The Impact of Second Loans on Subprime Mortgage Defaults

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1 The Impact of Second Loans on Subprime Mortgage Defaults by Michael D. Eriksen 1, James B. Kau 2, and Donald C. Keenan 3 Abstract An estimated 12.6% of primary mortgage loans were simultaneously originated with a second loan from 2004 until 2008, although relatively little is known about how the presence of such subordinate loans affects the default decisions of borrowers. We use a novel data series of loan servicing records from 2002 until 2010 to identify such borrowers and find evidence that the default behavior of these borrowers significantly differs from borrowers without second loans. Estimating a discrete-time proportional odds hazard model, we find borrowers with a second loan were 62.7% more likely to default each month on their primary loan when conditioning alone on the attributes of the primary loan. However, borrowers of second loans were 58.3% less likely to default on their primary loan as compared to single loan borrowers with equivalent current combined attributes (i.e., loan-to-value, balance, and interest rate). We hypothesize and provide empirical evidence this occurs because borrowers with second loans have the option to sequentially default on each loan since subordinate lenders will not pursue foreclosure if borrowers have insufficient equity. Lenders of defaulted subordinate debt may revisit their decision to foreclose in the future after housing markets start to recover, thus prompting a new round of foreclosures. Keywords: Subprime Mortgages. Foreclosure. Default. Second Loans. HMDA. March 19, Corresponding author. University of Georgia, Terry College of Business, Athens, GA 30602, phone: , fax: , eriksen@uga.edu 2 University of Georgia, Terry College of Business, Athens, GA 30602, phone: , fax: , jkau@uga.edu 3 Universite de Cergy-Pontoise & THEMA, 33 Boulevard du Port Cergy-Pontoise Cedex France, donald.keenan@u-cergy.fr

2 Introduction There was an estimated $955 billion in outstanding second mortgage loans at the end of 2009, with more than 50% of all borrowers having such a second loan (Goodman et al. (2010)). The existence of such secondary loans poses significant undocumented default risks for primary mortgage lenders because lenders are often unaware of their presence and borrowers would have significantly less housing equity than were they to have only the primary mortgage. Despite the importance of this question given the recent dramatic decrease in house prices and increase in foreclosures, relatively little empirical research has investigated how the presence of a second loan affects the underlying default behavior of borrowers towards their primary loan. This study furthers our understanding on this question, through use of a novel data series of loan originations and monthly servicing records from 2002 until 2010 of one of the nation s largest mortgage lenders. Borrowers have traditionally been able to take out a second mortgage subsequent to the origination of their primary mortgage, but increasingly over the last decade borrowers were additionally allowed to originate the primary and second mortgage loans simultaneously (Calhoun, 2005). This loan arrangement, commonly called a piggyback loan structure, proved particularly attractive for home purchasers with less than the traditional 20% down payment. Prior to the ability to co-originate a primary and subordinate loan, home buyers with less than a 20% down payment were required by lenders to take out a single primary loan in the full amount they wished to borrow and then purchase private mortgage insurance (PMI) covering the first portion of any losses incurred by the lender in the event of foreclosure. 1 In more recent times, lenders became 1 Borrowers with less than a 20% down payment were previously required to purchase PMI due to the eligibility requirements of Fannie Mae and Freddie Mac in purchasing the loan on the secondary mortgage market.

3 increasingly willing to allow borrowers to skirt this requirement on low down payment loans, by instead offering two separate loan products. The first was a conventional 80% loan-to-value (LTV) primary mortgage loan which would be paid first from any proceeds in the event of foreclosure. The second loan was for the remainder of the purchase price less down payment and came with a higher contract rate given its higher risk since that lender would only be paid from any foreclosure proceeds exceeding the amount owed to the primary mortgage holder and other more senior liens. 2 The majority of the prior literature on second mortgage loans, especially concerning those simultaneously originated, has been descriptive in nature due to an inability to identify unique borrowers of different loans within data commonly available for research (LaCour-Little, 2007a). Limited by this data constraint, prior research has examined the default patterns of borrowers on either their primary or second loan separately, but have largely been unable to examine both simultaneously for the same borrower. For example, Agarwal et al. (2006a) find important differences in default and prepayment patterns for borrowers of primary and second loans, but were unable to identify in their data which primary loans had a subsequent or simultaneously-originated second loan attached. More recent research has used data that identifies the presence of a second loan at origination, although such data usually contains no information on the subsequent performance and characteristics of these subordinate loans (e.g., see Demyanyk & Van Hemert (2009)). 3 This absence is especially problematic considering the important finding of Agarwal et al. (2006a) that subordinate loans have different default and prepayment patterns than 2 Despite lenders charging a higher interest rate on the second loan for their increased risks, the tax code enabled borrowers to deduct the interest of up to $100,000 of home equity debt from the their taxable income, but not their PMI premiums until the Mortgage Forgiveness Debt Relief Act was passed in 2007 (see Section 163(h) of the US Tax Code). 3 Two exceptions of research using subsequent information on second loans in their analysis are Goodman, Ashworth, Landy, & Yin (2010) and Jagtiani & Lang (2010). We discuss these studies in more detail in the next section. 2

4 primary loans. If borrowers treat the combined loans as one, as commonly assumed in the prior research on the topic, then we should expect the default patterns of borrowers with and without a second loan should be different. More specifically, we should anticipate borrowers with a known second loan, by having either less initial wealth or current housing equity, to be more likely to default on the primary loan. To further our understanding of how borrowers behave in the presence of such loans, we assembled a novel data series of origination and servicing records from one of the nation s largest residential mortgage lenders. We focus on the 64,209 primary 30-year fixed-rate mortgage loans originated by this lender from January, 2002 until February, From this data, we were able to identify 3,078 borrowers who simultaneously-originated a primary and second loan in our data by matching unique borrower and transaction characteristics available in the two samples (e.g., date of origination, zip code, FICO score, and appraised value). Through estimating a discrete-time proportional odds hazard model allowing for continuous and independent forms of unobserved heterogeneity, we then compare the incidence of default on the primary loan by borrowers with and without the known presence of second loans at origination. It is important to note that our data differ from earlier research in that we were able to identify not only the presence of a second loan at origination, but also the subsequent characteristics (e.g., current loan balance) and prepayment of these secondary loans on a monthly basis through December We find borrowers who simultaneously originated a second mortgage loan were significantly 4 While the individual loans in our data were all eventually securitized, we were still able to track subsequent characteristics of the loans since the company providing our data also served as master servicer in aggregating and monitoring payments for the trusts representing secondary market investors. 3

5 more likely to default on their primary loan, holding current attributes of that primary loan constant. Through use of a 0,1 indicator for such borrowers, we estimate these borrowers were 62.7% more likely to default on the primary loan each period. However, we also find borrowers with a second loan were 58.3% less likely to default on their primary loan than borrowers with a single loan of equivalent current combined attributes (hereafter referred to as single loan borrowers). We find this negative estimate is statistically significant and robust to a variety of alternative specifications including allowing for competing risks of prepayment, and restricting the sample to only high CLTV loans at origination to further control for the possibility of unobserved second loans originated by a different mortgage lender. This decreased likelihood of default suggests that current combined loan-to-value (CLTV) and other combined attributes of the two loans are not sufficient in predicting default, since borrowers with two separate loans behave differently than otherwise equivalent single loan borrowers. We argue this occurs because lenders of subordinate loans do not foreclose when borrowers have insufficient home equity given primary loan holders are paid first. Borrowers, aware of such disincentives for the subordinate lenders to pursue foreclosure, therefore treat their ability to default on each loan as separate put options with a subset choosing to default on the their second loan while remaining current on their primary loan payments. We provide supporting evidence of this hypothesis, but cannot rule out that borrowers of second loans may differ as well in other unobserved dimensions. Implications of the research are discussed in the conclusion. Background and Previous Research The use of second mortgage loans is not a recent phenomenon. Borrowers could previously 4

6 originate a subordinate mortgage loan and have found this option attractive when wishing to extract housing equity, and interest rates have increased since they originated their primary loan. However, the prevalence of simultaneously-originated second mortgage loans is a more recent phenomenon, although the historical prevalence of such loans is largely unknown due to a lack of data. This difficulty in collecting quality data is largely attributable to borrowers being able to originate separate loans through two different lenders. Furthermore, even in instances when the primary lender is aware of the second loan s presence, tracking the subsequent performance of both loans together often proves difficult as the two loans may be sold to different investors. Our best gauge of the prevalence of simultaneously-originated second loans is from data collected as a result of the Home Mortgage Disclosure Act (HMDA). This Act requires mortgage lenders in the United States to report, on an annual basis, loan and borrower characteristics for the loans they originate; and starting in 2004 they were also required to report the lien status of any loans originated. LaCour-Little, Calhoun, & Yu (2011) showed that, given reasonable assumptions, it was possible to identify simultaneous-originated second loans in HMDA data through matching unique borrower and loan characteristics present in the data. Using a nearly identical matching methodology, we expand their previous analysis using HMDA data of loans originated from 2004 through 2008 to create the estimates displayed in Table 1a. 5 Of the approximately 60 million primary mortgage loans originated over that time span present in the HMDA data, we identified 7,656,402 borrowers (12.6% of the total) who closed a second loan 5 To identify borrowers who originated a second loan within the same calendar year as a primary loan, we split the HMDA sample by lien status and re-merged the data based on their reported census tract, income, race, ethnicity, sex, property type and occupied status. 5

7 within the same calendar year. Those identified borrowers represent $385 billion in second loans and $1.73 trillion in primary loans. Through the use of unique lender identifiers in HMDA data, we were able to further determine that 45.1% of those loans were originated by the same lender, with the highest percentage (58.9%) occurring during Using the HMDA data, we were also able to identify whether the loans of borrowers with simultaneous primary and second loans were sold to the secondary market. Calhoun (2005), in outlining the institutional details of the mortgage industry, argued that the growth of piggyback loans reflects, in part, the failure of regulation to consider the lien priority of loans when establishing capital requirements for depository institutions. According to this hypothesis, mortgage lenders were more likely to sell the lower yield primary mortgage loan while retaining the higher-risk second loan in their own portfolio. We find evidence that this occurred using the HMDA records, as 46.2% of such primary loans were sold on the secondary market as compared to only 29.5% of associated second loans, a 16.7 percentage point difference. While it is feasible to identify simultaneously originated loans by the same borrower in HMDA data, such data do not contain information on subsequent characteristics and performance of these paired loans. Agarwal et al. (2006a) used individual loan data to compare the relative performance of primary and second loans, and found important differences in default and prepayment patterns for each type of loan. However, they were unable to distinguish which borrowers of primary loans in their sample additionally had a second loan. More recent research by Sherlund (2008), Demanyank & Van Hemert (2009) and Pennington-Cross & Ho (2010) has used data that identifies borrowers with a known second loan at origination, but lacked data on that subordinate 6

8 loan s subsequent characteristics (e.g., current loan balance and delinquency). This is problematic because the borrower s decision to terminate a loan is presumably decided on the basis of the current characteristics of both loans (e.g., loan size, contract rate, etc.) together with the then current economic environment (e.g., house price appreciation and prevailing term structure). Two recent studies have used records on matched primary and second mortgage loans in the First American CoreLogic LoanPerformance Securities (LPS) database. Goodman et al (2010) use the LPS data to illustrate the prevalence of second loans since 2005 and argue a much higher share of borrowers than previously thought have negative equity when both loans are taken into account. Jagtiani & Lang (2010) use the LPS data and attempt to explain why some borrowers chose to default on their primary loan while remaining current on their second loan during the 2008 financial crisis. 6 While our study is similar to Jagtiani & Lang in showing some borrowers with two separate loans may not choose to default on each loan simultaneously, we focus specifically on the default behavior of borrowers with regards to their primary loan given the presence of a second loan, which is much more common in our data. We describe the individual loan data we assembled in the next section and discuss implications of our results in the conclusion. Data Our data consist of primary and secondary mortgage loans originated by one of the nation s largest lenders of residential mortgage loans throughout the last decade. This lender specialized in originating and subsequently servicing higher credit risk loans that were eventually bundled into 6 Although the source of the discrepancy is unclear since both studies use data provided by LPS, Goodman et al (2010) found a much smaller percentage, only 7% as compared to 70% by Jagtiani & Lang (2010), of borrowers chose to default on their primary loan remained current on their second loan (see exhibit 11 on page 29 of Goodman et al, 2010). 7

9 non-agency residential mortgage-backed securities typically labeled as subprime. Our sample is restricted to loans originated by the lender from January, 2002 until February, 2007 when the lender ceased originating new loans, but continued to act as the master servicer for the trusts purchasing the loans on the secondary market. We restrict our sample to the 64,209 primary 30-year fixed-rate mortgage (FRM) loans with an LTV greater than 60% originated by this lender over this time period. Table 1b illustrates the geographic distribution of loans in our sample by Census Region as compared to all and identified subprime primary loans originated according to HMDA from 2004 until While the Southern Census region is over-represented (50.8%) in our own sample as compared to all loans originated over this time period, it is interesting to note that this region had the highest share of subprime loans with more than 41.5% of those originated. The origination data we draw upon is identical to information provided to private investors interested in purchasing loans from the secondary market, and accordingly, we have a rather complete set of borrower and loan characteristics. Table 2a provides a list and brief description of borrower and loan characteristics known at the time of origination in our sample. Table 2b lists the average and other summary measures of loan characteristics for the restricted sample. The average loan amount at origination was $136,000 and represented a loan-to-value (LTV) ratio of 81.4%. The high credit risk nature of borrowers within the sample is illustrated by their average Fair Isaac Credit score (FICO) of 623, although half of the borrowers did exceed the conventional subprime 7 Starting in 2004, lenders required to report HMDA data were also asked to identify primary loan borrowers with an APR more than 300 basis points higher than the US Treasury benchmark in effort to identify subprime borrowers. See Mayer & Pence (2008) for more description of alternative subprime loan when using HMDA data. 8

10 loan cutoff value of 620. The average contract interest rate of loans within the sample was 8.13%, approximately 207 basis points higher than the average 30-year conforming FRM interest rate of loans originated over the same period according to Freddie Mac. In addition, just over 21% of borrowers provided no or only a limited form of income documentation to the lender. Consistent with prior research on subprime mortgage loans, a relatively high percentage of the loans in our sample, 70%, also included a prepayment penalty. Given this lender s already noted specialization originating subprime loans, it is not surprising that the average credit risk of borrowers in our sample is apparently higher than what is typical of agency-conforming residential mortgage loans. The average annual contract rate in our sample was 8.14%, with the average contract rate in any month being 208 basis points greater than the corresponding average 30-year FRM loan prime contract rate, according to Freddie Mac. In addition, 21% of the borrowers provided a low level of income documentation, with 69% of them agreeing to some sort of prepayment penalty. As mentioned earlier, our data are unique in the ability to identify not only which borrowers had a second loan at origination, but also the subsequent characteristics of that second loan. This was accomplished by merging known closed-end second loans in our database with the 64,209 primary loans in our sample, based upon unique borrower and transaction characteristics. These unique characteristics used for the match were day of transaction, FICO score, zip code, structure-type, motivation, intended owner-occupancy status, and the appraised value of collateral. Using this procedure, we identified a second loan existed at origination for 3,078 primary loans, approximately 5% of our total sample. It is important to note we were only able to match second 9

11 loans simultaneously originated by the same lender of the borrower s primary loan. 8 Accordingly, we refer to primary loans without an identified second loan as having an unknown second loan status throughout the remainder of the analysis. Table 2c compares the average characteristics of primary loans with and without a known second loan at origination. Although the two sets of loans have nearly identical loan-to-value ratios of the primary loan, the combined loan-to-value (CLTV) of loans with a known second loan averages almost 100% at origination. The distributions of LTV and CLTV for individual loans (not shown), show the majority of loans in our sample with a known second had an 80% LTV of the primary loan and a 20% LTV second loan. It is interesting to note that while 37% of the primary loans were secured by private mortgage insurance (PMI) policies, we did not identify a single borrower with a second loan and PMI in our sample. We also found that borrowers who co-originated a second loan superficially appeared to offer lower credit and prepayment risks to investors. These borrowers had higher FICO scores, provided higher levels of income documentation, and were more likely to agree to a prepayment penalty. The bottom part of Table 2c reports the average characteristics of the second loans we successfully matched to 30 year fixed-rate primary loans in our sample. Despite merging our fixed-rate primary loans with second loans with both a fixed and adjustable rate, we found no instances where a primary loan was matched to an adjustable rate second loan. On average, successfully matched second loans had a contract interest rate of 8.9%, which was 116 basis points higher than the interest rate on the matched primary loan. 8 To the extent borrowers may have originated a simultaneous or subsequent second loan through a different lender is unknown. We discuss implications of these unobserved second loans on our results in the conclusion. 10

12 In addition to the above origination data, we were also able to obtain monthly servicing records for each of the primary and second loans in our sample, from January, 2002 until December, These data were matched to the origination data through a unique loan identification number established by the lender, which then provided the current payment, balance, and delinquency and prepayment status on a monthly basis. Note that, for the purposes of this study, we define default as the first occurrence of a borrower being 90-days delinquent on their payments, an occurrence which then results in a right-censored observation within our data. In addition, right-censoring of the data also occurs upon prepayment. For the 64,209 primary loans in our sample, we observe 2,315,167 unique loan-month observations where borrowers were at risk of default. Empirical Methods The option-theoretic model of default (Kau et al., 1992) takes the position that the borrower s choice to prepay, default, or continue a loan is solely dictated by the desire to minimize the objective market cost of the loan. Thus, these decisions were decided solely on the basis of the characteristics of the loan (e.g., loan size, contract rate, etc.) together with the relevant characteristics of the current economic environment, such as the current house price and prevailing term structure. Empirical applications of the option-theoretic approach additionally recognize the role of borrower-specific attributes and idiosyncrasies (e.g., reputation, liquidity constraints, etc.) affecting transaction costs associated with exercising their option to default. It remains theoretically unclear exactly how to incorporate the presence and current attributes of a second loan, for the subset of borrowers where one is known to exist. A common practice by 11

13 previous researchers is to combine the known attributes of the two loans and assume that borrowers treat the separate loans as a single loan and so consider only jointly their ability to prepay or default each loan together (e.g., see Demanyank & van Hemert, 2009 or Green, Rosenblatt, & Yao, 2010). More formally, this combined loan hypothesis requires that house price is a homogenous-of-degree-one process, which is needed, not for the simple logic that if the two loans prepay or default together they were no different than a single combined loan, but rather to ensure that CLTV is a sufficient description of the effect of house price on the default decision (see Kau & Keenan, 1995). According to the combined loan hypothesis, the relevant single outstanding loan balance of the combined loan (TotBal) would obviously be L 1 + L 2, where L 1 is the current size of the first loan, and L 2 the size of the second. The relevant single combined loan-to-value (CLTV) ratio would be, (1) where the superscripts denote lien status of the loan and H is the estimated current house value. 9 The relevant contract rate for the combined loan would be the weighted average of the two separate loans, which is to say,, (2) where Rate 1 is the first loan contract rate and Rate 2 is the rate on the secondary loan, with subscripts t removed since each loan s interest rate is fixed for the life of the loan. It is of some interest to observe that even with contract rates on the individual loans fixed, the combined 9 The current house value (H) is estimated each month by adjusting the original appraised value available in the data at the time of origination by an index of subsequent price changes according to the MSA-level house price index produced by the Federal Housing Finance Administration (see 12

14 contract rate is time-varying, because the different individual contract rates cause the different loan components to amortize differently. Using the above defined combined loan attributes, we can estimate the discrete choice P of borrowers to default each period t using a proportional odds estimator defined as log, (3) where we define default as first instance that borrower i is 90-days delinquent on their loan payments. 10 In estimating the above coefficients, we allow for a parametrically flexible piecewise constant baseline hazard (α t ) in three month blocks and control for observed initial borrower and loan attributes, X itk. 11 These additional control variables include: the borrower s Fair Issac credit score (FICO) at the time of origination, whether the borrower provided a low level of income documentation, and 0,1 indicators for whether the loan was secured by private mortgage insurance (Mortgage Insurance), had a prepayment penalty, if the purpose of the loan was for a home purchase, and the collateral was a single-family detached property. The estimated β s from equation (3) are interpreted as the conditional increase in the log odds of a representative borrower choosing to default in a particular month, conditional on not having defaulted in an earlier month, as the result of a one-unit increase in the corresponding attribute, holding other attributes constant. In addition, this estimate assumes any censoring (e.g., due to prepayment) is uninformative with regards to a borrower s decision to default We choose to define default as the first instance of borrower being 90 days delinquent on payments as this is the common threshold when they are declared in default by the lender and foreclosure proceedings typically begin. 11 We choose to estimate a piecewise constant baseline hazard in three months blocks to ensure a default occurs within each period, a necessary condition for identification of our estimates. 12 To account for possible systematic differences between borrowers in prepayment patterns, we additionally control for the spread between prime mortgage interest rates during current and origination month as suggested by Pennington-Cross & Ho (2010). 13

15 As first emphasized by Deng, Quigley & Van Order (2000), it is important to allow for unobserved heterogeneity among borrowers when estimating the above coefficients, although how best to incorporate the heterogeneity remains theoretically unclear. We first follow Nicolleti & Rondinelli (2010) and allow for unobserved heterogeneity v i that is independent, continuous, and normally distributed. A clear advantage of estimating our coefficients allowing for this form of unobserved heterogeneity is they can be derived using similar techniques used for estimating panel data with individual random effects. In addition, testing underlying assumptions of the model, including the combined loan hypothesis, using this estimator were relatively straightforward given its asymptotic properties are well established. An alternative estimation approach is to allow for discrete forms of unobserved heterogeneity as originally suggested by McCall (1996) and first implemented within a real estate context by Deng, Quigley, and Van Order (2000). Their mass-point mixed hazard (MMH) estimator assumes there are two or more different types of borrowers and has the added advantage of allowing for competing termination risks, such as prepayment of the underlying loan. The properties of this estimator, however, are less well established and the exact number of unique types of borrowers remains theoretically unclear. In addition to having to specify the exact number of distinct borrowers, this estimator often also requires the researcher to make stronger parametric assumptions about the baseline hazard function in order to converge (Deng, Clapp, & An, 2006). For these reasons, we choose to rely on the more traditional proportional odds estimator allowing for continuous independent and identically distributed (iid) forms of unobserved heterogeneity when first presenting our estimates, although show later in the paper the main results were robust 14

16 to choice of estimator. 13 It is important to emphasize that neither estimator properly controls for non-independent forms of unobserved heterogeneity. If such correlated and unobserved attributes exist, coefficients derived using either type of estimator will be biased and inconsistent. Results The first indication that borrowers of primary loans who simultaneously originated a second loan behave differently is illustrated at the bottom of Table 3. The first column of that table is restricted to the 61,131 primary 30-year FRM loans where we were unable to identify a second mortgage loan was originated by the same borrower within our data. The second column of that table is restricted to the 3,078 borrowers for whom we identified a second loan. Although a relatively high percent (24.3%) of borrowers with an unknown second loan status defaulted on their primary loan by December 2010, we find those borrowers with an identified second loan were much more likely to default on their primary loan (33.1%) within the same time span. The difference between the two samples (8.8 percentage points) is statistically different than 0 using a conventional t-test, although the timing as to when defaults occurred and the effect of differing loan and borrower characteristics between each of the samples remains unclear from such a simple comparison. The coefficient estimates reported in each column of Table 3 represent the percent change in the odds of default for a one-unit increase of each observed loan attribute, holding other characteristics of the primary loan constant through estimating a proportional odds model of the borrower 13 As a robustness check, we re-estimated all of the results in the paper using an alternative mass-point mixed hazard estimator allowing for the competing risk of prepayment and found qualitatively similar results. Estimates of our main results using this alternative estimator are reported in Table 7. 15

17 defaulting on the primary loan. 14 Standard errors obtained through using the delta method are reported below each estimate in parentheses. As described in the previous section, those estimates were obtained allowing for continuous iid forms of unobserved heterogeneity in a similar fashion to allowing for an individual random effect (RE) in panel data. We find inclusion of the random effect is supported through conducting a likelihood ratio (LR) test of its statistical significance in each model in the paper. 15 It is again important to emphasize including the continuous random effect does not control for correlated loan attributes. The signs of the estimates reported in Column 1 were consistent with past research on mortgage default. Borrowers with a higher current LTV, balance, and contract rate of the primary loan were more likely to default each period. We find that a 1 percentage point increase in current LTV is associated with a 6.1% increase in the odds of default, while a $10,000 increase in the current balance of the primary loan induces a 1.6% increase in these odds. Borrowers providing a low-level of income documentation at the time of origination were also more likely to default, while those with a higher FICO were less likely to do so. In addition, those borrowers using the loan for a home purchase, in contrast to refinancing an existing mortgage loan, were more likely to default each period, other things equal. We also find borrowers of primary loans secured by private mortgage insurance (PMI) with an unknown second loan status were 20.4% less likely to default each period. Conditional on the 14 The percent change in the odds ratio for a 1-unit change in each attribute is calculated for each estimated coefficient β by This transformed coefficient is the estimate reported in the tables. The standard error of the transformed coefficient is reported below each estimate and was obtained through using the delta method. 15 The test statistic of the random effect significance is distributed χ 2 with 1 degree of freedom. Estimates without allowing for iid unobserved heterogeneity were marginally closer to 0, although remained statistically significant at conventional levels. 16

18 characteristics of the primary mortgage, the presence of PMI premiums paid directly by borrowers is thought to make them more likely to default on the margin (e.g., see Epperson, Kau, Keenan, & Muller (1985)). This is not necessarily true with subprime mortgage loans, however, since lenders in the industry often decide to purchase policies and pay the premium themselves, and thus reflect the increased risk of the borrower through charging the borrower a relatively higher contract interest rate making the expected sign less clear (LaCour-Little, 2007b). A third consideration is that borrowers indicated as having PMI may be the borrowers least likely to have an unobserved second mortgage originated through a different lender. Although the determinants for why lenders required additional PMI protection for some borrowers are unobserved, it is reasonable to assume they would be less likely to require PMI for borrowers with a lower initial loan-to-value at origination. Given this, the presence of a PMI policy may serve as an indirect proxy variable for the borrower not having an unobserved second mortgage loan through a different lender since these borrowers would have lower initial loan-to-values. Although there is no way to confirm this hypothesis, this would explain the observed negative effect in our sample. 16 As explained above, the estimates reported in Column 2 of Table 3 were obtained from restricting the sample to only those 3,078 borrowers with a known second loan at the time of origination. While the estimated effects of individual borrower attributes of the two samples were similar, important differences were observed based on observed primary loan attributes. It is important to recognize that the model specified in column 2 is likely to be mis-specified, since LTV, size, and contract rate of the known second loan have been purposely omitted. Reported estimates are biased 16 It is interesting to note that when we restrict the sample to unmatched borrowers with a high loan-to-value at origination, who Ghent & Kundylak (2011) argue are the less likely to have unobserved second loans, the coefficient on PMI becomes positive. 17

19 and inconsistent if those omitted attributes of the second loan are correlated with included attributes of the primary loan and were themselves significant determinants of a borrower s decision to default. For our sample of loans where a second loan was known to exist at origination, we find a larger incremental effect of an increase in the current LTV and balance of only the primary loan on the likelihood of default of that loan. In all almost instances, with the exception of the loan having a prepayment penalty or being secured by a single-family detached property, estimates in each column were statistically different from 0 at the 1 percent level of significance. Table 4 pools the two loan samples. The first column ignores the presence and attributes of the known second loans entirely, as would be the case with prior analyses where this knowledge does not exist. As only 5% of the pooled borrowers were known to have a second loan at origination, the majority of estimated coefficients were similar to those reported in the first column of Table 3. Two interesting exceptions should be noted. The first is that the effect on PMI becomes slightly more negative, increasing from -19.6% in Table 3 to -22.8% in the pooled sample. Since no primary loans with a known second had PMI in our sample, this more negative result is presumably driven by the presence of PMI being highly correlated with not having a second loan originated through a different lender as explained above. We see a similar pattern with loan purpose also becoming more positive; since borrowers who simultaneously originated a primary and second loan were also more likely to do so for home purchase than for refinancing previous loans in our sample (see Table 2c). The second column in Table 4 incorporates a 0,1 indicator variable for the 5% of borrowers additionally known to have simultaneously originated a second loan. Holding all other attributes of 18

20 the primary loan constant, the presence of a second loan is associated with a 62.7% increase in the odds of the borrower defaulting during any given period, and is statistically different than 0 at the 1% level of significance. While this is a large increase, the result should not be that surprising since the option to default on the primary loan becomes considerably more attractive for these borrowers as, by definition, they have less equity than indicated alone by the LTV of their primary loan. Effects of the other observed attributes of the primary loan generally remain similar across the two columns, except for those of attributes argued above to be strongly correlated with the presence of an unobserved second loan (e.g., PMI and loan purpose). The last column of Table 4 replaces the 0,1 indicator for the known presence of a second loan with the observed current attributes of that subordinate loan. We find that a 1 percentage point increase in the LTV of the second loan is associated with a 5.3% increase in the likelihood of default, whereas a $10,000 increases in the second loan s balance results in a 120% increase. To allow a direct comparison of the estimated effect of the contract rate for each loan, we weighted the individual contract rates by the current total share of that loan s balance. Using such weights, we find that while borrowers with a 100 basis higher contract rate of the primary loan were 77.86% more likely to default on the primary loan each period, although we found no statistically significant difference from increasing the interest rate on the second loan. Combined Loan Hypothesis A common assumption in the prior literature is that borrowers with two separate loans behave in the same fashion as borrowers with a single loan of equivalent current combined attributes (e.g., see Demanyank & van Hemert, 2009). This combined loan hypothesis ignores the allocation of 19

21 loan attributes to either the primary or secondary loan and implicitly treats the borrower as having the decision to continue or terminate each loan simultaneously. For example, the researcher when relying on the current combined loan-to-value ratio (CLTV) is treating the borrower with two separate loans of 80% and 15% LTV ratios the same as a borrower with a single 95% LTV loan. If the above combined loan hypothesis is correct, we should find the coefficients for each loan attribute estimated separately in Column 3 of Table 4 to be statistically indistinguishable. Results of the three Wald tests of equivalence are found in Table 5, with the p-value of those test represented in brackets in the third column. While we do find the coefficients on loan balance and contract rate were statistically different from each other, we fail to reject the coefficients on LTV of each loan were different. Table 6 combines the known attributes of the primary and secondary loan and alternatively estimates a single coefficient for each attribute. A second implication of the combined loan hypothesis is that an indicator for presence of a second loan should not have any further descriptive power conditional upon the combined attributes of the two loans. The first column of Table 6 presents estimates combining the loan attributes, while the second column of that table additionally includes a 0,1 indicator for those loans where a second loan is known to currently exist. We find conditional upon the current combined attributes of the two loans, borrowers with a second loan were 58.3% less likely to default each period on their primary loan. Before exploring in more detail why borrowers with second loans with otherwise equivalent current loan attributes were less likely to default on their primary loan, we first provide evidence 20

22 this result is robust to alternative estimators and specifications. First, we re-estimated the specification in Column 2 of Table 6 using McCall s (1996) alternative mass point mixed hazard (MMH) estimator. Although the properties of this estimator are less well established and often require stronger parametric assumptions about the baseline hazard in order to converge, it is an attractive alternative given its allowances for discrete forms of unobserved heterogeneity and the competing termination risk of prepayment (Clapp, Deng, & An, 2006). We follow Pennington-Cross & Ho (2010) and allow for two discrete types of borrowers and a quadratic baseline hazard in estimating the coefficients in Table 7. Using this alternative estimator, we still find borrowers with second loans were still less likely to default on their primary loan conditional upon current combined attributes, although the magnitude of the estimate is somewhat reduced (-27.71%), but still statistically significant. It is interesting to note that while borrowers with known second loans were significantly less likely to default on the primary loan, we additionally find they were significantly less likely to prepay that primary loan as well. The robustness of the negative and significant effect of the second loan on the default of the primary loan holding combined attributes is further illustrated by 9 alternative specifications and sample restrictions in the appendix. These include controlling for higher order polynomials of current combined loan attributes (Table A-1) and further restricting the sample to only high LTV loans at origination to control for the possible presence of unknown second loans originated through different lenders (Table A-2). As explained earlier in the paper, there is a strong possibility that borrowers of primary loans in our sample may have originated simultaneous second loans through different lenders and thus we were unable to identify a second loan existed in our data. As argued by Ghent & Kudlyak (2011), the majority of borrowers who simultaneously originated a 21

23 second loan with a different lender would have an LTV of the primary loan less than or equal to 80% at origination since that loan would have a lower interest rate. By restricting the sample to only those borrowers with a CLTV greater than 80% at the time of origination, the number of borrowers with unobserved second loans should be significantly reduced. Reassuringly, our strong negative estimate of the effect a known second loan persists even after applying this further restriction as specified in Column 3 of Table A-2. Since only the lowest credit risk borrowers may be able to originate a subordinate loan, we place further restrictions on the sample in Table A-3. After limiting the sample to only those borrowers with a FICO score exceeding 620 at origination and providing complete documentation, we continue to find a strong negative and statistically significant effect of the presence of a second loan. We explore reasons behind this result in the next section. Evidence of Separate Default Options In the previous section, we first showed borrowers with a simultaneously originated second loan were more likely to default on their primary loan when only considering the other attributes of the primary loan. We then showed that borrowers with a second loan were less likely to default on the primary loan than single loan borrowers with otherwise equivalent current loan attributes. A possible explanation for this result is that borrowers view their option to default on each loan separately. It is apparent that if a borrower chooses to default on their payments to the lender of their primary loan, that lender will decide to foreclose if the value of the collateral exceeds the cost incurred by 22

24 the lender in acquiring legal title to the property. This foreclosure decision by the primary lender is independent of the status of any subordinate loans, since the primary lender will always be paid first from the proceeds of foreclosure. Given this, it is almost never a dominant strategy for the borrower to default on their primary mortgage loan while continuing to make payments on subordinate loans given that mortgage lender will pursue foreclosure. 17 The borrower, however, may find at least a temporary benefit in choosing to default on payments to subordinate lenders while continue to remain current on the primary loan. This decision hinges on the willingness of the lender of the subordinate loan to pursue foreclosure. Like the primary lender, subordinate lenders have the option to foreclose on property and will accordingly due so when the benefits exceed the costs of such an action. Unlike the primary lender though, subordinate lenders must also take into consideration the value of superior liens on the property when deciding to foreclose since those lenders will be paid first. 18 Even before considering any legal or court costs, the borrower may not have any equity beyond those superior claims on the property after a sufficiently large decrease in house values, making pursuing foreclosure by subordinate claimants essentially fruitless. Borrowers, aware of subordinate lenders in such predicaments, may then decide to suspend payments to those claimants while continuing to remain current on the primary mortgage loan. The main evidence we provide that borrowers actually behave in such a strategic fashion is the non-negligible percentage of borrowers who decide to default on their second loan while 17 Jagtiani & Lang (2010) mention borrowers may have an incentive to default on the primary mortgage while continuing payments on subordinate mortgage loans either due to an ability to borrow further against lines of credit or if default is required for future modification of the primary loan. 18 In addition to the primary mortgage on a property, the borrower may also have superior property tax and mechanics liens on the property. The presence of these additional liens would further erode the desire to pursue foreclosure since a foreclosing junior lien holder takes the title subject to these more senior liens as well. 23

25 continuing to make at least one additional payment towards their primary loan. Of the 3,078 borrowers of primary loans in our sample who we were able to identify simultaneously originated a second loan, 35.6%, or 1,096, decided to default on their second loan by December 2010, the end of our sample period. Of those borrowers deciding to default on their second loan, we found 280, or 25.5%, instances when the borrower defaulted on their second loan (i.e., being 90 days delinquent on payments) without defaulting on the primary loan. It is important to note that although the second lender may decide not to immediately exercise their option to foreclose on the property today; they could still revisit their decision to foreclose in the future if the borrower gains sufficient equity. This could occur to either future house price appreciation or through the scheduled amortization of the primary loan s principal. The defaulted borrower on the second loan, aware of this possibility, will only then continue to pay the primary lender if their implicit value of consumption placed on their continuing to occupy the property on a periodic basis exceeds payments on that primary mortgage loan. Conclusion This paper has shown the presence of second loans and their current attributes to be important determinants of the borrower s decision to default on primary loans. Data limitations have prevented previous researchers from considering the separate effect of such loans, but we have succeeded in assembling a novel data series of second loan simultaneously originated with subprime loans over the last decade through matching unique borrower and transaction characteristics. Through estimating a discrete-time proportional odds model, we show that borrowers with a known second loan were 62.7% more likely to default on their primary loan each 24