Personal Bankruptcy: Reconciling Adverse Events and Strategic Timing Hypotheses Using Heterogeneity in Filing Types

Transcription

1 Personal Bankruptcy: Reconcilin Aderse Eents and Strateic Timin Hypotheses Usin Heteroeneity in Filin Types By Li Gan, Tarun Sabarwal, and Shuoxun Zhan This ersion: March 8, 0 Abstract The strateic timin and aderse eents hypotheses of personal bankruptcy hae receied particular attention. Existin research focuses on proin or disproin either hypothesis, usin a strict interpretation of the role of financial benefit in the filin decision. Usin a more realistic framework in which financial benefit may affect the filin decision in both hypotheses, we show that endoeneity of financial benefit is a distinuishin factor between the two hypotheses. Usin two different datasets, we show that the endoeneity test faors the aderse eents hypothesis. Extendin the analysis to allow for both types, we find eidence of heteroeneity in filin types, consistent with both hypotheses. On aerae, approximately 6 percent of households are more likely to behae as strateic types and 84 percent as aderse eents types. Seeral implications of these results are explored. Keywords: Consumer bankruptcy, personal bankruptcy, aderse eents, strateic timin JEL Classification: D, D4 Gan: Department of Economics, Texas A&M Uniersity, and NBER, an@econmail.tamu.edu Sabarwal: Department of Economics, Uniersity of Kansas, sabarwal@ku.edu Zhan: Department of Economics, Texas A&M Uniersity, shuoxun@econmail.tamu.edu Pae

2 . Introduction Personal bankruptcy rates hae increased at an annual rate of 3.9 percent since 990, from about 78 thousand (non-business) bankruptcies in 990 to about.5 million in 00. There has been widespread debate about the causes of this increase and policy responses to this phenomenon. Partly as a response to this increase, the Conress passed the Bankruptcy Abuse Preention and Consumer Protection Act of 005, the larest oerhaul of bankruptcy laws since 980. This led to a spike in bankruptcies in 005 (about million non-business bankruptcies) just before the law took effect in 006 (about 600 thousand non-business bankruptcies). Since 006, bankruptcies hae continued to rise steadily once more, reachin a leel of about.5 million in 00. Althouh the literature on bankruptcy has rown, some basic questions hae not yet been settled, such as whether consumers behae strateically, and if so, how widespread is this phenomenon. Understandin the motiations of consumers to file for bankruptcy is central to the desin of appropriate policies to manae the number of filins. The study of consumer bankruptcy has hihlihted seeral reasons why a consumer files for bankruptcy. Two hypotheses, aderse eents hypothesis and strateic timin hypothesis, hae receied particular attention. This paper tried to understand and reconcile these hypotheses. The aderse eents hypothesis postulates that consumers file for bankruptcy mainly because they experience aderse eents, and financial stresses associated with such eents. Aderse eents occur, for example, in the form of a job loss, medical problems, and particular family issues such as diorce. Financial stresses associated with such eents arise, for example, in the form of income interruption, income reduction, or debt increase. The literature on consumer bankruptcy is ery lare. A partial list includes the followin. Girth (97) presents early work in this area. Sullian, Warren, and Westbrook (989, 994, and 000) present a ersion of the aderse eents theory. White (987, 998), Domowitz and Sartain (999), Gross and Souleles (00), Fay, Hurst, and White (00), Fan and White (003), Han and Li (004), Lishits, Macee, and Tertilt (007, 008) explore ersions of aderse eents and strateic timin theories and their impact on micro and macro decisions. Ausubel (99, 997) explores aspects of competition in the credit card industry. Theoretical models for default and bankruptcy with competitie and incomplete markets are considered in Zame (993), Modica, Rustichini, and Tallon (999), Araujo and Pascoa (00), Sabarwal (003), Dubey, Geanakoplos, and Shubik (005), Geanakoplos and Zame (007), and Hoelle (009), amon others. Pae

3 The strateic timin hypothesis postulates that a rational consumer incorporates in her decisionmakin, the bankruptcy option aailable under law, and its associated costs and benefits, makes the best use of her economic enironment, and chooses an optimal time to file for bankruptcy. In particular, if the best choice includes a strateic, and lawful, use of debt and the bankruptcy system, then that is reflected in consumer choice. At the heart of each hypothesis is the role of financial benefit in the bankruptcy filin decision. In the strict interpretation, strateic timin hypothesis holds, if, ceteris paribus, filin benefit affects the bankruptcy decision positiely, and aderse eents hypothesis holds, if, ceteris paribus, aderse eents ariables affect a consumer s decision to file. Usin data from the Panel Study of Income Dynamics (PSID), Fay, Hurst, and White (00), (henceforth, FHW,) show that financial benefit is positiely and sinificantly related to the filin decision, and after controllin for financial benefit, aderse eents ariables do not affect the bankruptcy decision (except for a marinally sinificant positie effect of diorce). Usin Surey of Consumer Finances (SCF) data, we document a similar effect of financial benefit, but a stronly sinificant and positie effect of diorce. Thus, usin the strict interpretation, the PSID dataset proides some support for the strateic hypothesis while the SCF dataset proides some support for both the strateic and the aderse eents hypothesis. The strict interpretation implicitly assumes that strateic behaior is the only behaior affectin financial benefit. More realistically, financial benefit from filin oes up when a consumer strateically increases unsecured debt before filin, consistent with strateic behaior; and it also oes up when she uses unsecured debt (e.. a credit card) to pay for expenses due to aderse eents, consistent with aderse eents behaior. Therefore, financial benefit is affected by both types of behaiors, and a positie coefficient on financial benefit alone may not be sufficient to distinuish between the two hypotheses. This point may be made more enerally; we show that in the standard random utility model underlyin the binary choice of filin and not filin, the coefficient on unsecured debt (and hence, on financial benefit from filin) is positie, reardless of how debt is accumulated. Pae 3

4 In this paper, we propose that een when financial benefit may affect the filin decision in either hypothesis, the inclusion of financial benefit as an optimizin ariable is a testable difference between the two hypotheses. In other words, strateic consumers may additionally manipulate debt before filin, but aderse eents consumers do not. We formalize this distinction by inquirin whether financial benefit is exoenous or endoenous to the filin decision. 4 The discussions proide a set of natural instrumental ariables, the aderse eents. Usin both PSID data and SCF data, we show that financial benefit is exoenous to the bankruptcy decision, consistent with aderse eents hypothesis. With both datasets, the coefficient on financial benefit from filin is stronly sinificantly positie. To inquire into the possibility of both types of behaior existin simultaneously, we extend the analysis by estimatin a model with two unobsered types. We find eidence of heteroeneity in types consistent with both behaiors. In particular, financial benefit is shown to be endoenous for the strateic type, and exoenous for the aderse eents type. The coefficient on financial benefit is sinificantly positie for the strateic type and positie but insinificant for the aderse eents type. These results show a role for both hypotheses. Moreoer, most of the ariables for aderse eents hae the same effect on financial benefit for both types, but with a larer absolute effect for strateic types. Not workin lowers financial benefit, increasin unemployment spell increases financial benefit, and diorce increases financial benefit. Health problems present a mixed picture, a positie (and marinally sinificant) effect on financial benefit for aderse types, but decreasin (and insinificant) effect for strateic types. These results document a financial-benefits channel for aderse eents. As the types are unobsered, a mixture-density type of model is used. The exclusion restriction includes access to debt markets (in terms of the number of credit cards), income, a measure of risk aersion, and a measure of financial sainess. Henry, Kitamura, and Salanie (00) proide conditions for the non-parametric identification of mixture-density models. Both Henry, Kitamura and Salanie (00) and Gan, Huan, and Mayer (0) suest a Hausman-type 4 FHW do not explore potential endoeneity of financial benefit. Pae 4

5 specification test. We find supportin eidence of the current two-type model when applyin the test. We find that lower access to debt markets and lower income sinificantly increase the chance of strateic behaior. There is little eidence, howeer, of the effect of risk aersion and financial sainess. On aerae, about 6 percent of the sample is strateic type, and 84 percent is aderse eents type, proidin support for the exoeneity of financial benefit in the one-type model. For comparisons between the two types, the population is diided into two roups. A household is of strateic type, if its type probability is reater than 0.5, and is of aderse eents type otherwise. We find that as compared to aderse eents types, strateic types hae hiher probability of filin and hiher (lo) financial benefit from filin, consistent with the theoretical framework. The estimated model is used to predict effects of hypothesized chanes in key ariables. In particular, we document the effects on filin probabilities resultin from the effect of aderse eents on financial benefits; exhibitin a financial-benefits channel for aderse eents effects. As bankruptcy is a form of insurance, the ideas here may be related to moral hazard in insurance markets, as follows. Moral hazard relates to increasin the benefit from insurance by takin some (additional) actions that increase insurance payoffs. In our ersion, strateic timin behaior is similar to moral hazard, in the sense that these consumers may additionally increase unsecured debt before filin to increase their financial benefit from filin. Aderse eents consumers do not exhibit such moral hazard. Thus, another way to formulate a distinction between the two hypotheses is to inquire whether, and to what extent, moral hazard is present in the bankruptcy decision. The question of aderse selection is not as releant here; in principle, eeryone under the U.S. leal jurisdiction has access to bankruptcy, without hain to pay somethin to be selected into hain a bankruptcy option. The paper proceeds as follows. Section presents the theoretical models and testable predictions, and section 3 presents the econometric specifications, data, and results. Pae 5

6 Theoretical Models and Predictions First, we show a positie relationship between unsecured debt and probability of filin for bankruptcy, reardless of how debt is accumulated. Next, we formulate simple models of aderse eents and strateic timin hypotheses, and hihliht their different predictions.. A Positie Correlation between Financial Benefit and Filin Probability FHW indicate that a positie and sinificant relationship between household financial benefit and probability of filin for bankruptcy sinals strateic behaior by a consumer. Similarly, Adams, Eina, and Lein (009) suest that an increase in probability of default with loan size is consistent with either moral hazard behaior or aderse selection behaior. In the same spirit, we present a simple model showin that financial benefit may affect the probability of filin, reardless of how debt is accumulated. In most empirical work, filin for bankruptcy is modeled as a binary choice model. Accordin to McFadden s Random Utility Maximization model, a person would file for bankruptcy if his utility difference between filin and not filin is positie. To inestiate this difference, let d be unsecured debt and w be assets minus secured debt. For simplicity, the exemptions are normalized to be zero. Financial benefit from filin, ien d, is file, d maxd w,0 financial benefit from not filin, ien d, is Not, d maxw d,0 file d Not d,, if and only if d w.. Notice that, and Let u denote utility from monetary outcomes. Assume that u is strictly increasin and continuously differentiable. We may write utility from filin, ien d as: file, d ufile d ; utility from not filin, ien d as U Not d unot, d U, difference in these utilities is U d U file, d U Not, d. Therefore, d u' file, d ' file, d u' Not, d ' Not d U ',., ; and the Consider the followin cases. Pae 6

7 d > w: In this case, ' file, d and ' Not, d 0. Therefore, ' d u' Not, d 0 U. d < w: In this case, ' file, d 0 and ' Not, d, whence, ' d u' Not, d 0 d = w: In this case, limu' file, d u' file, w u' 0 0 limu' dw dw Not, d u' Not, w u' 0 0 In all cases, we hae ' d 0 U.. U., and similarly, In terms of empirical prediction, this implies that the coefficient on unsecured debt (and consequently, on financial benefit from filin) is positie, reardless of how debt is accumulated. 5 Therefore, ien unsecured debt d, a positie relationship between financial benefit from filin and filin for bankruptcy is expected.. Aderse Eents Hypothesis Frequent support for aderse eents hypothesis has been adanced by Sullian, Warren, and Westbrook (989, 994, 000), amon others. Usin data from bankruptcy filins in 98 (for Illinois, Pennsylania, and Texas), and in 99 (for Illinois, Pennsylania, Texas, California, and Tennessee), these authors paint a rich portrait of consumers in bankruptcy, they present statistics that indicate similarities between bankrupt debtors and the eneral population, especially middle-class families, and they present a ariety of cases and statistics to conclude that while some cases of abuse of bankruptcy law may exist, bankruptcy is predominantly due to aderse eents. As they put it succinctly, 6 No one plans to o bankrupt. In terms of formulatin a model for this hypothesis, it is useful to keep in mind that a pattern that emeres consistently in this hypothesis is that there are some eents for which consumers do not plan (een if they may, in principle, be aware of the existence of such eents), and if such an eent occurs, then they may be compelled to file for bankruptcy. If such an eent does not occur, 5 Notice that all we used here was that u is strictly increasin and continuously differentiable. No additional restriction is imposed on utility. 6 Sullian, Warren, and Westbrook (000), pae 73. Pae 7

8 consumers do not consider filin for bankruptcy. For a statement like this to be true in a model of this hypothesis, it is important to answer at least two questions. First, why don't consumers plan for some eents? Second, een if they don't plan for some eents, why do they not include a bankruptcy option in the eents for which they do plan? Consumers miht not plan for some eents if they assin an eent a subjectie probability of zero. For example, we obsere that in sureys of indiidual mortality, some consumers list as zero their probability of next-period mortality (Gan, Hurd, and McFadden, 005). Such an assinment can arise if the cost of makin ery fine probability distinctions is relatiely hih, or it can arise as a mistake that has a miniscule impact. For example, in the PSID data, the probability of bankruptcy is , as reported in FHW. It is somewhat harder to justify theoretically why, in eents for which consumers otherwise plan, they do not include a bankruptcy option that is leally, and in principle, widely aailable. One explanation for this is that ex ante, the benefit from a bankruptcy filin is low relatie to costs; for example, as reported in FHW, for families that can ain from a bankruptcy filin, the mean benefit from filin is $7,83, and the probability of filin is , for an ex-ante filin benefit of about $5. This is less than the cost of a plannin session with a bankruptcy lawyer, or the resources expended to purchase and plan with a book on how-to-file. Another explanation can be proided in terms of utility penalties arisin from future reputation losses from filin; for example, see Dubey, Geanakoplos, and Shubik (005). Such losses can arise from a combination of restricted future access to debt markets, credit score impact (for seerity of credit score impact, see Musto 004,) and loss of option to re-file for some period (six years for a Chapter 7 filin). If such losses are ery hih when consumers file in the absence of aderse eents, and such losses outweih benefits of filin, then in non-aderse eents, consumers may optimally decide not to consider a bankruptcy option. For example, a bankruptcy fla on a consumer credit report is one of the worst deroatories on a credit report, and it stays there for ten years, but the leal system allows a Chapter 7 re-filin after six years. Consequently, the loner memory of financial institutions of a consumer bankruptcy filin increases the cost of filin by increasin future costs of accessin debt markets. Pae 8

9 Therefore, as a first approximation, we may iew aderse eents consumers as takin decisions sequentially; in period, they plan for some eents, and in such eents, they do not plan to file for bankruptcy, but they do not plan for other eents (termed aderse eents). In period, if a planned-for eent occurs, they consume as planned, and if an aderse eent occurs, they include a bankruptcy option in their decision-makin and re-optimize accordinly. In other words, in period, aderse eents consumers do not plan to o bankrupt. Consider a standard, two-period decision-makin framework. In the first period, there is one decision node. In the second period, one of three states of the world preails; a ood state, indexed, a bad state, b, and a terrible state, t, thouht of as an aderse eents state. Each state corresponds to a decision node, and the probability of each state is π, π b, and π t, respectiely, with π + π b + π t =. As usual, a consumer has to decide how much to consume at each node; his consumption is indexed c 0, c, c b, and c t. Moreoer, lendin markets are aailable to him at a one-period, riskadjusted, market interest rate r. As usual, a sinle consumer takes interest rates as ien. His endowment in consumption units at each node is denoted w 0, w, w b, and w t. (For conenience, suppose w 0 = 0, and 0 < w t < w b < w.) Moreoer, he has to decide how much debt to take, subject to some exoenously specified debt limit; indexed d 0. His twice continuously differentiable on Neumann-Morenstern utility is denoted u (c) with u 0, u 0,lim c 0 u ( c),limc u( c). His expected utility is U u( c 0 ) [ u( c ) b u( c b ) t u( c t )]. An aderse eents consumer takes decisions sequentially. In period, he plans for states, b, and he plans to remain solent in these states, but he does not plan for state t, the aderse eents state. In period, if or b occurs, he consumes as planned, but if t occurs, he considers the option to file for bankruptcy. There are some costs of filin for bankruptcy; usually some loss of assets, court fees, lawyer fees, limited future participation in debt markets, and so on. Benefits of filin include, amon others, dischare of debt, fresh start, and accompanyin wealth insurance. Adaptin a simple form of a Chapter 7 filin, 7 it is assumed that a filer ies up all his assets 7 Historically, Chapter 7 bankruptcies account for about 70 percent of all bankruptcies. Pae 9

10 except any exemptions from forfeiture proided by law, and his debt is dischared. 8 Exemptions specified under law are summarized by e. Consequently, an aderse eents consumer soles the followin problem. Stae subject Stae I : II : max d, c0, c, cb to If u( c t, c c c d c 0 b t 0 ) [ u( c then d w w d b ( r) d set : max( w ) u( c ( r) d t b ( r) d b )], min( w, e)) In Stae I, a consumer decides optimal debt and consumption (d, c 0, c, c b ), and by assumption, he does not file in, b. Gien d > 0, and w t < e, in Stae II, if t occurs, optimal choice is to file and consume c t = w t..3 Strateic Timin Hypothesis A strateic timin consumer is a standard fully rational consumer who includes the bankruptcy option in her maximization problem. Assumptions reardin decision nodes, endowments, utility functions, and expected utility are the same as in the preious case. Moreoer, it is assumed that the bankruptcy process is the same as in the preious case. Of course, the difference is in the optimization problem. In each state in the second period, a strateic timin consumer has an option to file for bankruptcy, and soles the followin problem. t 8 The other main personal bankruptcy cateory, Chapter 3 bankruptcy, accountin for about 9 percent of all cases, can be iewed in this formulation as follows. In this type of filin, a repayment plan proposed by the debtor is confirmed by the Court, and a dischare of remainin debt is proided on successful completion of the plan. In this case, net assets saed and debts dischared depend on the repayment plan, and can be mapped to this model after an appropriate discountin for period of plan. Exemptions proided under law are the same in both cases. Pae 0

11 max d, c 0, c, cb, File, Not subject to u( c ) [ u( c 0 c c c c d 0 b t ) u( c ) u( c )] b b d max( w ( r) d, min( w, e)) max( wb ( r) d, min( wb, e)) max( wt ( r) d, min( wt, e)) d t t The maximum operator for decision nodes in the second period corresponds to the bankruptcy decision. For example, if a consumer decides not to file in, her constraint is w - (+r)d, and if she decides to file, her constraint is min(w, e), where, as before, e captures exemptions permitted in bankruptcy..4 Comparisons between the Hypotheses and Empirical Predictions One distinction between strateic timin and aderse eents hypothesis is that for strateic timin consumers, the bankruptcy decision and the debt decision (and consequently, financial benefit) are jointly determined, whereas for aderse eents consumers, the debt decision (and consequently, financial benefit) is exoenous to the filin decision. This follows immediately from the construction of the two models. For the clearest distinctions between the two hypotheses in terms of financial benefits and probabilities of filin, suppose w w e w. That is, exemptions are sufficiently hih to 0 t b hae non-neatie financial benefit from filin in bad and terrible states, but not necessarily in a ood state. 9 In this case, strateic timin consumers file for bankruptcy in states t and b, and perhaps in as well, whereas aderse eents consumers file only in state t. Therefore, a second distinction is that aderse eents consumers may file less frequently (or equialently, with lower probability) than strateic timin consumers. Another intuitie comparatie statics result that can be seen here formally is that debt use by aderse eents consumers is sometimes less, and neer more than that for strateic timin 9 Appendix A presents details on utility maximizin solutions in this case. Pae

12 consumers. Of course, when debt limits are sufficiently low, both types miht decide to use maximum possible debt, and in this case, debt leels are the same. But notice that the optimal debt leel for aderse eents consumers can be lower than that for strateic timin consumers, because for eery d, MU AE ( d) u'( d) ( r) u u'( d) ( r) u' u'( d) ' w ( r) d ( r) bu' wb ( r) d ST w ( r) d MU not, d ST MU file, d Here, MU ST (not, d) is the marinal utility to the strateic consumer from not filin in state when debt is d, and MU ST (file, d) is the marinal utility to the strateic consumer from filin in state when debt is d. Therefore, if not filin in is optimal for the strateic consumer, then MU AE ST ST ST AE AE d MU not, d 0 MU d, whence d AE < d ST. (Here, d AE is the optimal debt leel for the aderse eents consumer, d ST for the strateic consumer, and we used the easy-to-check fact that MU AE ( d) / d 0.) Similarly, if filin in is optimal for the AE ST ST ST AE AE strateic consumer, then MU d MU file, d 0 MU d, and aain, d AE < d ST. Consequently, unsecured debt (and therefore, financial benefit from filin) is larer for strateic consumers than for aderse eents consumers. In summary, the empirical predictions from the theoretical analysis include: (a) financial benefit is endoenous to the bankruptcy decision in the strateic timin hypothesis and exoenous in the aderse eents hypothesis; and (b) financial benefit and probability of filin for bankruptcy are hiher in strateic timin hypothesis than in aderse eents hypothesis..5 Some Limitations The models presented aboe are simple models, and by no means capture all releant aspects of the bankruptcy decision. Issues related to choosin a particular period to file for bankruptcy, or to repeat interactions with credit markets, or to choice of bankruptcy chapter, or to role of leal adertisin, or to effects on supply of credit, or to effects on work incenties, and so on are not considered here. (Some of these are the subject of other papers, listed aboe.) It is possible to consider some of these issues here in a reduced form by includin parameters for expected ains Pae

13 and losses from delayin a decision, or reduced access to credit markets, or utility penalties for default, and then focusin on parameter alues which make particular ersions of the models more likely to occur, but it is unclear if such additions would yield tractable models, or hae additional applications ien the paucity of aailable data. The results here can be iewed as proidin an indication of alternatie hypotheses bein borne out in the data, rather than a definitie conclusion in faor of one hypothesis or the other. For example, in addition to research supportin different hypotheses, the reported sure in bankruptcy filins before the deadline of October 7, 005 for the new bankruptcy law to o into effect suests that other factors (perhaps informational spilloers emerin from declinin social stima, or lawyer adertisin) are important as well. No doubt, additional work may yield additional testable predictions, and additional research would be ery welcome. 3 Econometric Models and Results In this section, we first proide some information on the data and construction of ariables. Next, we present three specifications and estimation results for each specification. The specifications considered are: a simple Probit model, a one-type model (with joint maximum likelihood estimation), and a two-type model (with joint maximum likelihood estimation). 3. Data description and ariables We use two different datasets to check robustness of our results. One is the combined crosssection and time series sample of PSID households oer the period ; the same dataset is used in FHW. The other is the cross sectional dataset of SCF from 998. In 996, the PSID asked respondents whether they had eer filed for bankruptcy and if so, in which year. This information, combined with other household characteristics forms the basis of our first dataset. The PSID data are enerally of hih quality, but they hae some limitations for a study of this kind. In particular, wealth is only measured at 5-year interals, and it contains less detail on some aspects of use in this study. Moreoer, as documented in FHW, there are only 54 bankruptcy filins oer the period , and bankruptcy filins in the PSID are only about Pae 3

14 one-half of the national filin rate. There were 55 bankruptcy filins in 997, or about.8 percent of households, comparable to the 997 national bankruptcy filin rate of.6 percent. The SCF is cross-sectional only, so we lose the time-series aspect in this case; but there is some information for the year prior to the surey, and on future expectations. SCF also proides us with better wealth data, which reports 997 wealth information and 997 bankruptcy filins. (The surey itself was conducted between June and December of ) In table, we compare financial benefits (discussed below) and unsecured debt between filers and non-filers for both PSID and SCF. Similar patterns emere. In PSID, the mean lo(financial benefit) for filers is more than twice as much than those non-filers. In SCF, filers hae more than three times as much mean lo(financial benefits) than non-filers. In both SCF and PSID, the mean lo(unsecured debt) for filers is reater than that of non-filers. Financial benefit from filin is the key ariable in this paper. It is calculated as follows: max[ debt max( wealth exemption, 0), 0] In this formula, max( wealth exemption, 0) calculates the nonexempt assets that a filer loses in bankruptcy. It measures financial cost of filin for bankruptcy. The ariable debt measures the unsecured debt that will be dischared in bankruptcy; a measure of benefit of filin. As not filin dominates filin when debt max( wealth exemption, 0) is neatie, the financial benefit from filin is truncated at 0 to yield the aboe formula. To calculate financial benefit in the PSID, we use the same dataset as FHW. For the SCF, we make the followin adjustments. The SCF proides only reion codes; state codes are not released in public data. To et a relatie weiht for each state in a reion, we use Reional Economic Information System (REIS) from the Bureau of Economic Analysis. These 0 See Kennickell et. at (998). A more complete measure of costs would include both out-of-pocket filin costs, and future costs resultin from more restricted access to debt markets. Reliable data on these measures is not aailable. Addin a constant, of course, would not chane the qualitatie results. Pae 4

15 state weihts are based on the population of a state relatie to the reion in which it is included. These weihts are used to compute the composite exemption leel of a reion. Usin Elias, Renauer, and Leonard (999), we determine each state s exemption leels for 998 for homestead equity in owner-occupied homes, equity in ehicles, personal property, and wildcard exemptions. We adjust for state leel ariables to the extent we can. For example, if a state doubles exemptions for married households, we do the same. For the fifteen states allowin residents to choose between state or federal exemptions, we take the larer of the exemptions. For households in states with an unlimited homestead exemption, we take the homestead exemption to be the aerae of home alues in the entire sample. The ariable exemption is assumed to be the sum of these exemptions, because we do not obsere a household s state of residence. The ariable wealth is the sum of net worth of businesses a household owns, current alues of the ehicles it owns, and alue of real estate it owns. To make the two datasets consistent with each other, we include a ector of demoraphic ariables which may be related to households filin decisions, such as ae of household head, years of education of the head, family size, whether head owns their home. Moreoer, as aderse eents ariables, we include spell of unemployment, its squared term, whether the head is unemployed, whether the head s marital status is diorce, whether the head s health condition is poor. For the PSID dataset, these ariables are calculated usin the alues of correspondin ariables in the year prior to their bankruptcy. For the SCF data, we include only the reion dummies rather than macro information to capture the local fixed effects due to the lack of information reardin state of residency. 3. Simple Probit model Let s first consider a simple Probit reression, similar to FHW s specification. file X AE u 0 This specification explores the strateic timin and aderse eent hypotheses by runnin the Probit reression of whether households file for bankruptcy (file) as a function of their potential Pae 5

16 financial benefit,, from filin, their personal and state characteristics X, and the aderse eents they encountered in the preious year, AE. As described aboe, the strict interpretation focuses on the sinificance of the coefficients on financial benefit and on aderse eents. If strateic timin hypothesis is true, the coefficients of financial benefit should be positie and sinificant while the aderse eent ariables should not be sinificant. If aderse eent hypothesis is true, then aderse eent ariables should be positie and sinificant while the coefficient of financial benefit should be insinificant. Table illustrates this simple specification with PSID data and SCF data. (For ease of comparison, we keep the other ariables same as those in FHW.) As shown in table, usin PSID data, the coefficients on the ariables are comparable to those reported in FHW. In particular, financial benefit affects the filin decision positiely and hihly sinificantly, and its squared term is hihly sinificant. Amon statistically sinificant aderse eents, diorce is positie but only marinally sinificant. Moreoer, usin SCF data, financial benefit continues to be positie and hihly sinificant, but its squared term is not sinificant any more. The coefficient on diorce remains positie, but is hihly sinificant. Thus, usin the strict interpretation, and the simple Probit model, the PSID dataset proides support for the strateic hypothesis while the SCF dataset proides support for both the strateic and the aderse eents hypothesis. 3.3 One-type model (MLE) Gien the limitation of the strict interpretation, we propose to test the endoeneity of financial benefit by jointly estimatin financial benefit and the bankruptcy decision. The basic empirical model here is: file file if file 0 X ln( ) u, (3) file 0 if file 0 For all estimates, indicates sinificance at 90 percent, at 95 percent, and at 99 percent. Pae 6

17 if 0 ln( ) X AE, (4) 0 if 0 Notice that endoeneity of ln(+) is equialent to whether the error terms u and are correlated. The key difference between this model and FHW s specification is the role of the set of aderse eents, AE. Here, AE no loner directly affects a person s bankruptcy decision. Instead, it seres as the set of instrumental ariables that directly affects the financial benefits,, in (4). Another minor difference between these two models is that the loarithm of financial benefit is used here while FHW use the leel of financial benefits. As depends on the wealth leel, it is most likely to exhibit a lo-normal distribution, althouh censored at zero. With a loarithm transformation, we will assume that is normally distributed. Let Var(u) =, Var ( ), and assume the relationship between u and as follows: u, where Co(, ε) = 0, and Var ). In this ersion, testin if ln(+) is endoenous is ( equialent to testin if the parameter = 0. The probability a household files when financial benefit is zero is ien by Pr file,ln( ) 0 X AE X d, and therefore, the probability it does not file when financial benefit is zero is ien by Pr file 0,ln( ) 0 X AE - X d. Similarly, Pr( file,ln( )) X ln( ) ln( ) X AE ln( ) X AE, and Pae 7

18 Pr( file 0,ln( )) X ln( ) ln( ) X AE ln( ) X AE. The lo-likelihood function oer the sample is ien by l file0,ln( ) 0 ln Prbank 0,ln( ) 0 lnprbank,ln( ) 0 ln file0,ln( ) 0 file,ln( ) 0 Prbank 0,ln( ) 0 lnprbank,ln( ) 0 file,ln( ) 0 (5) Estimation results are presented in tables 3 and 4. 3 We find that usin either PSID data (table 3), or SCF data (table 4), the estimated parameter θ is not statistically different from zero, consistent with the aderse eents hypothesis. At the same time, lo financial benefit has a positie and hihly sinificant effect on the decision to file for bankruptcy in both datasets. Both datasets confirm the iew that aderse eents may affect financial benefit. In the PSID data (table 3), health shocks and period of unemployment increase financial benefit hihly sinificantly, whereas a switch from workin to not workin (no work dummy) decreases financial benefit. In the SCF data (table 4), diorce increases financial benefit hihly sinificantly, whereas no work decreases financial benefit. In both datasets, period of unemployment increases financial benefit (hihly sinificantly in the PSID data, but insinificantly in the SCF data), and its square term is neatie. 3.4 Two-type model (MLE) To inquire into the possibility of both types of behaior existin simultaneously, we extend the analysis to allow for heteroeneity in types by proposin a two-type model. Let a random ariable T = if a person is a strateic type, and T = if a person is a non-strateic (or aderse eents) type. For simplicity, we let 3 We apply a lo transformation to financial benefit, because this ariable exhibits a distribution that is similar to lo-normal but is left-censored at zero. In particular, we use lo(financial benefit + $). This is to capture the characteristics of censored data at zero. The transformed ariable is also left-censored at zero. Pae 8

19 Pr(T = ) = Φ(Wα), and Pr(T = ) = - Φ(Wα). W is a set of type-determinant ariables, which will be discussed more in detail later in this subsection. The filin decision may be impacted differently for each type, as follows. When T =, the filin equation is file X ln( ) u 0. (6.) When T =, the filin equation is file X ln( ) u 0. (6.) We normalize the ariances of the error terms for both types to be, i.e. Var u ) Var( u ). ( Similarly, we allow behaior in accumulatin debt or financial benefit to be different for each type. For the strateic type, financial benefit is assumed to be endoenous, and for the aderse eents type, it is assumed to be exoenous. Thus, for the strateic type, if 0 ln( ) X AE, and u, 0 if 0 where the ariance for the error term is For the aderse eents type, Var ( ), if we assume that Var if 0 ln( ) X AE,. 0 if 0 ( ). where Co u, ) 0. In empirical estimation, we will allow the possibility that Co u, ) 0, ( and estimate their correlation. ( Notice that the joint density of (bank, ln(+)) consists of four parts, (bank = 0, ln(+) = 0 ), (bank =, ln(+) = 0 ), (bank = 0, ln(+) ), and (bank =, ln(+)). In the last two cases ln(+) is positie and continuous. The density function for each of the four cases is ien in Appendix B. The model suested here belons to the class of the mixture density models. A well-known necessary identification condition of the model requires the exclusion restriction, i.e., the set W is Pae 9

20 different from X and AE. Henry, Kitamura, and Salanié (00) show that a correlation between W and T and the independence between W and the error terms (u and u ) in equations (6.) and (6.) are sufficient to identify the model up to a linear transformation non-parametrically. When the set W has more than one ariable, Henry, Kitamura, and Salanié (00) and Gan, Huan, and Mayer (0) show that a usin the full set of W and a subset of W would both produce consistent estimates of parameters of the model except the coefficients to determine the type. A Hausman-type specification test can be implemented by comparin estimates usin the full set of W with those usin a subset of W. 4 This test is similar to an oeridentification test in the instrumental ariable models. Here we suest a set of ariables that includes number of credit cards, loarithm of income, whether the person is risk aerse, 5 and whether the person shops around for the best term. 6. These ariables are not in the set of X that directly explains the bankruptcy decision. Our prior is that a person s credit worthiness may be an important factor in determinin her type. A better credit-scored person may be less likely to be the strateic type. Since credit scores are not aailable in the data set, seeral ariables that are related to credit scores are used. Therefore, the person with fewer numbers of cards is more likely to belon to the strateic type. Moreoer, it is reasonable to postulate that a person who shops around is more frual, and hence less likely to take on debt, and therefore, less focused on plannin for bankruptcy. Thus, a person who shops around more may be less likely to be a strateic type. The effect of risk aersion on determinin the type is unclear. It is not necessarily the case that a more risk-aerse person is 4 Gan, Huan, and Mayer (0) proide an economic interpretation of this type of mixture density model. 5 SCF asks its respondents: Which of the statements on this pae comes closest to the amount of financial risk that you are willin to take when you sae or make inestments? and we define the ariable risk aerse to be one if the respondent chooses not willin to take any financial risks. 6 SCF asks its respondents: When makin major sain and inestment decisions, some people shop around for the ery best terms while others don't. What number would you be on the scale?" And this ariable is a number between and 5, the larer the number, the reater the shoppin. Pae 0

21 more likely to file for bankruptcy. 7 The summary statistics of these four ariables can be found in table. All ariables hae substantial ariations. Table 5 shows estimation results for this model, usin SCF data. 8 This framework proides the clearest distinctions between the two models, as described in section aboe. One important distinction between the two models is endoeneity or exoeneity of financial benefit. Althouh we allow for the possibility of non-zero correlation between the error terms in the bankruptcy model and the financial benefit model for both types, only the strateic type exhibits a statistically sinificant (at the 90 percent leel) correlation, at (0.385), while the correlation for the aderse eents type is statistically insinificant, at 0.58 (0.463). Thus, financial benefit is endoenous to the bankruptcy decision for strateic types, and exoenous for aderse eents types, as predicted by the hypothesis. The coefficient on lo of financial benefit is positie and hihly sinificant for the strateic type, at (0.0570), but for aderse eents type, this coefficient is positie and insinificant, at 0.00 (0.0858). The coefficient for the strateic type is larer than the coefficient for the aderse eents type, as predicted by the hypothesis. Similarly, ariables for aderse eents (other than health problems) hae the same effect on both types, but with a larer absolute effect for strateic types. Not workin lowers financial benefit, increasin unemployment spell increases financial benefit, and diorce increases financial benefit. Health problems present a mixed picture, a positie (and marinally sinificant) effect on financial benefit for aderse types, but decreasin (and insinificant) effect for strateic types. These results document a financial-benefits channel for aderse eents. The last panel in table 5 shows that fewer numbers of credit cards increases the chance of strateic behaior, as does an increase in risk aersion. Consumers who shop around more are less likely to be strateic type. A lower income also increases the chance of strateic behaior. 7 Gan and Mosquera (008) (Appendix ) show that a more risk aerse person may or may not hae a hiher probability of default, dependin on relatie current income and future income. 8 The two-type model could only be estimated usin SCF data, partly because PSID does not hae the typedetermination ariables similar to those in SCF. Pae

22 As shown in table 6, the aerae probability of bein a strateic type is This proides additional confirmation for the exoeneity of financial benefit in the one-type model. For additional analysis of the two types, we diide the population into two roups. A household is of strateic type, if its type probability is reater than 0.5, and is of aderse eents type otherwise. Accordin to this criterion, 80 households are strateic type and 3,503 households are aderse eents type, as shown in table 6. Notably, on aerae, a strateic type has a 3.37% chance to file for bankruptcy, more than 4 times hiher than the 0.8% chance of the aderse type. This reater filin probability is consistent with the empirical prediction of the model in section. Similarly, in terms of the predicted probabilities, a strateic type is expected to hae 9.84% chance to file for bankruptcy while the aderse eents type would hae 0. 6% chance to file for bankruptcy. Moreoer, the two types exhibit different leels of financial benefits. The aerae leel of lo of financial benefit is.453 for the strateic type, about 34 percent larer than.887 for the aderse eents type. The larer financial benefit for strateic type is aain consistent with the prediction of the model. Similarly, on aerae, about 30.8% of strateic type consumers hae strictly positie financial benefit, as compared to 0.8% of aderse eents type. As shown in table 6, the predicted probability of filin for bankruptcy is hiher than actual for both types. One possible explanation is that financial benefit from filin for bankruptcy is heaily censored at zero (about 80 percent of the financial benefit calculations take the alue of zero), and the predicted alue is close to the true data of the percentae of those zeroes. This may also proide a reason why the bias of mean of lo financial benefit is so lare. Table 7 shows the effects of hypothesized chanes in particular ariables on the probability of filin. 9 For example, if financial benefit oes up by $,000, and all other characteristics are held constant at sample means, the aerae strateic type s filin probability oes up 0.0 percentae points (equialently, the filin probability increases by 0.0), that of an aderse 9 The columns for percentae point marinal effect show the chane in filin probability. The column labeled Total ies the weihted aerae of the chanes, usin probability of strateic type as and that of aderse eents type as Pae

23 eents type oes up neliibly, and the total filin probability oes up about percentae points. In terms of a percentae chane in the filin rate, filin rates for strateic types o up by percent, those for aderse types o up by 0.4 percent, and total filins o up by 7.4 percent. 0 Similarly, if home-ownership increases by 5 percentae points, the filin rates of strateic types o up about percent, those of aderse types o down neliibly, and the oerall filin rate oes up about 9 percent. Our framework allows estimates of the effects of aderse eents on filin probabilities throuh the channel of financial benefit. Table 8 presents some of these effects. If the aerae spell of unemployment oes down by week, the filin rate of strateic types oes down 93 percent, that of aderse eents oes down neliibly, and the oerall filin rate oes down 38 percent. A 5 percentae point decrease in the proportion of people not workin leads to an increase in filin rate of strateic types by 7 percent, a neliible increase for aderse types, and an percent increase in the oerall filin rate. Similarly, a decrease of 5 percentae points in diorce, lowers the oerall filin rate by about 8 percent. Notice that the comparatiely smaller effects for aderse type (as compared to strateic type) are in part due to their much lower responsieness to financial benefit in the bankruptcy equation. Finally, table 9 lists the Hausman specification test suested in Henry, Kitamura, and Salanié (00), and Gan, Huan, and Mayer (0). As described in table 5, the full set of type determination ariables includes ln(income), number of credit cards, an indicator for risk aersion, and an index ariable for financial sainess (shoppin around). The first column in table 9 presents estimates of seeral key ariables of the model usin the full set of W. The second column has the estimation results without the indicator for risk aersion and the shoppin around ariable. The test shows that different of the coefficients for all parameters (except type-determination ariables in W) from the full set of W and from a subset of W are not statistically different. This result proides supportin eidence on the specification of the current model. Column 3, howeer, tells a different story. This column is estimated without the 0 The last three columns in table 7 translate the marinal effects into the correspondin percentae chane in the filin rate, as follows: diide the marinal effect of the strateic type by the filin probability of strateic type, which is in the sample, that of aderse type by their filin probability, which is 0.008, and the total by the total filin probability, which is Pae 3

24 "ln(income)" and number of credit card ariables. The difference of coefficient estimates with the estimates from the full set of W is statistically sinificant. This contradictory testin result is likely due to the rather weak relationship between the unobsered type and the risk aersion ariable and the shoppin around ariable (both of these two ariables are statistically insinificant in table 5). 4. Conclusions The aderse eents and strateic timin hypotheses hae receied particular attention in the debate on bankruptcy. Existin work proposes to distinuish between these hypotheses in a strict manner, which does not allow aderse eents to affect probability of filin throuh the channel of financial benefits. We propose testin for endoeneity of financial benefit as a distinuishin feature between the hypotheses. Financial benefit is endoenous to the filin decision for strateic types, and exoenous for aderse eents types. This test allows aderse eents to affect probability of filin in both hypotheses throuh the channel of financial benefit. Usin a sinle-type model, we show that both the PSID and the SCF data support the aderse eents hypothesis. Extendin the analysis to allow for the more realistic case of both types existin simultaneously, we propose and estimate a mixture-density type model with two types. We find eidence of both types of behaior in the data. In particular, financial benefit is endoenous for the strateic type and exoenous for the aderse eents type. On aerae, about 6 percent of the sample is strateic type, and 84 percent is aderse eents type, proidin support for the exoeneity of financial benefit in the one-type model. These results show a role for both hypotheses. A specification test proides some supportin eidence of this two-type model. The estimates here are broadly consistent with theoretical predictions: the probability of filin and the financial benefit from filin are both larer for strateic type than for aderse eents type. There is some eidence of a financial-benefits channel of the effect of aderse eents on Pae 4