Finance and Economics Discussion SeriesDivisions of Research & Statistics and Monetary AffairsFederal Reserve Board, Washington, D.C.The Dynamics of Adjustable-Rate Subprime Mortgage Default: AStructural EstimationHanming Fang, You Suk Kim, and Wenli Li2015-114Please cite this paper as:Fang, Hanming, You Suk Kim, and Wenli Li (2015). “The Dynamics of Adjustable-RateSubprime Mortgage Default: A Structural Estimation,” Finance and Economics Discussion Series 2015-114. Washington: Board of Governors of the Federal Reserve TE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminarymaterials circulated to stimulate discussion and critical comment. The analysis and conclusions set forthare those of the authors and do not indicate concurrence by other members of the research staff or theBoard of Governors. References in publications to the Finance and Economics Discussion Series (other thanacknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

The Dynamics of Adjustable-Rate Subprime Mortgage Default:A Structural Estimation Hanming Fang†You Suk Kim‡Wenli Li§December 9, 2015AbstractWe present a dynamic structural model of subprime adjustable-rate mortgage (ARM) borrowers making payment decisions taking into account possible consequences of different degreesof delinquency from their lenders. We empirically implement the model using unique data setsthat contain information on borrowers’ mortgage payment history, their broad balance sheets,and lender responses. Our investigation of the factors that drive borrowers’ decisions revealsthat subprime ARMs are not all alike. For loans originated in 2004 and 2005, the interest rateresets associated with ARMs, as well as the housing and labor market conditions were not asimportant in borrowers’ delinquency decisions as in their decisions to pay off their loans. Forloans originated in 2006, interest rate resets, housing price declines, and worsening labor marketconditions all contributed importantly to their high delinquency rates. Counterfactual policysimulations reveal that even if the Libor rate could be lowered to zero by aggressive traditionalmonetary policies, it would have a limited effect on reducing the delinquency rates. We findthat automatic modification mortgage designs under which the monthly payment or the principal balance of the loans are automatically reduced when housing prices decline can be effectivein reducing both delinquency and foreclosure. Importantly, we find that automatic modificationmortgages with a cushion, under which the monthly payment or principal balance reductions aretriggered only when housing price declines exceed a certain percentage may result in a Paretoimprovement in that borrowers and lenders are both made better off than under the baseline,with a lower delinquency and foreclosure rates. Our counterfactual analysis also suggests thatlimited commitment power on the part of the lenders to loan modification policies may be animportant reason for the relatively small rate of modifications observed during the housing crisis.Keywords: Adjustable-Rate Mortgage, Default, Loan Modification, Automatic Modificationwith a CushionJEL Classification Codes: D12, D14; G2, G21, G33 We thank Shane Sherlund and seminar/conference participants at the Econometric Society World Congress(2015), University of New South Wales and University of Technology Sydney for their comments. The views expressedare those of the authors and do not necessarily reflect those of the Board of Governors of the Federal Reserve, theFederal Reserve Bank of Philadelphia, or the Federal Reserve System.†Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104 and the NBER.Email: [email protected].‡Division of Research and Statistics, Board of Governors of the Federal Reserve System. Email: [email protected].§Department of Research, Federal Reserve Bank of Philadelphia. Email: [email protected].

1IntroductionThe collapse of the subprime residential mortgage market played a crucial role in the recenthousing crisis that subsequently led to the Great Recession.1 At the end of 2007, subprime mortgages accounted for about 13 percent of all outstanding first-lien residential mortgages but overhalf of the foreclosures. The majority of the subprime mortgages, both by number and by value,were adjustable interest rates mortgages (ARMs); and these mortgages had a foreclosure rate of17 percent, much higher than the 5 percent foreclosure rate for the fixed-rate subprime mortgages(Frame, Lehnert, and Prescott 2008, Table 1). In response to these developments, many government policies were designed and implemented to change the default incentives of the subprime ARMborrowers.2 Few structural models, however, exist that can guide us in these efforts, and that canhelp us understand why most of the programs had limited success.3In this paper, we develop a dynamic structural model to study the incentives of the adjustablerate subprime borrowers to default, and investigate how these incentives change under variouspolicies. In our model, at each period, a borrower decides whether to pay the amount due (andbe current) or not pay (and stay in various delinquent status), taking into account the lender’sresponses such as mortgage modification, liquidation, or waiting (i.e., doing nothing). Relative tothe existing structural models on mortgage defaults which we review below, our model has two keydistinguishing features: first, in our model default is not the terminal and absorbing state as weallow borrowers to self cure their delinquency; second, we consider loan modification as one of thelenders’ loss mitigation practices while the existing models only allow for liquidation.We empirically implement our model using unique mortgage loan level data sets that containnot only detailed information on borrowers’ mortgage payment history and lenders’ responses, butalso credit bureau information about borrowers’ broader balance sheet. We are thus one of the firstto utilize borrowers’ credit bureau information to understand their mortgage payment decisions.4To track movements in the local housing and labor markets, we further merge our data with zipcode level home price indices and county level unemployment rates.1There is no standard definition of subprime mortgage loans. Typically, they refer to loans made to borrowerswith poor credit history (e.g., a FICO score below 620) and/or with a high leverage as measured by either the debtto-income ratio or the loan-to-value ratio. For the data used in this paper, subprime mortgages are defined as thosein private-label mortgage-backed securities marketed as subprime, as in Mayer, Pence, and Sherlund (2009).2To name a few of such programs, the FHASecure program approved by Congress in September 2007; the HopeNow Alliance program (HOPENOW) created by then-Treasury Secretary Henry Paulson in October 2007; Hope forHomeowners refinancing program passed by Congress in the spring of 2008; Making Home Affordable (MHA) initiativein conjunction with the Home Affordable Modification Program (HAMP) and the Home Affordable Refinance Program(HARP) launched by the Obama administration in March 2009 (HAMP). See Gerardi and Li (2010) for more details.3Over the first two and a half years, HARP refinancing activity remained subdued relative to model-basedextrapolations from historical experience. From its inception to the end of 2011, 1.1 million mortgages refinanced through HARP, compared to the initial announced goal of three to four million mortgages. In December, HARP 2.0 was introduced and HARP refinance volume picked up, reaching 3.2 million by June inance-Report-February-2014.aspx. Similarly, HAMP was designed to help as many as 4 million borrowers avoid foreclosure by the end of 2012. By February 2010, one year intothe program, only 168,708 trial plans had been converted into permanent revisions. Through January 2012, a population of 621,000 loans had received HAMP modifications. See 70912FINAL.pdf4Elul, Souleles, Chomsisengphet, Glennon, and Hunt (2010) also use credit bureau information to study mortgagedefault decisions in their empirical analysis.1

Three main factors drive ARM borrowers’ mortgage payment decisions: home equity, income,and monthly mortgage payment; importantly, both the current levels of these factors and the expectations of their future changes matter. Borrowers with negative home equity have little financialgains from continuing with their mortgage payments, especially when they do not expect houseprices to recover and when costs associated with defaults and foreclosures are low. Changes inincomes and expenses, including changes in monthly mortgage payments due to interest rate resets for example, affect borrowers’ liquidity position. In principle, borrowers can refinance theirmortgages to lower interest rates or sell their houses to improve their liquidity positions, but theseoptions may not be available in the presence of declining house prices, increasing unemploymentrates, and/or tightened lending standards. These constrained borrowers thus may find it optimalto default on their mortgages despite the possible consequences of foreclosure.To quantify the relative importance of these different drivers of default, we simulate our structurally estimated model under various counterfactual scenarios. Our simulation results suggestthat the factors that drive the borrower delinquency and foreclosure differ substantially by loanorigination year. For loans originated in 2004 and 2005, which preceded the severe downturn of thehousing and labor markets, the interest rate resets associated with ARMs as well as the housing andlabor market conditions do not seem to be as important factors for borrowers’ delinquency behavioras they are in determining whether the borrowers would pay off their loans (i.e., sell their housesor refinance). However, for loans that originated in 2006, interest rate reset, housing price declines,and worsening labor market conditions all contributed to their high delinquency rates with housingprice declines being the most significant contributing factor.5 These results arise because for loansoriginated in 2004 and 2005, interest rates did not reset until 2006 or 2007 at which time houseprices have just begun to decline. More importantly, since house prices continued to appreciate in2004, 2005, and part of 2006, these borrowers have accumulated some home equity by the time oftheir interest rates reset; in fact, in many places house price did not go all the way down to their2004 levels until 2008. Additionally, the labor market did not deteriorate significantly until 2008 or2009. In contrast, borrowers whose loans originated in 2006 had the perfect storm in 2008 or 2009when their interest rates reset, as house prices had depreciated substantially and unemploymentrates had risen sharply.Counterfactual policy simulations reveal that even if the Libor rate could be lowered to zero byaggressive traditional monetary policies, it would have a limited effect on reducing the delinquencyrates. We find that automatic modification mortgage designs under which the monthly paymentor the principal balance of the loans are automatically reduced when housing prices decline canbe effective in reducing both delinquency and foreclosure. Importantly, we find that automaticmodification mortgages with a cushion, under which the monthly payment or principal balancereductions are triggered only when housing price declines exceed a certain percentage may resultin a Pareto improvement in that borrowers and lenders are both made better off than under the5Our finding is consistent with those in the literature including Bhutta, Dokko, and Shan (2010), Foote, Gerardi,and Willen (2012), and Fuster and Willen (2015). Bhutta, Dokko, and Shan (2010) also find that 80 percent of thedefaults in their sample (2006 loans originated in the crisis states) are the results of income shocks combined withnegative house equity. Foote, Gerardi, and Willen (2012) find that interest rate reset raised the default rates of 2006loans.2

baseline, with a lower delinquency and foreclosure rates. Our counterfactual analysis also suggeststhat limited commitment power on the part of the lenders to loan modification policies may be animportant reason for the relatively small rate of modifications observed during the housing crisis.There are several structural models on mortgage defaults and foreclosures. Bajari, Chu, Nekipelov,and Park (2013) is most related to our paper both in questions addressed and in the empiricalmethodology. However, there are several key differences. First, we incorporate mortgage modification as a possible lender response while they do not. Second, we allow for borrowers to self curewhile they treat default as a terminal event that leads to liquidation with certainty.6 Third, wefocus on adjustable-rate subprime mortgages which were much more prevalent than the fixed-ratesubprime mortgages that they focus on. Fourth, the two papers differ in the way we examinethe effect of counterfactual policies. There differences enable us to study the effects of exogenouslychanging lenders’ actions on a borrowers’ behavior and to shed light on why lenders were not willingto modify loans. More importantly, the effects of alternative policies such as automatic modification mortgages with a cushion can be studied in our framework because this involves changingborrowers’ expectation about the co-evolution of house prices, mortgage balances and paymentsizes.Campbell and Cocco (2014) study a dynamic model of households’ mortgage decisions incorporating labor income, house price, inflation, and interest rate risk to quantify the effects of adjustableversus fixed mortgage rates, mortgage loan-to-value ratio, and mortgage affordability measures onmortgage premia and default. Corbae and Quintin (2015) solve an equilibrium model to evaluate the extent to which low down payments and interest-only mortgages were responsible for theincrease in foreclosures in the late 2000s. Garriga and Schlagenhauf (2009) study the effects ofleverage on default using long-term mortgage contract. Hatchondo, Martinez, and Sanchez (2011)investigate the effect of broader recourse on default rates and welfare. Mitman (2012) considersthe interaction of recourse and bankruptcy on mortgage defaults. Chatterjee and Eyigungor (2015)analyze the default of long-duration collateralized debt. None of these papers make use of mortgageloan level data as in our paper and in Bajari et al. (2013).There are also several recent empirical papers that use regression analysis to study lenders’loss mitigation practices and the impact of government intervention policies on these practices. Forexample, Haughwout, Okah, and Tracy (2010) estimate a competing risk model using modifications(excluding capitalization modifications) of subprime loans that were originated between December2004 and March 2009. They find a substantial impact of payment reduction on mortgage re-defaultrates. Agarwal, Amromin, Ben-David, Chomsisengphet, and Evanoff (2015) analyze lenders’ lossmitigation practices including liquidation, repayment plans, loan modification, and refinance ofmortgages that originated between October 2007 and May 2009 from OCC-OTS Mortgage Metricsdata and find a much more modest effect of mortgage modification on defaults. In a subsequentpaper, Agarwal, Amromin, Ben-David, Chomsisengphet, Piskorski, and Seru (2012) study theimpact of the 2009 Home Modification Program on lenders’ incentives to renegotiate mortgages.Finally, our paper also adds to the growing literature on the recent subprime mortgage cri6Adelino, Gerardi and Willen (2013) show the importance of self-cure as a hinderance for loan modifications.3

sis, including, among many others, Foote, Gerardi, and Willen (2008), Demyanyk and van Hemert(2011), Keys, Mukherjee, Seru, and Vig (2010), and Gerardi, Lehnert, Sherlund, and Willen (2008).Additionally, Piskorski, Seru, and Vig (2010) find that securitization reduced mortgage renegotiation and led to more foreclosures. In contrast, Adelino, Gerardi, and Willen (2013) show that it isinformation asymmetries rather than securitization that hindered mortgage renegotiation.The remainder of the paper is organized as follows. In Section 2 we describe the data sets weuse in our empirical analysis and present the descriptive statistics. In Section 3 we present ourmodel of borrowers’ behavior and their interactions with the lenders in a stochastic environmentwith shocks to housing prices, unemployment rates and Libor interest rates. In Section 4 we brieflydiscuss how we solve and estimate our model. In Section 5 we present our estimation results. InSection 6 we describe the goodness-of-fit between the predictions of our model under the estimatedparameters and their data analogs. In Section 7 we present results from several counterfactualexperiments. In Section 8 we conclude and discuss avenues for future research.22.1DataData SourceOur data on mortgages and their modifications come from three different sources, the CoreLogicPrivate Label Securities data – ABS, the CoreLogic Loan Modification data, and the TransUnionConsumer Risk Indicators for Non-Agency RMBS data (also known as “TransUnion-CoreLogicCredit Match Data”). The CoreLogic ABS data consist of loans that were originated as subprimeand Alt-A loans and represents about 90 percent of the market. The data include loan level attributes generally required of issuers of these securities when they originate the loans as well as theirhistorical performance, which are updated monthly. The attributes include borrower characteristics(credit scores, owner occupancy, documentation type, and loan purpose); collateral characteristics(mortgage loan-to-value ratio, property type, zip code); and loan characteristics (product type,loan balance, and loan status).The CoreLogic Loan Modification data contain information on modifications on loans in theCoreLogic ABS data. The data include detailed information about modification terms includingwhether the new loan is of fixed interest rate, the new interest rate, whether some principal is forgiven, whether the mortgage term is changed, etc. The merge of the two data sets is straightforwardas each loan is uniquely identified by the same loan ID in both data sets.The TransUnion Consumer Risk Indicators for Non-Agency RMBS data provide consumer creditinformation from TransUnion for matched mortgage loans in CoreLogic’s private label securitiesdatabases. TransUnion employs a proprietary match algorithm to link loans from the CoreLogicdatabases to borrowers from TransUnion credit repository databases, allowing us to access manyborrower level consumer risk indicator variables, including borrowers’ credit scores, income at origination, among many others.We then merge our data with CoreLogic monthly zip code level repeat-sales house price indexand county level unemployment rates from the Bureau of Labor Statistics. Thus our constructed4

data have several advantages over most of those used in the literature. First, the match withthe mortgage modification data allows us to accurately identify lenders’ actions, and separatedelinquent mortgages that are self-cured from delinquent mortgages that become current afterlender modification. Second, the TransUnion data enable us to capture borrowers’ other liabilities aswell as the payment history of these liabilities as summarized by credit scores, which are importantfor borrowers’ mortgage payment decisions.2.2Mortgage Loans: Summary StatisticsWe focus on subprime adjustable-rate mortgage loans originated in four major housing crisisstates, Arizona, California, Florida, and Nevada, between 2004 and 2007.7 In particular, we takea 1.75 percent random sample of adjustable-rate mortgages with an initial fixed interest rate for aperiod of two or three years and a mortgage maturity of 30 years, which are for borrowers’ primaryresidence, are first lien, and are not guaranteed by government agencies such as Fannie Mae,Freddie Mac, the Federal Housing Administration (FHA), and Veterans Administration (VA). Wefollow these loans until February 2009 before the first coordinated large-scale government effort tomodify mortgage loans – the “Making Home Affordable” program was unveiled. In total, we have16,347 mortgages and 337,811 monthly observations. Of the 16,347 mortgages, 11 percent wereoriginated in Arizona, 55 percent in California, 28 percent in Florida, and 6 percent in Nevada.Not surprisingly, the largest fraction of the loans were originated in 2005 (43 percent), followed by2004 (37 percent), 2006 (17 percent), and then 2007 (2 percent).Table 1 provides summary statistics of the mortgage loans at origination and of the wholedynamic sample period. The average age of the loan is 16 months in the sample and the median is 14months. At origination, 81 percent of the sample are loans with two-year fixed-rates. Through thesample period, however, 76 percent of the sample are loans originated with two-year initial fixed-rateperiod indicating that more of those loans have terminated via payoff/refinance or foreclosure. Over90 percent of the loans have prepayment penalty. About 40 percent of the mortgages at originationare interest-only mortgages and the fraction becomes slightly higher in the whole dynamic sample.About half of the mortgages have full documentation both at origination and through the sampleperiod. While 43 percent of the mortgages are purchase loans at the origination, the ratio increasesto 48 percent. Consistent with being subprime, mortgage borrowers in the sample all have relativelylow risk scores, averaging 445 at origination, and the scores deteriorate somewhat as the loans age.8Additionally, both the average and the median mortgage loan-to-value ratios at origination are botharound 80 percent and they do not change much as the loans age. The annual household incomeestimated by TransUnion averages 72,000 at origination with a median of 67,000. Loan balancesaverage 259,000 at origination with a median of 228,000. These numbers are not very differentfrom their dynamic counterparts. The mortgage interest rates average 7.13 percent at originationwith a median of 6.99 percent. Dynamically, both the mean and median mortgage interest ratesare higher by 20 and 15 basis points, respectively, as many of these adjustable-rate mortgages reset7The subprime mortgage market dried up after 2007.The risk scores are estimated by TransUnion. They range between 150 and 950 with a high score indicating lowrisk.85

VariableAge of the loan (months)Share of 2-year fixed period (%)Prepayment penalty (%)Interest-only mortgages (%)Full document at origination (%)Purchase loan (%)Risk scoreLTV ratio at origination (%)Annual income ( 1000)Principal balance ( 1000)Current interest rate (%)Remaining mortgage terms (months)Monthly payment ( 1000)Maximum lifetime interest rate (%)Minimum lifetime interest rate (%)Periodic interest rate cap (%)Periodic interest rate floor (%)First interest rate cap (%)Margin for adjustable rate loans (%)30 days delinquent (%)60 days delinquent (%)90 days delinquent (%)120 days delinquent (%)150 days delinquent (%)180 days delinquent (%)180 days more delinquent (%)House liquidation (%)Loan modification (%)Deviation local unemployment rates (%)Local house price growth rates (%)Number of 613.506.701.200.012.505.74000000000At OriginationMedianStd. 1.621.401.251.143.860.640.26-1.51-0.3216,347Table 1: Summary Statistics of Selected Mortgage Loans.6Dynamic SampleMedianStd. 15

to higher rates after the initial fixed-rate period expires. The ARMs in our data have a lifetimemaximum interest rate of 13.50 percent on average at origination, similar to the dynamic averageof 13.42 percent; and the lifetime minimum interest rate averages 6.7 percent at origination and6.59 percent in the dynamic sample. The margin above Libor rate when interest rates are adjustedaverages 5.74 percent at origination and 5.67 percent in the dynamic sample. Both at originationand in the dynamic sample, the period interest rate adjustment has a cap of 1.2 percent and afloor of 0.01 percent on average. The first interest rate adjustment cap, however, is higher at 2.5percent on average at origination and 2.53 percent in the dynamic sample. Unemployment ratestend to be lower than their recent local historical averages. Local house prices, on the other hand,all depreciate in our sample period.Two observations emerge from Table 1. First, some mortgages stay in delinquency status fora long time without being liquidated. Particularly, in our loan-month dynamic sample, close to7 percent of loans are 30-day delinquent, 3 percent are 60-day delinquent, 2 percent are 90-daydelinquent, etc. Close to 4 percent of the loans are delinquent for over half a year. The liquidationrate, in contrast, is only 0.64 percent if measured at loan-month level.9 Of course, at the loan level,2,177 out of the 16,347 loans in our random sample were liquidated (see Table 2), resulting in a13.3% foreclosure rate, similar to what others have documented in the literature. Second, at theloan-month level, about 0.26 percent of all mortgage loans are modified by their lenders. This ratiois obviously much higher if we condition on loans that are delinquent. At the loan level, out of 857out of the 16,347 loans in our randomly selected sample were modified, resulting in a modificationrate of about 5.24%. We elaborate on the second observation regarding lenders’ decisions in moredetails in the next subsection.In the appendix, we provide summary statistics of the mortgage loans separately by the origination year, both at the time of origination and over time in Tables A1 to A3. As can be seen, theloans originated in later years are riskier, more likely to have two-year interest fixed period insteadof three-year, more likely to be interest-only mortgages, less likely to have full documentation, andmore likely to be purchase loans instead of refinance loans. Their principals, the initial interest rate,and monthly payment are also larger. Furthermore, the maximum and minimum lifetime interestrates and margins have risen over time. Given these differences at origination, not surprisingly,mortgage delinquency rates are much higher for loans originated in later years than earlier years.2.3Lenders’ Choices: Descriptive StatisticsFrom Table 1, we observe that lenders do not always respond to borrowers’ mortgage delinquencyimmediately by liquidating them. In this subsection we describe lenders’ decisions in more details.Table 2 presents the delinquency status (in months) at the beginning of the month when theloan was liquidated and modified. It shows that mortgage liquidation typically occurs when theborrower is between 6 and 9 months delinquent. While houses with loans less than 3 monthsdelinquent are rarely liquidated, many houses are liquidated when the mortgage is over one year9House foreclosure can be a long and expensive process especially in states with judicial foreclosure laws (Li 2009).Of the four states that we study, Florida requires judicial foreclosure. Arizona, California, and Nevada allow for bothjudicial and nonjudicial foreclosures, but most of the foreclosures are nonjudicial foreclosures.7

Begnning-of-the-MonthLoan StatusCurrent1 months2 months3 months4 months5 months6 months7 months8 months9 months10 months11 months12 months13 months14 months15 months16 monthsMore than 17 monthsNumber of observationsAt .489.007.355.193.814.,177At 5.314.042.541.961.500.921.731.150.812.31857Table 2: Loan Status at the Beginning of the Month when Liquidation or Modification Occurs.delinquent; indeed, about 4.46 percent of the loans liquidated is over 17 months delinquent. As aside note, the average loan age at liquidation is 27 months; about half of the liquidation occurredin 2008, 30 percent in 2007, and 8 percent in 2006, and about 6 percent in the first two months of2009.Loan modifications are offered generally to loans already in distress. Nearly 60 percent ofthe loans are three months or more behind payments at the time of modification. Close to 9percent are one year or more behind on payments. What is interesting, however, is that about 17percent of the loans are modified when they are listed as current at the beginning of the period.The majority of these loans (55 percent) are originated in 2005 and the rest mostly in 2006 (37percent). Furthermore, the majority of the modifications occur within three months of interest ratereset.10Table 3 presents the modification terms. The majority of the modification results in moreaffordable mortgages as 83 percent of them have a reduction in monthly payments of about 542on average. However, 8.6 percent of the modifications produce higher payments of about 287 onaverage; and 8 percent of the modified loans lead to less than 50 of monthly payment changes.Capitalization in modification is very common with arrears added to the principal balance. Indeedov

Homeowners re nancing program passed by Congress in the spring of 2008; Making Home A ordable (MHA) initiative in conjunction with the Home A ordable Modi cation Program (HAMP) and the Home A ordable Re nance Program (HARP) launched by the Obama administration in March 2009 (HAMP). See Gerardi and Li (2010) for more details.