Risky Borrowers or Risky Mortgages Disaggregating Effects Using Propensity Score Models

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2 Risky Borrowers or Risky Mortgages Disaggregating Effects Using Propensity Score Models Abstract: This research examined the relative risk of loans from two broad categories: subprime mortgages and special lending programs targeted to low- and moderate-income (LMI) purchasers. Using the propensity score match method, we constructed a sample of comparable borrowers with similar risk characteristics but holding different loan products. We found that loans in a LMI-targeted community-lending program have a lower default risk than subprime loans, very likely because they were not originated by brokers and lack risky features such as adjustable rates and prepayment penalties. Our results suggest that the higher default risk of subprime loans may not be attributed to borrower risk profile only but is instead significantly associated with certain characteristics of loan products and the origination channel in the subprime market. Keywords Mortgage, Subprime, Default, Propensity Score Match, Low- and Moderate-Income Introduction Prior to the housing meltdown that began in late 2005, conventional, FHA, and subprime loan products had been competing for borrowers, particularly those lowand moderate- income (LMI) borrowers with marginal credit quality in the United States (Ambrose, Pennington-Cross, and Yezer, 2002; Rodda, Schmidt, and Patrabansh, 2005). Traditionally, FHA-insured mortgages were designed to allow households with relatively low down payments and high debt ratios to purchase moderately priced housing. However, from the 1990s, the mortgage industry responded to increased housing demand, technological innovations, and policymakers incentives to promote homeownership with an expanded set of mortgage financing products. Beyond the conventional and government-insured options, the new products may generally be classified into two main categories: (1) subprime mortgage products; 1 and (2) LMI-targeted prime mortgage products. Originally, subprime mortgages were designed as refinancing tools to help borrowers consolidate debt. But recent surprime home-purchase loans became available to borrowers who may have had impaired credit history or were perceived to have elevated credit risks, such as low-doc or no doc borrowers, low-down or zerodown payment borrowers, or borrowers with high debt-to-income ratios (DTI). Subprime mortgages usually do not involve income or geographic limitations but 1

3 studies have generally documented that subprime lending is more likely to be concentrated in certain neighborhoods and among certain racial and ethnic groups (Calem, Gillen, and Wachter, 2004). The LMI-targeted lending programs have been important options for LMI borrows. The Community Reinvestment Act (CRA), which regulates banking organizations, 2 and the Affordable Housing Goals for government-sponsored enterprises (GSEs), 3 are intended to encourage efforts to broaden the supply of mortgage credit and thereby increase homeownership. Such efforts, manifested in the various affordable lending programs of secondary market institutions and individual banks, have helped to expand access to mortgage credit for many LMI borrowers. In general, they offer reduced down payment requirements and greater underwriting flexibility and usually have some income and geographic restrictions (Quercia, McCarthy and Wachter, 2003). Such programs generally involve greater credit risk than traditional prime mortgage lending but are seldom regarded as subprime. Compared to other loan products, subprime loans typically have higher delinquency and default rates. For example, the subprime serious delinquency (90+day or in foreclosure process) rate was 14.4% in the fourth quarter 2007 compared to 1.67 % of prime loans and 6.0% of FHA loans. In addition, subprime mortgages represented 54 percent of newly started foreclosures but only 13 percent of the loans outstanding (MBA, 2008). Immergluck (2008) indicates that subprime loans foreclose at rates 10 times to 20 times the rate of prime loans, when different measures of foreclosures and different definitions of subprime loans are used. The high default rate may reflect the higher level of risk that is more characteristic of subprime borrowers than average prime borrowers. However, many researchers have identified products or features that are more common in the subprime market and that are associated with elevated default risk of subprime loans (e.g. Quercia, Stegman, and Davis, 2007; Pennington- Cross and Ho, 2006). The higher default rates reported in subprime lending may be a result of lending to risky borrowers, risky loan products, or a combination of both. However, how to separate the impact of these two factors is still an empirical research question. The purpose of this study is to investigate the impact of some key loan characteristics of subprime mortgages by comparing the relative risk of loan products in a special lending program and a sample of subprime loans from a proprietary dataset. There are some fundamental questions that need to be addressed if we want to compare the performance of different loan products directly. We typically only observe realized outcomes, conditional on the borrower holding the particular loan product. In that case, receiving a particular loan product would be considered a treatment, and the assignment/selection biases among borrowers of different mortgage products need to be addressed. However, if we focus on similar borrowers holding two types of loans, we should be able to identify whether the difference in their performance is due solely to borrower risk characteristics or to loan terms and features. This would help us answer whether the high default rate of subprime loans is attributable to risky borrowers, risky products, or both. 2

4 In this study, we employed a method called propensity score match (PSM) to create a new sample by matching borrowers holding subprime loans with borrowers holding alternative loan products in a LMI-targeted program based on borrower, loan, and local risk characteristics. A well-specified PSM model is able to reduce bias nearly as well as a randomized controlled trial (see review in Guo, Barth, and Gibbons, 2006). By comparing the performance of the new sample, we can better identify differences between borrowers who received subprime loans and similar borrowers but who received alternative prime products. In other words, instead of focusing on the whole population, we used a matched group to compare the relative risk of borrowers holding different loan products. In this case, it is highly likely that there is significant overlap between the special lending program and the subprime market, as both of them are focusing on LMI households with marginal credit quality. Freddie Mac, for example, finds that about 20 percent of subprime borrowers could have qualified for a prime rate mortgage (Hudson and Reckard, 2005). Because a significant portion of borrowers with marginal credit quality could have gone to either market, the overlap allows us to conduct a meaningful analysis of the performance of different loan products. We included one such program here developed by a nonprofit community development financial institution, Self-Help Ventures Fund (Self-Help). Through the Community Advantage Program (CAP, also called the Secondary Market Program), Self-Help purchases affordable mortgages, such as Community Reinvestment Act (CRA) loans, from participating lenders and then sells them to the secondary market. These loans could not otherwise be sold readily in the secondary market because borrowers typically have high debt ratios, high loan-to-value ratios, limited assets, nontraditional employment, or poor credit history; the loans may also lack private mortgage insurance. Though borrowers in this program usually have greater credit risk than traditional prime borrowers, the vast majority of loans originated under this program feature terms associated with the prime market: thirty-year fixed-rate loans amortizing with prime-level interest rates, no prepayment penalties, no balloons, escrows for taxes and insurance, documented income, and standard prime-level fees. We constructed the sample of subprime loans from a large proprietary database. The results of this study suggest that mortgage default risk may not be attributed to borrower credit risk only; the high default risk seems significantly associated with characteristics of loans products. For borrowers with similar levels of credit risk and who could qualify for the CAP program, the default rate is much higher for those holding subprime loans than for those who obtained CAP loans. The brokerorigination channel, the adjustable-rate terms, and the prepayment penalty all more common in the subprime market seem to contribute substantially to the elevated default risk among subprime loans. The results have important policy implications for how to provide LMI borrowers with sustainable products in the current situation. Literature Review 3

5 Mortgage Choice and Market Overlap in the LMI Market There is an overlap among different mortgage market sectors, meaning that there is a set of borrowers that could have gone to any sector. Research indicates that conventional, FHA, and subprime loan products had been competing for many borrowers, particularly those LMI borrowers with marginal credit quality (Ambrose, et al., 2002; Rodda, et al., 2005). During the beginning stages of the subprime loan market, the subprime lending channel focused almost exclusively on subprime borrowers, who are perceived to be more risky relative to the average borrower, usually because of a poor credit history. 4 However, with the rapid technology development and product innovation in the financial industry, as well as the recent growth in house prices nationwide, subprime mortgages evolved from loans originated to borrowers with a poor credit history to borrowers who might have an acceptable credit score but had perceived elevated credit risk because of other risk characteristics. These could be borrowers who had low-down or zero-down payment, limited ability to cover living expenses after debts (DTI of 50% or more), or no docs or low docs. Based on Loan Performance data, Cutts and Merrill (2007) estimates that the share of subprime loans with limited or no income or asset documentation grew from less than 30 percent in 2001 to over 50 percent by 2006; in the Alt-A segment these loans increased to over 80 percent. As recently as 2002, subprime lending represented only 7 percent of total mortgage originations, but by 2006 its market share was more than 20 percent (Inside Mortgage Finance, 2008). Except for the FHA program, various affordable products provided by special lending programs comprise another product array. Many are conventional programs sponsored by GSEs, such as Fannie Mae s Community Home Buyer s Program and Freddie Mac s Affordable Gold initiative. Some are lender-specific, such as a special lending program developed by a national bank in partnership with a major GSE, described in LaCour-Little (2007). As summarized by Quercia, et al. (2003), affordable products may include an enhanced marketing strategy to attract loan applicants from targeted groups or an automatic second review of some mortgage denials. Most include the use of flexible or non-traditional underwriting guidelines and a requirement for homeownership education or counseling. Flexible underwriting guidelines may include such elements as allowing lower down payments, higher debt ratios, and/or accepting alternative proofs of creditworthiness, typically underwritten by lenders, not brokers and most of them are fixed-rate mortgages. Recent empirical studies suggest that borrowers sort to subprime, prime, or FHA mortgages based on credit characteristics, among other factors. Borrower income and wealth constraints, loan size limits, and differences in underwriting criteria play a role in borrowers choice or assignment of different mortgage products, while there is mixed evidence on the effect of demographics (Pennington-Cross and Nichols, 2000; Courchane, Surette, and Zorn, 2004; LaCour-Little, 2007). In a study investigating mortgage pricing for different racial/ethnicity groups in the prime and subprime market, Courchane (2007) further controls neighborhood risk characteristics, 4

6 including the level of market competition, mortgage denial rate, and the share of population with different levels of education attainments. There are even more reasons why borrowers, especially borrowers with marginal qualification, receive different mortgage products. First, there may be limited access to credit, especially on favorable terms, for LMI borrowers and borrowers in certain neighborhoods. Ambrose et al. (2002) find that conventional underwriting does not adjust to local risk factors to maintain market share; this leaves FHA and surprime lenders to maintain the mortgage credit supply in declining housing markets. More importantly, some studies (for example, NTIC, 2002 and Renuart, 2004) highlight the role of loan steering and abusive push-marketing of FHA and subprime lending practices. This may be a issue serious in the subprime market since lenders have relied heavily on brokers for loan originations. In this paper, we observe that many CAP borrowers have very similar characteristics to subprime borrowers. Some CAP borrowers have high debt-to-income levels, low down payments, limited assets, and/or are somewhat credit impaired, or the loans may lack private mortgage insurance. It seems there is a significant overlap between the CAP program with the subprime sector many subprime borrowers may have qualified for the CAP program and this overlap allows us to conduct a meaningful analysis of the performance of these two loan products. Risk of Subprime Mortgages Generally, research has documented that subprime loans typically have higher delinquency and default rates. Pennington-Cross (2003) suggests that usually nonprime loans 5 do prepay more quickly and default more often than prime loans. Gerardi, et al. (2007) analyze homeownership experiences in Massachusetts over the period and find that home purchases that begin with a subprime mortgage end up in foreclosure almost 20 percent of the time over six times more often than purchases that begin with prime mortgages. As summarized by Immergluck (2008), subprime loans of all types generally foreclose at rates over 10 times the rate of prime loans. To some subprime loans, the high default rate reflects high-risk characteristics of borrowers, such as impaired credit scores, limited household income and assets, or other traits that increase the credit risk to lenders. But some features and loan terms that are more prevalent in subprime products are found to be associated with higher default risk. As summarized by Cutts and Van Order (2005) and Immergluck (2008), characteristics of subprime loans relative to prime loans include: 1) high interest rates and high points and fees; 2) prevalence of prepayment penalties; 3) prevalence of balloon payments; 4) prevalence of adjustable-rate mortgages; 5) popularity of broker originations. Quercia, Stegman, and Davis (2007) find that refinance loans with prepayment penalties are 20 percent more likely to experience a foreclosure than loans without 5

7 these characteristics. Danis and Pennington-Cross (2005) find that prepayment penalties do tend to reduce prepayments and increase the likelihood of delinquency and default among subprime loans. Quercia, et al. (2007) also find that refinance loans with balloon payments are about 50 percent more likely to experience a foreclosure than loans without balloon payments. Subprime borrowers with adjustable-rate mortgages (ARMs) are also found to have a higher risk of foreclosure because of the higher interest-rate risk (Calhoun and Deng, 2002, Quercia, et al, 2007). At the aggregate level, the share of ARMs appears to be positively associated with market risk as measured by the probability of the property value to decline in the next two years (Immergluck, 2008). Subprime hybrid ARMs which have fixed rates for the first two or three years of the mortgage before converting to semi-annual ARMs and usually have prepayment penalties bear particularly high risk of default at the time the interest rate is reset, as recent studies have found (Ambrose, LaCour-Little, and Huszar, 2005; Pennington-Cross and Ho, 2006). Mortgage brokers have been playing an important role in the mortgage market, originating about 30 percent of all mortgages by volume in recent years (Inside Mortgage Finance, 2008). Several recent studies started to compare the pricing of broker-originated and lender originated mortgages (Ernst, Bocian and Li, 2008; Anshasy, Elliehausen, and Shimazaki, 2005). Though it is possible brokers can reduce borrowers search costs and enable them to obtain lower-cost credit, the broker origination channel has been blamed for inadequate disclosure, lack of borrower sophistication, and the compensation system (Belsky and Essene, 2007). Especially, the incentives mechanism of brokers that that ties broker s compensation to loan origination, such as the yield spread premium, 6 may lead to a lack of concern about long term performance of mortgages. Usually these problems are not so pronounced for retail loans because of better internal control, more regulation, and the existence of reputational risk in the retail channel. Empirical evidence on the behavior of broker-originated mortgages is scarce. One exception is based on loan-level data; LaCour-Little and Chun (1999) find that for each of four types of mortgages analyzed, loans originated by a third party were more likely to prepay than loans originated by a lender. Thus, the higher default rates reported in subprime lending may be because of risky borrowers, risky loan products, or a combination of both. Below, we describe the propensity score match method used to clarity this issue. The Propensity Score Match method As noted earlier, data on borrowers mortgage products are not generated by randomized experiments. Usually, researchers are only able to work with observation data of realized outcomes, which is conditional on borrowers obtaining a particular loan product and does not address borrowers assignment/selection biases of different mortgage products. In other words, the borrower s assessment of default risk and the 6

8 decision to apply to a particular loan product may affect the choice of loan terms. Moreover, the lender s subsequent decision to approve or not based on borrower default risk may also be a factor. Especially, for subprime borrowers with low credit scores, they do not have the many choices and in most cases they are told by lenders what they qualify for (Courchane, et al., 2004). Propensity score match (PSM) method was first developed by Rosenbaum and Rubin (1983) as an effort to more rigorously estimate causal effects from observational data. The key assumption of the framework is that individuals selected into treatment and nontreatment groups have potential outcomes in both states: the one in which they are observed and the one in which they are not observed. Thus, the PSM framework assumes that there exists an unobserved outcome under the condition of nontreatment for the treated group, as well as an observed outcome under the condition of treatment. Similarly, subjects of the nontreatment group have both observed and unobserved outcomes. To be fair, we must compare treated and nontreated groups that are similar in everything that affects the outcome, except the receipt of treatment. PSM provides a means for adjusting for selection bias in observational studies of causal effects. The PSM method entails the use of a three-phase procedure. In the first phase, the PSM method summarizes all of the background (covariate) information about treatment selection into a scalar, or propensity score. The propensity score is described as the conditional probability of assignment to a particular treatment given a vector of observed covariates (Rosenbaum and Rubin, 1983). A set of covariates is used to estimate the propensity score of the treatment; and the derived propensity scores can facilitate meaningful comparisons of borrowers. In the second, resampling phase, treated cases are matched to nontreated cases based on the estimated propensity scores; the resulting sample usually is a subset of the original sample. In the last step, regression models or other methods can be applied to the matched group to compare the outcomes of treated and nontreated groups. The advantage of PSM is that it provides an adjustment for selection bias to help support strong inferences about program effects, even though the data come from an observational study and not an experiment. It summarizes multidimensional covariates into a one-dimentional score, while in conventional matching one can hardly find a match from the control group when the number of matching variables increases. The PSM approach has gained increasing popularity among researchers from a variety of disciplines, including biomedical research, epidemiology, education, sociology, psychology, and social welfare (see review in Guo, et al., 2006). But there have been few discussions and applications of PSM in the field of mortgage finance and real estate research. Researchers in this field have been using selection models, instrumental variables, control endogenous switching regression, difference-indifference estimator, or other econometric techniques to perform nonexperimental evaluations of program intervention (Courchane, 2007; Elliehausen, Staten, and Steinbuks, 2007; Di, Ma, and Murdoch, 2007). In this analysis, we used propensity 7

9 score analyses to construct a comparison group of individual subprime borrowers who are well matched to CAP borrowers on a range of characteristics. Data Data for this study come from one LMI-targeted lending program, the Community Advantage Program (CAP), developed by Self-Help in partnership with a group of lenders, Fannie Mae, and the Ford Foundation. Stimulated by the Community Reinvestment Act (CRA), CAP loans were originated under lender-crafted affordable mortgage programs. These programs feature customized loan guidelines tailored to meet lenders CRA goals as well as local market needs. Many of these nonconforming loans are held in lenders portfolios because most of them meet neither the underwriting guidelines used by secondary mortgage market institutions nor the underwriting guidelines for FHA loans. However, under the CAP program, participating lenders are able to sell these nonconforming mortgages to Self-Help, which then securitizes and sells them to Fannie Mae or other investors. Participating lenders originate and service the loans under contract with Self-Help. It should be emphasized that, while many of the borrowers are somewhat credit impaired, the program cannot be characterized as subprime. The CAP portfolio, which is made up of retail originations (in contrast to broker or correspondence originated), features loans with prime terms and conditions with no prepayment penalties and no balloons. The data of subprime loans come from a proprietary database from McDash Analytics, which provides loan information collected from approximately 15 mortgage servicers. While McDash s coverage in the conventional market varies from year to year, during 2004 to 2006 it covered roughly 40 percent of that of the Home Mortgage Disclosure Act (HMDA) data (Ernst, et al., 2008). Its coverage in the subprime market by volume increased from 14 percent in 2004 to over 30 percent in 2006, based on our estimation using data from Inside Mortgage Finance. The McDash data is rich in detail, including over 70 variables related to loan characteristics and performance, such as FICO score, DTI, loan amount, property value, contract rate type (fixed or adjustable), loan purpose (purchase money or refinance), loan type (conventional, FHA, or VA), occupancy status (owner-occupied or not), documentation status (full documentation or not), existence of a prepayment penalty, loan term to maturity, origination channel (wholesale or retail), and delinquency and foreclosure status in each month as well as each property s zip code. There has been no universally accepted definition of a subprime mortgage. Many researchers base the definition on the secondary market s categorization of mortgages, some define a subprime mortgage as a mortgage originated by a subprime lender identified by HUD s annual list, and others use HUD s definition of a highcost mortgage (Gerardi, et al., 2007). For the purposes of this paper we primarily follow the first definition, since we can identify those B&C loans in McDash data. We further consider high-cost ARMs as subprime in this analysis. Less than 20% of loans in our McDash study sample are included solely because they are considered 8

10 high-cost, defined as having a margin greater than 300 basis points. See Poole (2007) for a discussion of the ARM margin in the prime and nonprime market. In addition, we appended to our data selected census and aggregated HMDA variables at a zip code level, including the Herfindahl-Hirschman Index ( HHI ) from HMDA, racial and educational distribution from census, and average FICO scores for all loan originations in the preceding year calculated from the McDash data. We started from a sample of 9,221 CAP loans originated from 2003 to All are first-lien, owner-occupied, fixed-rate conforming home purchase loans with full or alternative documentation. To make sure subprime loans are roughly comparable to CAP loans, as Table 1 shows, we limited our analysis to first lien, single-family, purchase-money, conforming subprime mortgages with full or alternative documentation that originated during the same period. We further excluded loans with missing values for some key underwriting variables (FICO score, LTV, DTI, and documentation status) and loans without complete payment history. Finally, because we want to compare CAP and subprime loans in the same market, we excluded those subprime loans in areas without CAP lending activities and ended up with a sample of 42,065 subprime loans. Table 2 summarizes some important characteristics of both CAP loans and subprime loans in this analysis. Compared to subprime loans, CAP borrowers generally have higher credit score and lower debt-to-income ratios. Figure 1 shows the distribution of credit scores for CAP and subprime borrowers. It is obvious that subprime borrowers tend to have lower FICO scores than CAP borrowers have, but there is a significant overlap in these distributions. About 28 percent of CAP borrowers considerably less than subprime borrowers (about 50 percent) have a DTI higher than 42 percent. Significance tests show that almost all variables across the two groups differ by a statistically significant amount before matching, indicating that the covariate distributions are different between CAP and subprime loans in the original sample. In summary, the CAP and subprime samples have identical characteristics for the following important underwriting variables: lien status, amortization period, loan purpose, occupancy status, and documentation type. They were originated during the same time period and roughly in the same geographic areas. But the two samples differ in other underwriting factors, including DTI, LTV, and FICO score, and in loan amount and some loan features that are more common only for subprime loans. In the next section, we use the PSM method to develop a new sample by matching CAP loans with comparable subprime loans. Modeling using Propensity Score Match Because receiving a subprime is a choice/assignment variable and is not randomly assigned, we used the propensity score match method to adjust the selection bias. In this case, the first step using a well-specified model to estimate the propensity score is the key for the propensity score match method. We used logistic regression 9

11 models to predict the propensity scores (e(x i )) for borrower i (i=1,,n) of receiving subprime loans (W i =1) using a set of conditioning variables (x i ). e(x i )=pr(w i =1 X i = x i ) (1) The choice of explanatory variables for the logistic model serves a paramount role in the entire propensity score analysis. We chose these conditional variables based on a review of mortgage overlap and mortgage choice literature (for example, Courchane, 2007; LaCour-Little, 2007) to determine what characteristics were associated with the use of subprime loans. Specifically, we included the key underwriting factors of FICO score and DTI in our analysis. These variables are assumed to directly affect credit risk and therefore affect mortgage choice/assignment, since higher credit risk is hypothesized to be associated with a greater probability of taking out a subprime mortgage. Lower FICO scores are assumed to be associated with higher credit risk, so we expect subprime loans to capture the majority of the borrowers in the lower ranges. Because higher DTIs are also assumed to be associated with higher credit risk, we hypothesized that borrowers with high DTIs are more likely to take subprime loans. LTV, another important underwriting variable, is also the variable generally considered to raise endogeniety concerns (LaCour-Little, 2007). In this case, higher LTV is one distinctive characteristic of most CAP loans, with over 82 percent of CAP loans having an LTV equal to or higher than 97 percent. By contrast, most subprime loans have an LTV of less than 90 percent. This is consistent with the observation that subprime loans mainly provide additional flexibility for households who are able to make a relatively large down payment. Courchane et al. (2004) also suggest that high LTV may be associated with higher risk but is not necessarily associated with getting a subprime mortgage. We decided not to include LTV variables in the model as our focus is the impact of borrower and neighborhood characteristics on borrowers choice/assignment of mortgages. 7 In addition to underwriting variables, we included loan amount as an explanatory variable since fixed costs are usually a large component of loan originations. We further included several factors measuring local market dynamics and credit risk. We constructed a zip code-level credit risk measure: the mean FICO score for mortgages originated in the preceding year from the McDash data. Our hypothesis is that subprime lenders tend to market in neighborhoods or areas with a larger share of potential borrowers who have impaired credit history. The zip code educational distribution is included as a proxy of residents financial knowledge and literacy. We assume that education attainment is associated with greater financial knowledge and literacy and we expect that borrowers who are more financially knowledgeable are less likely to take out a subprime mortgage. Because some literature suggests that subprime lending is more likely to be concentrated in minority neighborhoods (Calem, et al., 2004), we included the share of minority in the zip code in the models. 10

12 Furthermore, we constructed a zip code-level HHI using HMDA data to measure the extent of competition in the market in which borrowers properties are located. 8 The HHI measure also partially represents the volume of transactions in the area, since more transactions in a hot market could, though not necessarily would, attract more lenders to the market. In addition, we included quarterly calendar dummy variables to account for fluctuations in the yield curve that could affect market dynamics. Table 3 presents the results from logistic regression models for different vintages. Across different years, credit risk measures are highly predictive: Borrower FICO score, coded into buckets with above 720 as the holdout category, is highly predictive of the use of subprime loans; coefficients are relatively large and decrease monotonically as credit score categories increase. In other words, as expected, the higher the FICO score, the lower the probability of taking out a subprime mortgage. Compared to those with very high DTI (>42%), borrowers with lower DTIs are generally less likely to receive subprime loans with only exceptions for the buckets with low DTI (<28%) for the 2005 and 2006 samples. While it seems CAP borrowers had very high DTIs in 2006, the results generally suggest that borrowers with very high DTIs are more likely to receive subprime loans. In all the models, loan amount is positive for the use of subprime loans, consistent with the hypothesis that subprime borrowing involves higher costs, with costs being driven by large fixed components. Further, zip code-level average credit score is statistically significant and negatively related to the probability of taking out a subprime mortgage, suggesting that borrowers in areas with a higher share of low-score population are more likely to receive subprime loans. Zip code-level education performs about as expected, with higher educational attainment roughly associated with a reduced probability of receiving a subprime mortgage. Borrowers in areas with a higher share of minorities are also found to be more likely to use subprime mortgages. Finally, higher HHIs are associated with a lower probability of taking out a subprime mortgage suggesting that, at least in the period from , subprime loans were more likely to be in the markets with more intensive competition and/or more transactions. The PSM method uses propensity scores obtained from the logistic regression to create a new sample of cases that share the approximately similar likelihood of receiving the particular treatment. In this analysis, we defined the logit rather than the predicted probability as the propensity score, because the logit is approximately normally distributed. There are many matching algorithms and this study focuses on the nearest neighbor with caliper matching methods. 9 For the one-to-one nearest neighbor with caliper match, we selected the subprime loan with the closest propensity score within a caliper for the first CAP loan after the subprime and CAP loans were randomly ordered. We then removed both cases from further consideration and continue to select the subprime loan to match the next CAP loan. For the one-tomany match, we matched subprime loans with CAP loans with the closest propensity score within a caliper after all the loans were randomly sorted. Instead of removing the matched cases after matching as in the one-to-one match, we kept the matched CAP loans in the sample and continued to find the matching CAP loan for the next 11

13 subprime loan. This allows us to match as many subprime loans as possible for each CAP loan. The size of the caliper was determined by the investigator; Rosenbaum and Rubin (1985) suggest using a caliper that is a quarter of a standard deviation of propensity score, and we also tried two different calipers (0.1, or 0.25 times of standard error). In other words, we tried two matching algorithms, allowing us to match one CAP loan with one or multiple subprime loans, and we also tried two caliper sizes to test the sensitivity of the findings to varying caliper sizes. Table 4 describes the four matching schemes and numbers of loans for the resamples: Match 1 and Match 2 are based on the one-to-one match; Match 3 and Match 4 are based on one-to-many match. Match 1 and Match 3 use nearest neighbor matching within a more restrictive caliper of 0.1, while other matching schemes employ a wider caliper (a quarter of the standard deviation of the propensity scores, about 0.5 in different models). In theory, a wider caliper increases the matching rate, but it also increases the likelihood of producing inexact matching. The results show that the more restrictive caliper does not result in a dramatic reduction in sample size; we lost about 791 cases (12%) from Match 2 to Match 1 and only one CAP loan from Match 4 to Match 3. Because the qualitative results do not change as we checked and a restrictive caliper can lower the likelihood of producing inexact matching, we focused on the schemes using the more restrictive caliper size of 0.1 (Matches 1 and 3) in our analysis of loan performance in the next step. For the one-to-one match (Match 1), we ended up with a sample of 5,558 CAP loans and the same number of matching subprime loans. For the one-to-many match, a total of 35,971 subprime loans were matched to 3,943 CAP loans (Match 3). Because of using different matching algorithms, the numbers of matched CAP loans are different for the two matches. We checked covariate distributions after matching. Both Match 1 and Match 3 remove the all significant differences between groups except the LTV variables. For the matched groups, as Table 5 shows, borrowers are remarkably similar across all groups except LTV ratios, and we got a reduced but more balanced sample of CAP and subprime borrowers. Compared to CAP loans, which are usually fixed-rate retail loans with no prepayment penalty, subprime loans have distinctive features and terms. A vast majority (86 percent) of subprime loans are adjustable rate mortgages; most (70 percent) were obtained through brokers; and many (41 percent) have prepayment penalties. In summary, we employed a logistic regression models to predict the propensity scores of receiving a subprime loan and two matching algorithms and two matching specifications using different caliper sizes for the nearest neighbor within caliper approach. This design helps us test the sensitivity of study findings to varying matching algorithms and various bandwidth of matching. Performance of the Matched Sample We turn now to the comparison of CAP loans and subprime loans with similar characteristics based on the more balanced matched sample from the propensity score 12

14 match. We observed their outcomes as of March CAP loans had a lower serious delinquency rate: 9.0 percent of CAP loans had ever experienced 90-day delinquencies before March 2008, compared to 19.8 percent of comparable subprime loans (Table 6). Subprime loans also had a higher prepayment rate, with over 38 percent of subprime loans prepaid, compared to about 18 percent for the matched CAP loans. The propensity score match method allows us to construct a more balanced sample of CAP and subprime borrowers based on loan origination information. To study the performance of the new sample, we employed a multinomial regression model to further control factors, many of which are timevarying, that may influence the behavior of borrowers. This study follows the option theory; we can think of mortgage borrowers as having three options each month: DEFAULT: This study treats the incidence of the first 90-day delinquency as a proxy of default because of several reasons. First, it is still a little early to observe the final outcomes, especially foreclosures, of these recent originations. Further, the duration of foreclosures may vary significantly across states and across servicers after a loan enters the foreclosure process, which makes it complicated to compare foreclosure rates of CAP and subprime loans. It is also difficult to construct comparable foreclosure measures for CAP and subprime loans as some seriously delinquent loans were returned to their original lenders primarily because of the limited indemnity rule (see Ding, Quercia, Ratcliffe, 2008, for a detailed discussion). In fact, delinquency is frequently used as a measure of default, especially for recent originations since a certain share of delinquencies usually go to foreclosure eventually (Cutts and Merrill, 2008). PREPAID: If a loan was prepaid before it is seriously delinquent, it is considered a prepayment. ACTIVE: Active and not default (not seriously delinquent in some models) We used a multinomial logit (MNL) to model outcomes with multiple possible states. In each month the loan can be in only one state or outcome (active, default, or prepaid). Since the sum of the probabilities of each outcome must equal one, the increase in the probability of one outcome necessitates a decrease in the probability of at least one competing outcome. Thus the multinomial logit model is a competing risk model. The probability of observing a particular loan outcome is given by: 13

15 Pr( y Pr( y it it ln L = = j) = 1 + T N t= 1 i= 1 j= 0 d βjzit+ γ jsit e = j) = e 2 k = 1 k = 1 ijt 2 e βkzit+ γ k Sit 1 βkzit+ γ k Sit ln(pr( y it = j)) for for j = 1,2 j = 0 (2) where j=0,1,2 represents the three possible outcomes of a loan and the omitted category (j=0) remains active and not delinquent (ACTIVE). d ijt is an indicator variable taking on the value 1 if outcome j occurs to loan i at time t, and zero otherwise. Z contains a set of explanatory variables and β is the coefficient. To identify the difference between the performance of CAP loans and subprime loans, S contains a subprime dummy variable or indicators of subprime loan characteristics. Specifically, we considered the impact of some loan characteristics and terms that are common in the subprime market, such as prepayment penalty, adjustable rates, and the broker origination channel. We constructed eight mutually exclusive dummy variables for all combinations of these three characteristics, such as sub_bro&arm&ppp for broker-originated subprime loans with adjustable rates and prepayment penalties and sub_arm for retail-originated subprime loans with adjustable interest rates and no prepayment penalties. Unfortunately, there are too few loans in the matched sample for retail-originated fixed-rate mortgages (less than 20 for the one-to-one match for each category), which does not allow us to conduct meaningful analysis, and so they were dropped from further analysis. None of the CAP loans have these features, and they are set as the reference group in both models. For the one-to-many matched sample, to ensure that our analysis is representative of the matched set, we apply a system of weights, where the weight is the inverse of number of subprime loans that matched to one single CAP loan. As to other control variables, we considered important underwriting variables, including borrower debt-to-income ratio, credit history, loan age, and loan amount in the model, as well as the put option. According to the option-based theory, home equity plays a central role in determining the probability of foreclosure (Quercia and Stegman, 1992). The value of the put option indicates the ratio of negative equity (unpaid balance minus estimated house price) to the original house price and it is calculated using the unpaid mortgage balance and the estimated house price using the original house price and the house price index (HPI) of the Office of Federal Housing Enterprise Oversight (OFHEO). We recognize that the inclusion of the put option may overestimate the risk of subprime loans since, since as suggested in Zelman, McGill, Speer and Ratner (2007), some subprime loans may have second mortgages that are not captured here. We tried the same models without including the put option variable; although the estimated default rate for the subprime loans are smaller, the qualitative results are fairly consistent with those listed in Table 7 and Table 8. 14

16 The zip code average credit score and county average unemployment rate were included to reflect area credit risk and economic conditions, respectively. Falling interest rates may lead to faster prepayments and drive down delinquency rates as borrowers refinance their way out of potential problems. Rising interest rates can cause payment shocks at the reset date for adjustable-rate mortgages and reduce the ability of borrowers to afford a fixed-rate refinance. To capture the change in interest rate environment, we used the difference between the prevailing interest rates, which is proxyed by the average interest rate of 30-year fixed-rate mortgages from the Freddie Mac Primary Mortgage Market Survey (PMMS), and the temporal average of the prevailing interest rates during the study period (Q to Q1 2008). Consistent with prior work, we further separated the matched sample into two cohorts based years of originations. Subprime loans that originated in 2003 and 2004 were underwritten during a time of historically low interest rates and a strong economy, leading to a relatively good performance with very low default rates (Cutts and Merrill, 2008). Many of them were able to refinance the mortgages or sell the houses because of lax underwriting and high house price appreciation before 2007, which extinguish the default option. Instead, subprime loans that originated in 2005 and 2006, especially subprime ARMs, have not performed as well because of a relaxed underwriting criteria to credit score, lax documentation and verification of income, higher combined loan-to-value ratios, and the popularity of risky loan terms (Bernanke, 2008; Belsky and Essene, 2007). Beginning in late 2005, home prices and economic conditions also worsened significantly, with a sharp deceleration in the national house price index and then outright decline in some markets from the fourth quarter of 2005, rising interest rates from late 2005, and in more recent years a weakening economy. By constructing these two cohorts, we are able to compare the performance of CAP loans and subprime loans that originated in a booming housing market to those that originated in a softening housing market. The results from the MNL regressions based on different matching samples are listed in Table 7 (one-to-one match) and Table 8 (one-to-many match). Model 1 considers the subprime dummy variable only, while Model 2 helps us explain the difference in performance between CAP and subprime loans. The results-based samples using varying algorithms are quite consistent; estimated coefficients for the explanatory variables are of the same sign and similar size. The subprime variables are significant and have expected signs except for a few insignificant coefficients for the prepayment outcome. Since it is not easy to interpret the results based on the coefficients from the MNL regressions, we estimated the cumulative default and prepayment rates in the first 24 months after origination for borrowers with impaired credit score (FICO score ) and with mean value of other regressors, except loan age and loan characteristics, based on the MNL regression results. The estimation results are listed in Table 9. Note that all the estimation results discussed below are based on borrowers with the same characteristics described above. We considered a 90-day delinquency as a proxy of default and a serious delinquency as termination of the loan, although it may still be active after the delinquency. 15

17 Here we summarize some primary findings. First, not surprisingly, the default rate of the cohort is significantly higher than that of the cohort for loans with same loan features. For example, the cumulative default rate (in the first 24 months after origination) increases from 16.3 percent for a 2004-originated subprime loan to 47.0 percent for a 2006-originated one. The estimated default rates of CAP loans, though more muted, have a similar pattern. As mentioned earlier, changes in the underwriting standard, decline in house prices, and changes in economic conditions may help explain performance of different cohorts. Second, there is consistent evidence that subprime loans have a higher default risk and a higher prepayment probability than CAP loans. As mentioned earlier, the estimated cumulative default rate for a 2004 subprime loan is 16.3 percent, about four times that of CAP loans (4.1 percent). For a 2006 subprime loan, the cumulative default rate is over 47.0 percent, about 3.5 times that of comparable CAP loans (13.3 percent). In other words, CAP loans are over 70 percent less likely to default than a comparable subprime loan across different vintages. Third, we found that subprime loans with adjustable rates have a significantly higher default rate than comparable CAP loans. And when the adjustablerate term is combined with the prepayment-penalty feature, the default risk of subprime loans becomes even higher. For a 2004 sub_arm loan (retail-originated subprime ARM without prepayment penalty), the estimated cumulative default rate would be 6.5 percent, slightly higher than that of CAP loans (4.1 percent). But if the adjustable rate subprime mortgage has a prepayment penalty, the estimated default rate increases to 13.5 percent for a 2004 sub_arm&ppp loan (retail-originated subprime ARM with prepayment penalty), over 100 percent higher than that of sub_arm. The same pattern also holds for the 2006 originations. This is consistent with the observation that subprime ARMs have performed worse than fixed-rate products (Bernanke, 2008). Finally, we found that the broker-origination channel is significantly associated with an increased level of default. For example, the estimated cumulative default rate for a 2004 sub_bro&arm loan (broker-originated adjustable-rate subprime loan without prepayment penalty) is 17.3 percent, significantly higher than the 6.5 percent of the sub_arm loans. For a 2006 sub_bro&arm loan, the estimated cumulative default rate is as high as 51 percent, much higher than the 16.8 percent of the sub_arm loans. The same pattern also holds for adjustable-rate subprime loans with prepayment penalties. When broker-originated subprime loans have both an adjustable rate and a prepayment penalty, the default risk for 2004 origination is 5.1 times as high as that of CAP loans (21.8% vs. 4.1%) and for 2006 originations 4.0 times as high(53.8% vs. 13.3%). The results suggest that, all other characteristics being equal, borrowers are three to five times more likely to default if they obtained their mortgages through brokers. When the feature broker-origination channel is combined with the adjustable rate 16