An Empirical Model of Subprime Mortgage Default from 2000 to 2007 Patrick Bajari, Sean Chu, and Minjung Park MEA 3/22/2009 1
Introduction In 2005 Q3 10.76% subprime mortgages delinquent 3.31% subprime mortgages in the process of foreclosure In 2008 Q3 20.03% subprime mortgages delinquent 12.55% subprime mortgages in the process of foreclosure Troubles in the subprime mortgage market generated broader instability in financial markets Prospect of the worst recession since the Great Depression 2
Introduction (cont d) What are the key drivers of subprime mortgage defaults? Potential triggers of default 1. Financial incentives (eqn 1) Borrower s equity eroded by falling house prices Expected price appreciation downward revisions? Contractual v. market interest rates 2. Credit constraints (eqn 2) Payment or income shocks, ability to get credit Relative magnitudes: useful input to policy debates 3
Introduction (cont d) Rich data on (almost) universe of US subprime mortgages This paper Our first cut at the data Since the data are so rich, we want to be flexible in investigating data patterns while being consistent with a simple model Captures first-order effects Next paper A more structural approach: solve borrowers DP problem Use the results from this paper as inputs 4
Literature Mortgage literature Kau, Keenan and Kim (1994) Deng, Quigley, and van Order (2000) Crawford and Rosenblatt (1996) Archer, Ling, and McGill (1996) Recent subprime Demyanyk and van Hemert (2007) Gerardi, Shapiro, and Willen (2008) Keys, Mukherjee, Seru, and Vig (2008) Danis and Pennington-Cross (2008) 5
Model of Default 1. Optimal Default without Credit Constraints a. Static world without transaction costs: Home equity t it io it ' t ' 1 Default iff V L 0 V V (1 g ) : market value of borrower i's home at time t g it it : nominal rate of increase in home prices b/w time periods t-1 and t it L it : outstanding principal on i's mortgage at time t 6
b. Expectations about home prices Default iff V ( Eg Vg ) L 0 it 1 2 it 3 it it Eg it, Vg it : expected home price trend and volatility Measuring Eg it and Vg it a. No-arbitrage condition: user cost of owning = rental cost Himmelberg, Mayer, and Sinai (2005) recover Eg it from the noarbitrage condition Exp_HMS b. Backward-looking measure: extrapolate from recent past Exp_Bwd for Eg it ; Past Volatility for Vg it 7
c. Future interest payments Default iff V ( Eg Vg ) L (1 IR MR ) 0 it 1 2 it 3 it it 4 it 5 it IR it : measure of how overpriced contractual interest rates are, relative to the market rate P : monthly payments it TM r m it r c it it : number of remaining months until maturity : market interest rate for : contractual interest rate for i i MR it : number of months before next rate reset (for ARMs) 8
2. Credit Constraint a. Period-by-period budget constraint Constraint binds iff Y it Credit it C it P it Y it : income P it : monthly mortgage payments C it : consumption of the composite commodity Credit it : access to credit Proxy Credit it by various measures of credit quality Cit Assume a minimum required level of Y = c i it 9
b. Borrower heterogeneity P Pit Constraint binds iff Z Z ( ) 0 Y it 0i 1 it 2 3 it Yit Z it : borrower's overall credit quality - FICO scores, level of documentation, loan-to-value ratio at origination, monthly unemployment rate at the county level, etc. it 10
3. Empirical Model Bivariate probit with partial observability (Poirier, 1980): Default results from either of two latent causes V U α ( Eg Vg ) ( IR MR ) it 1,it 0i 1 2 it 3 it 4 it 5 it 1, it Lit P P U Z Z ( ) it it 2,it 0i 1 it 2 3 it 2, it Yit Yit (ε 1,it, ε 2,it ) ~ BVN(0, 0, 1, 1, σ) Dependent variable: ND it =1 if NOT default ND 0 (default) U 0 or U 0 it 1, it 2, it 11
Data Loan Performance 85% of securitized subprime and Alt-A mortgages originated 2000-2007 (46-75% of subprime securitized) Contract terms and borrower characteristics Loan amount, mortgage type, contractual interest rates, reset dates, etc. LTV, documentation, FICO, debt/income at origination, etc. Month-by-month performance Actual payments, delinquency- and foreclosure status 12
Data (cont d) Case-Shiller housing price indices for 20 MSAs Impute current value of house by adjusting appraised value at origination by index Zip-code-level demographics (Census) Monthly unemployment rate for counties (BLS) 13
Summary statistics: loan-level variables Prepaid Defaulted Censored All Std dev Fixed-rate 0.268 0.184 0.463 0.315 (0.47) Multiple Liens 0.093 0.150 0.176 0.123 (0.328) LTV at origination 0.766 0.798 0.747 0.764 (0.14) FICO 619 584 646 623 (73.6) FICO<620 0.526 0.717 0.377 0.504 (0.50) 620<=FICO<700 0.320 0.238 0.375 0.327 (0.47) 700<=FICO 0.154 0.045 0.248 0.169 (0.38) Low doc 0.397 0.354 0.445 0.407 (0.49) No. obs. 81,758 14,459 38,735 134,952 14
Time-varying variables in last observed period for each loan Prepaid Defaulted Censored All Std dev log(v/l) 0.524 0.361 0.457 0.487 (0.39) Monthly payment/income 0.320 0.345 0.281 0.312 (0.14) Loan age in months 19.653 20.07 28.84 22.33 (14.09) Months until next reset* 13.95 14.23 13.06 13.74 (10.53) Exp_Bwd 0.118 0.055-0.047 0.064 (0.12) Exp_HMS 1.119 1.086 1.206 1.140 (0.19) Recent volatility of V 1.888 1.033 1.235 1.609 (1.40) No. obs. 81,758 14,459 38,735 134,952 * For ARMs 15
Results: baseline estimates 16
Spec A, eq. 1 Spec B, eq. 1 Log( LV ) 0.613 (0.103)*** 0.659 (0.173)*** Log( LV ) Exp_Bwd 7.416 (1.109)*** 10.459 (2.298)*** Log( LV ) Past Volatility 0.541 (0.111)*** 0.598 (0.155)*** IR -0.171 (0.076)** 0.067 (0.112) MR 0.012 (0.0008)*** 0.015 (0.001)*** FRM 0.693 (0.037)*** 2.049 (0.998)** 17
Spec A, eq. 2 Spec. B, eq. 2 Low Doc -0.153 (0.010)*** -0.160 (0.009)*** FICO/100 0.464 (0.014)*** 0.389 (0.012)*** Original LTV -0.498 (0.042)*** -0.615 (0.038)*** Multiple Liens -0.380 (0.014)*** -0.328 (0.012)*** Unemployment -0.019 (0.003)*** -0.020 (0.004)*** PI ratio Low FICO -0.536 (0.093)*** -0.420 (0.064)*** PI ratio Med FICO -0.657 (0.069)*** -0.558 (0.051)*** PI ratio High FICO -0.381 (0.121)*** -0.361 (0.086)*** Loan Age -0.029 (0.001)*** -0.030 (0.001)*** Loan Age 2 /100 0.038 (0.002)*** 0.039 (0.002)*** Corr(ε 1, ε 2 ) -0.711 (0.091) -0.513 (0.061) No. Obs 2472282 2439607 LL -75917.13-74276.22 18
Marginal effects 19
Marginal effects associated with 1 s.d. change in regressors Spec A Spec B Log( LV ) 44.63% 7.55% Exp_Bwd 21.16% 4.22% Past Volatility 23.52% 2.77% IR -1.04% 0.06% MR 7.25% 1.34% FRM 26.98% 12.00% Low Doc -40.37% -48.54% FICO/100 82.83% 79.90% Original LTV -16.76% -23.82% Multiple Liens -137.40% -127.25% Unemployment -6.43% -7.75% PI Low FICO -23.96% -21.62% PI Med FICO -24.19% -23.61% PI High FICO -10.47% -11.41% 20
Comparing 2004 and 2006 vintages 21
2004 Mean 2006 Mean Δ in Default Probability Log( LV ) 0.539 0.307 55.84% Exp_Bwd 0.123 0.023 39.92% Past Volatility 2.111 1.118 30.26% IR -0.039-0.003 0.68% MR 13.255 16.417-4.09% FRM 0.288 0.242 2.33% Low Doc 0.515 0.434-6.21% FICO/100 6.507 6.181 69.57% Original LTV 0.758 0.771 2.94% Multiple Liens 0.169 0.242 19.01% Unemployment 5.667 4.612-9.01% PI Low FICO 0.347 0.529 44.68% PI Med FICO 0.369 0.362-2.14% PI High FICO 0.284 0.109-30.51% 22
Key Results 1. Falling home prices important driver of mortgage default. eg. 30-yr FRM w/ no downpayment + 20% in home price within first year of purchase 15.4% more likely to default 2. Borrower and loan characteristics affecting ability to pay and credit constraints are as empirically important in predicting default as declining house prices Increase in defaults in recent years is linked to changes over time in the composition of mortgage recipients 3. For any foreclosure mitigation policy to be effective, it must address both declining home equity as well as borrowers ability to pay in the short run. eg. write-downs on loan principal amounts 23
Conclusion Estimate a model of default that Nests competing explanations for borrower behavior Accounts for the interaction of financial incentives with borrower credit constraints in determining outcomes Recent wave of subprime defaults largely explained by decreasing net equity, but also by apparent deterioration in the ability of borrowers to make their monthly payments Next step: fully dynamic model 24
25
Supplements Source: The New York Times 26
For Prime In 2005 Q3 2.34% prime mortgages delinquent 0.41% prime mortgages in the process of foreclosure In 2008 Q3 4.34% prime mortgages delinquent 1.58% prime mortgages in process of foreclosure 27
Source: Inside Mortgage Finance 28
29
Source: Office of Federal Housing Enterprise Oversight 30
FRBSF annual report 31
Source: FRBSF 2007 Economic Letter at the MSA level 32
List of MSAs included in the analysis: Atlanta, Boston, Charlotte, Chicago, Cleveland, Dallas, Denver, Detroit, Las Vegas, Los Angeles, Miami, Minneapolis, New York, Phoenix, Portland, San Diego, San Francisco, Seattle, Tampa, and Washington D.C. 33