom and 34% of defaults as prices fell during the bust. Finally, I introduce a preference shock that accounts for the residual heterogeneity in the default decisions of underwater homeowners. This residual shock gives the model the flexibility to reproduce many of the patterns of household default decisions while maintaining income and house price shocks that are calibrated to match observabledata. I estimate the parameters of the model by matching a set of moments computed from the borrowing and default outcomes recorded in the CoreLogic mortgage data. In addition, the estimationdrawsonotherdatasourcesthatcontaininformationabouttherelationshipbetween the model’s unobserved states and observable information such as location, time period and features of the mortgages. I then use the estimated model to study the role of both income and housepriceshocksinhomeowners’decisionstoextractequityanddefault. The model provides two key mechanisms that connect homeowners’ equity extraction during the boom and their decision to default during the bust. First, homeowners who withdraw more equity end up with larger mortgage balances and larger mortgage payments, both of whichdirectlyincreasetheprobabilityofdefault. Second,liquidityconstrainedhouseholdsare more likely to extract equity in order to smooth consumption when hit by a negative income shock. This introducesa selectioneffect wherebythose homeownerswho takeout largermortgages are more likely to have fewer liquid assets and a history of negative income shocks, a conditionthatinitselfincreasestheriskofdefault. Quantitatively,Ifinditisthedirecteffectof equity extraction rather than this selection effect that explains most of the connection between equity extraction and default. Income shocks and liquidity constraints account for only 30% of defaultsfollowingthedeclineinprices. Using this estimated model, I study two counterfactual policies that would reduce homeowners’ ability or incentive to extract equity. The first policy limits the amount of equity that existing homeowners can withdraw by prohibiting cash-out refinances from exceeding 80% of the current house value. This restriction is similar to a key provision of refinance policies currently in effect in Texas. In the second policy, I treat mortgages as full recourse loans. This means that after leaving the house, a defaulting borrower would continue to be obligated to repay the portion of the mortgage not covered by the sale price of the house. Most states allow the lender to take legal action against defaulting homeowners to enforce this obligation. California, however, where the present study is focused, is generally classified as a “non-recourse” stateswheresuchactionsareprohibited.6 2009PSID,16%ofmortgagorsinforeclosurehaveanunemployedheadofhousehold. 6This is somewhat of a simplification. Under California law, a mortgage used to purchase a house is non- 4

In the first policy experiment, I find that limiting the amount of equity that homeowners can extract reduces the amount of equity extracted during the boom by 23%. Because of the decreased collateral value of housing, prices fall by an average of 14% and the combination of lowerhousepricesandlessabilitytoborrowcauseshouseholdstoholdlessdebtandtherefore to default at a lower rate. Of the homeowners who default in the baseline model, 41% do not under this policy. However, the overall default rate is only 28% lower. This is because of an offsetting increase in defaults that arises from the reduced borrowing opportunities for homeownerswithsmallbutpositiveamountsofequity. Theinabilityofthesehomeownerstoaccess this equity has two consequences. The first is to close a borrowing channel that could be used to prevent default should they experience a negative income shock and become liquidity constrained. The second effect is to reduce the value of staying in the home for homeowners with negative equity and the prospect of regaining some positive equity through price growth. By decreasingthevalueofhavingsmalllevelsofpositiveequity,thisincreasestheprobabilitythat such households will default when presented with an opportunity to do so. The welfare gain of this restriction for new homeowners is equivalent to 3.2% of consumption due to the lower prices at which they can purchase housing. Under a more extreme version of the policy that prohibitshomeownersfromextractinganyequityatall,thedefaultratefallsto20%ofitsoriginalvalue. Ithereforeconcludethatequityextractionwasresponsiblefor80%ofdefaultsamong theseearlyhome-buyers,representingapproximately30%ofthetotalnumberofdefaultsinLos AngelesCountyfrom2006to2009. In the other policy experiment, I find that granting full recourse to lenders reduces defaults significantly. First, because the mortgages that can be secured by the house are less valuable, house prices fall by 12% so homeowners have less expensive houses and smaller mortgages at the time of purchase. Second, because homeowners can no longer expect to be relieved of their repayment obligations upon default, they take on less debt, reducing their equity extractionduringtheboomby18%. Finally,thepolicycreatesastrongdisincentivetodefaultamong homeowners who already have negative equity. The total default rate falls by 45%. I estimate that the overall welfare gain to new homeowners from this policy is equivalent to 2.7% of consumption,againduetothelowerpriceofhousing. recourse but refinances originated before January 1, 2013, as well as all second mortgages and the portion of cash-out refinances beyond the original mortgage balance plus fees, are not. In order to collect the outstanding balance,however,lendersmustpursueajudicialforeclosure,whileotherwisethestategivesthemaquickerand less-expensive non-judicial option. Even then, lenders run the risk that the borrower will discharge the debt by declaring bankruptcy. In practice, therefore, lenders rarely choose this option. In my analysis, I assume that Californiaborrowersthoughtofallmortgagesasnon-recourse. 5

1.1 Related Literature This paper contributes to several strands of the existing literature on default. Empirical studies of mortgage default such as by Deng, Quigley and Van Order (2000) and Bajari, Chu and Park(2008)haveprovidedevidencefortheimportanceoftheLTVratiointhedefaultdecision. Thispaper,incontrast,focusesonhomeownersforwhomtheLTVratioisendogenouslydetermined so that quantifying the relationship between LTV ratios and defaults requires a model that also explains differences in borrowing decisions. Elul et al. (2009) further demonstrate the importance of the interaction between high LTV ratios and liquidity constraints in producing defaults. In the model presented in this paper, spending decisions made by households can causethemtoexhausttheirliquidassetssothatthebindingliquidityconstraintsalsoemergeas endogenous outcomes. Ghent and Kudlyak (2011) find that at a fixed level of negative equity, recourse decreases the probability of default by 30%. I argue that in addition to this effect, the threat of recourse results in homeowners approaching the default decision with less negative equity. On the subject of equity extraction, Hurst and Stafford (2004) show that homeowners withfewliquidassetsandahistoryofnegativeincomeshocksaremorelikelytoextractequity. Mymodelisconsistentwiththeirfindings. Regardingtherelationshipbetweenrefinancinganddefault,Foote,GerardiandWillen(2008a) findthatforeclosedhomesinNewEnglandexhibitedgreaterrefinancingactivityandtendedto have more life-time mortgages than those that were not foreclosed upon. Mian and Sufi (2011) identify a correlation at the regional level between the rate of house price appreciation from 2002-2006 and the default rate between 2006-2008. Based on this relationship, they conclude that house price growth and the resulting equity withdrawal can account for 35% of the total numberofdefaultsinthisperiod. Theconclusionsupportedbytheiranalysisisthathadprices notrisenfrom2002-2006,inducinghomeownerstoborrowagainstaccumulatedequity,thedefault rate during 2006-2008 might have been 35% lower. This differs from the counterfactual experiment that motivates the present study, in which house price growth is left unaltered but theborrowingopportunitiesofhomeownersarechanged. Earlier structural models that include homeowners’ mortgage choices and the option to default include Campbell and Cocco (2003), and Yao and Zhang (2008). More recently, Campbell and Cocco (2011) develop a model which focuses more on defaults but does not allow homeowners to refinance. An important difference between these papers and the present study is that I estimate my model using household-level data and am able to quantitatively match the cross-sectionalandtimeseriespatternsofdefaultfoundinthatdata. Thisprovidesmearealisticbaselinemodelfromwhichtoruncounter-factualpolicyexperiments. Li,LuiandYao(2008) also estimate a model of housing and mortgage choices using household data from the PSID, butintheirmodel,homeownersneverhaveanincentivetodefault. A growing literature in macroeconomics studies the mortgage choices of homeowners in a 6

general equilibrium setting in which prices are determined endogenously. Papers that study the effects of default risk on interest rates include Jeske, Krueger and Mittman (2010), Guler (2008), and Corbae and Quintin (2010). Chatterjee and Eyigungor (2009) study the equilibrium effectsofdefaultonhousepricesandincludeananalysisoftheeffectsofforeclosureprevention policies on prices. Favilukis, Ludvigson, and Van Nieuwerburgh (2011) account for the boom and bust in U.S. aggregate house prices in a model where credit constraints on mortgages are relaxed and later re-tightened. The current paper does not attempt to solve for equilibrium interest rates. Also, while I do allow the overall level of house prices to adjust in response to policy changes, I the rate at which prices grow each period. This allows me to include a more realisticmodeloftheincomeandhousepricerisksthatdriveequityextractionanddefault. The rest of the paper is organized as follows. In Section 2, I present a structural model of equity extraction and default. In Section 3, I describe my mortgage data set and the other sources of data on income and assets which I use to estimate the parameters of the model. I explain the estimation of this model in Section 4 and discuss the results of the estimation in Section 5. The policy experiments are described in Section 6. Finally, Section 7 concludes and discussespotentialimplicationsofmyfindingsforcurrentpolicydiscussions. 2 Model In this section, I describe a dynamic model of a homeowner who makes decisions about consumptionandsavings,isabletoadjusthismortgagebalance,andhastheoptionstopayoffhis mortgage and sell the house or to default on the mortgage. The key novel feature is the set of shocks that allow the model to match the data: a large discrete unemployment shock, changing expectations about future house prices, and a continuous preference shock that captures residualheterogeneityinthedefaultchoicesofunderwaterhomeowners. 2.1 Preferences Time in the model is discrete and households are infinitely lived. Each period, households consumehousingservices h andnon-housingconsumption c andreceiveutility t t (cαh (1−α) )(1−γ) u(c ,h ) = t t . t t 1−γ In addition to the quantity of housing and non-housing consumption, households have timevarying preferences each period over whether to remain in their current house or to move to a differenthouse. Idenotetheutilityderivedeachperiodfromthedecisionoverwhethertostay Ω ormoveby withthedetailstobedescribedbelow. t 7

Preferences are time-separable with discount factor β so that at time t , households have 0 preferencesover ∞ E ∑ β (t−t 0 )(u(c ,h )+Ω ) t t t t 0 t=t 0 2.2 Income HouseholdshaveriskylaborincomeY thatfollowsaprocess t Y = Pε P = P ν t t t t t−1 t where P is the permanent component of income subject to shocks ν with logν ∼ N(µ ,σ2) t t t ν ν and ε are transitory shocks. The transitory shock has two components, a discrete component t e corresponding to whether the household is unemployed for the period, and a continuous t componentε0 thatcapturesallothertransitoryvariationinhouseholdincome. Anunemployed t householdlosesafraction (1−δ)ofitspermanentincome,so e = δ whenthethehouseholdis t unemployed and e = 1 otherwise. Employment follows a Markov process with constant trant sition probabilities into and out of unemployment given by π e→u and π u→e respectively. The continuous component ε0 is i.i.d. and has a distribution logε0 ∼ N(0,σ2). The total transitory t t ε shockistheproductofthetwocomponents: ε = e ·ε0. t t t The discrete unemployment shock in the income process is not standard in this literature.7 I introduce it for two reasons. First, a large and persistent income shock is likely an important factor in a household’s default decision. Second, the observed measure of income shocks present in the data is an estimate of the local unemployment rate. When I simulate the model, I draw realizations of this unemployment shock in a way that is consistent with the patterns of unemploymentfoundinthedata.8 2.3 Assets Households hold three kinds of assets, a one-period bond, their house, and a mortgage. The bond a earnsarisk-freesavingsrate rs andmustbeheldinpositivequantity. t 7ThedisastrouslaborincomeshockconsideredbyCocco,GomesandMaenhout(2005)andothersissimilarin spirit 8Note that my treatment of unemployment assumes that household income is derived from a single wage earner, andabstractsawayfromthepossibilityofmultipleearnersornon-laborincome. However, Idocalibrate theincomeprocesstomatchmomentsoftotalhouseholdincomesototheextentthatthisassumptionaboutunemploymenthascounterfactualimplicationsfortotalhouseholdincome, thecalibratedprocessfortheothershocks ν andε0willadjusttocompensate. t t 8

2.3.1 Housing The household must hold an amount of the housing asset equal to the amount of housing services consumed that period, so both are identified with the quantity h . The price per unit of t housing is p so the value of the house is H = h p . There is maintenance cost each period t t t t proportional to the value of the house, χH . Households may sell their house and purchase a t house of different size h (cid:54)= h , also priced at p , by paying a fixed cost θ P and a transaction t+1 t t 0 t cost proportional to the value of the house being sold, θ H . Finally, a household that moves to 1 t adifferenthouseincursautilitypenaltyequalto Θ = θ P 1−γ p (1−α)(γ−1) u u t t The proportionality factor which multiplies θ maintains the size of this penalty relative to u changesinincomeandpricelevels.9 AsIdonotmodelthedecisionofthehouseholdtobecome an owner, I also assume that it does not consider the option of selling the house to become a renter. Innovations to house prices have three components, two of which are common within the household’sgeographicregion,indexedbyj,andonethatthatisidiosyncratictothehousehold. First, there is a persistent regional component µ , which can take one of two values, µ ∈ jt jt {µ 1 ,µ 2 } and follows a Markov process with transition matrix Π µ,µ(cid:48). Without loss of generality, I assume that µ > µ so that µ represents the high-price-growth state. Second, there is an 2 1 2 i.i.d. component to regional house prices η ∼ N(0,σ2). Finally, the is an i.i.d. idiosyncratic jt η component ζ ∼ N(0,σ2) so that the total time-t price appreciation of house i in region j is it ζ givenby: ∆ p = µ +η +ζ . ijt jt jt it Theexpectedpricegrowthinthesubsequentperiod, E ∆ p = E(µ |µ ), t ij,t+1 j,t+1 jt isnotconstantovertime,butdependsonthecurrentvalueof µ . jt Iassumethathouseholdsdonotobservethetruestate µ ,butrathertheyobserveahistory jt ofregionalhouseprices{µ jt(cid:48) +η jt(cid:48) }t t(cid:48)=−∞ andsolveafilteringproblemtodeterminetheprobability distribution f (µ) over the two states {µ ,µ } in each period.10 This distribution, which jt 1 2 can be summarized by f (µ ), the probability that region j is in the high-appreciation state at jt 2 time t,becomesastatevariableinthehouseholdproblem.11 9Specifically,ithasconstantmagnituderelativetotheutilitythehouseholdcanachievebyspendingitscurrent permanentincomeonanoptimalbundleofhousingandnon-housingconsumption. 10Thisfilteringproblemisdescribedinanappendix. SeeKimandNelson(1999)foramorein-depthdiscussion. 11Indecidingwhethertomovetoadifferentsizehouse,homeownersonlyconsiderotherhousesthatarealso 9

2.3.2 Mortgages Thehouseholdholdsamortgageofsize M onwhichitmakesinterestpaymentsrmM butdoes t t not pay down the principal.12 Homeowners may change the size of their mortgage, subject to tworestrictionsonthenewmortgage. Thefirstrestrictionisthatthenewtotalmortgagebalance maynotexceedafractionφ ofthecurrenthousevalue. ThislimitontheLTVratiomaydepend jt on current beliefs about future house prices, so that lending standards are looser if prices are expected to rise, i.e. φ = φ(f (µ )), where the function φ(·) is increasing. There is no periodjt jt 2 by period borrowing constraint so the LTV ratio, M /H , may become arbitrarily high if house t t prices decline. The second restriction is that mortgage payments may not exceed a fraction ψ i ofpermanentincome,rmM < ψ P,wherei ∈ {P,R} dependingonwhetherthemortgageis t+1 i t foranewpurchase(P)ortorefinancethemortgageonthecurrenthome(R). Therearetwocostsassociatedwithrefinancingamortgage,afixedcost,whichisfractionk 0 of permanent income, and a fraction k of the the total size of the new mortgage. Although the 1 interest rate on all allowed mortgages is the same, households wishing to borrow an amount greater than m of the house value pay an additional one-time cost k M . This additional 2 t+1 cost captures actual costs such as mortgage insurance, as well as higher interest rates paid by borrowerstakingoutriskiermortgages.13 Thereisnocostassociatedwithpayingoffthecurrent mortgageandnottakingoutanewone. Thusthetotalcostofchoosinganewmortgage M (cid:54)= t+1 M with M > 0is K(M ) = k P +(k +k ·1(M > mH ))M . t t+1 t+1 0 t 1 2 t+1 t t+1 When the house is sold, the balance of the mortgage is repaid from the proceeds of the sale. If M > (1− θ )p h , then the funds generated by the sale are insufficient to repay the t 1 t t mortgagedebt. Inthedata,Idoseesalesoccurringforhousesthatappeartobeworthlessthan the outstanding mortgage balance. To capture this feature of the data, I allow homeowners to repay the balance of the mortgage in excess of (1−θ )p h out of savings. However, to do 1 t t so, they incur a cost κ ·(M −(1−θ )p h ), which is proportional to the amount of mortgage t 1 t t debt being repaid from sources other than sale of the home. If κ = 0, then homeowners freely availableatprice p ,thepriceoftheircurrenthouse. Thisrestrictsthemfromchoosingamonghousesindifferent t regions with different prices, which would be a significantly harder problem to solve. (See Van Nieuwerburg and Weill (2010) for an example of agents solving such a problem.) Further, this assumption requires that the idiosyncraticshockζ issharedbytheowner’scurrenthouseaswellastheladderofotherhousesthattheowner it hastheoptionofbuying.Therefore,theidiosyncraticshockshouldbeinterpretedasaffectingalocalneighborhood withintheregion,withalltheotherhousesavailabletotheownerlocatedwithinthatsameneighborhood. 12Principal payments would depend on the age of the mortgage, which is not a state variable in this model. Also,omittingprincipalpaymentsisareasonableassumptionfortworeasons. First,thesampleperiodextendsa maximumofonlysevenyearspastthepurchasedateandtheamountofprincipalrepaidduringtheinitialyearsof amortgageissmall. Second,duringaperiodofsuchlargehousepricemovements,itisthefluctuationsinhouse priceratherthanprincipalpaymentsthatareimportantindeterminingtheamountofequityinthehouse. While I assume that all households face the same interest rate, I do use household specific interest rates in assigning startingvaluesofincomeandassetsinthemodelsimulations. 13By introducing this cost as a a one-time up-front fee, analogous to “points” in the real mortgage industry, I avoidhavingtokeeptrackofinterestratesasanadditionalstatevariable. 10

pay off excess mortgage debt from their liquid assets. As κ → ∞ , households are unable (or unwilling) to use funds from other sources in order to pay off the mortgage. In reality, there is little evidence that homeowners contribute other funds towards the repayment of a mortgage balance that is not covered by the sale price of the house. Rather, a finite value of κ likely describesthewillingnessofbankstoengageinshortsalesandtoreleasethelienandacceptthe sale price as repayment even if it falls short of the outstanding debt. However, I do not model suchshortsalesexplicitly.14 2.4 Default Mortgage default is modeled in a way to capture the fact that loans in California are nonrecourse. Homeowners defaulting on their mortgages remain in their houses for the current period but do not have to make mortgage or maintenance payments. At the end of the period, they pay moving costs θ P (but not the transaction cost θ H ) and retain any remaining liquid 0 t 1 t Θ assets a . They incur the non-monetary moving cost and permanently enter a frictionless t+1 u rental market in which housing services are available at price ρp . A household that cannot aft forditsmortgageandmaintenancepaymentsanddoesnothavefeasibleoptionsamongchanging its mortgage position or house size is forced to default. A household that does have other feasibleoptionsmaystillchoosetodefaultasanoptimaldecision. 2.5 Preference Shocks Every period, the household receives a preference shock of strength ω that controls its prefert ence for remaining in the current house. If the household leaves its house during this period, eitherbysellingordefaulting,itreceivesadditionalutility Ω = ω P 1−γ p (1−α)(γ−1) . t t t t With probability λ, the “strength” of the preference shock ω is non-zero and follows an i.i.d. t distribution ω ∼ N(µ ,σ2). With probability (1− λ), there is no shock and ω = 0. The t ω ω t Ω proportionality factor between the strength of the shock ω and the total utility is the same t t Θ oneusedfor ,thedis-utilityofmoving. u This preference shock generalizes the “moving shock” that Cocco (2005) and others have introducedinordertomatchtherateatwhichhomeownersselltheirhomes. Inthelimit µ → ω ∞ ,homeownersalwaysmoveinresponsetothisshockanditbecomesequivalenttothemoving shock of previous models. Allowing this shock to arrive with different strengths provides a range of realizations for which homeowners whose mortgage balances far exceed their house 14SeeClauretieandDaneshvary(2011)foranempiricaldiscussionofthevalueofshortsalerelativetodefault. 11

values will default but those with mortgages only slightly above their hose house values will remain in their homes. This allows me to better match the increasing rate of default among homeownerswithhigheramountsofnegativeequity. 2.6 Household Problem The problem faced by the homeowner each period can be written recursively. The solution to thisproblemisgivenbyavaluefunction V(P,a˜,h,e,p,M, Ω , f) where P ispermanentincome, a˜ = a+Pε iscash-onhand, h isthesizeofthehouse, e indicates ifthehomeownerisemployed,thepriceofhousingisgivenby p sothatthevalueofthehouse is H = ph, M is the mortgage balance, Ω is the current realization of the preference shock and f = f(µ ) is the filtered probability of being in the high-price-growth state. The household 2 then has a choice over the following four options with regard to housing and mortgages, each with an associated value function. In each option, the household also chooses non-housing consumption c.15 1. Continuetopaythemortgage V0(P,a˜,h,e,p,M, Ω , f) = maxu(c,h)+βEV(P (cid:48) ,a˜ (cid:48) ,h,e (cid:48) ,p (cid:48) ,M, Ω(cid:48) , f (cid:48)) c a (cid:48) = (1+rs)·(a˜−χph−rmM−c), a (cid:48) ≥ 0 2. Refinance into a new mortgage of size M (cid:48) (cid:54)= M. The amount of equity extracted is equal to (M (cid:48) − M) VR(P,a˜,h,e,p,M, Ω , f) = maxu(c,h)+βEV(P (cid:48) ,a˜ (cid:48) ,e (cid:48) ,h,p (cid:48) ,M (cid:48) , Ω(cid:48) , f (cid:48)) c,M(cid:48) a (cid:48) = (1+rs)·(a˜+(M (cid:48)−M)−rmM−χph−K(M (cid:48))−c), a (cid:48) ≥ 0, M (cid:48) < φ(f)ph, rmM < ψ P t+1 R (cid:48) (cid:48) 3. Sellthehouseandpurchaseanewhouseofsize h withanewmortgage M VS(P,a˜,h,e,p,M, Ω , f) = max u(c,h)+Ω−Θ +βEV(P (cid:48) ,a˜ (cid:48) ,e (cid:48) ,h (cid:48) ,p (cid:48) ,M (cid:48) , Ω(cid:48) , f (cid:48)) u c,h(cid:48),M(cid:48) a (cid:48) = (1+rs)·(a˜+(1−θ −χ)ph−θ P−(1+rm)M− ph (cid:48) + M (cid:48) 1 0 −κ(M−(1−θ )ph)·1((1−θ )ph < M)−c) 1 1 15Following the standard convention, unprimed variables refer to the current period and primed variables to thefollowingperiod. 12

a (cid:48) ≥ 0, M (cid:48) < φ(f)ph (cid:48) , rmM < ψ P t+1 P 4. Default VD(P,a˜,h,e,p,M, Ω , f) = maxu(c,h)+Ω−Θ +βEVrent(P (cid:48) ,a˜ (cid:48) ,e (cid:48) ,p (cid:48)) u c a (cid:48) = (1+rs)·(a˜−c−θ P), a (cid:48) ≥ 0, 0 where Vrent solvestherenter’sproblem,definedbelow. Expectationsaretakenoverthepossiblerealizationsofthepermanentandtransitoryincome shocks, the unemployment shock, the regional and idiosyncratic house price shocks and the preferenceshock.16 Thevaluefunctionisthemaximumvalueofthesefourchoices V(P,a˜,h,e,p,M, Ω , f) = max(V0(·),VR(·),VS(·),VD(·)). Afterdefault,rentersmakedecisionsoverthehousingandnon-housingconsumption. Renters arenotresponsibleformaintenancecostsandcancostlesslyadjusttheirhousingconsumption. Therenter’sproblemcanbewritten Vrent(P,a˜,e,p) = maxu(c,h)+βEVrent(P (cid:48) ,a˜ (cid:48) ,e (cid:48) ,p (cid:48)) c,h a (cid:48) = (1+rs)·(a˜−c−ρph), a (cid:48) ≥ 0. 2.7 Model Solution Themodelhasbeenconstructedsothatitispossibletoreducethedimensionofthestatespace by rewriting the problem in terms of variables that are normalized by permanent income: aˆ = a˜/P,Hˆ = H/P,and mˆ = M/H.17 Inthisformulation,neitherthelevelofpermanentincome P, nor the level of housing prices p enters the household problem explicitly, greatly reducing the size of the state space and the computational burden of solving the model. Details are shown inanappendix. Once the problem has been expressed in these normalized variables, I discretize the state space and the control space and then solve the household problem using value function iteration. At values in between these discrete points, I approximate the value function using linear interpolation. 16Although the household does not directly care about the decomposition of the house price shock into its regionalandidiosyncraticcomponents,onlythetheobservedrealizationoftheregionalcomponentaffectstheupdatingof f(µ ). Seetheappendixfordetails. 2 17This construction is similar to Yao and Zhang (2005), who normalize the state variables by the household’s totalwealth. 13

3 Data In this section, I describe the sources of data that I use to estimate the parameters of the model presentedabove. 3.1 Liens Data The main data set used in this analysis is a series of quarterly “open lien searches” conducted by CoreLogic on all single family residences in Los Angeles County, California from 2000 to 2009.18 Thesesearchesidentifyalloutstandingmortgagescurrentlyopenagainsteachproperty. As described in the introduction, the novel feature of this data set is that the unit of analysis is the property rather than the mortgage. Because it is possible to link together all the mortgages taken out against each property, I can compute the total mortgage balance and measure equity extraction. At the start of 2000, the data contains 1.2 million properties. As new residences are built, the number rises, reaching 1.3 million by the end of the sample. Each property is identified by unique numerical identifier as well as the postal address, which I use to identify the 2000 census tract and other geographical information. For each quarterly observation, the data include information about the most recent sale, including the date, the purchase price, a calculation of the combined LTV ratio at purchase, and whether it was a foreclosure sale. Including multiple ownersofthesameproperty,thedatacontains1.9milliondistinctownershipepisodes. 3.1.1 Mortgages In each quarter, the data includes information on up to four mortgages held against the property. For each mortgage, the data identifies the date and original amount of the loan, the maturity date, whether it was a purchase, refinance or junior mortgage, and the type of mortgage(conventional,FHA,VAetc.) Thereisadditionalinformationonjuniormortgagessuchas whetheritisasecondorrevolvingmortgage. Formostmortgages,thedataalsoincludestheinterest rate and whether that rate is fixed or adjustable.19 A subset of adjustable rate mortgages, 18LosAngelesCountyisthemostpopulouscountyinthecountrywithapopulationofover9.8millionaccording tothe2010census. Ofthe88incorporatedcities,thelargestareLosAngeles,LongBeach,Glendale,SantaClarita andPomona. ThehousingmarketinLosAngelesisnotnationallyrepresentative. Mostnotably, cyclesofhouse pricesaremorepronounced. TheCoreLogichousepriceindexforsinglefamilyhomesintheLosAngelesmetro area climbed 183% from January 2000 through its peak in September 2006 and then declined 34% by December 2009. Thesameindexforthenationasawholeroseonly100%withasubsequentdeclineof28%. 19Forhousespurchasedafterthestartofthesamplein2000,theinterestrateonthepurchasemortgageispresent in71%oftheobservations,andtheinterestratetypein59%ofcases.Becausethelikelihoodthatthisinformationis missingdoesdependonthetypeofmortgage,itisnotpossibletoreachconclusionsabouttheoveralldistribution. SeeKoijen,vanHemert,andVanNieuwerburgh(2009)forananalysisofthevariationinmortgagetypeovertime. Ingeneral,Californiahasamuchlargershareofadjustableratemortgagesthantherestofthecountry. 14

mostly from the end of the sample, also includes detailed information on the the contractual detailsgoverningrateadjustments. There is no information about FICO scores or whether the loan is prime or sub-prime, but for many mortgages, there is an indicator of whether the mortgage lender is identified as a lender specializing in sub-prime mortgages. Gerardi et al. (2007) show that this measure is highly correlated with whether the loan itself can be categorized as sub-prime. Of the houses purchased after the start of the sample period, this indicator is present for 79% of purchase mortgages in the sample, with 22% of those mortgages classified as sub-prime. As shown in Table 1, the fraction of homes purchased with mortgages from sub-prime lenders grows from 14%in2001to28%in2004-2005anddropsoffdramaticallyafter2006. Although the data does not include payment history, CoreLogic calculates the outstanding balanceoneachmortgageeachquarterusingaproprietaryalgorithm. Thisallowsidentification ofwhichrefinancesinvolvetheextractionofequity. Figure5showsthenumberandtypeofnew mortgagestakenouteachquarter,dividingthesemortgagesintocash-outrefinances,non-cashout refinances and junior mortgages. The rate at which new mortgages are taken out grows by a factor of five from 2000 to 2003, driven largely by cash-out refinances, and by a surge of non-cash-out refinances as interest rates reached historically low levels in 2003. From 2004 to 2007, approximately one in 12 homeowners took out an additional mortgage or withdrew cash through refinancing each quarter. The rate of cash-out refinancing falls as housing prices begin to decline in 2007, reaching a low point at the height of the financial crisis in 2008 before reboundingslightlyin2009. 3.1.2 Default Thedatadoesnotincludeinformationaboutwhetheraborrowerhasbecomedelinquent. However, if the bank files a notice of default, which it must do to begin the foreclosure process, or a notice of trustee sale, indicating that it has set a date to sell the property, the types and dates of such filings are recorded in the data. The first filing of either of these notices is my measure of mortgage default. Although the notice of default can be filed up to one year after the borrower becomesdelinquent,commonpracticeinCaliforniaistoissuesuchanoticewhenthemortgage becomes90daysdelinquent. InFigure1,Iplotthetotalnumberofhomeownersdefaultingontheirmortgageseachquarter, broken down by the year of purchase. The default rate starts rising dramatically in 2006 whenlocalhousepricesstoprisingandbegintofall. By2009,over12,000borrowers(morethan 1%ofallhomeowners)aredefaultingeachquarter. Thoughtheseborrowersaredisproportionately owners who purchased after 2003, a significant and increasing number of defaulters are drawn from earlier cohorts of purchasers. As I described in the introduction, only for these earlier homeowners did equity extraction play an important role in determining whether they 15

laterdefaulted. In Figure 6, I show the fraction of each cohort of buyers who are observed to sell or default by the end of the sample. Of the buyers who purchase in 2006, 40% have already defaulted by the end of 2009. The default rate is far lower for earlier cohorts, with only 7-8% of buyers from 2000-2002havingdefaultedbytheendofthesampleperiod. 3.1.3 HousePricesandLoan-to-ValueRatios The borrower’s combined LTV (cLTV) ratio is a key state variable in the model. The cLTV ratio at the time of purchase is included in the data. Table 1 shows that the mean cLTV ratio at purchase is 0.86-0.87 for most of the sample, rises to 0.88 in 2005 and then jumps to .90 in 2006 before falling down to 0.85 in 2007. The median cLTV ratio shows a similar behavior. A morestrikingpatterncanbeseenbylookingatthefractionofpurchaseseachquarterthatwere financed with mortgages with a cLTV ratio greater than or equal to 1.0. I plot this measure in Figure 7. The fraction rises from 10% to over 50% in the last quarter of 2006 and then declines precipitouslytolessthan2%bythemiddleof2008.20 In subsequent periods, computing the LTV ratio21 requires first having an estimate of the current house value. To estimate the house value in each period, I first compute a local zipcode-level house price index. I then construct an estimate of the value of each house each quarterbystartingwiththeobservedpurchasepriceandassumingthattherateofappreciation each quarter is equal to the growth in the local price index. By combining this value estimate with the total outstanding mortgage balance, I can construct an estimate of the LTV ratio for eachobservation.22 To calculate the house price index, I use the purchase information in the liens data to identify properties for which I observe multiple sales. I use these sales to construct a zip-code level repeat-sales housing price index, following the modification of Deng, Quigley and Van Order (2000) to the original algorithm of Case and Shiller. I perform kernel-weighted local polynomial smoothing across time on the resulting quarterly price estimates. Properties in the data arespreadover302zipcodes,andthereareasufficientnumberoftransactionstogeneratereasonable house price series for approximately 250 of these zip-codes for the period 1986-2009. Thoughthereissubstantialvariationinthesizeofthepricefluctuations,mostzip-codesexhibit 20Mian and Sufi (2009) argue that this expansion of credit in the early 2000’s was an important factor in the housing boom and Favilukis et al. (2011, 2013) further argue that the tightening of lending standards in 2006 contributedsignificantlytothesubsequentfallinpricesaswell. 21Becausethemodelabstractsfromtheissueofhowthetotalmortgagedebtisdividedbetweenindividualloans, Iuse“LTVratio”and“cLTVratio”interchangeablyintherestofthepaper. 22Thisratiocanbeconstructedfromthepurchaseprice,thelocalhousepriceindex,andtheoutstandingmortgagebalance. Becauseitisobservablefromthedata,IrefertothisestimateoftheLTVratioasthethe“observed” LTV ratio and this is the ratio used in all the moment calculations. However, the true LTV ratio, which also includestheidiosyncraticcomponentofthehousepriceobservableonlytothehousehold,istheonethatwillenter thehousehold’soptimizationproblem. 16

similar trends, a peak in house prices around 1990, followed by a moderate decline and then a rapid appreciation starting around 2000. Prices peak in 2006 before declining dramatically and thenappear tolevel offor evenslightly recoverin thefinal quartersof 2009. Averageprice increases from 2000 to 2006 were approximately 150% followed by a decline of almost 50%. A sampleofhousepriceindicesforseveralzip-codesisshowninFigure8. 3.1.4 EstimationSample I focus the analysis on earlier cohorts for whom equity extraction was an important factor in determiningiftheyultimatelydefaulted. Formyestimation,Iselecthousespurchasedin2002- 2004. Iexcludeownerswhohavepurchasedtheirhousethroughaforeclosuresale,housesthat arenotowner-occupied,andthosewithmissingoroutlyingvaluesofanyvariablesusedinthe analysis. I further exclude homeowners with government loans insured by the Federal Housing Administration or guaranteed by the Veterans’ Administration, mortgages with terms less than 15 year or greater than 40 years, those houses in zip-codes with fewer than 1000 observed repeated house sales, and houses that do not appear in the data in the quarter in which they were purchased. Of the 100,000 houses meeting these criteria, I randomly select 20% to keep the computations manageable. I include observations from the time of purchase through the secondquarterof2009. The resulting sample contains 20,531 homeowners across 1,691 census tracts and 230 zipcodes. Themedianpurchasepriceis$375,000withameanof$462,000andastandarddeviation of $341,000. Twenty-seven percent of the sample borrowed their purchase mortgages from a sub-prime lender. Fifty percent took out a second mortgage at the time of purchase and the combined LTV ratio at purchase has a mean of .875, a median of 0.9 and it is greater than or equaltounityfor26.2%ofpurchasers.23 The42.7%ofhomeownerswhopurchasedtheirhomes with a fixed-rate mortgage have an average interest rate of 6.2%, with a standard deviation of 0.5%. Homeowners with adjustable-rate mortgages have an average interest rate of 5.9% with a standard deviation of 1.1%. The average household in this sample takes out 2.5 new mortgages during the sample period. Of these, 10% are non-cash-out refinances, 45% are cashout refinances, 10% are home equity lines of credit and another 22% are classified as equity mortgages. By the end of the sample, 11% have defaulted and 27% have sold their homes withoutdefaulting. 3.2 American Community Survey ThoughIdonothaveobservationsofincomeshocksforindividualhouseholds,Icomputemeasures of local income shocks from the American Community Survey (ACS), an annual survey 23Itisstrictlygreaterthanoneforonly2.7%oftheseborrowers,lessthan1%ofthetotalsample. 17

conductedbytheU.S.CensusBureausince2001.24 Unemploymentratescanbecomputedfrom this data for each congressional district, broken down by race and age group.25 I use software purchasedfromGeolyticstoidentifythecongressionaldistrictofeachpropertyintheliensdata, which spans 17 districts. Within each congressional district, I compute a local unemployment rate as a weighted average of the age-race specific rates. For weights, I use the demographic distribution of homeowners in the property’s census tract from the 2000 census, also identified using the Geolytics software. When averaged across the sample, this rate begins below 5% in 2002-2003andreaches9.2%in2009duringtherecession. The ACS also reports median annual household income among homeowners for each congressionaldistrict. Iusegrowthinthisstatisticasanadditionalmeasureoflocalincomeshocks. Theaveragegrowthratefluctuatesbetweenthreeandfivepercentovermostofthisperiodbut becomesnegativeinthefinalyearofthesample. 3.3 Panel Study of Income Dynamics The mortgage data includes no information about income or assets. Instead, I impute starting income and asset values for these homeowners by using observations of new homeowners in the Panel Study of Income Dynamics (PSID). The PSID is a longitudinal household survey conducted by the University of Michigan that has followed approximately 5000 families since 1968. The survey has been conducted biannually since 1997 and each wave since 1999 contains self-reportedhousevalues,adetailedbreakdownofhouseholdincomeandassetholdings,and information about mortgages, including the principal balances, monthly payments, and interest rates. In particular, I am interested in the empirical relationship between assets and income and household characteristics present in my mortgage data set, such as initial LTV ratios and interestratetypesandspreads. I construct a sample of homeowners from the 1999-2007 waves who report having moved intotheircurrentresidenceswithinthe12monthsprecedingtheinterviewandhaveamortgage. For each household, I calculate two variables: the ratio of their after-tax household income to their mortgage payments and the total amount of liquid assets.26 The logarithm of the ratio of 24The related literature uses quarterly measures of county-level unemployment rates as its measure of local income shocks. Since my data is all within a single county, this approach would not provide any cross-sectional variation. 25Thenumberofindividualsemployed,unemployed,oroutofthelaborforceistabulatedforagebrackets16- 25,26-55 and 56-65 for each of the following race categories: white (not Hispanic), Hispanic, black, Asian, and other. 26Themeasureoftotalincomeincludeswageincomeoftheheadandspouse(ifpresent),pensions,unemploymentbenefits,andsocialsecurityincome. TaxliabilitieswerecalculatedusingNBER’sTAXSIMsoftware. Liquid assetsaredefinedfromresponsestothefollowingthreequestions:”Doyou(oranyoneinyourfamilylivingthere) have any shares of stock in publicly held corporations, mutual funds, or investment trusts, including stocks in IRAs?”,”Doyou(oranyoneinyourfamilylivingthere)haveanymoneyincheckingorsavingsaccounts,money marketbonds,orTreasurybills,includingIRA’s?”,”Doyou(oranyoneinyourfamilylivingthere)haveanyother 18

income to mortgage payments is well approximated by a normal distribution with mean of 1.4 (an absolute value of 4.1) and a standard deviation of 0.6. The median value of liquid assets is is $5000 and the 75th percentile is $20,000. Ten percent of new homeowners report no liquid assets. I regress the logarithm of both variables on a set of covariates that can be computed from both the PSID and the liens data set: the combined LTV at purchase, whether there was a second mortgage at the time of purchase, a dummy for whether the purchase mortgage had an adjustable interest rate, a measure of the interest rate spread,27 and a dummy for whether the purchase occurred after 2005. Summary statistics for these covariates are shown in Table 2 and theresultsoftheseregressionsarepresentedinTable3. Theregressionoftheratioofincometo mortgage payments uses 782 observations. Home buyers with higher LTV ratios have higher mortgage payments relative to their incomes. The 12% of buyers who purchase their homes using more than one mortgage have payments that are 20% higher than those without a second mortgage, and those buying after 2005 have higher payments by 13%. None of the other coefficients are significant. For assets, I estimate a Tobit model on 706 households with leftcensoringat$1000. ThosewhopurchasehouseswithahighercombinedLTVhavesignificantly fewer assets, as do those paying higher interest rates. Each additional percent on the interest ratecorrespondstoadecreaseinassetsof38%forthosewithfixed-ratemortgagesand52%for borrowerswithadjustable-ratemortgages. ThePSIDalsocontainspaneldataonhouseholdincome,whichIusetocalibratetheincome processofthestructuralmodelpresentedabove. Iusethedatasetofafter-taxhouseholdincome constructed by Heathcote, Perri and Violante (2010), keeping only recent observations (after 1980) and only observations of homeowners, so as to better match my sample of post-2000 homeowners. This leaves me with 33,725 observations in which I can measure the growth of household income from one year to the next. I describe the calibration of the income process basedonthisdatawhenIdiscustheparameterizationofthemodelbelow. 3.4 Empirical Results Beforedescribingtheestimationofthefullstructuralmodel,Ifirstestimateanempiricalmodel of sales, equity extraction and default to study the dependence of these outcomes on observable household and local characteristics. I use the same estimation sample described above, dropping355observationswithoutlyingvaluesofsomevariablesusedintheestimation. Ifollow each house from purchase through the second quarter of 2009, creating a panel of 311,367 savings or assets, such as bond funds, cash value in a life insurance policy, a valuable collection for investment purposes,orrightsinatrustorestatethatyouhaven’talreadytoldusabout?” 27Forfixedratemortgages,thespreadisoverthemonthlyaveragecommitmentrateon30-yearfixed-ratemortgagesfromFreddieMac’sPrimaryMortgageMarketSurvey. Foradjustableratemortgages,thespreadisoverthe 6-monthLIBOR. 19

household-quarter observations of 20,176 distinct households. As I follow my estimation sampleacrosstime,Iobserveregionalincomeshocks. Mymeasureoftheunemploymentrateaverages5.7%withastandarddeviationof1.7%. Annualchangesinmedianincomelevelsaverage 4.0% with a standard deviation of 6.6%. Local house prices are recorded at the zip-code level. The sample spans 230 zip codes. One year house price appreciation averages 6.4% with a large standarddeviation(17.0%)thatcapturesatremendouspriceincreasethrough2006followedby asteepdecline. Ineachquarter,Iconsiderfourpossibleoutcomes, 1. The owner chooses to extract equity, either through a cash-out refinance or an additional juniormortgage. 2. Theownersellsthehouseandpaysoffthemortgage. 3. Theownerdefaultsonthemortgage,whichIseeinthedatawhenthebankissuesanotice ofdefault. 4. The owner makes none of the above choices, either continuing to pay all mortgages or refinancingwithoutwithdrawingequity. I estimate a multinomial logistic regression with these four possible choices, with the last option, continuing to make payments, as the reference category. The estimation includes a set of fixed effects for the year of observation interacted with the year of purchase. Table 4 gives definitions and summary statistics for the variables used in the regression. Results are shown inTable5. High cumulative loan-to-value ratios at purchase, high interest rates, having an adjustable rate mortgage, and borrowing from lenders specializing in sub-prime mortgages are all associated with a greater propensity both to extract equity and to default. Comparisons to other data sets, such as the PSID, that include both mortgage information and other asset holdings suggest that high LTV ratios and high interest rates at purchase are both associated with low holdings of liquid assets. Households with LTV ratios above unity are more likely to default andthisriskincreasessomewhatwithhigherLTVratios. AstheLTVratiosincreasesaboveone, households are also less likely to extract equity as there is no longer any equity to withdraw. High price growth leads to greater equity extraction, while negative house price appreciation is associated with higher default rates. Higher local unemployment rates are also associated with a greater likelihood of defaulting. Turning to local demographics from the 2000 census, I find that in locations with more educated populations, homeowners are somewhat more likely to take advantage of opportunities to extract equity and also somewhat less likely to default. Thesefindingsareconsistentwithalargebodyofpreviouswork. With regard to selling one’s house, I find that households in areas with more homeowners under age 35 are more likely to sell, as are home buyers who purchase their homes with an 20

adjustableratemortgage,ahigh-LTVmortgage,oramortgagewithahigherinterestrate. These latter measures are probably also indicative of younger owners with lower accumulations of liquid savings. Positive house price growth also increases the probability of sale as it give homeownersthepositiveequitytheyneedtobeabletosell. I next attempt to match the moments from this estimation using the full structural model presentedabove. 4 Model Estimation I estimate the key parameters of the model using the simulated method of moments. Several parameters, however, such as the processes for household income and house prices, rely on otherdataandareestimatedseparately. Aperiodinthemodelcorrespondstoonequarter. Allquantitiesinthemodelarenominal. 4.1 Income The income process has three components: the permanent shock, the discrete unemployment state,andthecontinuoustransitoryshock. Icalibrateeachoftheseoutsidetheestimation. The probability that an employed worker will become unemployed, π e→u is an important parameter in matching the default rate and I estimate it jointly with the other parameters of the model, as described below. Conditional on its value, I fix the transition rate out of unemployment π u→e to achieve a steady state level of unemployment consistent with the data. The average unemployment rate in my sample is 6.2%. However, this rate combines both homeowners and non-homeowners, while I am interested only in the rate among homeowners. In order to estimate the difference in unemployment rate by homeownership status, I use PSID data to estimate a logistic regression of the unemployment status of the head of household on homeownership status, also including dummies for race and a quartic polynomial in the age of the head. I estimate an odds ratio of 0.31 for homeownership, meaning that controlling for age and race, a homeowner is only 31% as likely as a renter to be unemployed. Assuming the total population contains 63% homeowners, which is the average census-tract-level homeownershiprateinmysamplefromthe2000census,thisimpliesthattheunemploymentrateamong homeowners is 55% of the overall rate. Therefore I target a steady-state unemployment rate of 0.55×6.2% = 3.4%. I estimate a value π e→u = 0.020, which implies a job finding probability π u→e =0.60, implying a median unemployment spell of just under one quarter. The average wagereplacementrateinCaliforniais50%soIsetthereplacementrate δ = .5. Following Heathcote, Perri and Violante (2010), I calibrate the remaining parameters of the incomeprocesstomatchthemean,thevarianceandtheone-periodauto-covarianceoftheoneyear growth in household after-tax log income, using only recent observations of homeowners 21

intheirdata.28 Givenmyestimatesfortheunemploymentprocess,theresultingparametersare µ = .008,σ = .096forthepermanentshockand σ = .233forthetransitoryone. ν ν ε 4.2 House Prices Toestimatetheparametersofthehouse-priceprocess,Iusepropertiesfromtheliensdatawith multiplerecordedsalesafter1986toconstructquarterly,zip-code-levelrepeat-saleshouseprice indices using the algorithm from Deng, Quigley and Van Order (2000). The long-run growth rate of housing prices is poorly identified from this window, which contains approximately twofullcyclesofpricegrowthanddecline. WhenIestimatethemodelofregionalhouseprices using these zip-code-level indices, I impose the additional constraint that the annual nominal longrungrowthrateinhousepricesequal4%. Iestimatemeanappreciationinthetworegimes to be µ = −.018,µ = 0.038 with transition probabilities Π = .092, Π = .046 and a 1 2 1,2 2,1 standard deviation of the regional i.i.d. house shock σ = .02. This means that during a boom, η homeowners expect prices to grow at 3.8% quarterly and for this appreciation to continue on average for 22 quarters. In periods of declining house prices, average declines are 1.8% per quarterandlastfor11quartersonaverage. Inadditiontochangesinregionalhouseprices,householdsfacequarterlyidiosyncraticprice shocks ζ ∼ N(0,σ2). Consider a house i in region j that sells in period τ at price p and then it ζ iτ (cid:48) again in period τ at price p iτ(cid:48). If the zip-code level house prices indices at the times of the two salesare p jτ and p jτ(cid:48),thentheidiosyncraticportionofthechangeinprices τ(cid:48) ∑ (p iτ(cid:48) − p iτ )−(p jτ(cid:48) − p jτ ) = ζ it τ+1 isdistributed N(0,(τ (cid:48) −τ)σ2) andIcanidentify σ2 asthesamplevarianceof ζ ζ (p iτ(cid:48) − p iτ )−(p jτ(cid:48) − p jτ ) . (τ(cid:48) −τ) Dependingonhow Ichoosethethe sampleofrepeatsales forthisestimation,I get valuesof σ ζ between.015and.019. Ichoosethemiddleofthisrange, σ = .017. ζ In the data, I observe a correlation of 0.17 between the growth rates of median income and the zip-code-level house price index. However, there is also a significant amount of additional idiosyncratic variation in both income and house price growth for individual households. Usingthecalibratedparametersofmyincomeandhousepriceprocesses,Iestimatethatthecorre- 28Afterdroppingthehighestandlowest2%ofincomechanges,Icalculateameanof0.0313,astandarddeviation of0.2504andaone-periodauto-covarianceof-0.012. 22

lationbetweenhousepricesandpermanentincomeforanindividualhomeownerisonly0.03.29 ThisisthevalueIuseinthemodel. 4.3 Other Parameters I fix the quarterly return on savings at r = .01 and the mortgage interest rate at r = .0155, s m the average interest rate in my sample. Quarterly maintenance costs are fixed at a fraction χ = .003 of the house price, consistent with spending on alterations and repairs reported by respondents in the American Housing Survey.30 During the boom, it was common to take out a mortgage equal to 100% of one’s house value so I set the limit on LTV ratios for new mortgages during periods of positive expected price growth to φ(f(µ ) = 1) = 1.0. After the 2 crash,lendingstandardstightenedandIusean80%limitforperiodsofnegativeexpectedprice growth, φ(f(µ ) = 0) = 0.8. At intermediate values, I assume the limit is piecewise linear and 2 include the value of φ(f(µ ) = 0.5) in the list of estimated parameters. Finally, I impose the 2 additionalborrowingcostsforriskiermortgagesonmortgagesthatexceedathresholdfraction m = 0.8ofthevalueofthehome. ThisistheLTVratioabovewhichprivatemortgageinsurance istypicallyrequired. 4.4 Simulations This leaves 18 model parameters that are key for matching patterns of sales, equity extraction and default found in the data: the three preference parameters β,γ,α, borrowing limits ψ , ψ P R and φ(f(µ ) = 0.5), mortgage costs k ,k ,k ,κ, moving costs θ ,θ ,θ , the rent-price ratio for 2 0 1 2 0 1 u defaulters ρ, parameters of the preference shocks λ,µ ω ,σ ω and the rate of job loss π e→u . These parametersareestimatedusingthesimulatedmethodofmoments. Each of the 20,531 households in my estimation sample is simulated 25 times. Simulations begin at the time of purchase and end when the homeowner moves or defaults, or reaches the end of the sample period, which extends to second quarter of 2009. This creates a maximum sample period of 30 quarters. The probability that an employed homeowner loses his job is held constant at π u→e and I vary the probability with which an unemployed worker becomes employed to reproduce the current local unemployment rate.31 Shocks to permanent income are drawn from a normal distribution with a mean to match the period and region specific growthrateofmedianincome. The evolution of regional house prices follows the observed zip-code level house price indicescalculatedfromthedata. Foreachperiod,ineachzip-code,Iupdate f(µ )usingthesame 2 29YaoandZhang(2005)useacorrelationof0.2betweenhousepricegrowthandlaborincomegrowth. 30Cocco(2005)usesanannualmaintenancecostof1%. 31ThischoicefollowstheconclusionofShimer(2007)thatvariationintheunemploymentrateoverthebusiness cycleisdrivenmostlybyfluctuationsinthejobfindingrateratherthanthejobseparationrate. 23

filteringalgorithmattributedtoagentsinthemodel. InFigure9,Iplotthedistributionof f(µ ) 2 across zip-codes at different times. This graph shows that until mid-2005, all households expected prices to continue rising. By the end of the boom in mid-2006, approximately half of households still believed that the probability of continued price growth was greater than 50%. Themodelpredictsthatbythestartof2008,allhomeownersinthesamplewouldhavebelieved thatpriceswouldcontinuetofall. The continuous transitory income shocks and idiosyncratic house price shocks are drawn fromtheirunconditionaldistributions. I match a set of 190 observable moments motivated by the empirical analysis of the Section 3.4. These moments include the rates of new mortgage origination (excluding non-cash-out refinances), default and sale each quarter, plus the interaction of these rates with unemployment, median income growth, house price appreciation, LTV ratio at purchase and the current observed LTV ratio. I also target the rates of default and sale by LTV ratio, the LTV ratio of homeowners each period who do and do not default, the total number of households who sell and default, and the rate of equity extraction by purchase year and outcome. From the PSID data on new homeowners, I target the average value of mortgage payments as a fraction of incomeandthethe50thand75thpercentilesofthedistributionofliquidassets.32 Due to the computational demands of this estimation, I use a parallelized implementation oftheNelder-Meadsimplexalgorithm,asdescribedinLeeandWiswall(2007).33 4.4.1 InitialConditions Each simulated household begins with a level of permanent income and an endowment of liquid assets, already having decided to purchase a house and now optimizing over the size of that house and a starting mortgage balance. Equivalently, the household makes choices over the starting LTV ratio and the fraction of its income consumed by its mortgage payments. The procedure by which I assign these starting values for income and assets is designed to satisfy two objectives. First, the model makes predictions about the optimal choice of house size and mortgage balance for each starting value of income and assets. Starting values should be assigned so that, on average, household are making choices consistent with these predictions. Second, based on my analysis of new homeowners in the PSID, there is significant heterogeneityinassetsandincomeofhomeownersimmediatelyafterpurchase. Mostofthisheterogeneity cannotbeexplainedbasedonobservablecharacteristicsofthehousehold. However,analysisof 32AllcomparisonsofmomentsinvolvingtheLTVratiorefertothe“observed”LTVratio,wherethehousevalue is calculated from the purchase price and the evolution local house price index. For consistency, I calculate momentsfromthesimulationsusingthis“observed”LTVratio,eventhoughtheLTVratiothatentersthehousehold’s problemalsoincludestheidiosyncraticcomponentofthehouseprice. SeeKortewegandSorensen(2012)foran analysisthatfocusesontheroleofidiosyncratichousepriceshocksinstudyingforeclosureandtradebehavior. 33TheFortrancodeforthisalgorithmisavailableuponrequest. 24

thesenewhomeownersrevealsthattherearestatisticallysignificantcorrelationsbetweenstarting income and assets and some characteristics that are observable in the data. Most notably, homeownerswithhigherinterestratestendtobeginwithlowerassetholdingsbutdonothave larger mortgage payments relative to their income. (See Section 3.3.) These correlations should be reproduced in the simulations. The procedure by which I assign the initial conditions satisfies these two objectives. Details are described in an appendix. This procedure defines three additionalfreeparameters,whichIestimatejointlywiththeotherparametersofthemodel. The definitions and estimated values of these parameters are contained in the appendix. Finally, I assumethathomeownersareemployedatthetimeofpurchase. 5 Estimation Results 5.1 Parameter Estimates Parameter estimates are are shown in Table 6. I find a quarterly discount factor of 0.94. This low value is consistent with the fact that households only extract equity when they deplete their liquid assets and in the data, new equity-extracting mortgages are initiated every 10-12 quarters. Inthemodel,allspendingbeyondmortgageandmaintenancepaymentsisattributed to consumption and so the rapid rate at which assets are exhausted means that the desire for immediateconsumptionisveryhighandthediscountfactormustbelow.34 Theestimateofrisk aversion is γ = 1.52. The share of housing consumption in the utility function is (1−α) = .26, slightlyhigherthan,forexample,the19%shareof2005expendituresspentonshelteraccording to the Consumer Expenditure Survey, and consistent with the fact that housing costs in Los Angelesarehigherthanthenationalaverage. Theestimatedvaluesofmortgagecostsk andk 0 1 meanthatthecostofnewmortgagesis15%ofquarterlyincomeincome,whichisapproximately ten days worth of earnings, plus 1.2% of the value of the mortgage. This is slightly higher than actual initial mortgage fees, which averaged approximately 0.5% during this period according totheFederalHousingFinancingBoard’sMonthlyInterestRateSurvey. Homeowners wishing to take out loans with LTV greater than 0.8 must pay a fraction k = 2 .07oftheentirebalance. Thiscanbethoughtofasapproximatelyseventotenyearsofmortgage insurance payments, which are typically just under one percent of the total loan balance per year. New buyers are restricted from taking out mortgages whose payments are greater than ψ = 38% of their after-tax income. For the sake of comparison, guidelines for conforming p conventional loans call for mortgage payments not to exceed 28% of the borrower’s gross income. I estimate that there are no income limits on homeowners wishing to refinance, i.e. a 34GreenspanandKennedy(2007)documentthatinfactmostextractedequityisappliedtowardshomerenovationsandpayingdownnon-mortgagedebt. 25

value of ψ sufficiently large that it is a non-binding constraint. This estimate is necessary for r themodeltoreproducethehigherrateofequityextractionamongdefaulterscomparedtonondefaulters. Homeowners who ultimately defaulted tended to already have larger mortgages at the time of purchase, but this group of homeowners nevertheless extracted equity at a greater ratethanthosewhodidnotdefault. Thissuggeststhathouseholdswhoalreadyhadsignificant mortgageobligationswerecommittingincreasinglylargefractionsoftheirincometodebtpayments as prices climbed. Overall, the median household in my estimation sample increases its mortgage balance by 20% and a quarter of homeowners expand their debt by over 50%, rates that far exceed the growth of income during these years. The availability of mortgages with such high debt-to-income ratios is consistent with the popularity of “low-doc” and “no-doc” mortgagesduringthisperiod. The rent-price ratio that prevails in the post-default rental market is ρ = .17, which equals 0.68 in annual terms. This estimate captures not just the true cost of rental housing but all the costsassociatedwithdefaultincludingthedistasteforrenting,theimpactonthehomeowner’s credit score and any potential stigma. This value is approximately ten times the true rent-price ratio, indicating a high cost of default. If the true rent-price ratio is 6%, this default cost is equivalent to sacrificing 51% of future consumption. This high value reflects the low rate at which underwater homeowners default despite their strong financial incentive to do so. Even atLTVratiosabove1.5,thedefaultrateisstilllessthan4.5%perquarter. In the data, there is a considerable amount of default among homeowners with positive equity. Homeowners with an LTV ratio less than .75 default at a rate of 0.14% per quarter, which is more than half the total default rate during the early part of the sample. Even after accounting for the fact that these LTV ratios ignore the unobserved idiosyncratic component of house values,Iestimatelargemovingcoststoexplainwhythesehomeownersdefaultratherthansell. The estimated values are a fixed cost of θ = 3.3 times quarterly income and transaction costs 0 (θ )equalto20%ofthesaleprice. Withthesevalues,themodelsuccessfullyreproducesdefault 1 ratesatdifferentLTVratiosasshowninTable7. IhaveassumedthatthelimitonLTVratiosfornewmortgagesis1.0duringperiodsofpositiveexpectedpricegrowthand0.8whenpricesareexpectedtodecline. Basedontheamountof borrowing inthe data,I estimatethat at theintermediate value,when theprobability of aprice declineis0.5,theLTVlimitonnewloans, φ(f(µ ) = 0.5),isequalto0.9. 2 5.2 Comparing Data and Simulations The success of the model in matching aggregate rates of equity extraction, sales and default can be seen in Figure 10. The model successfully captures both the timing and quantity of new equity extractions, which rise dramatically starting in 2003 to a rate of approximately 10- 12% per quarter and then remain steady before dropping off rapidly in late 2006 after prices 26

have started to decline. It is matching this time series of equity withdrawal rates that requires the model to have a lower maximum LTV ratio when future price growth is expected to be negative. Withoutthisdecrease,themodelpredictsaspikeinequityextractioninlate2006that is not found in the data. This happens because when households begin to expect that future prices will be lower, they want to convert equity into liquid assets before it is erased by falling prices. This creates additional demand for mortgage debt. A tightening of the supply of credit by lenders in response to this same change in expectations is necessary to prevent this spike in borrowingandbringthemodelsimulationsintobetteragreementwiththedata. Next, I look at the rate at which homeowners sell their homes, shown in the upper-right panel of Figure 10. As house prices rise, homeowners accumulate positive equity and a greater proportion can afford to sell. When prices fall, more homeowners have negative equity and cannot. Inthedata,therateatwhichhomeownersselltheirhomesclimbsfrom1.0%perquarter at the beginning of the sample to 2.4% at the start of 2005. As prices decline, this rate falls to 0.4%. The model matches this pattern with the fraction of homeowners selling each quarter climbingfrom0.7%to2.2%andthenfallingto0.3%afterpricesfall. Model predictions for the default rate also match the data well. Default rates remain low at aratearound0.2%perquarteruntiltheybegintorisedramaticallywiththefallinhouseprices at the end of 2006. In the data, there is a dip in the default rate during the financial crisis of 2008. Thisdropisnot present inthesimulations. Apossibleexplanationforthisdiscrepancyis that I observe a default in the data only when the lender files a notice of default and begins the foreclosure process. Therefore a change in the rate at which banks foreclose will appear in the dataasachangeinthedefaultrate. Thesimulationsareconsistentwiththeriseindelinquency ratesduringthisperiodratherthanthefallinforeclosures. ThemodelalsocapturesthedefaultratesatdifferentLTVratios.35 WhentheestimatedLTV ratio is less than 0.75, quarterly default rates are 0.14% in the data and 0.09% in the model. Theobserveddefaultrateincreasesto0.75%astheLTVratioapproachesunityandthenjumps to 1.56% at ratios between 1.0 and 1.25. At higher levels of negative equity, the default rate continues to climb, reaching 4.2% per quarter at LTV ratios above 1.5. The model is consistent with this pattern, with default rates of 0.50% for homeowners with LTV ratios between 0.75 and1.0and1.83%atratiosbetween1.0and1.25. Theseareslightlyhigherthanthecomparable rates in the data. Then, to match the overall default rate, it under-predicts defaults by a similar marginathigherLTVratios. AfullcomparisonisshowninTable7. In the data, earlier homeowners have the opportunity to extract more equity and for each cohort, homeowners who have extracted more equity are more likely to default. The model reproduces these patterns, as shown in Table 8. The rate of equity extraction among defaulters who had purchased their homes in 2002 is 11.8% per year compared to 7.1% for 2002 buyers 35Theseofcourseareagainthe“observed”LTVratios,whichignoretheidiosyncratichousepriceshocks. 27

who do not default by the end of the sample. In the simulations, the comparable statistics are 12.6% and 7.8%. Among 2004 buyers, defaulters extract equity at a rate of 8.8% per year while those who do not default do so at a rate of 5.9%. In the simulations, these numbers are 7.4% and4.2%respectively. Oneareawherethemodelhassomedifficultyisinexplainingthedefaultrateofhomeowners immediately after purchase. New homeowners with LTV ratios near unity have no equity and tend to have almost no liquid assets. The model predicts that they should default when they become unemployed. Twenty-six percent of the sample begins with a LTV ratio greater than or equal to one and 2% of employed homeowners become unemployed each quarter, yet the default rate for homeowners in each of the first two quarters after purchase is only 0.13%. Inordertobettermatchthislowdefaultrate,themodelassignsstartingassetswhicharehigher than those found in the data. The median value of liquid assets for new homeowners is 1.9 times quarterly income in the model, compared to 0.4 in the data. Because new homeowners hold more liquid assets in the model, they extract equity at a lower rate. This explains why the model under-predicts equity extraction at the start of the sample, as can be seen in Figure 10. Even so, the model over-predicts default rates in 2002.36 In reality, Mayer and Engelhardt (1996) find that more than 10% of down-payments come from gifts from relatives so that new homeowners may have access to other financial resources that could let them avoid default. Alternatively,householdsmaybemorelikelytopurchaseahomewhentheirriskofunemploymentisparticularlylow. 5.3 Policy Functions To understand these simulations, I next explore what drives agents in the model to extract equityanddefault. Asanillustrativeexample,Ifocusonahomeownerlivinginahousevalued at25timeshisquarterlypermanentincome,approximatelythemedianhomevalueinlate2004 whentherateofborrowingwasatitspeakaswellasin2008whenthefractionofhomeowners defaultingeachquarterhadexceededonepercent. First, when do homeowners extract equity? In Figure 11, I depict the values of liquid assets and LTV ratios for which homeowners increase the size of their mortgages. The most salient feature of this graph is that equity extraction only occurs when liquid assets are near zero (and of course only when there is positive equity to be withdrawn). Because the mortgage interest rate is higher than the return on savings, homeowners with liquid assets prefer to spend those assets rather than take on additional debt. There is also a difference in household borrowing behaviorthatdependsonfutureexpectedpricegrowth. AthighLTVratios,additionalborrowingisonlyallowedunderthelooserborrowinglimitsthatexistwhenhousepricesareexpected 36Because the 2003 and 2004 purchasers have not yet entered the sample and the default rate is so low, these momentsinthedataaremeasuredwithlowprecision. 28

to increase. Conversely, for households with LTV ratios just below the 80% limit, there is an extra incentive to borrow when prices are falling. This is because for homeowners with little equity to borrow against, falling prices threaten to erase that collateral value completely. By converting this wealth into the risk-free asset, households can preserve their ability to spend theseresourcesevenifpricesfall. Forhouseholdswithlittletotalwealth,thisbenefitoutweighs thecostofhavingtomaintaintheadditionaldebtatthehigherinterestrate. If homeowners only extract equity when they hold few or no liquid assets, then it is important to understand what causes them to reach this state. In Figure 12, I show total household spending (non-housing consumption plus mortgage and maintenance payments) at different values of liquid assets and mortgage debt, again for a homeowner with a house valued at 25 times his permanent income. In this figure, I depict contours of constant spending under the belief that prices are expected to rise and under the belief that they are expected to decline. Except at very low asset holdings, spending is higher than income so that households are depleting their assets. For example, a household with a LTV ratio of 0.7, liquid assets equal to four quarters of permanent income, and an expectation that prices are increasing chooses total spending equal to 150% of income. The same household with financial wealth equal to 10 quarters of income chooses total spending equal to 200% of its income. The figure shows that as long as equity is positive, spending increases quickly with asset holdings, with a marginal propensity to consume (MPC) out of financial wealth equal to approximately 7%. At higher mortgagebalances,however,spendingincreasesmoreslowlywithassets,withanMPCofonly 5%. Households with positive equity expect to be able to extract this equity and are therefore eagertospendoutoftheirliquidassets. Thisalsoexplainstheincreaseinspendingwhenprices are expected to rise compared to when they are expected to fall. The same median homeowner who spends 150% of his income under the belief that prices are rising spends 14% less (nonhousing consumption is 18% lower) if he believes prices are falling. As the LTV ratio increases significantly above one, the probability of being able to extract equity becomes small, even if pricesarerising. Inthiscase,theimpactofhousepriceexpectationsonspendingbecomesmuch smaller. The high rate of spending for homeowners who expect to be able to withdraw equity suggest that it is the decision to increase consumption rather than negative income shocks that drives these homeowners to deplete their liquid assets and take out additional debt. I explore thisquestionfurtherinacounter-factualexperimentbelow. The final policy rules to consider are those for default. In Figure 13, I plot contours showing regions with different probabilities of default, again at different values of liquid assets and mortgage debt for a homeowner with a house valued at 25 times his permanent income. The contours divide the state space into three regions. In the upper-left region of the graph, the homeowner has no equity and liquid assets that approach zero. For these homeowners, the optionstosellorrefinancearenotavailableandthebudgetconstraintassociatedwithcontinuing to pay the mortgage either cannot be satisfied or requires a very low level of non-housing 29

consumption. Default is the optimal decision and occurs with probability one.37 At the bottom ofthegraph,householdshavepositiveequityandwouldalwayschoosetosellthehouserather than default so the probability of default in this region is zero. In the upper-right region of the graph, households have negative equity but sufficient liquid resources to afford their housing paymentsandanacceptablelevelofconsumption. Iftheyreceiveapreferenceshock,theyhave the option to default but cannot afford to sell. Whether or not they default when they receive a preference shock depends on the strength of that shock and the value of defaulting relative to remaining in the house. As the LTV ratio increases (and to a smaller degree as asset levels decrease), the financial incentive to default is larger and the value of remaining in the house is lower. Therefore the homeowner will default for a wider range of preference shocks and the totalprobabilityofdefaultincreases. Theaboveparagraphanalyzesdefaultpolicieswhenhousepricesareincreasing. Thedashed linesofFigure14showthechangeintheprobabilityofdefaultifhousepricesaredecreasing. If prices are expected to fall, this reduces that probability that the household will regain positive equityandbeabletosellthehousewithoutdefaultingortoengageinadditionalborrowing. As a result, the value of remaining in the house declines and the household is willing to default at significantlylowerLTVratios. Inthisexample,homeownersdonotdefaultatLTVratioslower than 1.2 if they have some minimum amount liquid assets and expect prices to rise. However, if prices are falling, the model predicts that some homeowners will default as soon as equity becomesnegative. 5.4 Causes of Equity Extraction In order to understand why homeowners extracted equity during the boom, I simulate several variations of the baseline model. In each variation, I turn off one shock in the model and calculate the change in the amount of equity extracted. For each household, I measure equity extraction as a fraction of the purchase price. Then I sum this measure over all the households inthe sample. Ireportthe totalamountof equityextractedfrom thestartof the modelthrough thethirdquarterof2006. First,towhatdegreearehouseholdextractingequitytosmoothconsumptioninresponseto negative income shocks? To answer this question I repeat the baseline simulations but never allowhouseholdstobecomeunemployed. Equityextractiondropsbyonly2%comparedtothe baselinemodel. Optimalpolicieshavenotchangedfromthebaselinemodelsoequityextraction stillonlyoccurswhenthehouseholdapproachestheliquidityconstraint. Withouttheseincome shocks, households reach this constraint more slowly. However, these shocks explain only a 37AthigherLTVratios,wellasforlargerhousevaluesholdingtheLTVratiofixed,thehomeownerdefaultsat a wider range of assets. In other words, the number of states at which default is optimal increases as mortgage paymentsconsumealargerfractionofhouseholdincome. ThisresultisexploredindetailbyCoccoandCampbell (2011). 30

verysmallfractionofequityextraction. Alternatively,householdsreachtheliquidityconstraintbecauseofhighconsumption. Inthe discussion of households’ spending, I showed that households have a high MPC out of liquid assetsiftheyhavepositiveequity. Additionally,theyspendtheirwealthfasteriftheyexpectto accumulateadditionalequitythroughfuturepricegrowth. Inotherwords,actualpricegrowth increases spending by increasing current equity while expected price growth increases spending by increasing the expected amount of future equity. To quantify these two effects, I run two additional simulations. First, I eliminate the accumulation of equity by setting the realized house price growth each period to zero. In this simulation, equity extraction falls by 92% compared with the baseline. Unsurprisingly, strong price growth is necessary to explain the large amount of equity extraction observed in the data. In the second exercise, I leave the realization of house prices unaltered but change households’ expectations about future house prices. In the baseline model, I showed that most households expect positive house price growth until the middle of 2006. If instead, I assign to all homeowners a belief that the probability of being in the high growth state is only 0.5 each quarter, equity extraction falls by 20%. I conclude that approximately one-fifth of equity extraction during the boom is attributable to the belief that priceswouldcontinuetorise. 5.5 Understanding Defaults Next, I study the determinants of default. In the model, homeowners with negative equity default for one of two reasons. First, homeowners with no liquid assets default because they cannotaffordtheirmortgagepayments. Thesedefaultscanbeexplainedbytheincomeprocess together with the household’s consumption decisions. Second, homeowners who are not liquidityconstraineddefaultforotherreasons,whichIhavemodeledasapreferenceshock. These defaultsmayreflectstrategicbehavior,joborfamilysituationsthatrequirethehouseholdtorelocate, or they may be wealth shocks such as high medical expenditures that are not captured bytheincomeprocess. At the start of the sample, the majority of defaults are attributed to liquidity constraints. These are mostly new homeowners who have little assets and have not had the opportunity to accumulate any equity. When these homeowners experience a job loss or other income shock, they are driven to default. By 2005-2006, almost all households have built up equity and have had the opportunity to borrow against this equity. The total default rate falls and very little is attributed to liquidity constraints. After house prices begin to decline in 2006, the model attributes most of the rise in defaults to the preference shock. Income shocks and liquidity constraints explain only 30% of defaults during this period. This conclusion is driven by the empirical observation that defaults begin to increase dramatically in 2006 even though unem- 31

ploymentratesdonotriseuntil2008.38 Rather than income shocks, the model attributes the surge in defaults in the late 2000’s to the collapse of house prices and the growth of negative equity. If prices had remained flat after 2006, I estimate that the default rate in the subsequent years would have been 49% lower. Anotherimportantdriverofdefaultswasthechangeinexpectations. Intheprecedingdiscussion, Ishowedthathomeownerswithnegativeequityaremorelikelytodefaultiftheyexpecthouse prices to fall. Figure 9 shows that under my model of house price expectations, some households begin in late 2005 to place increasing weight the possibility that prices might decline. By the start of 2008, all homeowners in the sample would have believed that prices would continue to fall. To quantify the contribution of this expectation to the wave of defaults, I repeat the simulations, but starting in the fourth quarter of 2006, I set the probability of being in the highgrowthstateto0.5eachquarter. Evenwiththesamefallinprices,defaultsovertherestof thesampleperiodfallby34%. Formanydefaultinghomeownersinthemodel,especiallythose withonlysmallamountsofnegativeequity,thebeliefthatpriceswerenotlikelytorecoverwas animportantfactorintheirdecisiontodefault. 6 Policy Experiments Given the important role that equity extraction played in the default crisis that emerged from the boom-bust house prices cycle of the 2000’s, it makes sense to consider policies that would limit homeowners’ ability or incentive to extract equity. Within my estimated model, I implementtwosuchpoliciesandanalyzetheireffectsonhouseprices,defaultratesandhomeowners’ welfare. 6.1 Tighter Borrowing Limits on Refinances One example of a policy that limits the equity homeowners can extract is currently in place in the state of Texas. The Texas Homestead Act of 1997 regulates cash-out refinances, all new loans taken against a primary residence, plus the refinancing of such loans. In addition to a list of borrower protections, the law prohibits borrowers from refinancing the loan within twelve 38Bhutta et al. (2010) study a sample of 2006 non-prime borrowers and estimate that the fraction of defaults driven purely by negative equity rather than income shocks is only 20%. I attribute a much larger fraction of defaultsinmydatatocausesotherthanincomeshocks. Thetworesultsareactuallyconsistentinthatbothstudies findthecausebeinginvestigatedexplainsonlyasmallfractionofthetotalnumberofdefaults.Inthecurrentpaper, thiscauseisincomeshocks. InBhuttaetal. (2010),thecauseisnegativeequity. Bothstudiesattributethemajority of defaults to the residual shock in the model and both therefore leave ample room for other drivers of default. Inaddition, thesamplesinthetwopapersarequitedifferent. Guiso, SapienzaandZingales(2011)estimatethat 26%ofexistingdefaultsarestrategic. Amongthedefaultsinthecurrentmodelnotcausedbyincomeshocks,my analysisoffersnoinsightintowhatfractionwouldproperlybecharacterizedasstrategic. 32

monthsoforiginationandlimitstheowner’scombinedLTVratioatoriginationto80%.39 What is the effect of such regulations on default? Default rates in Texas following the collapse of the housing market were lower than in other states. (The delinquency rate was 5.8% comparedtothenationalaverageof8.8%inthefirstquarterof2010.) Tosomedegree,thismay reflect the tighter regulations on housing finance, but it is also in large part attributable to the very small decline in Texas house prices, which fell only 7% after the peak. What would the effects of these regulations have been in a housing market with a more pronounced cycle of prices such as California’s? Specifically, I focus on the provision of the Texas law that cash-out refinancesmaynotexceed80%ofthehouse’scurrentvalue. Inordertoanswerthisquestion,Isolveandsimulatethemodelattheestimatedparameters but change the maximum allowed LTV ratio when homeowners refinance to 80%. This restriction decreases the collateral value of the house and lowers the demand for housing. To assess the effect of this decreased demand on house prices, I impose a market clearing condition that eachhomeownerstillchoosestopurchasethesamehouseasinthebaseline. Thisidentifiesthe new price level for each house at the time of purchase. In the simulations, I assume the rate of subsequenthousepricegrowthisunchanged. Ialsoassumethemortgageinterestrateremains thesameasinthebaselinemodel.40 Underthiscounter-factualpolicy,theaveragehousevaluefallsby14%. Thetotalnumberof homeownerswhodefaultduringthesampleperiodfallsfrom10.6%ofhouseholdsinthebaseline mode to 7.6%, a decline of 28%. This decrease is the combination of several effects. First, becausehouseholdspurchaselessexpensivehouses,theyhavesmallermortgagepaymentsrelative to their income and more liquid assets after the purchase. This effect explains most of the decline in defaults. In an alternative specification where I force homeowners to purchase a house of the same value as in the baseline, the default rate only falls to 9.5%. The second effect is that with the tighter lending regulations and lower house prices, homeowners now take out lessequityduringtheboom. Theaverageamountofequityextractedthroughthethirdquarter of2006,expressedasafractionofthepurchaseprice,fallsby23%. Although the overall default rate falls by 28% this total decline is actually the net result of several competing mechanisms. In Table 9, I show the joint distribution of outcomes in 39 The Texas state constitution tightly regulates the ability of a homeowner to borrow against his house, or “homestead,” and prior to this act, did not allow any market for cash-out refinancing. The section of the law regulatingthissetofloansisArticleA,Section6andmortgagessubjecttotheseprovisionshavecometobeknown as Texas A6 Home Equity Loans. In addition to the refinancing limits, the act requires a number of borrower protectionsincludinga12-dayreviewperiod, alimitonclosingcoststo3%ofthemortgagevalue, aprohibition againstpre-paymentpenaltiesandarequirementthatlendersforeclosethroughajudicialforeclosureprocess. The restrictionsofthissectiondonotapplyiftheextractedcashisusedentirelyforhomerenovationsorthepayment ofbacktaxes. 40GhentandKudlyak(2009)findthatinterestratesarenotlowerinrecoursestatesdespitetheirlowerdefault rates.Therefore,inthefollowingsection,whereIstudyhomeownerbehaviorunderafull-recoursepolicy,Iassume the interest rate is unchanged. I make the same assumption here, where the impact on default rates is actually smaller. 33

the baseline model and outcomes in this counterfactual. The third row of this table shows that of homeowners who default in the baseline model, 41% do not under this counterfactual policy. The reason the overall default rate falls by less is that there are two offsetting effects which cause 1.6% of those who either sell or remain in their houses in the baseline model to defaultinthecounterfactualexperiment. BotheffectscanbeseeninFigure15,whichcompares default policies in the baseline model and under these tighter borrowing limits. The first effect concerns homeowners who reach the liquidity constraint with a small but positive amount of equity. In the baseline model, these homeowners are allowed to withdraw all their remaining equity. This extra source of funds allows them to make their mortgage payments and finance consumption. However, if their borrowing is limited to 80% of their house value, they may instead have to sell their house or default. The second channel that increases defaults affects underwater homeowners who are considering whether to default or remain in their homes. For homeowners comparing these two options, part of the value of remaining in the house comes from the possibility that prices will rise and they will again have positive equity in their houses. If this happens, they would again be able to extract this equity to finance additional consumption or to sell the house without defaulting. By reducing their ability to extract this equity, the regulation reduces the future value of remaining in the house. This increases the likelihood that default will be the optimal decision. Together, these two effects offset some of thedecreaseindefaultscausedbythelowerhousepricesandthereductioninborrowing. The reduction in welfare caused by the decreased borrowing opportunities of homeowners is compensated for by their ability to purchase their houses at lower prices. Overall, the average welfare gain for a household entering the housing market, expressed as a consumption equivalentvariation,is3.1%. 6.1.1 AlternativeBorrowingLimitsonRefinances While an 80% LTV ratio was the limit that Texas lawmakers actually implemented, it is natural to examine alternative values for this limit. In a series of counterfactual exercises similar to the onejustpresented,IimposeprogressivelytighterrestrictionsontheLTVratiosthathomeowners may select when refinancing. The results for limits at 80%, 60% and 0% are compared in Figure 16.41 As the maximum LTV ratio is lowered, the amount of equity extraction naturally falls. Since homeowners can no longer borrow as much against their rising house values, they insteadbecomemorelikelytogenerateliquidassetsbysellingtheircurrenthomesandmoving to smaller ones. The fraction of homeowners who sell without defaulting climbs from 27% in baseline model to 31% when the LTV ratio is limited to 80%, and up to 44% when there is no cash-out refinancing at all.42 With the further reduction in borrowing, the number of defaults 41AmorecompletesetofresultsthatalsoincludesotherlimitsispresentedinTable10. 42This of course may be seen as alternative way of extracting equity from an appreciating house. Because of thenatureofmydata, Idonotfocusonthismechanisminthecurrentpaper, butitisstudiedinGreenspanand 34

also continues to decline, with most of the decrease in defaults realized by the point at which the maximum LTV ratio is lowered to 60%. When the ability to withdraw equity is removed completely, the default rate among this cohort of homeowners falls to 2.1%, a decline of 80% relativetothebaseline. 6.2 Strengthening Recourse I next consider a policy that preserves the ability of homeowners to borrow but reduces their incentive to do so. California is one of nine “non-recourse” states. This means that when a homeowner defaults on his mortgage, the lien holder takes possession of the house and receives the proceeds from its sale. However, if the sale price does not cover the outstanding mortgage balance, the lender is not entitled to recover the difference. This creates an incentive for the homeowner to borrow larger sums with the expectation that if house prices fall, he can default and not repay the debt. This is sometimes referred to as “strategic borrowing.” Under an alternative policy in which the borrower maintains his obligation to repay the outstanding mortgage balance, this incentive does not exist. In addition to directly reducing the incentive to default, such a policy should therefore be expected to decrease the amount of borrowing as well. In order to quantify the amount of strategic borrowing and estimate the effects of a fullrecourse policy, I solve and simulate an alternative specification of the model in which a defaultinghomeownercarriestheunpaidmortgagebalancewithhimintotherentalmarketafter defaulting. A renter with such a debt continues to pay only interest and the quarterly rate of interest remains rm = .0155. While the renter is free to pay down the balance of this debt if he chooses, he may never increase the principal beyond its current value.43. In this sense, the policy does not give the renters additional borrowing opportunities that were not available in the baseline model. Importantly, there is no bankruptcy in the model so that the borrower cannot default on this debt. In reality, the ability of a borrower to declare bankruptcy represents an important limitation on the lender’s ability to collect the outstanding balance and significantly reduces the difference between recourse and non-recourse policy regimes.44 I impose the same market clearing conditions as described in the previous section, allowing house prices but not interestratestorespondtothischangeinpolicy. Because borrowers cannot escape repayment under the full-recourse policy, mortgages are now less attractive assets and the houses used to secure them less valuable as collateral. As a result, house prices are on average 12% lower. A comparison of outcomes under this policy to Kennedy’s(2007)moregeneralanalysisofequityextraction. 43Inotherwords,thisdebtisnotarevolvinglineofcredit. 44SeeLiandWhite(2009)foranempiricalanalysisanddiscussionofthejointdecisiontodefaultonamortgage anddeclarebankruptcy. Mittman(2011)studiestheinteractionsbetweenpoliciesregulatingmortgagedefaultand bankruptcyinageneralequilibriumsetting. 35

outcomes in the baseline model is shown in Figure 17. With less incentive to borrow, as well as lower house prices, equity extraction during the boom falls by 18%.45 Most of this decrease is attributable to the reduction in house prices. In an alternative experiment where I do not let house prices adjust, equity extraction falls by 6%. This may be interpreted as the model’s estimateofthefractionofborrowingduringtheboomthatcouldbeconsidered“strategic.” The total number of defaults during the sample period falls by 45%, from 10.6% of the sample in the baseline to 5.8% under the counterfactual policy. The lower left panel of Figure 17 showsthatessentiallyallofthisdecreaseoccursamonghomeownerswhointhebaselinemodel default after house prices begin to decline in 2006. This reduction in defaults is a combination of two effects. First, homeowners now have smaller mortgages. As a result, 13% of defaulters in the baseline model are now able to sell rather than default when they receive a preference shock. Second, because defaulting is now much less attractive, 41% of homeowners who default in the baseline model choose instead to remain in their houses. In Figure 18, I compare the default policies in this counterfactual to those of the baseline model. Except at low levels of liquid assets, homeowners under the full-recourse policy do not default until the LTV ratio exceeds1.5,comparedtoathresholdof1.2inthebaselinemodel. As in the previous policy experiment, I find that the reduction in welfare cause by homeowners’ inability to discharge their debt is offset by their ability to purchase houses at a lower price. The average welfare gain for a household entering the housing market, again expressed asaconsumptionequivalentvariation,is2.7%. 7 Conclusion Manyofthehomeownerswhorecentlydefaultedontheirmortgageswouldhavebeenunlikely todefaulthadtheynotextractedequityduringtheprecedingboominhouseprices. Inthispaper, I have presented an estimated structural model capable of explaining the patterns of both equity extraction and default observed among this group of homeowners. One key finding of this study is that changing expectations about future price growth can lead to additional borrowingaspricesriseandlargerdefaultratesafterpricesbegintofall. Themodelpredictsthatif households have small amounts of negative equity and prices are expected to rise, the number of defaults will be small. However, if there is a larger degree of negative equity and prices are not expected to recover, default rates may be much higher. This could explain the difference between the current situation, where the default rate is high, and past housing markets where defaultrateswerelowdespitemanyhomeownershavingnegativeequity.46 45Asinthepreviousexercise,thisfiguremeasuresthetotalequityextractionthroughthethirdquarterof2006, calculatedasafractionofthepurchaseprice. 46For example, the housing market in Massachusetts during the 1990’s, studied by Foote, Gerardi and Willen (2008b). 36

Ihaveusedmymodeltostudytwopoliciesintendedtoreducedefaultbylimitingexantethe amountofequitythathomeownersextractduringperiodsofappreciatinghousevalues. While it might be useful to consider such policies as a part of future housing regulations, they do little to address the question of how policy makers should respond ex post to a housing market suchasthecurrentoneinwhichmanyhomeownersfindthemselveswithnegativeequity. One conclusion of this analysis is that in my model, only a small portion of defaults following a boom-bust cycle is attributable to negative income realizations. Most defaults result instead from the non-income shocks that I have modeled as preference shocks. This implies that most defaults in the model could not be prevented by providing relief to unemployed homeowners. Unsurprisingly, the model implies that reducing the principal balances of homeowners with negativeequitywouldlowerthetotalnumberoffutureforeclosures. Anotherpredictionisthat suchpoliciesaremorelikelytobesuccessfulifhomeownersexpectpricestorise,eitherbecause ofrealpricegrowthorasaresultofhigherinflation. Thispaperstudiesthebehaviorofhouseholdsonlyaftertheyhavedecidedtobecomehomeowners. It would be natural to extend the model to include the home-ownership decision as well. In response to a policy that changes the value of being a homeowner, some renters may choose to become homeowners while other households may choose to rent rather than to own. Given additional data, it might also be useful to redo the analysis using a more nationally representativesampleofhomeowners. A Initial Conditions In this appendix, I describe the procedure by which I assign values of initial income and liquid assetstoeachhouseholdinmysimulations. Each simulated household begins with a level of permanent income and an endowment of liquid assets, already having decided to purchase a house and now optimizing over the size of that house and a starting mortgage balance. The model is constructed so that only the ratio of assets to income matters in solving the household’s problem. At low initial endowments of assets, there exists a range of endowments for which the optimal choice includes a starting LTV ratio of 100%. This range begins at zero and extends to an upper bound above which the household would prefer a lower starting mortgage balance. At higher initial endowments, the optimal starting LTV-ratio is a decreasing function of the endowment. The optimal choice of startinghousevalueandmortgagebalancefordifferentstartingassetendowmentsisplottedin Figure19. I choose the starting asset endowment for each simulated household such that its optimal starting LTV ratio matches the observed initial LTV ratio found in the data. If the LTV ratio is lessthanone,thisgivesauniquevalueforthestartingendowment. Ifitisequaltoone,thereis 37

afiniteintervalofstartingendowmentsconsistentwiththischoice. Fromthisinterval,Idrawa random starting value from a distribution with a c.d.f. given by a power law with exponent ξ. Specifically,iftheintervalisgivenby [a,a],thenthedistributionofstartingassets A satisfy (cid:18) a−a (cid:19)ξ Prob(A < a) = . a−a Ifξ islarge,mostofthedistributionisconcentratedtotherightoftheinterval,meaningmore of these homeowners were close to making a non-zero down payment. I estimate ξ together with the other parameters of the model. From this starting endowment of assets, households make choices over the value of their house, starting liquid assets and mortgage balances. By construction,thechoiceofmortgagebalancewillmatchthatfoundinthedata. Thehousehold’s optimal policy specifies a house value as a multiple of its permanent income. From this policy plus the house value observed in the data, I am able to construct the household’s permanent income. For each household, this procedure therefore gives me starting values for permanent income(P(cid:99) 0i )andassets(a (cid:99)0i ). After choosing a starting house value and mortgage balance, each household then draws shockstotheirassetsandpermanentincomethatcapturestheheterogeneityamongnewhomebuyers found in the data. In addition to capturing the effects of unobserved heterogeneity, I construct these shocks so that they reflect patterns of observable heterogeneity from my sample of new home buyers in the PSID. Specifically, the starting values of permanent income and assetsincludingtheseshocksaregivenby P 0i = P(cid:99) 0i ·exp(β0 P 0 +β P 0 X i +ε P 0 i ) and a 0i = a (cid:99)0i ·exp(β0 a 0 +β a 0 X i +ε a 0 i ) where X are the covariates from the PSID data that are found to be correlated with starting i income and assets and β and β are the coefficients from those regressions (See Section 3.3). P a 0 0 Relative to the results of those regressions, I make three adjustments. First, I set to zero all coefficients that are statistically insignificant. Second, I set to zero the coefficient on the LTV ratiointheshocktostartingassets. Ratherthanimposingitexogenously,thestrongcorrelation betweenassetsandtheLTVratiofornewhomeownersemergesendogenouslyfromthebuyer’s optimization problem. Third, I fix the constant terms β0 and β0 such that the expected mean P 0 a 0 of both shocks across the sample is equal to zero. The random terms ε and ε are i.i.d and P i a i 0 0 arenormallydistributed ε ∼ N(0,σ2 ), ε ∼ N(0,σ2 ). P 0 i P 0 a 0 i a 0 This procedure gives three parameters that I estimate jointly with the other parameters of the model: the exponent on the distribution of starting assets among those with LTV ratios equal to 100%, ξ, and the standard deviations of the shocks to the starting values for assets and income, σ and σ . The estimated values, with standard errors, are: ξ = 0.121(0.013), P a 0 0 σ = 0.346(0.036) and σ = 0.948(0.044). P a 0 0 38

B House Price Expectations In this appendix, I describe the procedure by which I update the beliefs about future house pricegrowth. Let g denotethegrowthinloghouseprices g = logp −logp . t t t t−1 Attime t,homeownersobservepricegrowth g = µ +η . t t t Thepersistentcomponentµ t ∈ {µ 1 ,µ 2 },followsaMarkovprocesswithtransitionmatrix Π µ,µ(cid:48). The i.i.d component η is distributed N(0,σ2). Note that the p.d.f. of g conditional on µ is t η t t givenby (cid:18) (cid:19) 1 g −µ f(g |µ ) ≡ φ t t (1) t t σ σ η η where φ isthep.d.f. ofthestandardnormaldistribution. Assumethatbasedonobservationsofpasthouseprices,whichIdenotebygt−1 ≡ {g }t−1 , t t(cid:48)=−∞ the household enters period t with a value for the probability Pr(µ = µ |gt−1) and then obt−1 2 serves g . We need to calculate the updated probability: Pr(µ = µ |gt−1,g ). There are two t t 2 t steps. First,calculate Pr(µ = µ |gt−1): t 2 Pr(µ = µ |gt−1) = ∑ Pr(µ = µ ,µ = µ |gt−1) = ∑ Pr(µ = µ |µ = µ )·Pr(µ = µ |gt−1) t 2 t 2 t−1 i t 2 t−1 i t−1 i i=1,2 i=1,2 The quantity Pr(µ = µ |µ = µ ) is defined by the Markov process. By assumption, we t 2 t−1 i already know Pr(µ = µ |gt−1) and of course Pr(µ = µ |gt−1) = 1−Pr(µ = µ |gt−1) t−1 2 t−1 1 t−1 2 sowecanwrite Pr(µ = µ |gt−1) = Π (1−Pr(µ = µ |gt−1))+Π Pr(µ = µ |gt−1). t 2 12 t−1 2 22 t−1 2 ThesecondstepistoapplyBayes’ruletowrite f(µ = µ ,g |gt−1) Pr(µ = µ |gt) = Pr(µ = µ |gt−1,g ) = t 2 t . t 2 t 2 t f(g |gt−1) t Conditional on the value of µ , g does not depend on gt−1. This observation lets us rewrite the t t denominatorandalsoletsususeBayes’ruleagaintoexpandthenumerator: f(µ = µ ,g |gt−1) f(g |µ = µ )·Pr(µ = µ |gt−1) Pr(µ = µ |gt) = Pr(µ = µ |gt−1,g ) = t 2 t = t t 2 t 2 . t 2 t 2 t f(g |gt−1) ∑ f(g |µ = µ )·Pr(µ = µ |gt−1) t i=1,2 t t i t i Thevalueof f(g |µ ) isgivenbyEquation1andwederivedanexpressionfor Pr(µ = µ |gt−1) t t t i inthepreviousstep. 39

C Normalizing the Model by Permanent Income Inthisappendix,Ishowhowtoreformulatethemodelintermsofvariablesthatarenormalized by the household’s permanent income. Define normalized values of consumption cˆ = c /P, t t t assets aˆ = a /P,andcash-on-hand t t t aˆ˜ = a˜/P = (a +Pε )/P = aˆ +ε . t t t t t t t t t Definethenormalizedhousevalue hˆ = h p /P anddefinetheLTVratio mˆ = M /h p . t t t t t t t t Householdspreferences,originallygivenby E ∑ ∞ β (t−t 0 ) (cid:32) (cα t h ( t 1−α) )(1−γ) +Ω (cid:33) , t 0 1−γ t t=t 0 with Ω = ω P (1−γ) p (1−α)(γ−1) cannowberewrittenas t t t t ∞ (cid:16) cˆαhˆ(1−α) (cid:17)(1−γ)  E ∑ β (t−t 0 ) t t +ω · (cid:16) P (1−γ) p (1−α)(γ−1) (cid:17) . t 0  1−γ t t t t=t 0 Fromthisexpression,weseethatwhenthemodelisexpressedintermsofthesenormalized variables,therateatwhichtimetutilityisdiscountedrelativetotime(t−1)utilityisdependent onrealizationsof p and P. Definethegrowthratesof p and P: t t t t g = p /p G = P/P . t t t−1 t t t−1 Itisalsonaturaltodefineadiscountfactor (cid:18) (cid:19)(1−γ)(cid:18) (cid:19)(1−α)(γ−1) βˆ = β P t p t = βG (1−γ) g (1−α)(γ−1) . t P p t t t−1 t−1 Themortgagecostfunctioncanbewritten Kˆ(mˆ ,hˆ ) = K(M )/P = k +(k +k ·1(m > m))mˆ hˆ . t+1 t+1 t+1 t 0 1 2 t+1 t+1 t+1 In the recursive formulation of the household problem, neither the current level of permanentincomenorthepriceofhousingarestatevariables. Thehouseholdproblemissolvedbya valuefunction Vˆ(aˆ˜,hˆ ,e,mˆ,ω, f), wherenowthestatevariablesarethenormalizedcash-on-handaˆ˜,thenormalizedhousevaluehˆ , 40

theemploymentstatee,theLTVratiomˆ,therealizationofthepreferenceshockωandlikelihood ofbeinginthehighpricegrowthstate f. Unlikeintheoriginalformulationofthemodel,householdsdonotdirectlychoosethestate variables which capture the size of the house and the mortgage balance: hˆ(cid:48) and mˆ (cid:48) . Rather, they choose the value of next period’s house value relative to the current permanent income, which I denote by h ˆ˜(cid:48) , and the ratio of the new mortgage balance relative to the current value of the the house they choose to live in next period, mˆ˜ (cid:48) . Next period’s state variables hˆ(cid:48) and mˆ (cid:48) depend on the realizations of the shocks to house prices and permanent income: hˆ(cid:48) = h ˆ˜(cid:48) /G (cid:48) and mˆ (cid:48) = mˆ˜ (cid:48) /g (cid:48) . Thevaluefunctionisagainthemaximumofthevaluesoffouroptions: Vˆ(aˆ˜,hˆ ,e,mˆ,ω, f) = max(Vˆ0(·),VˆR(·),VˆS(·),VˆD(·)) where 1. Thevalueofcontinuingtopaythemortgageis Vˆ0(aˆ˜,hˆ ,e,mˆ,ω, f) = maxu(cˆ,hˆ)+Eβˆ(cid:48) V(aˆ˜ (cid:48) ,hˆ(cid:48) ,e (cid:48) ,mˆ (cid:48) ,ω (cid:48) , f (cid:48)) cˆ aˆ (cid:48) = (1+rs)·(aˆ˜−(χ+rmmˆ)hˆ −cˆ), aˆ (cid:48) ≥ 0, hˆ(cid:48) = hˆ /G (cid:48) mˆ (cid:48) = mˆ/g (cid:48) 2. ThevalueofrefinanceintoanewmortgagewithLTV-ratio mˆ˜ (cid:48) (cid:54)= mˆ is VR(aˆ˜,hˆ ,e,mˆ,ω, f) = maxu(cˆ,hˆ)+Eβˆ(cid:48) V(aˆ˜ (cid:48) ,hˆ(cid:48) ,e (cid:48) ,mˆ (cid:48) ,ω (cid:48) , f (cid:48)) cˆ,mˆ˜(cid:48) aˆ (cid:48) = (1+rs)·(aˆ˜+(mˆ˜ (cid:48) −mˆ)hˆ −(χ+rmmˆ)hˆ −Kˆ(mˆ (cid:48) ,hˆ)−cˆ) aˆ (cid:48) ≥ 0, hˆ(cid:48) = hˆ /G (cid:48) , mˆ˜ (cid:48) < φ(f), rmmˆ˜ (cid:48) hˆ < ψ , mˆ (cid:48) = mˆ˜ (cid:48) /g (cid:48) R 3. The value of selling the house and purchase a new house of size h ˆ˜(cid:48) with a new mortgage withLTV-ratio mˆ˜ (cid:48) is VS(aˆ˜,hˆ ,e,mˆ,ω, f) = max u(cˆ,hˆ)+ω−θ +Eβˆ(cid:48) V(aˆ˜ (cid:48) ,hˆ(cid:48) ,e (cid:48) ,mˆ (cid:48) ,ω (cid:48) , f (cid:48)) u cˆ,h ˆ˜(cid:48),mˆ˜(cid:48) aˆ (cid:48) = (1+rs)·(aˆ˜+(1−θ −χ)hˆ −θ −(1+rm)hˆmˆ −(1−mˆ˜ (cid:48))h ˆ˜(cid:48) 1 0 −κ(mˆ −(1−θ ))hˆ ·1((1−θ ) < mˆ)−cˆ) 1 1 aˆ (cid:48) ≥ 0, hˆ(cid:48) = h ˆ˜(cid:48) /G (cid:48) , mˆ˜ (cid:48) < φ(f), rmmˆ˜ (cid:48) h ˆ˜(cid:48) < ψ , mˆ (cid:48) = mˆ˜ (cid:48) /g (cid:48) P 41

4. Thevalueofdefaultingis VˆD(aˆ˜,hˆ ,e,mˆ,ω, f) = maxu(cˆ,hˆ)+ω−θ +Eβˆ(cid:48) Vˆrent(aˆ˜ (cid:48) ,e (cid:48)) u cˆ aˆ (cid:48) = (1+rs)·(aˆ˜−cˆ−θ ), aˆ (cid:48) ≥ 0 0 Therenter’sproblemcanbewritten Vˆrent(aˆ˜,e) = maxu(cˆ,hˆ)+Eβˆ(cid:48) Vˆrent(aˆ˜ (cid:48) ,e (cid:48)) cˆ,hˆ aˆ (cid:48) = (1+rs)·(aˆ˜−cˆ−ρhˆ), aˆ (cid:48) ≥ 0 References [1] Aragon, Diego, Andrew Caplin, Sumit Chopra, John V. Leahy, Yann LeCun, Marco Scoffier and JosephTracy,2010.“ReassessingFHARisk.”NBERWorkingPaper15802. [2] Bajari, Patrick, Chenghuan Sean Chu and Minjung Park, 2008. “An Empirical Model of Subprime MortgageDefaultfrom2000-2007.”NBERWorkingPaper14625. [3] Bhutta,N.,J.Dokko,andH.Shan,2010.“TheDepthofNegativeEquityandMortgageDefaultDecisions. ”Finance and Economics Discussion Series Working Paper 201035, Federal Reserve Board ofGovernors. [4] Campbell, John and Joao F. Cocco , 2003. “Household Risk Management and Optimal Mortgage Choice.”QuarterlyJournalofEconomics,Vol.118,1149-1194. [5] Campbell, JohnandJoaoF.Cocco, 2011.“AModelofMortgageDefault”WorkingPaper, Harvard University. [6] Case, Karl and Robert Shiller, 1989. “The Efficiency of the Market for Single-Family Homes.”AmericanEconomicReview,Vol.79(1),pages125-37 [7] Chatterjee, Satyajit, and Burcu Eyigungor, 2011. “A Quantitative Analysis of the U.S. Housing and Mortgage Markets and the Foreclosure Crisis.”Working Papers 11-26, Federal Reserve Bank ofPhiladelphia [8] Clauretie,TerrenceandNasserDeneshvary2011.“TheOptimalChoiceforLendersFacingDefaults: ShortSale,Foreclose,orREO.”JRealEstateFinanEconVol.42504-521. 42

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Table1: SamplebyPurchaseYear ThistableshowssummarystatisticsforhousesintheCoreLogicopenliensdatapurchasedbetween2000and2007. “cLTV”isthecombined LTVratioatthetimeofpurchase. “Subprime”isthefractionofhousespurchasedwithamortgagefromalenderspecializinginsub-prime loans.“Default”isthefractionofhomeownersfromthatcohortwhohavedefaultedbytheendofthedatasamplein2009Q4. Purchase Mean Median Year N(1000) cLTV cLTV Subprime Default 2000 103 .87 .90 .40 .07 2001 88 .87 .90 .14 .08 2002 94 .86 .90 .18 .08 2003 94 .86 .90 .25 .11 2004 91 .87 .90 .29 .19 2005 88 .88 .91 .28 .32 2006 72 .90 1.00 .22 .42 2007 53 .85 .90 .05 .19 Table2: SummaryStatisticsofPSIDSampleofNewHomeowners This table shows summary statistics for homeowners from the 1999-2007 waves of the PSID who report having moved into their current residenceswithinthe12monthsprecedingtheinterviewandhaveamortgagewithanon-missinginterestrate.The“income/payment”ratio istheratioofafter-taxhouseholdincometoannualmortgagepayments.“cLTVratio”istheratioofthetotaloutstandingmortgagebalanceto theself-reportedhomevalue.Dummyvariablesindicatewhetherthereisasecondmortgage,whetherthepurchasemortgagehasanadjustable interestrate,andwhetherthehousewaspurchasedafter2005. Forfixed-ratemortgages,theinterestratespreadisoverthemonthlyaverage commitmentrateon30-yearfixed-ratemortgagesfromFreddieMac’sPrimaryMortgageMarketSurvey. Foradjustableratemortgages,the spreadisoverthe6-monthLIBOR.Thesampleexcludeshouseholdswithoutlyingvaluesfortheratioofincometomortgagepayments(less than.13orgreaterthan55).Theresultingsampleincludes782observations,ofwhich694havenon-missingandnon-zeroassets. Variable N Mean StdDev Min Max log(assets) 694 1.95 1.94 -3.91 8.30 log(income/mortgagepayment) 782 1.38 0.52 -0.75 3.58 cLTVratio 782 0.77 0.19 0.00 1.15 Secondmortgagedummy 782 0.12 0.32 0 1 ARMdummy 782 0.12 0.32 0 1 FRMspread 782 0.06 0.84 -2.65 5.85 ARMspread 782 0.17 0.64 -2.94 5.23 purchaseafter2005 782 0.28 0.44 0 1 Table3: RegressionofIncomeandAssetsforNewHomeowners ThistableshowstheresultsoftworegressionsusingthesampleofnewhomeownersfromthePSID.Thedependentvariablesinthetwo regressionsarethelogarithmsoftheratioofafter-taxhouseholdincometomortgagepaymentsandthetotalamountofliquidassets. The sampleandallvariablesaredefinedinTable2.Theregressionofliquidassetsusesatobitmodelwithleftcensoringatlog($1000)andhas706 observations.Theregressionforincomeincludes782observations. log(income/payment) log(liquidassets) Variable Coef. Std.Err. p-val Coef. Std.Err. p-val cLTVratio -.350 .096 .000 -3.708 .360 .000 secondmortgagedummy -.208 .058 .000 -.055 .207 .791 ARMdummy .009 .086 .913 .768 .311 .014 FRMspread -.027 .022 .215 -.383 .083 .000 ARMspread -.044 .043 .307 -.528 .159 .001 purchaseafter2005 -.134 .041 .001 -.208 .148 .163 constant 1.72 .078 .000 4.949 .288 .000 R2 .046 .053 46

Table4: SummaryStatisticsofEstimationSample Thistablepresentssummarystatisticsforthesampleof2002-2004homebuyersusedinthemultinomiallogisticregressiondescribedinSection 3.4. “Subprime”iswhetherthepurchasemortgagewasobtainedfromasub-primelender. “PurchaseLTV”istheLTVratioofthepurchase mortgage,“PurchasecLTV”thecombinedLTVratioatpurchase. “Purchaserate”and“currentrate”aretheinterestratesonthepurchase mortgageandonthecurrentprimarymortgage. “ARM”isadummyvariableindicatingthatthecurrentprimarymortgagehasavariable interestrate. “∆HPI -1yr”isthechangeinzip-code-levelhousepricesoverthelastfourquarters. “2000Unemp,”“2000FracYoung”and “2000FracCollege”arethecensus-tract-levelunemploymentrate,fractionofhomeownersunderage35andfractionofresidentsage25and overwithatleastsomecollege,allfromthe2000census.Thesamplecontains311,367quarterlyobservationsof20,176homeowners. Variable Mean StdDev Min Max Subprime .230 .421 0 1 PurchaseLTV 0.789 0.115 .088 1.098 PurchasecLTV .865 .133 .010 1.100 PurchaseRate 6.03 .879 3.50 9.99 CurrentRate 5.92 .955 1.00 14.93 ARM .500 .500 0 1 ∆HPI-1yr .064 .170 -.951 .352 cLTV>1 .065 .247 0 1 cLTV×(cLTV>1) .088 .339 0 3.98 ∆med.inc. .040 .066 -.329 .484 Unemployment .057 .017 .016 .181 2000Unemp. .067 .037 .000 .481 2000FracYoung .185 .092 .000 .585 2000Frac.College .521 .209 .030 .924 Outcome=extractequity .081 .273 0 1 Outcome=sell .016 .124 0 1 Ooutcome=default .005 .073 0 1 Table5: EmpiricalDescriptionofOutcomes ThistableshowstheestimatedcoefficientsofthemultinomiallogisticregressiondescribedinSection3.4. VariablesaredefinedinTable4. Allvariablesarenormalizedtohaveunitstandarddeviationpriortotheestimationsothatcoefficientsdescribetheeffectofaonestandard deviationchangeineachvariableontheoutcome.Theregressionincludesfixedeffectsforeachyearofobservation,foreachyearofpurchase. Theomittedcategoryisthechoicetocontinuetopayonesmortgageortorefinancewithoutwithdrawingequity.Thesamplecontains311,367 quarterlyobservationsof20,176homeowners.Standarderrorsareclusteredbyzip-code,whichistheregionforwhichhousepriceindicesare computed. ExtractEquity Sell Default Variable Coef. Std.Err. p-val Coef. Std.Err. p-val Coef. Std.Err. p-val Subprime .047 .007 .000 .062 .016 .000 .160 .025 .000 PurchaseLTV .029 .011 .007 .110 .023 .000 -.011 .042 .803 PurchasecLTV .175 .011 .000 -.017 .024 .472 .260 .047 .000 PurchaseRate .033 .011 .002 .075 .020 .000 .210 .031 .000 CurrentRate .089 .008 .000 .026 .018 .146 .330 .021 .000 ARM .186 .008 .000 .362 .017 .000 .717 .046 .000 ∆HPI-1yr .348 .024 .000 .600 .047 .000 -.103 .054 .057 cLTV>1 -.303 .051 .000 .009 .101 .931 .154 .070 .029 cLTV×(cLTV>1) .144 .051 .005 -.023 .104 .827 .122 .072 .090 ∆med.inc. .012 .008 .111 .028 .016 .077 -.041 .037 .266 Unemp. .003 .009 .726 .015 .023 .497 .096 .036 .008 2000Unemp. .000 .011 .973 .050 .018 .006 .000 .029 .994 2000FracYoung -.026 .011 .019 .066 .022 .003 -.058 .036 .103 2000Frac.College .019 .010 .083 .145 .027 .000 -.097 .045 .029 Pseudo-R2=.065,Loglikelihood=-114511. 47

Table6: ParameterEstimates Thistableshowstheparameterestimateswithstandarderrorsinparentheses. discountfactor β .941 (.002) weightonnon-housingconsumption α .742 (.006) riskaversion γ 1.52 (.06) mortgagecost(fractionofincome) k0 .147 (.032) mortgagecost(fractionofmortgagebalance) k 1 .012 (.002) mortgagecost(forLTV>.8) k2 .073 (.006) repaymentcost κ 6.82 (3.74) mortgagepayment/incomelimit(purchase) ψp .384 (.011) mortgagepayment/incomelimit(refinance) ψr >1 (-) movingcost(fractionofincome) θ0 3.28 (.20) movingcost(fractionofhousevalue) θ1 .198 (.003) movingcost(utility) θu 0.25 (.14) defaultrent-priceratio ρ .170 (.016) probabilityofpreferenceshock λ .028 (.001) meanofpreferenceshock µω 10.21 (.55) varianceofpreferenceshock σω .398 (.24) jobseparationrate Π e E →u .021 (.002) LTVlimitformediumexpectedpricegrowth φ(f(µ2 )=0.5) .90 (.02) Table7: DefaultRatesbyLTVRatio ThistableshowstheprobabilityofdefaulteachquarterbycurrentestimatedLTVratio.IncomputingtheLTVratio,Iusethevalueofthehouse calculatedfromthepurchasepriceandthezip-code-levelhousepriceindex.Becauseoftheunobservedidiosyncratichousepriceshocks,this isnotequaltothetruevalueofthehousethatentersthehousehold’sdecisionproblem. LTVRatio Data Model <.75 .001 .001 .75-1.0 .004 .005 1.0-1.25 .016 .018 1.25-1.5 .030 .027 >1.5 .042 .035 Table8: RatesofEquityExtractionbyPurchaseYearandOutcome Thistableshowsthenumberofnewmortgagesperyear,includingsecondmortgagesandcash-outrefinancesbutexcludingnon-cash-out refinances,bypurchaseyearandoutcome.“Outcome”iswhetherthehouseholdhassoldordefaultedbytheendofthesamplein2009Q2. Purchase NewMortgages/Year Year Outcome Data Model Stay .062 .074 2002 Sell .091 .085 Default .118 .126 Stay .062 .063 2003 Sell .089 .076 Default .118 .115 Stay .053 .039 2004 Sell .073 .057 Default .088 .074 48

Table9: OutcomeswithRefinanceLTV<.8 ThistableshowsthejointdistributionofoutcomesinthebaselinemodelandwhenrefinancesarelimitedtoanLTVratioof0.8. Tableentries givethedistributionofoutcomesunderthecounterfactualpolicyforeachoutcomeunderthebaselinemodel. Numbersinparenthesesshow thedistributionofoutcomesinthebaselinemodel.Thebottomrowshowsthetotaldistributionofoutcomesofunderthecounterfactualpolicy. Baseline OutcomewithRefinanceLTV<.8 Outcome Stay Sell Default Stay(62.7%) 93.8% 4.6% 1.6% Sell(26.7%) 0.9% 97.5% 1.6% Default(10.6%) 24.8% 16.4% 58.8% Total 61.7% 30.7% 7.6% Table10: OutcomesUnderAlternativeLimitsonRefinancing ThistableshowsoutcomesofmodelsimulationswithalternativelimitsonthemaximumLTVratiosthathomeownersareabletoachieve whentheyrefinance.Thecolumnsshowthelevelofhouseprices,theamountofequityextractedduringtheboom(measuredasafractionof thepurchaseprice),thefractionofhomeownersdefaulting,thefractionofhomeownerssellingwithoutdefaulting,andthewelfarefornew homeowners.HousePrices,equityextractionandwelfarearenormalizedtounityinthebaselinemodel. LTVLimit HousePrices EquityExtracted DefaultRate SaleRate Welfare 100%(baseline) 1.00 1.00 .106 .267 1.00 90% .87 .79 .077 .305 1.03 80% .86 .77 .076 .307 1.03 70% .65 .48 .033 .385 1.10 60% .64 .27 .025 .419 1.09 30% .62 .05 .020 .436 1.09 0% .63 .00 .021 .436 1.08 Table11: OutcomeswithRecourse Thistableshowsthejointdistributionofoutcomesinthebaselinemodelandunderfullrecourse.Tableentriesgivethedistributionofoutcomes underthecounterfactualpolicyforeachoutcomeunderthebaselinemodel.Numbersinparenthesesshowthedistributionofoutcomesinthe baselinemodel.Thebottomrowshowsthetotaldistributionofoutcomesofunderthecounterfactualpolicy. Baseline OutcomewithRecourse Outcome Stay Sell Default Stay(62.7%) 94.9% 4.1% 1.0% Sell(26.7%) 1.1% 97.7% 1.3% Default(10.6%) 40.9% 13.1% 46.0% Total 64.1% 30.1% 5.8% 49

Figure1: DefaultsbyYearofPurchase Thisfigureshowsthedistributionoftheyearofpurchaseforhomeownerswhodefaulteachquarter. Defaultisdefinedasthefirstfilingofa noticeofdefaultornoticeoftrusteesale.Thetotalsamplecontains1.2millionhomeowners. stluafeD 00051 00001 0005 0 Defaults by Purchase Year 2002 2004 2006 2008 2010 Quarter <1998 1998−9 2000−1 2002−3 2004 2005 2006 2007−9 50

Figure2: FractionofDebtduetoEquityExtractionatDefaultbyYearofPurchase Debtduetoequityextractionisdefinedasthedifferencebetweenthetotalmortgagebalanceandwhatthemortgagebalancewouldhavebeen hadthehomeownernotextractedequityorotherwisechangedhismortgagebalanceafterpurchase. Thisfigureplotsthefractionofthetotal debtatthetimeofdefaultthatcanbeattributedtoequityextraction. Thinlinesshowthe10th,25th,50th,75thand90thpercentilesofthis measureamonghouseholdspurchasingeachquarterwhoareobservedtodefaultbytheendofthesample.Thethicklineshowsthemean. noitcarF 1 8. 6. 4. 2. 0 Fraction of Debt at Default due to Equity Extraction 2002 2003 2004 2005 2006 2007 Quarter of Purchase Mean 10% 25% 50% 75% 90% 51

Figure3: LTVDistributionofDefaulters ThisfigureshowsthedistributionofcombinedLTVratiosamonghomeownerswhopurchasedtheirhomesduring2000-2003anddefaultedby 2009. Thethreehistogramsshowthedistributionatthetimeofpurchase(yellow),atthetimeofdefault(red),andwhattheLTVratiowould havebeenatthetimeofdefaultunderacounterfactualinwhichthemortgagebalanceremainsthesameasthetimeofpurchase,i.e. without anyequityextraction(blue). tnecreP 05 04 03 02 01 0 0 .5 1 1.5 2 2.5 LTV LTV at Purchase LTV at Default Without Equity Extraction LTV at Default Figure4: EquityExtractionbyPurchaseYearandOutcome Thisfigureshowstherateatwhichhomeownersextractequityduringtheirtenureinthecurrenthome. EquityExtractionincludesbothnew juniormortgagesandcash-outrefinancing.Theoutcomeisdefinedaswhethertheownerhasdefaultedorsoldthehouseby2009Q4. raeY rep segagtroM weN 6. 4. 2. 0 Rate of Equity−Extracting Mortgages by Outcome 2000 2002 2004 2006 2008 2010 Purchase Year Sale Default Neither 52

Figure5: NewMortgages Thisfigureshowsthenumberandtypesofnewmortgagesinitiatedbyexistinghomeownerseachquarter.Thetotalsamplecontains1.2million homeowners. )sdnasuohT( segagtroM weN fo rebmuN 051 001 05 0 New Mortgages 2000 2002 2004 2006 2008 2010 Quarter Non−Cash−Out Refinacnes New Junior Mortgages Cash−Out Refinacnes 53

Figure6: OutcomesbyYearofPurchase Thisfigureshowsthefractionofeachcohortofhome-buyerswhohavedefaultedorsoldtheirhomesby2009Q4. semoctuO fo noitcarF 4. 3. 2. 1. 0 Outcomes by Purchase Year 2000 2002 2004 2006 2008 2010 Purchase Year Sale Default Figure7: CLTVatPurchase ThisfigureshowsthefractionofhouseseachquarterthatarepurchasedwithacombinedLTVratiogreaterthanorequalto100%. Homes purchasedwithnon-conventionalloans(e.g.FHA,VA)areexcluded. noitcarF 6. 4. 2. 0 Fraction of Purchases with cLTV Greater Than or Equal to 100% 2000 2002 2004 2006 2008 2010 Quarter 54

Figure8: HousePriceIndices Thisfigureshowsasampleofcalculatedhousepricesforselectedzip-codes. Eachzip-codecontains1-1.5%oftheestimationsample. The indicesarenormalizedto100in2000Q1. IPH 003 002 001 0 Zip−code House Price Index 1985 1990 1995 2000 2005 2010 Quarter 90066 90650 91344 91506 Figure9: DistributionofHousePriceExpectations Ineachperiod,thisfigureshowsthedistributionacrosszip-codesoftheprobabilitythathomeownerswouldhaveassignedtoincreasinghouse pricesbasedonthefilteringalgorithmdefinedinthetext. Thinlinesshowthe10th,25th,50th,75thand90thpercentilesofthisdistribution. Thethicklineshowsthemean. 1 8. 6. 4. 2. 0 Probability of High House Price Growth 2002 2004 2006 2008 2010 Quarter Mean 10% 25% 50% 75% 90% 55

Figure10: AggregateRatesofEquityExtraction,SaleandDefault Thisfigureshowstheratesofequityextraction,saleanddefaultinthemodelandinthedata.Equityextractionisdefinedinthedataaseither acash-outrefinanceoranewjuniormortgage.Thesolidlineshowsthedata,thedashedlinethemodelsimulations. Fraction Extracting Equity Fraction Selling 0.15 0.03 0.025 0.1 0.02 0.015 0.05 0.01 0.005 0 0 2002 2004 2006 2008 2002 2004 2006 2008 Fraction Defaulting 0.015 Data Model 0.01 0.005 0 2002 2004 2006 2008 Quarter Figure11: EquityExtraction Thisfigureshowsthestatesinwhichhomeownersextractequityforanemployedhouseholdlivinginahousevaluedat25timesitspermanent income.Thehorizontalaxisshowscash-on-handasamultipleofpermanentincome.TheverticalaxisshowsthecurrentLTVratio.Thethree regionsshowstatesinwhichthehomeownerwouldextractequityunderthebeliefthathousepricesareincreasing,decreasing,andwhether increasingordecreasing. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 Liquid Assets (A/P) )H/M( oitaR VTL Whether Extract Equity Increasing Prices Decreasing Prices Increasing or Decreasing Prices 56

Figure12: TotalHouseholdSpending This figure shows the total household spending (consumption, mortgage and maintenance payments) in different states for an employed householdlivinginahousevaluedat25timesitspermanentincome. Thehorizontalaxisshowscash-on-handasamultipleofpermanent income. TheverticalaxisshowsthecurrentLTVratio. Spendingisconstantalongeachcontourandisexpressedasmultipleofpermanent income. Solidlinesshowspendingifthehouseholdbelievesthathousepricesareexpectedtoincrease,dashedlinesiftheyareexpectedto decrease. 2 1 .5 1 2 1 .5 2 1 2 2.5 5 1. 2 2.5 3 1 2 2.5 3 Liquid Assets (A/P) )H/M( oitaR VTL Total Spending by Expected Price Growth 2 Increasing Prices Decreasing Prices 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 5 10 15 20 25 57

Figure13: DefaultProbabilities Thisfigureshowstheprobabilityofdefaultindifferentstatesforanemployedhouseholdlivinginahousevaluedat25timesitspermanent income. Thehorizontalaxisshowscash-on-handasamultipleofpermanentincome. TheverticalaxisshowsthecurrentLTVratio. The probabilityisconstantalongeachcontour. Intheupper-leftregionofthegraph,defaultistheoptimaldecisionandoccurswithprobability one. Atthebottomofthegraph,defaultisneveroptimalandthedefaultrateiszero. Intheupper-rightregionofthegraph,defaultoccurs withalowbutnon-zeroprobability. Liquid Assets (A/P) )H/M( oitaR VTL Probability of Default 1.6 0<Prob(Default)<1 1.5 1 0.025 Default 1.4 0.015 0.025 1.3 0.015 1.2 1 0.0001 1.1 0.025 0.015 0.0001 1 0.0001 0.9 1 No Default 0.8 0.7 0.6 0.5 1 1.5 2 2.5 3 3.5 4 58

Figure14: DefaultProbabilities Thisfigureshowstheprobabilityofdefaultindifferentstatesforanemployedhouseholdlivinginahousevaluedat25timesitspermanent income. Thehorizontalaxisshowscash-on-handasamultipleofpermanentincome. TheverticalaxisshowsthecurrentLTVratio. The probabilityisconstantalongeachcontour.Solidlinesshowtheprobabilityifthehouseholdbelievesthathousepricesareexpectedtoincrease, dashedlinesiftheyareexpectedtodecrease. Liquid Assets (A/P) )H/M( oitaR VTL Probability of Default by Expected Price Growth Increasing Prices 1.6 Decreasing Prices 1.5 1 0.025 1.4 0.015 0.025 1.3 0.015 1.2 1 0.0001 1.1 0.025 0.015 0.0001 1 0.0001 0.9 1 0.8 0.7 0.6 0.5 1 1.5 2 2.5 3 3.5 4 59

Figure15: DefaultProbabilitieswith80%RefinancingLimits Thisfigureshowstheprobabilityofdefaultindifferentstatesforanemployedhouseholdlivinginahousevaluedat25timesitspermanent income,withtheexpectationthatpriceswillincrease.Thehorizontalaxisshowscash-on-handasamultipleofpermanentincome.Thevertical axisshowsthecurrentLTVratio. Theprobabilityisconstantalongeachcontour. Solidlinesshowtheprobabilityunderthebaselinemodel, dashedlinesunderthepolicywithcash-outrefinancinglimitedto80%ofthehousevalue. Liquid Assets (A/P) )H/M( oitaR VTL Probability of Default Baseline Refinance LTV<.8 1.6 1 0.025 1.4 0.015 1.2 1 0 0 . . 0 02 1 5 5 0.0001 0.0001 1 1 0.8 0.6 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Figure16: AggregateRateswithTighterRefinancingLimits Thisfigureshowsthefractionofhouseholdseachperiodextractingequity,sellinganddefaulting.Thesolidlineshowssimulationsunderthe baselinemodel,thethreedashedlinesshowsimulationsunderpolicieswithcash-outrefinancinglimitedto80%ofthehousevalue,60%ofthe housevalueandwithnocash-outrefinancing. Fraction Extracting Equity Fraction Selling 0.2 0.04 0.15 0.03 0.1 0.02 0.05 0.01 0 0 2002 2004 2006 2008 2002 2004 2006 2008 Quarter Quarter Fraction Defaulting 0.02 Baseline Refinance LTV<.8 0.015 Refinance LTV<.6 No Refinancing 0.01 0.005 0 2002 2004 2006 2008 Quarter 60

Figure17: AggregateRateswithFullRecourse Thisfigureshowsthefractionofhouseholdseachperiodextractingequity,sellinganddefaulting.Thesolidlineshowssimulationsunderthe baselinemodel,thedashedlineunderapolicywithfullrecourse. Fraction Extracting Equity Fraction Selling 0.2 0.03 0.025 0.15 0.02 0.1 0.015 0.01 0.05 0.005 0 0 2002 2004 2006 2008 2002 2004 2006 2008 Quarter Quarter Fraction Defaulting 0.02 Model(Baseline) Model(Recourse) 0.015 0.01 0.005 0 2002 2004 2006 2008 Quarter Figure18: DefaultProbabilitiesUnderFullRecourse Thisfigureshowstheprobabilityofdefaultindifferentstatesforanemployedhouseholdlivinginahousevaluedat25timesitspermanent income,withtheexpectationthatpriceswillincrease.Thehorizontalaxisshowscash-on-handasamultipleofpermanentincome.Thevertical axisshowsthecurrentLTVratio. Theprobabilityisconstantalongeachcontour. Solidlinesshowtheprobabilityunderthebaselinemodel, dashedlinesunderthepolicywithfullrecourse. Liquid Assets (A/P) )H/M( oitaR VTL Probability of Default Baseline Recourse 1.6 1 0.025 1.4 0.025 0.015 0.015 1.2 1 0.0001 0.0001 1 1 0.8 0.6 1 2 3 4 5 6 61

Figure19: PurchasePolicies ThisfigureshowstheoptimalhousevalueandLTVratioforahouseholdpurchasingahouse,startingwithdifferentamountsofliquidassets, underthebeliefthatpricesareincreasing.Thehorizontalaxisshowsstartingassetsasamultipleofpermanentincome.Thedashedlineshows theoptimalhousevalue,expressedasamultipleofpermanentincome,plottedagainsttheleftverticalaxis. Thesolidlineshowstheoptimal LTVratio,plottedagainsttherightverticalaxis. 30 25 20 15 10 5 0 5 10 15 20 25 30 35 Liquid Assets (A/P) )P/’H( eziS esuoH New Purchase Policies 1 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30 35 )’H/’M( oitaR VTL 62