An Analysis of SBA Loan Defaults by Maturity Structure. Dennis Glennon * Risk Analysis Division Office of the Comptroller of the Currency

Transcription

1 An Analysis of SBA Loan Defaults by Maturity Structure Dennis Glennon * Risk Analysis Division Office of the Comptroller of the Currency Peter Nigro Department of Finance Bryant College September 2003 Preliminary Draft: DO NOT QUOTE ABSTRACT The financial intermediation literature on small business lending focuses on the determinants and costs to credit access. There is, however, little research examining the repayment behavior of small firms that actually receive loans. In this paper, we address this shortcoming in the literature by examining the default behavior of a sample of Small Business Administration 7(a) guaranteed loans with three distinct maturity structures. We employ a discrete-time hazard approach and show that small-business defaults are time-dependent and that the factors impacting default behavior, as well as its timing, are maturity specific. These results are important to financial regulators in assessing capital requirements for small business loans under Basel II. Specifically, we show the importance of loan maturity, seasoning, economic conditions and other firmspecific factors in assessing capital adequacy for small business credits. Moreover, the detailed results on default and its timing enhance the probability of further deepening in credit markets by encouraging the development of a secondary market for small business loans. JEL code: Keywords: G21 Small Business Loans, Default Risk, Survival Analysis. * The opinions expressed in this paper are those of the authors and do not necessarily reflect those of the Office of the Comptroller of the Currency or the SBA. All errors are the responsibilities of the authors. Correspondence: dennis.glennon@occ.treas.gov, Risk Analysis Division, The Office of the Comptroller of the Currency, 250 E Street, SW, Washington, DC 20219; Tel.: (202) or pnigro@bryant.edu, Department of Finance, Bryant College, 1150 Douglas Pike, Smithfield, RI 02917; Tel (401)

2 I. Introduction Commercial banks play a critical role in financing small firms in the U.S. and loans to these firms represent a relatively large proportion of the exposure to loss within the commercial banking sector. 1 For example, in 1999 U.S. commercial banks held roughly $105 billion in small business loans (i.e., commercial and industrial (C&I) loans less than $250,000) representing 11 percent of their total holdings of C&I loans. 2 Despite the importance of small business lending to bank portfolios, very little is known about their performance. This lack of information makes their treatment under Basel II an issue of concern. In July 2002, the BIS Basel Committee reached agreement on a proposal for the treatment of small firms for banks choosing the IRB approach. Under the proposal, small and medium enterprises (SME) borrowers would be assessed up to a 20 percent lower capital charge relative to the same exposure to a large-firm borrower (Allen, et al., 2003). Moreover, banks could treat their SME exposures as a homogenous portfolio similar to that of retail credits a provision that reflects the fact that both retail and small-business loans are (i) typically made to unrated borrowers; (ii) the credit-risk exposure to any single loan will not cause bank insolvency; and (iii) are typically credit scored. The use of credit scoring models is a relatively new, but growing practice, in the area of small business lending. Akhavein, et al. (2001) find that of the 95 largest banking organizations in their sample, 55 (i.e., 58 percent) had implemented small business scoring models by the late 1990's. Mester (1997) suggests that 70 percent of all banks used credit scoring in their small business lending during a similar time period. More recently, Allen, et al. (2003) state that in 2002 over 350 lenders used the Fair Isaac system alone in the analysis of more than one million loan applicants. 3 The adoption of scoring models as underwriting and account 1 The prominent role of small firms in the economy and banking sector is not unique to the U.S. In fact, in the European Union over 99 percent of all enterprises are also classified as small and medium enterprises (SME). These firms are also heavily dependent on bank loans. For more detail, see the European Business Position on New Capital Adequacy Framework for Banks and Investment Firms, at 2 Banks report their volume of C&I lending by loan size once a year in the June Call Report. models. 3 Some other lenders, such as Wells Fargo, have developed their own proprietary small business scoring

3 management tools has significantly altered the way bank s approach underwriting and managing their smallbusiness loans. Banks are moving away from the more traditional relationship-based approach (Petersen and Rajan, 1994; and Berger and Udell, 1995) and adopting a transactional-based approach similar to that used for retail lending. 4 As a result, small-business lending has become more amenable to the application of more advanced portfolio-risk measurement techniques outlined in the proposed Basel II Accord. Although credit scoring modeling appears to go hand in hand with the use of ratings-based, portfoliorisk measurement techniques, there are limitations to their use as risk-management tools. Credit scoring models are generally developed for the purpose of ranking the population by relative credit quality similar to the way rating-agencies ratings provide a relative measure of credit quality as opposed to predicting the default frequency. Under that objective, these models are developed to discriminate between potentially good and bad accounts using a maximum divergence criterion. 5 Performance is typically defined over a two-year time horizon with defaults identified as charge off or seriously delinquent at any time during the performance period. The timing of default is a factor not considered in the development of these models. However, for amortizing loans (e.g., mortgage, auto, and small-business, but generally not retail, loans), the dollars-at-risk changes over the life of the loans. If the probability of default is also time sensitive, scoring models will tend to under estimate losses initially during that period when the lender s exposure is greatest. For that reason, we argue that the timing of default is as important a factor in loss forecasting as the realization of the event itself and, therefore, should be incorporated directly into the estimation of the default model. 4 Some smaller community banks remain relationship lenders due to their competitive advantages in this type of lending (Berger and Udell 1996). These small institutions, however, will not be subject to the Basel II Accord. 5 Under a maximum divergence criterion, the model is identified (i.e., the factors are selected and their weights derived) by the set of factors that generate the greatest distance between the performance distribution of good accounts and that of bad accounts in the model development sample. In practice, the industry focuses on the size of the KS statistic as the selection criteria. See Thomas (2001) and Rosenberg and Gleit (1994) for a more detailed discussion of the modeling techniques used to develop credit scoring models. 2

4 Credit scoring models also do not typically take into account the effect of changing economic conditions on loan performance. The likelihood of default of loans that fall within the same score range, yet originated at different points in the business cycle, will be very different unless the model explicitly captures the effect of changing economic conditions. Under the static sample design used to develop credit scoring models changing economic conditions cannot be introduced, but must be captured indirectly through ad hoc calibration methods. Data availability problems have limited the amount of research designed specifically to examine the timing and factors influencing small business defaults. In this paper, we use a sample of loans originated under the SBA 7(a) loan guarantee program to gain insight into the time-sensitive of default on small-business loans. 6 Our data set includes loans with varying times to maturity representing short, medium, and long-term loans (i.e., three, seven, and fifteen years to maturity). The different maturity structures allow us to explicitly evaluate the potential impact of both time and the length of time to maturity (i.e., loan duration) on the likelihood of default or loss exposure. In general, we believe that the amortizing structure of small-business loans raises the importance of analyzing the effect of longer maturities on default probabilities; and, if valid, suggests small-business loans of longer maturity should be treated differently under Basel II than other retail credits. Our results show that the default behavior of small business credits varies over the life of the loan. This suggests that, even within a fairly homogenous pool of small business borrowers, the lender s exposure to loss depend on the average duration of the loans. We also find that the determinants of default are maturity specific. For example, we find that longer term credits to small firms are more sensitive to economic conditions than their medium and short-term loans counterparts. Alternatively, we find that corporate structure 6 Although losses on SBA 7(a) guaranteed loans are shared on a pro-rata basis between the lender and the SBA the greater portion borne by the SBA, these loans may not be representative of the full market of loans to small business. 3

5 (corporation and partnerships) has a large influence on the odds of default for short term loans. In addition, we find that, for all three maturity structures, the default rate increases initially, peaks within six to 12 quarters, then declines over the remainder of the time-to-maturity; a result that indicates the timing of default is likely to be an important factor in estimating a lender s exposure to losses for reserve and capital allocation purposes. Finally, because of the relatively long duration of the amortization small-business loans, the loss behavior of small-business loans is likely to be different from that of other retail credits. The remainder of the paper is organized as follows. In Section II, we provide descriptive statistics on the timing of default, as well as default rates by loan, lender and borrower characteristics. We compare the default statistics using pooled (across time) data to that based on a simple non-parametric hazard model. These results show the importance of both maturity and seasoning on the default process. In Section III we develop a discrete-time hazard model incorporating both time-invariant and time-varying factors to better capture the time-dependent default process. We estimate both pooled-sample and maturity-specific models to demonstrate the importance of loan seasoning on the estimates of default to assess if maturity matters for capital adequacy purposes. Finally, we conclude in Section IV with a summary of results and a brief discussion of other potential areas of research. II. Data Our data set includes a randomly selected sample of short (three years), medium (seven years), and long-term (fifteen years) SBA 7(a) loans disbursed between Loan performance was tracked through the third quarter of Although the SBA underwrites loans with fewer than three years to maturity, those loans (primarily lines of credit) span a performance period too short to reflect a time-dependent 7 The data were obtained directly from the SBA and include information on booked accounts only. The sample is truncated in the second quarter The observation period ends in the third quarter of

6 process. 8 As a result, we define the short-term loan category using three-year maturity. The medium maturity group represents the most common loan tenor originated under the 7(a) program. These loans are typically used for working capital and equipment purchase purposes. The fifteen-year maturity is used to represent longer-term credits. These loans typically have a real estate focus. 9 The data set includes information on: (i) loan-specific characteristics such as the guarantee percentage, loan amount, initial interest rate, interest-rate type, a low-documentation indicator and whether the loan was sold in the secondary market; (ii) lender characteristics such as SBA lender type, bank or on-bank, and region (geographic location) (iii) borrower characteristics such as corporate structure, SIC division (industry classification), number of employees, and new/existing-firm status; and (iv) macroeconomic and industry conditions (state-level and industry specific business activity). 10 Table 1 provides an overview of the sample statistics, including a breakdown of the number of both disbursed loans and defaults by the maturity structure and loan cohort. As shown in the table, the sample is heavily weighted toward loans disbursed in the 1990's. This reflects the recent growth in the SBA program. In addition, because the SBA lenders concentrate primarily on mid- to long-term credit needs of small firms, our sample includes a high concentration of medium (i.e., seven-year) and longer-term (i.e., fifteen-year) loans. 8 The majority of the loans with terms to maturity under three years are one-year maturity loans. Although the likelihood of default of the one-year maturity loans is likely to be affected by post-origination changes in macroeconomic an industry conditions, the timing of default is generally monotonically increasing over the performance period. For that reason, we use three-year maturity loans as the shortest period over which a pattern in the time dependency of loan performance is observed. 9 Although loans with tenor greater than fifteen years are available under the 7(a) program (i.e., loans with 20, 25, and 30 years are not uncommon), we use a the fifteen-year term as our long-term category so that, at least, a few cohort groups reach maturity during the performance period ending in The primary strength of the data set is the coverage in both numbers of loan and the long time-period that includes a full business cycle. The cross sectional-time series nature of the data and the fact that it covers a substantial time period greatly increases the power of our statistical analysis. A primary weakness of the data set, however, is the lack of extensive borrower-level and firm-specific characteristics, such as credit history of the borrower and firm, as well as balance sheet and collateral information. 5

7 As a result, short-term (i.e., three-year) loans make up only a small percentage of the pooled sample. 11 The statistics reported in Table 1 also reveal that the mean default rates vary dramatically across maturity length, with the medium maturity default rate twice as high as the short-term rate (22.0 percent vs percent) and the longer term default rate falling in between (18.8 percent). The table also shows a general improvement in loan performance in recent years, when compared to earlier cohorts. For example, the pooled default rate for the 1986 cohort is 26.9 percent, while for the 1993 cohort it is only 12.2 percent. However, the cumulative default rates for the more current cohort groups (i.e., ) appear to have increased possible due to the effects of the 2001 recession. A simple comparison of mean default rates, however, can be misleading due to the fact that several of the more recent loan cohorts and longer term loans have not reached full maturity. Insofar as loans of different maturities, originated over different points in the business cycle, may exhibit different performance behavior over time, the mean default rate values are skewed. To take into account the time at risk, we estimate the hazard rates using a non-parametric estimation technique (i.e., life-table method) in which a specific functional form for the distribution of the underlying duration data is not imposed. Instead, an empirical hazard rate defined as the ratio of the number of events (e.g., defaults) in a given time period to the number of accounts at risk at the beginning of the time period is calculated directly from the data. The results of the non-parametric estimator are plotted in Figure 1, by maturity structure. The plots shows that, in general, the hazard curves are inverted U-shaped functions of time, although the actual shape of the hazard function appears to vary by maturity. For example, the long-term hazard function is relatively flat, increasing slowly over the first eleven to twelve quarters, then falling off gradually over time. The medium and shortterm default rates, however, increase sharply and reach a peak earlier (i.e., within six quarters after origination) 11 The concentration of loans by maturity in our sample reflects the maturity mix in the population of SBA loans and the SBA s focus on the long-term credit needs of small firms. The large percentage of seven- and fifteenyear maturity loans allowed us to use a 20 percent random sample for each of these maturity bucket. However, there are far fewer short-term loans. For that reason, we used a 70 percent sample of three-year maturity loans. 6

8 than the long-term loans. Moreover, the medium and short-term hazard functions exhibit a more distinct decline in the hazard rate over time. We tested for differences in the hazard by maturity structure using several statistic measures (i.e., log-rank, Wilcoxan, and log-likelihood). Although not reported, these tests support the conclusion that the hazard function varies significantly by maturity structure. Table 2 provides descriptive statistics by loan, lender, and borrower characteristics for each of the maturity groups. In Panel A, the average values for several loan characteristics are reported by maturity structure and for the total (or, pooled) sample. These results show that the average guarantee percentage is fairly constant across the three maturity structures, with a mean of 83 percent for the pooled sample. The average loan amount, however, increases with the length of maturity ranging from $60,000 for a three-year maturity loan to roughly $245,000 for a fifteen-year loan. The interest rate at time of origination is relatively constant across maturity groups averaging 10.2 percent overall. Longer maturity loans, however, are less likely to have a fixed interest rate as lenders appear to be shifting more of the interest rate risk onto borrowers. For example, roughly 28 percent of the short-term loans have fixed rates compared to only 20 percent of the long term loans. Finally, in Panel A, we show that a greater percentage of short-term loans are underwritten through the low-doc program. This is not a surprising result, given the loan-size restrictions under the low doc program and the average loan size of each of the three maturities. In Panel B of Table 2, we report the percentage of loans by lender characteristics and maturity length. Regular lenders underwrite the largest percentage of SBA loans (i.e., 69.2 percent overall) relative to CLP (19.7 percent) and PLP (10.5 percent ) lenders. 12 CLP and PLP lenders, however, underwrite a greater share of both the medium and longer term loans. Panel B also reveals that over 96 percent of the loans in our sample were originated by commercial bank lenders and that the percentage is relatively constant across the three maturities. 12 Percentages reported in the tables may not add to 100 percent due to incomplete reporting of all information for a small percentage of loans. 7

9 In Panel C we show that, on average, several borrower characteristics vary by maturity length. The result show that overall the percentage of loans made to new firms is relatively high (31.9 percent) and varies across maturities. However, there is no specific pattern of loans to new firms across the maturity structure (i.e., medium-maturity loans have the highest percentage of loans to new firms). In addition, the average number of employees, which is used as a proxy for firm size, shows no pattern with respect to maturity. In terms of corporate structure (i.e., corporate, partnership, and sole/individual proprietor), the majority of the loans are underwritten to corporations (54.2 percent) followed by individuals (37.1 percent) and partnerships (8.6 percent). Interestingly, a much greater percentage of loans to partnerships, 13.1 percent, are for fifteen-year loans compared to only 7.2 percent and 7.1 percent to three-year and seven-year maturity loans respectively. In Table 3 we provide the descriptive statistics by firm-specific SIC division and geographic location (i.e., region) of the borrower. Panel A shows that the breakdown of SIC divisions is relatively similar across maturity structure. The largest percentage of SBA loans in our sample are to borrowers in the retail trade (Division G) and services (Division I) divisions i.e., 34.2 percent and 30.1 percent respectively. There are, however, some notable differences in the percent of loans originated by borrower location. In Panel B, we report the percentage of loans to firms by census region. The largest percentage of loans were originated in the West region (i.e., over 23 percent of the pooled sample); however, this varies slightly by maturity structure (e.g., the largest percentage of three-year maturity loans were originated in the Northeast region followed by the Midwest). The descriptive statistics reported in Tables 1 through 3 reveal the wide scope and coverage in terms of time period, maturity, geography, business, borrower and loan characteristics of our sample of SBA guaranteed loans. Table 4 summarizes the default behavior by several of these characteristics by presenting the pair-wise comparisons of default rates for all borrowers possessing the specific characteristic compared to those that do not. The pair-wise comparisons of mean default rates, however, do not control for time at 8

10 risk. 13 Panel A of Table 4 shows the pair-wise comparison of mean default rates by various business characteristics. These results suggest that the borrower s corporate structure is an important factor in identifying the credit quality of short-term, but not medium- or long-term loans. For example, three-year maturity SBA loans to corporations are significantly less likely to default than non-corporate borrowers (9.1 percent and 13.1 percent, respectively). Partnerships (17.7 percent vs percent) and individuals (12.3 percent vs percent) are more likely to default relative to their counterparts. For both medium and long term loans, however, there is no statistical difference in the default rates by corporate structure except for seven-year maturity loans to individuals. These loans have a slightly higher default rate (22.9 percent vs percent). New firms are statistically more likely to default than established firms (i.e., pooled sample: 21.1 percent vs percent, respectively). Previous research has shown that factors such as firm age and size have a strong influence on loan default. For example, Bates and Nucci (1990), Evans (1987) and Dunne, Roberts and Samuelson (1989) have found that in the U.S., the probability that a firm will fail over a given period of time decreases with both firm size and age. 14 This result holds for all maturity lengths: short-term (13.6 percent vs. 9.7 percent), medium term (24.0 vs. 21.0) and long-term (17.3 percent vs percent) maturity loans. These results lend support to the hypothesis that new firms are generally more information opaque; that is, in the sense that it is more difficult to judge the relative creditworthiness of those firms in the absence of an extended performance history. 13 Although, the averages figures do not control for time at risk, all loans have been at risk a minimum of 20 quarters. Thus, the short-term loans have matured (or defaulted), while even the youngest of the medium and longerterm cohorts have, at a minimum, reached their peak hazard quarters. 14 These results are not only specific to firms in the U.S. For example, Good and Graves (1993) find in Canada that 45 percent of new firms failed within the first three years during the period, while Honjo (2000) finds that in Japan, firm age and size is related to business failure. 9

11 Although, there is no specific evidence on small firm failure rates by industry classification, Audrestsch (1991) finds that business survival rates vary by industry, while others have found that certain industries are more information opaque and are likely to be subject to credit rationing (Guiso, 2000). 15 In Panel A of Table 4 we report the pair-wise comparison of default rates for four of the eleven SIC classifications. The differences in default rates for long-term loans show that agriculture, forestry, and fishing (SIC division A) and services (SIC division I) industries exhibit much lower default rates, and that borrowers in the manufacturing (SIC division D) and retail trade (SIC division G) industries exhibit statistically higher default rates relative to borrowers operating outside their respective industries. These results appear to be driving those for the pooled data. The differences in default rates for the three and seven-year maturity loan, however, are statistically different for loans in the manufacturing and retail trade industries. There is strong evidence in the literature that regional or industry economic conditions impact failure rates (e.g., mortgage default, see Pavlov, 2000; bond defaults, see McDonald and Van de Gucht, 1999; bank failure, see Calormaris and Mason 2000; firm survival, see Audretsch and Mahmood, 1995, and Kane, Graybeal, and Richardson, 1996). Panel B of Table 4 presents results of the pair-wise comparison of default rates by borrower region. For the pooled sample, we find that four of the five regions exhibit significantly different default rates relative to borrowers outside their respective regions. The Southeast is significantly worse than its counterparts for all maturity groups, while several of the other regions appear to have some strengths and weaknesses. Interestingly, the regions that exhibit the greatest difference in mean default rates within maturity structure are generally different across maturities (i.e., Southeast differential is 8.1 percent for three year; Southwest differential is 4.2 percent for seven year; and West differential is 3.4 percent for 15 year loans). These results suggest that there may be non-specific regional factors that influence small-firm default behavior. 15 The bond rating companies have shown that for large firms differences in bond defaults by industry do exist. For example, see Moody s Historical Default Rates of Corporate Bond Issuers, , January

12 In Panel C and D of Table 4 we report the results of the pair-wise comparisons of mean default rates by several loan and lender characteristics. Variable and fixed interest rate loans have statistically similar default rates across all maturities. Loans originated under the low-doc program exhibit significantly higher default rates for all but the three-year maturity. For example, the seven-year low-doc loans have a 23.9 percent mean default rate compared to a 21.2 percent default rate overall. Finally, in the pooled sample, loans that have there guaranteed portions sold on the secondary market exhibit significantly higher default rates (20.1 percent vs percent) and these results hold for all but the three year maturity length. The univariate analysis in Panel D supports the hypothesis that specialized lenders who have a strong history in underwriting small business credits (i.e., Certified and Preferred) generally underwrite loans to higher credit-quality borrowers. Preferred (PLP) lenders outperform Certified (CLP) and regular lenders over all maturity structures. CLP lenders, however, perform better for only the seven year maturity loans. In addition, the table shows that bank lenders overall experience significantly lower default rates (18.5 percent vs percent); a result that is consistent across the three maturity structures. These results indicate that banks may have some informational advantages over non-bank lenders and support the hypothesis that relationship lending is an important factor in successfully lending to small firms (see Berger and Udell, 1995; Petersen and Rajan, 1994; Mester, Nakamura and Renault (2002); and Cole, 1998). In Table 5, we report the pair-wise comparison of the mean default rates by SBA guarantee percentages and the number of employees. The results in Panel A show that for the pooled sample, the greater the guarantee percentage, the higher the mean default rate. These results suggest that lenders may have less of an incentive to carefully underwrite and closely monitor these loans with higher guarantee percentages given their reduced exposure to loss in the event of default. 16 Alternatively, the higher percentage guarantee 16 Loan monitoring involves paying close attention to firm specific attributes such as investment policy, use of other credit, management changes, personnel changes, strategic plans and project choices (see Mester, 1992). In our sample, the role of monitoring is likely greatest for seven year maturity, since fifteen year loans are typically for real estate purposes which do not require large degrees of monitoring, while the three year length is less susceptible 11

13 may reflect the increased risk associated with borrowers that fail to qualify under the lender s conventional guidelines, or the result of cohort effects since the higher guarantee percentages are from earlier cohorts. In Panel B, pair-wise comparisons of mean default rates by firm size (as represented by the number of employees) are presented. The results show that the average default rate appears to be relatively stable across firm size. In the next section we examine several of the hypotheses discussed above for both the pooled sample and for each separate maturity structure. Using a discrete-time hazard modeling approach, we study the effect of borrower, lender, and loan-specific factors on likelihood of default. The discrete-time hazard approach allows us to capture the effect of time on the likelihood of default and avoid the statistical issues that arise using a single-period (i.e., static) classification modeling technique (Shumway, 2001). Furthermore, this approach allows us to isolate the individual effects of each factor, all else equal, while controlling for the impact of time-at-risk on a borrower s default behavior. Given the different maturity structures, time at risk, and the use of loan proceeds, the impact of several of the factors outlined above may differ across the different maturity structures. Thus, we assess whether we need to estimate separate models for each maturity length and whether small business loans of varying maturities can be treated similarly for capital purposes. III. Discrete Time Hazard Model In this section we model the time-dependent default rate conditional on borrower, lender, and loanspecific characteristics, and regional economic conditions for our sample of SBA 7(a) loans using a discretetime hazard model. The discrete-time hazard model is an empirical analogue to semi-parametric Cox Proportional Hazard model. 17 It is designed specifically to capture the effect of time on the likelihood of default. Under this approach, we can incorporate time-varying covariates such as economic and market to many of these due to their limited time horizon. 17 The discrete time hazard models have been shown to be statistically equivalent to a Cox Proportional Hazard (CPH) model (Allison, 1990; Shumway, 2001; Brown and Goetzmann, 1995; and Deng, 1995). 12

14 indicators directly into the model. We use a hazard model approach to identify the likelihood and timing of default over the life of the loan. Under this approach, the model is designed to measure the probability a loan will default in time t, given that it has survived up until that time (see Appendix 1). At any time t, the hazard rate corresponds to the notion of risk of default in period t a property of a default model that best reflects our objective of measuring the SBA s exposure to loss over time. Under a discrete-time hazard approach, however, the data must be reported in an event history format. That is, for every loan there is an observation for each point in time (i.e., each quarter) over the loan s life-cycle. 18 For that reason, the dependent variable is defined as a binary indicator variable that equals one if the loan defaulted in that period and zero otherwise. 19 More specifically, the dependent variable would be derived as a series of (stacked) binary variables, D i (1),...D i (t) for each loan i over t periods. Each observation D i (t j ) is assigned the value 0 if the loan survives over the period (t j-1, t j.); and a value 1 if the loan is terminated within the specific interval. 20 This design captures the conditional probability of default within the interval (t j-1, t j ), given that the loan survived to t j-1. From our sample of roughly 21,301 SBA 7(a) loans, we generate an event-history sample of almost 390,000 loan-quarter observations, including more than four thousand loans that migrate into default status. The event-history sample design allows us to estimate the hazard model using qualitative dependent variable 18 To illustrate, suppose the data set contains five loans all of which have contractual two-year maturity dates. Moreover, suppose that, of these five, two pay as agreed (eight quarters of payment history for each loan), one pre-pays after one year (four quarters of payment history), one defaults after six months (two quarters of payment history), and the fifth prepays after 18 months (six quarters of payment history). Instead of five observations with a dependent variable assigned a value equal to the number of quarters to termination (either by default or censoring), we would have a total of 28 observations under an event-history sample design. In this example, the first two loans would generate 16 observations, the third loan 4 additional observations, the fourth loan 2 observations, and the fifth loan an additional 6 observations for a total of 28 observations. 19 This is in contrast with a survival time design in which the dependent variable is measured in the number of time periods to default or censoring. 20 For example, for a five-year (i.e., 20 quarters) maturity loan that defaulted in the fourth quarter after origination will contribute a total of only four (out of a possible 20) observations to the development sample in which the dependent variable takes the values D i t = 0, for t = 1, 2, 3; and D i,4 = 1 in the terminal period. 13

15 estimation techniques. More specifically, if we define D * it as a latent index value that represents the unobserved propensity to default conditional on the covariates (Gross and Souleles, 1998), we can model the default propensity as: D * it = x i $ + z i,t N +, (1) = w2 +, where x i is a vector of time-invariant covariates (e.g., borrower, loan, and lender characteristic), z i,t is a vector of time-varying covariates (e.g., economic variables), and $ and N are the corresponding vectors of timeinvariant and time-varying parameters. We write the propensity equation more compactly using w and 2 to represent the full set of covariates and parameters, respectively. If we assume, is distributed as a standard logistic and define: D it = 1 if D * it > 0, D it = 0 if D * it # 0, then the probability that D it = 1 is pr(d * it > 0) = pr(w2 +, > 0) pr(d * it > 0) = pr(, > -w2) pr(d it = 1) = 7(w2) (2) where 7(.) indicates the logistic cumulative distribution function. Equation (2) can be estimated as a standard logit model. In addition to the time-varying covariates z i,t, we include several trend variables to capture the inverted U-shape of the hazard function identified in the non-parametric graph (Figure 1). We test several transformations including a piecewise transformation using annual and quarterly dummies, a quadratic function of time since origination (i.e., age), and higher-order polynomials of the age variable. Although the full results not reported here, we found among all the possibilities that a sixth-order polynomial best fits the shape 14

16 of the pooled data hazard function. The discrete-time model incorporates several time-invariant covariates known at time of origination such as: corporate structure (i.e., Corporation, Partnership, or Individual), number of employees, new or established firm, the borrower s SIC classification, borrower s region, loan amount, interest rate type, low-doc program, SBA lender type (PLP, CLP, or Regular, and bank/nonbank), SBA guarantee percentage, and a regime shift variables that represents the implementation of the FCRA and the expansion of the SBA loan guarantee program (D91). 21 In addition, we test several time-varying economic variables. We utilize region (i.e., state) and industry (i.e., SIC division) specific time-series data that reflect the economic conditions of the region and industry division of the borrowers. For example, we include both the quarterly growth in the state- and industry-specific income and the change in employment from the state and industry division in which the borrower operates from the time of origination. The time-series economic data was then calibrated to match the performance period of the loans. For example, a five-year loan originated in the third quarter 1990 to a wholesaler operating in New York would be matched with the income and employment growth in the wholesale trade industry, in the state of New York, for the full 20-quarters beginning in the third quarter of The next section analyzes several distinct discrete time hazard models. IV. Empirical Results In this section, we summarize the results from several specifications of the discrete-time hazard model. Our initial results are based on a pooled sample across all three maturity groups. The pooled sample results 21 In 1990, the Federal Credit Reform Act (FCRA) was implemented and its purpose was to improve the allocation of resources between government credit programs and other spending initiatives by providing more accurate information to policymakers on their true costs. FCRA requires the SBA to more accurately measure the costs and risk of their credit programs, and placed the cost on a budgetary basis equivalent to other Federal spending programs. 15

17 appear promising. The graphical analysis shows, however, that although the pooled sample model appears to do a reasonable job of predicting defaults on a pooled basis (Figure 2), the model systematically under (over) predicts the number of defaults for short and medium (long) maturity loans (Figure 3a-c). Using the pooled results as a benchmark, we estimate separate models for each of the three maturity structures using the same model specification. The results for the restricted, maturity-specific models show that both the magnitude and level of significance of the covariates vary across models. The maturity-specific models, however, appear to perform better at predicting defaults (Figure 4a-c) relative to the pooled model, especially for the short and long term maturity loans. For that reason, we develop separate unrestricted hazard models for each of the maturity groups. IV.1 Pooled Sample Results The pooled-sample model is presented in Tables 6. These results support the conclusion from the nonparametric hazard analysis that the default probabilities are time dependent. A sixth-order polynomial in age is used to capture the effect of loan seasoning on the likelihood of default. The coefficients on the higher-order age variables are all highly significant. In addition, we find that several borrower, loan, and lender-specific characteristics are associated with the overall credit quality of the loan and the likelihood and timing of default. In general, the impact of each of these factors is consistent with the results of the univariate analysis discussed above (see Tables 4 and 5). A large loan to a new business underwritten using the regular lender low-doc program guidelines, by a non-bank lender with a relatively high SBA guarantee percentage has a higher odds of default over the life of the loan (i.e., experience shorter survival times). These results support several hypotheses about small business lending. First, the results support the hypothesis new firms are generally more opaque and therefore potentially more risky than established firms. Second, it concurs with the previous 16

18 literature that banks have a comparative advantage in underwriting and monitoring loans to small business. 22 Third, the specialized lender programs that SBA identifies as good lenders (i.e., PLP and CLP) are successful at identifying better quality loans, while loans underwritten with limited documentation than conventionally underwritten SBA loans perform worse. In addition, the pooled-sample results suggest that loans made to partnerships are less likely to default, all else equal; a result suggesting that multiple ownership may increase the resources available to avoid bankruptcy. Contrary to the literature on small firms, however, the odds of default increases as the size of the firm based on the number of employees increases, all else equal. 23 The magnitude of this effect, however, is very small (i.e., for every 10 employee increase in firm size, the odds of default increases by 0.4 percent). 24 We also find that industry-specific and regional effects are important determinants of default. Loans made to borrowers in SIC Division G (i.e., Retail Trade) are more likely to default, with a 11.4 percent higher odds of default relative to firms in other SIC categories. Moreover, SIC Division A (i.e. Agriculture, Fishing and Forestry) and Division I (Finance, Insurance and Real Estate) are less likely to default, with odds of default 48.1 and 18.9 percent respectively. Loans originate to firms located in the Southeast region of the US have a higher likelihood of default relative to all but the Southwest region, all else equal. There appears to be no statistical difference in the odds of default of loans to firms in the Southwest and Southeast regions It could also be that nonbanks preferences for risk are greater and, therefore, they underwrite loans that are inherently more risky than their bank counterparts. 23 This result is due in part to selection bias. Larger small firms relying on SBA guarantees are very risky since after attaining this size they should have migrated to the traditional bank loan market. Thus, larger firms in the SBA program are likely to be among the riskiest in this size category. 24 The odds ratios for the discrete covariates reported in Table 6 are calculated as e $. It can be shown that the odds ratio corresponding to an increase in a continuous covariate X from, say, a value x a to x b (b>a) is R= [exp($)] c where c=x b - x a. R is interpreted as the change in the odds for any increase of c-units in the corresponding risk factor X. 25 We analyzed the role of interest rate (spread over prime) and find that a risk-based price relationship does not to hold for several reasons. First, SBA loans are subject to statutory constraints on the rate lenders can charge borrowers. Second, small business loan pricing is often driven primarily by local market conditions and the strength 17

19 Most surprisingly, the size of the SBA guarantee has no impact on the hazard. Given the downward trend in guarantee rates from 1991, part of this effect might be captured in the dummy variable controlling for Federal Credit Reform Act (FCRA). Following the implementation of FCRA in 1990, the SBA modified its lending programs to be consistent with the goal of streamlining risk assessment of government credit programs which included the lowering of maximum guarantee rates. During this same time frame, commercial banks also began implementing the 1992 Basle Accord which altered the capital charges on all commercial loans. The Basle Accord which implemented risk-based capital regulations (RBC) greatly increased the capital charges relative to other assets and may have caused banks to become more active players in the SBA loan market. Whatever the true cause, the odds of default are 30.3 percent lower for loans originated after We introduce time-varying economic conditions factors using a combination of local economic/industryspecific variables. Our results show that an increase in the growth in employment and industry income both calculated from time of origination, decreases the likelihood of default and increases the survival time. If income growth improves by its average amount (i.e., ), the odds of default is reduced by roughly 1.2. percent (i.e., exp(.0548) = 0.988). If employment growth increases by its average amount from origination (i.e., ), the odds of default is reduced by a much higher amount roughly 6 percent (i.e., exp( ) = 0.939). These results support the hypothesis that economic conditions have a significant effect on the estimate of the default probabilities. In the next section, we estimate separate models for each of the maturity structures using the pooledsample model specification (i.e., restricted models). We compare the results of the maturity-specific models to that of the pooled-sample model to determine if our results are sensitive to aggregating over maturity structure. Under a pooled-sample design, it is implicitly assumed that the impact of loan, borrower, and lender characteristics, and economic conditions on default behavior are the same irrespective of the terms to maturity. of the borrower/lender relationship, neither of which is captured directly in the data. 18

20 To the extent that the estimated coefficients are stable across the maturity-specific models, a pooled sample design is justified. IV.2 Maturity-Specific Models: A Comparison to the Pooled-Sample Results In Table 7, we present the parameter estimates from the maturity-specific models using the identical specification as the previous section. 26 Under the hypothesis of no difference in the relationship between borrower, lender, and loan characteristics and economic conditions, and default behavior across maturity length, we should find a relatively stable relationship between the estimated coefficients across the maturity-specific models. Moreover, the magnitude of the maturity-specific coefficients should closely resemble those of the pooled-sample model. The regression parameters reported in Table 7, however, show that the estimated coefficients vary across the three maturity classes and in many cases differ from the pooled results in terms of magnitude and significance. Among the three maturity-specific models, the seven-year model most closely resembles the pooledsample results. This is not surprising given that the seven-year maturity constitutes roughly 60 percent of the event-history observations and more than 70 percent of the defaults. Nevertheless, several of the estimated coefficients for the seven-year model are notably different from those estimated in the pooled sample model. For example, under the maturity-specific model, the odds of default for a new business is only 14.8 percent, which is almost half the amount (27.17) in the pooled-sample model. Second, the variables capturing the shape of the hazard (i.e., age i, i=1,2,..., 6) ) change dramatically to better capture the impact of the seven year maturity, as opposed to fitting a pooled maturity sample. Third, the magnitudes of the impacts of the regional variables (Northeast, Midwest, Central and West) are much smaller than their pooled counterparts suggesting that the role of regional conditions are less important when analyzing the seven year maturity in isolation. Finally, the role 26 See Appendix for a detailed reporting of the maturity-specific regression results. 19

21 of regional/industry employment growth is significantly less under the seven-year model. Income growth is not, however, statistically significant in the seven-year model. The difference between the maturity-specific and the pooled-sample coefficients are even more pronounced for the three-year and fifteen-year maturity models. Consistent with the non-parametric results that show that the shape of the hazard rate is much different for the shortest term loans, the three-year model shows the greatest deviation from the pooled-sample results. First, the shape of the hazard function for the three-year maturity loans is not well represented by a sixth-order polynomial in age. None of the age-related coefficients are statistically significant. 27 Second, although far fewer borrower, lender, and loan characteristics are statistically related to the hazard rate, those that are tend to play a more important role in explaining the expected default behavior. For example, unlike the pooled sample, corporate structure has an important role in explaining default. For example, short-term loans to corporations have a 26.9.percent lower odds of default and partnerships have a 38.3 higher odds of default both relative the missing category individual. For the shortest maturity length, lender type variables do not appear to play any role, while the role of the regional dummies is more pronounced. These results suggest that the regional area where the loan was originated has more of an influence on loan performance than who originated the loan. Finally, the shorter-term loans are not sensitive to region/industry income growth. Given the short term nature of these loans, the role of economic conditions on performance is minimized. The hazard model for the fifteen-year maturity more closely resembles the pooled and seven-year models than the three-year model. The fifteen-year model, however, has some striking results. First, the seasoning coefficients that capture the shape of the hazard are different from the pooled, three and seven year mode and 27 The order of the polynomial was derived from an analysis of pooled-sample data and is applied to the three-given maturity loans for comparative purposes. It is more likely that the sixth-order polynomial is over specified for the three-year maturity loans a result that may affect the statistical significance of the transformed age variables. Preliminary work on the three-year maturity data reveals that a third-order polynomial is a statistically better fit for the shape of short-term loan hazard function. 20