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  • 标题:Strategic or nonstrategic: the role of financial benefit in bankruptcy.
  • 作者:Zhang, Shuoxun ; Sabarwal, Tarun ; Gan, Li
  • 期刊名称:Economic Inquiry
  • 印刷版ISSN:0095-2583
  • 出版年度:2015
  • 期号:April
  • 语种:English
  • 出版社:Western Economic Association International
  • 摘要:Personal bankruptcy rates have increased at an annual rate of 3.9% since 1990, from about 718 thousand (non-business) bankruptcies in 1990 to about 1.5 million in 2010. Partly as a response to this increase, the Congress passed the Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA) of 2005, the largest overhaul of bankruptcy laws since 1980. Although recent data are too sparse to determine the longer-term effectiveness of the law, we know that there was a spike in bankruptcy filings in 2005 (just before the law took effect on October 17, 2005) and a corresponding decline in 2006. Since then, bankruptcies have continued to rise, reaching a level of about 1.5 million in 2010, the same level as in 2004 (the bankruptcy rate has also begun to creep up to the earlier levels). One of the major purposes of the new bankruptcy law was to cut down on abusive or fraudulent uses of the bankruptcy system, or in other words, strategic use of the law. Therefore, it is important to understand the motivations of consumers who file for bankruptcy, what constitutes "strategic" use of bankruptcy law, and how widespread is its incidence.
  • 关键词:Bankruptcy law;Consumer research;Econometric models;Marketing research

Strategic or nonstrategic: the role of financial benefit in bankruptcy.


Zhang, Shuoxun ; Sabarwal, Tarun ; Gan, Li 等


I. INTRODUCTION

Personal bankruptcy rates have increased at an annual rate of 3.9% since 1990, from about 718 thousand (non-business) bankruptcies in 1990 to about 1.5 million in 2010. Partly as a response to this increase, the Congress passed the Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA) of 2005, the largest overhaul of bankruptcy laws since 1980. Although recent data are too sparse to determine the longer-term effectiveness of the law, we know that there was a spike in bankruptcy filings in 2005 (just before the law took effect on October 17, 2005) and a corresponding decline in 2006. Since then, bankruptcies have continued to rise, reaching a level of about 1.5 million in 2010, the same level as in 2004 (the bankruptcy rate has also begun to creep up to the earlier levels). One of the major purposes of the new bankruptcy law was to cut down on abusive or fraudulent uses of the bankruptcy system, or in other words, strategic use of the law. Therefore, it is important to understand the motivations of consumers who file for bankruptcy, what constitutes "strategic" use of bankruptcy law, and how widespread is its incidence.

In the literature, there is no clear definition of what constitutes a strategic bankruptcy filing. We shall consider strategic behavior to be a conscious decision to benefit from bankruptcy law. To make this tractable, consider a simple two-period model of decision-making. In the first period, consumers receive a noisy signal of experiencing a financial shock in the second period. Based on this signal, consumers may update their probability of an adverse shock and choose their debt level. In the second period, the shock is realized and consumers decide whether to file for bankruptcy or not. A strategic consumer is one who, in the first period, chooses her debt level after conditioning on the signal; that is, a strategic consumer takes on debt after accounting for the chance of filing for bankruptcy. In other words, a strategic consumer is one who is fully rational and takes decisions to maximize her benefit. A nonstrategic consumer is one who chooses debt level without conditioning on the signal; he plans to repay his debt in the absence of adverse events. Such a consumer is myopic and may be exhibiting rational inattention (as described below).

Consistent with this view, we may distinguish between strategic and nonstrategic behavior by testing whether consumers make their debt and filing decision jointly, or not. Strategic behavior is consistent with a joint decision, whereas nonstrategic behavior is not. In terms of empirical strategy, this is implemented by testing whether financial benefit is endogenous to the filing decision or not.

Our test is different from the one in the study by Fay, Hurst, and White (2002) (henceforth, FHW). In that approach, a positive relationship between filing for bankruptcy and financial benefit from filing, ceteris paribus, is taken as evidence of strategic behavior; and a positive relationship between filing for bankruptcy and adverse events (such as divorce, health shocks, employment shocks, etc.) is taken as evidence of nonstrategic behavior. Using data from the Panel Study of Income Dynamics (PSID), FHW show that financial benefit is positively and significantly related to the filing decision, and after controlling for financial benefit, adverse event variables do not affect the bankruptcy decision (except for a marginally significant positive effect of divorce). (1)

This simple empirical relationship between bankruptcy filing and financial benefit does not consider more realistic relationships among financial benefit, adverse events, and strategic behavior. For example, financial benefit from filing may go up due to adverse events, regardless of whether a consumer is trying to abuse bankruptcy law or not. That is, financial benefit goes up when a consumer consciously increases unsecured debts before filing, consistent with strategic behavior; and it also goes up when she uses unsecured debt (e.g., a credit card) to pay for expenses due to adverse events, consistent with nonstrategic behavior. Moreover, a nonstrategic consumer may appear strategic to the analyst, if he rolls over debt as long as there is hope of repaying it. This leads to greater measured financial benefit before filing, despite no intent to abuse bankruptcy law. Indeed, equilibrium models of default typically include such features. (2)

In other words, financial benefit is affected by both strategic and nonstrategic behavior, and a positive coefficient on financial benefit alone is insufficient to distinguish between the two behaviors. (3)

Our test partially disentangles the role of financial benefit, adverse events, and strategic behavior: it allows for a positive relationship between bankruptcy filing and financial benefit for both strategic and nonstrategic consumers and still may distinguish between the two. This test cannot distinguish between strategic consumers and nonstrategic consumers who may appear strategic due to a nonstrategic run-up of debt before filing.

Consequently, if the test result shows that financial benefit is endogenous to the filing decision, that result can be consistent with both strategic and nonstrategic behavior. If the test result shows that financial benefit is exogenous to the filing decision, the result supports nonstrategic filing behavior (and shows that the incidence of both strategic filings and nonstrategic filings that may appear strategic is statistically insignificant in the data).

We propose a model in which financial benefit and the filing decision are jointly determined, estimate it using joint maximum likelihood, and test for endogeneity of financial benefit and the filing decision. The discussion provides a set of natural instrumental variables, the adverse events.

Using two different datasets (PSID and Survey of Consumer Finances [SCF]), (4) the test results are consistent with nonstrategic behavior, in contrast to FHW. With both datasets, financial benefit is exogenous to the filing decision. Moreover, with both datasets, the coefficient on financial benefit is strongly significantly positive.

Our finding is consistent with "rational inattention" to rare events such as bankruptcy; that is, ex ante, the benefit from a bankruptcy filing is very low relative to costs, leaving little incentive for consumers to actively "plan" to file for bankruptcy. For example, as reported in FHW, for families that can gain from a bankruptcy filing, the mean benefit from filing is $7,813, and the probability of filing is 0.003017, for an ex ante filing benefit of about $25. This is less than the cost of a planning session with a bankruptcy lawyer, or the resources expended to purchase and plan with a book on how to file for bankruptcy. Note that planning for a strategic bankruptcy would have to be done early enough, because legal restrictions disallow wealth reallocations designed to gain from bankruptcy, especially if these are within about six months prior to a bankruptcy filing.

This article proceeds as follows: Section II describes the basic theory and a theoretical result on positive correlation between financial benefit and filing probability. Section III presents the econometric specifications and results, and Section IV concludes.

II. BASIC THEORY AND POSITIVE CORRELATION BETWEEN FINANCIAL BENEFIT AND FILING PROBABILITY

Bankruptcy filers typically have a choice between filing for chapter 7 or 13 bankruptcy. (5) A chapter 7 bankruptcy process liquidates a filer's estate and, net of exemptions, makes payments to creditors based on law. This is sometimes termed a straight bankruptcy. In a chapter 13 filing, a filer typically keeps his assets, proposes a plan of repayment, and on plan completion, gets discharge from remaining debts. Historically, about 70% of bankruptcies are chapter 7, and most of the remainder are chapter 13. Moreover, a filing under chapter 13 may be moved to chapter 7, if the chapter 13 repayment plan is not completed successfully. In practice, this can happen in a significant proportion of chapter 13 filings. (6) Therefore, most research models chapter 7 bankruptcy filing. We follow the same approach. (7)

Consider a simple two-period model of decision-making. Prior to the first period, consumers receive a noisy signal of experiencing a financial shock. The shock may be viewed as an adverse event: job loss, health problem, divorce, and so on. Based on this signal, consumers may update their probability of an adverse shock. In the first period, they choose their debt level. Then the shock is realized and in the second period, consumers decide whether to file for bankruptcy or not.

As shown in Figure 1, a strategic consumer is one who, in the first period, chooses her debt level after conditioning on the signal. A strategic consumer understands that based on an adverse event there is some chance of a bankruptcy filing, in which case some debt is forgiven. She plans accordingly, and chooses a debt level to achieve the highest benefit available under law. In other words, a strategic consumer is one who is fully rational, and takes decisions to maximize her benefit.

A nonstrategic consumer is one who chooses debt level without conditioning on the signal. Intuitively, a nonstrategic consumer understands that based on an adverse event there is some chance of a bankruptcy filing, but does not plan to benefit additionally from a filing. He plans to repay his debt in the absence of adverse events. Such a consumer is myopic, but that may not necessarily imply he is irrational.

This situation can be formalized using a simple two-period model of expected utility maximization (Gan and Sabarwal 2005). In the first period, there is one decision node. In the second period, depending on a shock (that we may assume occurs at an intermediate stage) one of two states may occur: a good state, indexed g, and an adverse events state, indexed a. State-contingent consumption is indexed [c.sub.0], [c.sub.g], [c.sub.a]. A consumer's von-Neumann-Morgenstern utility index is given by u(c), with standard assumptions (u' > 0, u" < 0, [lim.sub.c[right arrow]0] u' (c) = [infinity], [lim.sub.c[right arrow][infinity]], u' (c) = [infinity]). Expected utility is given by u([c.sub.0]) + [delta][[pi].sub.g]u([c.sub.g]) + [[pi].sub.a] u([c.sub.a])]], the distribution ([[pi].sub.g], [[pi].sub.a]) captures uncertainty in the second stage. Consumer's state-contingent wealth is given by [w.sub.0], [w.sub.g], [w.sub.a]. For convenience, we assume 0 = [w.sub.0] < [w.sub.a] < [w.sub.g].

Consumption in first period is financed by debt d > 0, available at a (risk-adjusted) interest rate r > 0. (8) For nontrivial solution, we assume debt limit for a consumer is given by [bar.d] > 0, so that d is constrained to satisfy d [less than or equal to] d. Exemptions in bankruptcy are given by d > 0. A natural assumption in this setting is [w.sub.a] < e < [w.sub.g].

A strategic consumer is fully rational, maximizing m([c.sub.0]) + [delta] + [delta][[pi].sub.g]u([c.sub.g]) + [[pi].sub.a]u([c.sub.a])] subject to (1) [c.sub.0] = d, (2) [c.sub.g] = max[[w.sub.g] - (1 + r)d, min([w.sub.g], e)], and (3) [c.sub.a] = max[[w.sub.a] - (1 + r)d, min([w.sub.g], e)]. Here, ([[pi].sub.g], [[pi].sub.a]) is the (updated) belief of the probability of an adverse event, based on the signal received. The minimum operation is a proxy for loss of nonexempt assets in a bankruptcy filing, and the maximum operation corresponds to the bankruptcy decision: file when nonexempt assets are greater than net wealth remaining after debt repayment. The effective decision variable is d. Notice that our assumptions imply that in the adverse event state, the consumer files for bankruptcy and consumes [c.sub.a] = [w.sub.a].

A nonstrategic consumer does not condition debt decision on the adverse events signal captured by the (updated) distribution ([[pi].sub.g], [[pi].sub.a]). Such a consumer may be viewed as taking decision sequentially. In period 1, the consumer maximizes u([c.sub.0]) + [delta]u([c.sub.g]), subject to (1) [c.sub.0] = d and (2) [c.sub.g] = [w.sub.g] - (1 + r)d. Effectively, a nonstrategic consumer is not planning for a bankruptcy filing and plans to repay his debt in period 2. If, however, an adverse event occurs in period 2, the consumer reoptimizes to set [c.sub.a] = max[[w.sub.a] - (1 + r)d, min([w.sub.a], e)]. Our assumptions imply that in the adverse events state, consumer files for bankruptcy and consumes [c.sub.a] = [w.sub.a].

By construction, this formulation shows immediately that for a strategic consumer, debt and filing decisions are determined jointly, whereas for a nonstrategic consumer, this is not the case. (9) Moreover, a strategic consumer may file for bankruptcy in a good state (in which exemption is low relative to wealth), if debt elimination from bankruptcy can offset the loss of nonexempt assets. A nonstrategic consumer does not engage in such behavior.

One way to motivate nonstrategic behavior is in terms of rational inattention to rare events. In other words, ex ante, a nonstrategic consumer behaves as if his subjective probability of an adverse event is zero. This might not necessarily be irrational, if we expand the model to include some ex ante cost of determining the probability of an adverse event and planning for a bankruptcy filing, and the ex ante benefit from a bankruptcy filing, and then consider a behavioral choice whether a consumer would want to behave strategically or nonstrategically. Such an extension is beyond the scope of this study, but as reported in FHW, for families that can gain from a bankruptcy filing, the mean benefit from filing is $7,813, and the probability of filing is 0.003017, for an ex ante filing benefit of about $25. If a consumer were to plan to gain from a bankruptcy filing, he would include the ex ante cost of a planning session with a bankruptcy lawyer, or the resources expended to purchase and plan with a book on how to file for bankruptcy; this is typically greater than $25. This would have to be done early enough, because legal restrictions disallow wealth reallocations designed to gain from bankruptcy, especially if these are within about 6 months prior to a bankruptcy filing.

An immediate consequence of this model is that for a strategic consumer, financial benefit is endogenous to the filing decision, and for a non-strategic consumer, it is exogenous. This leads us to the empirical test used here.

As mentioned above, this empirical test only partly disentangles the endogeneity, because even for a nonstrategic consumer, there might be some debt accumulation after the shock is realized, if the consumer is trying to roll over debt with the hope of repaying it. But a finding of exogeneity favors nonstrategic behavior.

In empirical work, filing for bankruptcy is typically modeled as a binary choice model. FHW indicate that a positive and significant relationship between household financial benefit and probability of filing for bankruptcy signals strategic behavior by a consumer. Similarly, Adams, Einav, and Levin (2009) suggest that an increase in probability of default with loan size is consistent with either moral hazard behavior or adverse selection behavior. In the same spirit, we show that financial benefit may affect the probability of filing, regardless of how debt is accumulated.

According to McFadden's Random Utility Maximization model (Gan, Hurd, and McFadden 2005), the probability that a person files for bankruptcy is increasing in the utility difference between filing and not filing. To investigate 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 filing, given d, is B(file, d) = max(d - w, 0), and financial benefit from not filing, given d, is B(Not, d) = max(w - d, 0). Notice that B(file, d) [greater than or equal to] B(Not, d) if and only if d [greater than or equal to] w.

Let u denote utility from monetary outcomes. Assume that u is strictly increasing and continuously differentiable. We may write utility from filing, given d as: U(file, d) = u(B(file, d)); utility from not filing, given d as U(Not, d) = u(B(Not, d)); and the difference in these utilities is [DELTA] U(d)=U(file, d) -- U(Not, d). Therefore, [DELTA] U' (d) = u' (B(file, d))B ' (file, d) - u'(B(Not, d))B' (Not, d).

Consider the following cases. Case 1: d > w. In this case, B' (file, d)= 1 and B' (Not, d) = 0. Therefore, [DELTA] U' (d) = u'(B(Not, d))> 0. Case 2: d<w. In this case, B' (file, d) = 0 and B' (Not, d) = - 1, whence, [DELTA] U' (d) = u' (B(Not, d))> 0. Case 3: d = w. In this case, [lim.sub.d[down arrow]w], u' (B (file, d)) = u' (B (file, w)) = u' (0) > 0, and similarly, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] u' (B (Not, d)) = u' (B (Not, w)) = u' (0) > 0. In all cases, we have [DELTA]U' (d) > 0.

In terms of empirical prediction, this implies that the coefficient on unsecured debt (and consequently, on financial benefit from filing) is positive, regardless of how debt is accumulated. (10) Therefore, given unsecured debt d, a positive relationship between financial benefit from filing and filing for bankruptcy is expected.

III. ECONOMETRIC MODELS AND RESULTS

In this section, we first provide some information on the data and construction of variables. Next, we replicate the FHW's specification using two different datasets. Then we present test results for endogeneity of financial benefit (using joint maximum likelihood estimation) with two different datasets. Finally, we use comparative statics to predict the bankruptcy filing rates with hypothetical changes in key variables.

A. Data Description and Variables

We use two different datasets to check robustness of our results. One is the combined cross-section and time-series sample of PSID households over the period 1984-1995; the same dataset is used in FHW. The other is the cross-sectional dataset of SCF from 1998. (11)

In 1996, the PSID asked respondents whether they had ever 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 generally of high quality, but they have some limitations for a study of this kind. In particular, wealth is only measured at 5-year intervals, and it contains less detail on some aspects of use in this study. Moreover, as documented in FHW, there are only 254 bankruptcy filings over the period 1984-1995, and bankruptcy filings in the PSID are only about one-half of the national filing rate.

SCF, in contrast, has 55 bankruptcy filings in 1997, or about 1.28% of households, comparable to the 1997 national bankruptcy filing rate of 1.16%. 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 survey, and on future expectations.

SCF also provides better wealth data, which reports 1997 wealth information and 1997 bankruptcy filings (the SCF survey was conducted in 1998, between June and December). (12)

We do not distinguish chapter 7 and 13 filings in this study (although consumers are able to make choices), because the financial benefit from filing under chapter 13 is closely related to that from filing under chapter 7. It usually takes between 4 and 6 months for a chapter 7 filing procedure, but between 36 and 60 months for a typical chapter 13 case. The 1998 SCF does not provide information on chapter choice. Financial benefit from filing is the key variable in this study. As in FHW, it is calculated as follows:

(1) [B.sub.i,t] = max [D.sub.i,t] - max (W.sub.i,t] - [E.sub.i,t], 0), 0] ,

where [B.sub.i,t] is the financial benefit from filing for household i in period t, [D.sub.i,t] is the unsecured debt discharged in bankruptcy for household i in period f, [W.sub.i,t] is the value of wealth for household i in period t, and [E.sub.i,t] is value of exemptions under law for household i in period f, in the household's state of residence. In this formula, max([W.sub.i,t], - [E.sub.i,t] 0) calculates the nonexempt assets that a filer loses in bankruptcy. It is a measure of financial cost of filing for bankruptcy. The variable [D.sub.i,t] t is the part that will be discharged in bankruptcy, thus is a measure of benefit of filing. As not filing dominates filing when [D.sub.i] - max([W.sub.i,t], - [E.sub.i,t], 0) is negative, the financial benefit from filing is truncated at 0 to yield the above formula.

Notice that this calculation does not include the full economic cost of a bankruptcy filing. For example, a more complete measure of the economic cost of filing would include future and dynamic costs of a bankruptcy filing as well, such as loss of future stream of profits from liquidated assets, or effects on future creditworthiness, which determines future access to debt markets and the price of debt. (13) A more complete accounting of the cost of bankruptcy would include such costs and also out-of-pocket filing costs. Reliable data on these measures are unavailable, and including a reduced form constant would not change the qualitative results. This is a limitation of our approach, as also that of FHW.

To calculate financial benefit in the PSID, we use the same dataset and calculation as FHW. In the PSID, housing equity is reported every year, but nonhousing wealth is reported only in the 5-yearly wealth supplements from 1984, 1989, and 1994. These data are used to construct unsecured debt, [D.sub.i,t], that will be discharged in bankruptcy. Wealth includes current year housing equity (reported every year) and the value of the most recent prior report on nonhousing wealth. (14) IV, t is the wealth net of secured debts (such as mortgages and car loans). [E.sub.i,t] is the exemption in the state of residence of household i in period t.

For the SCF, variables are constructed similarly. The variable [D.sub.i,t] measures unsecured debt that will be discharged in bankruptcy. Unsecured debts include both credit card debt and installment loans. (15) Wealth, Wit, is total assets net of the secured debt. Total assets include all financial assets and nonfinancial assets. (16) For exemption, [E.sub.it], we make the following adjustments.

The SCF provides only region codes; state codes are not released in public data. To get a relative weight for each state in a region, we use Regional Economic Information System from the Bureau of Economic Analysis. These state weights are based on the population of a state relative to the region in which it is included. These weights are used to compute the composite exemption level of a region. Moreover, using the study by Elias, Renauer, and Leonard (1999), we determine each state's exemption levels for 1998 for homestead equity in owner-occupied homes, equity in vehicles, personal property, and wildcard exemptions. We adjust for state-level variables to the extent we can. For example, if a state doubles exemptions for married households, we do the same. For the 15 states allowing residents to choose between state or federal exemptions, we take the larger of the exemptions. For households in states with an unlimited homestead exemption, we take the homestead exemption to be the average of home values in the entire sample. The exemption variable, [E.sub.i,t], is the sum of these exemptions. (17) To make the two datasets consistent with each other, we include a vector of demographic variables that may be related to households' filing decisions, such as age of household head, years of education of the head, family size, whether head owns their home, and whether head owns business. For SCF data, we include only region dummies rather than macro information to capture local fixed effects, due to lack of information regarding state of residency.

For adverse event variables, we include whether the head was ever unemployed during the prior 12 months (labeled "unemployed"), total weeks of unemployment during the prior 12 months (labeled "period of unemployment"), (18) its squared term, whether the head is recently divorced (labeled "divorce"), (19) and whether the head's (self-reported) health condition is poor (labeled "health"). (20)

In Table I, we present financial benefit and unsecured debt between filers and nonfilers for both PSID and SCF. Similar patterns emerge. In PSID, the mean log (financial benefit) for filers is more than twice as much as for nonfilers. In SCF, filers have more than three times as much mean log(financial benefit) as nonfilers. In both SCF and PSID, the mean log(unsecured debt) for filers is greater than that of nonfilers.

As in FHW, our debt calculation is for the period of filing, and the adverse event variables are for the prior period. This is consistent with our model (with adverse events realized before the bankruptcy decision).

There is the issue that in the data, it is possible that debt (and therefore, financial benefit) changes after an adverse event occurs and before a bankruptcy filing. We can consider two cases.

First, an adverse event (which here is assumed to occur with an exogenous probability) itself leads to an increase in debt. This is captured in the model in a reduced form by a reduction in state-contingent wealth, and empirically in the financial benefit calculation.

Second, a consumer might take some actions that change debt just before filing. For example, a strategic consumer could try and consciously increase unsecured debts just before filing in order to increase benefit from filing. As mentioned above, there are legal restrictions for such moves and creditors are likely to have these enforced strictly. However, debt may go up when a nonstrategic consumer rolls over debt in the hope of repaying it. As mentioned earlier, our test cannot distinguish between strategic consumers and nonstrategic consumers who may appear strategic due to a nonstrategic run-up of debt before filing.

Consequently, if the test result shows that financial benefit is endogenous to the filing decision, that result can be consistent with both strategic and nonstrategic behavior. If the test result shows that financial benefit is exogenous to the filing decision, the result supports nonstrategic filing behavior (and shows that the incidence of both strategic filings and nonstrategic filings that may appear strategic is statistically insignificant in the data).

B. Simple Probit Model

Let us first consider a simple Probit regression, similar to FHW's specification.

(2) file = 1 ([gamma]B + X[beta] + [alpha]A + u > 0)

This specification explores strategic and non-strategic behavior by running the Probit regression of whether households file for bankruptcy (file) as a function of their potential financial benefit, B, from filing, their personal and state characteristics X, and the adverse events they encountered in the previous year, A.

As described above, one test of strategic behavior focuses on the significance of the coefficients on financial benefit and on adverse events, as in FHW. If strategic behavior hypothesis is true, the coefficients of financial benefit should be positive and significant while the adverse event variables should not be significant. If nonstrategic behavior hypothesis is true, then adverse event variables should be positive and significant while the coefficient of financial benefit should be insignificant.

Table 2 illustrates this simple specification with PSID and SCF data (21) (for ease of comparison, we keep the other variables same as those in FHW). As shown in Table 2, (22) using PSID data, the coefficients on the variables are comparable to those reported in FHW. In particular, financial benefit affects the filing decision positively and highly significantly, and its squared term is highly significant. And, among statistically significant adverse events, divorce is positive but only marginally significant. When using SCF data, financial benefit continues to be positive and highly significant, but its squared term is marginally significant. The coefficient on divorce remains positive, but is highly significant.

Thus, using the simple Probit model, the PSID dataset provides support for strategic behavior, as in FHW, while the SCF dataset provides support for both strategic and nonstrategic behavior, providing an indication of alternative behavior in the data.

C. Model with Joint Determination of Financial Benefit and Filing Decision

As mentioned in the introduction, a simple empirical relationship between filing for bankruptcy and financial benefit from filing conflates more realistic relationships between financial benefit, adverse events, and strategic behavior. To disentangle some of these relationships, we propose to test the endogeneity of financial benefit in a more general model in which financial benefit and the bankruptcy decision are allowed to be determined jointly. It is reasonable to believe that consumers' attitude toward debt (and thus financial benefit), which is unobserved, determines both how they accumulate debt and whether or not they file for bankruptcy.

As discussed above, nonstrategic households would respond to income shocks, but not respond additionally to financial benefit upon filing. Strategic households could manipulate their debts so that their financial benefits from bankruptcy are maximized; in other words, their financial benefits and bankruptcy decision are simultaneously determined. To test these two hypotheses is equivalent to testing whether financial benefit is endogeneous or not.

Hence, we have the basic empirical model as follows:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The key difference between this model and FHW's specification is the role of the set of adverse events, A. Here, A no longer directly affects a person's bankruptcy decision. Instead, it serves as the set of instrumental variables that directly affects the financial benefits, B, in Equation (4). As adverse events are exogenous to a household's bankruptcy decision, they act more as a negative shock to a household's income/wealth.

Another minor difference between these two models is that the logarithm of financial benefit is used here while FHW use the level of financial benefits. As B depends on the wealth level, it is most likely to exhibit a log-normal distribution, although censored at zero. (23) With a logarithm transformation, we will assume that v is normally distributed.

Notice that endogeneity of ln(B + 1) is equivalent to whether the error terms u and v are correlated. Let Var(u) = 1, Var(v) - [[sigma].sup.2.sub.v], and assume the relationship between u and v as follows:

u = [theta] v + [epsilon],

where Cov(v, [epsilon]) = 0, and Var([epsilon]) = 1 - [[theta].sup.2][[sigma].sup.2.sub.v]. In this version, the exogeneity of ln(B + 1) is equivalent to the hypothesis that the parameter [theta] = 0. The probability a household files when financial benefit is zero is given by

Pr (file = 1, ln (B+ 1) = 0)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and accordingly, the probability it does not file when financial benefit is zero is given by

Pr (file = 0, ln(B + 1) = 0)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Similarly,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The log-likelihood function over the sample is given by

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Estimation results are presented in Tables 3 and 4. (24) We find that using either PSID (Table 3) or SCF data (Table 4), the estimated parameter [theta] is not statistically different from zero, consistent with nonstrategic behavior.

At the same time, log financial benefit has a positive and highly significant effect on the decision to file for bankruptcy in both datasets.

Both datasets confirm the view that adverse events may affect financial benefit. Results using PSID data are presented in Table 3 and those with SCF data in Table 4. (25) Both show similar results, with some differences in terms of statistical significance. Intuitively, health problems would lead to a larger amount of debt and thus a potentially higher financial benefit (highly significant in PSID data, not in SCF). In the absence of divorce, there is a greater chance of repaying higher levels of debt (due to joint earnings), leading to lower probability of filing. Or there may be lower levels of debts, due to greater production of services at home (in case one spouse is not working), leading to lower financial benefit from filing. (26) Conversely, conditional on divorce, financial benefit may be higher (highly significant in SCF data, not in PSID). Moreover, greater financial benefit may also be due to more joint (and individual) debts being discharged to give both partners a fresh start after divorce. Transitioning into unemployment typically lowers access to debt markets, lowering financial benefit from filing (highly significant in PSID, not in SCF). Conditional on being unemployed, an increase in duration of unemployment is more likely to imply utilizing existing debt lines more completely, or increases in debts outstanding due to nonservicing of debt, both increasing financial benefit. This increase may be tempered by more stringent conditions from creditors, leading to an increasing and concave impact on financial benefit (highly significant in PSID data, marginally significant in SCF).

It is possible that not all adverse events have the same impact on filing behavior. For example, a health shock may be less predictable than divorce, and may have a different impact on filing behavior. Therefore, in principle, different adverse events could lead to differing strategic behavior depending on type of adverse event. For robustness, we run the joint determination model with different combinations of adverse events. The main results are unchanged, as shown in Tables 5 and 6.

D. Interpretation

Tables 7 and 8 show how hypothetical changes in key variables affect financial benefit from filing and probability of filing. Table 7 shows information for the joint determination model using PSID data, whereas Table 8 shows the same information using SCF data.

Suppose financial benefit from filing increases by $1,000 for each household. (27) In this case, the average filing probability is predicted to increase by 0.216 percentage points (PSID data, Table 7) and by 0.56 percentage points (SCF data, Table 8). Given that filing probability is 0.3017% (PSID data) and 1.28% (SCF data), an increase in financial benefit of $1,000 predicts that bankruptcy filing rates would increase by 71.6% per year (using PSID data), and by 43.8% (using SCF data). Thus, consistent with the basic theory outlined above, even with nonstrategic behavior, financial benefit can have a large effect on bankruptcy filings. (28)

We also present predictions for changes in some household characteristics, such as age of head of household, education level, family size, and home ownership.

If age of head of the average household increases by 10 years, using Equation (4), we see that log financial benefit would decrease, on average, by 0.0433 (PSID data) and by 0.0102 (SCF), which would lead to 18.0% (PSID) and 4.7% (SCF) reduction in annual bankruptcy filing rate.

If head of the average household receives one more year of education, the predicted change in financial benefit is -0.001 (PSID) and -0.1041 (SCF). Bankruptcy filing rates would decrease by 4.7% (PSID) and 6.25% (SCF).

If the average household adds one member, bankruptcy filing rate increases by 6.0% (PSID) and 7.8% (SCF).

Home ownership has a different effect in the two samples. If every household turns from having no home to having at least one home, the bankruptcy filing rate using PSID data is predicted to decrease by 24% (PSID) while the filing rate using SCF data is predicted to drop only 0.3%. This might be due to the fact that SCF does not release state information, and we might underestimate the homestead exemption if the state does not set a cap on homestead exemption.

Tables 7 and 8 present predictions based on changes in adverse event variables as well, especially if adverse events did not occur. Broadly, except for unemployment, absence of adverse events is predicted to decrease bankruptcy rates, as expected.

If the head of an average household turned from being unemployed to having a job, financial benefits are predicted to be higher on average, increasing predicted filing rates by 1.3% (PSID) and 3.5% (SCF). Given that a head of household is unemployed, if spell of unemployment is 1 week shorter, then financial benefits as well as the bankruptcy filing rate is predicted to decrease by 0.23% (PSID) and 0.94% (SCF).

If the average household head turned from having health problem to not having health problem. both predicted financial benefits and predicted bankruptcy filing rates would decrease. The reduction in average bankruptcy rate is 3.7% (PSID) and 3.6% (SCF), respectively.

Finally, suppose divorce did not occur, probability of bankruptcy filing is predicted to decrease by 0.5% (PSID) and 34.4% (SCF).

IV. CONCLUSION

Understanding the motivations of consumers to file for bankruptcy is central to the design of appropriate policies to manage the number of filings. For example, if consumers typically file strategically, and it is determined that filings are too high, then policies to reduce filings could include, among others, those that tighten access to bankruptcy courts, or make bankruptcy more expensive, perhaps by restricting access to particular types of bankruptcy provisions, lowering exemptions, diverting more debtors to longer repayment plans, lengthening minimum time between repeat filings, or requiring debt management programs outside of bankruptcy. (29) However, if consumers typically file nonstrategically, then policies to reduce bankruptcy filings could include, among others, those that minimize the impact of adverse events, or increase financial literacy for planning for such events. (30)

This article proposes a test to detect strategic or nonstrategic behavior in bankruptcy filings. The test is based on endogeneity or exogeneity of financial benefit and the bankruptcy decision. The proposed test is more realistic than a simple estimation of the sign of the coefficient on financial benefit and on adverse shocks. The test is partial in that it cannot distinguish between strategic filing and a filing that

appears to be strategic due to nonstrategic reasons. Nevertheless, test results are consistent with nonstrategic filing behavior, and rule out significant strategic behavior. The same results hold in two different datasets.

The models used in this study are simplified and by no means capture all relevant aspects of the bankruptcy decision. Issues related to choosing a particular period to file for bankruptcy, or to repeat interactions with credit markets, or to choice of bankruptcy chapter, or to role of legal advertising, or to effects on supply of credit, or to effects on work incentives, and so on are not considered here (some of these are the subject of other papers, listed above). It is possible to consider some of these issues here in a reduced form by including parameters for expected gains and losses from delaying a decision, or reduced access to credit markets, or utility penalties for default, and then focusing on parameter values which make particular versions of the models more likely to occur, but it is unclear if such additions would have additional applications given the paucity of available data.

The results here can be viewed as providing an indication of some nonstrategic behavior in bankruptcy filings, rather than a definitive conclusion in favor of one hypothesis or the other. For example, in addition to research supporting different hypotheses, the reported surge in bankruptcy filings before the deadline of October 17, 2005 for the new bankruptcy law to go into effect suggests that other factors (perhaps informational spillovers emerging from declining social stigma, or lawyer advertising) are important as well. No doubt, additional work may yield additional testable predictions, and additional research would be very welcome.

ABBREVIATIONS

BAPCPA: Bankruptcy Abuse Prevention and Consumer Protection Act

FHW: Fay, Hurst, and White (2002)

PSID: Panel Study of Income Dynamics

SCF: Survey of Consumer Finances

doi: 10.1111/ecin.12163

REFERENCES

Adams, W., L. Einav, and J. Levin. "Liquidity Constraints and Imperfect Information in Subprime Lending." American Economic Review, 99(1), 2009, 49-84.

Arabmazar, A., and P. Schmidt. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality." Econometrica, 50, 1982, 1055-64.

Araujo, A., and M. Pascoa. "Bankruptcy in a Model of Unsecured Claims." Economic Theory, 20(3), 2002, 455-81.

Athreya, K. "Equilibrium Models of Personal Bankruptcy: A Survey." Federal Reserve Bank of Richmond Economic Quarterly, 91(2), 2005, 73-98.

Ausubel. L. M. "The Failure of Competition in the Credit Card Market." American Economic Review, 81(1), 1991, 50-81.

--. "Credit Card Defaults, Credit Card Profits, and Bankruptcy." The American Bankruptcy Law Journal, 71, 1997, 249-70.

Berkowitz, J., and R. Hynes. "Bankruptcy Exemptions and the Market for Mortgage Loans." Journal of Law and Economics, 42(2), 1999, 809-30.

Crow, E. L., and K. E. Shimizu. Lognormal Distributions: Theory and Applications. New York: Dekker, 1988.

Domowitz, L. and T. L. Eovaldi. "The Impact of the Bankruptcy Reform Act of 1978 on Consumer Bankruptcy." Journal of Law and Economics, 36(2), 1993, 803-35.

Domowitz, P. J., and R. L. Sartain. "Determinants of the Consumer Bankruptcy Decision." Journal of Finance, 54(1), 1999, 403-20."

Dubey, P., J. Geanakoplos, and M. Shubik. "Default and Punishment in General Equilibrium." Econometrica, 73(1), 2005, 1-37.

Eaton, J., and M. Gersovitz. "Debt with Potential Repudiation: Theoretical and Empirical Analysis." Review of Economic Studies, 48(2), 1981, 289-309.

Elias, S., A. Renauer, and R. Leonard. How to File for Chapter 7 Bankruptcy. 8th ed. Berkeley, CA: Nolo Press, 1999.

Fan, W., and M. J. White. "Personal Bankruptcy and the Level of Entrepreneurial Activity." Journal of Law and Economics, 46(2), 2003, 543-68.

Fay, S., E. Hurst, and M. J. White. "The Household Bankruptcy Decision." American Economic Review, 92(3), 2002, 706-18.

Gan, L., and T. Sabarwal. "A Simple Test of Adverse Events and Strategic Timing Theories of Consumer Bankruptcy." NBER Working Paper Series No. 11763, November 2005.

Gan, L., M. Hurd, and D. McFadden "Individual Subjective Survival Curves," in Analyses of Economics of Aging, edited by D. Wise. Chicago: University of Chicago Press, 2005, 377-411.

Geanakoplos, J., and W. Zame. "Collateralized Asset Markets." Working Paper, University of California at Los Angeles, 2007.

Gropp, R. E., J. K. Scholz, and M. J. White. "Personal Bankruptcy and Credit Supply and Demand." Quarterly Journal of Economics, 112, 1997, 217-52.

Gross, D. B., and N. S. Souleles. "Do Liquidity Constraints and Interest Rates Matter for Consumer Behavior? Evidence from Credit Card Data." Quarterly Journal of Economics, 117(1), 2002, 149-85.

Gross, T., M. J. Notowidigdo, and J. Wang. "Liquidity Constraints and Consumer Bankruptcy: Evidence from Tax Rebates." NBER Working Paper Series No. 17807, 2012.

Han, S., and G. Li. "Household Borrowing after Personal Bankruptcy." Journal of Money, Credit and Banking, 43(2-3), 2011, 491-517.

Kennickell, A., M. Starr-McCluer, and B. J. Surette. Recent Change in U.S. Family Finances: Results from the 1998 Survey of Consumer Finances. Washington, DC: Federal Reserve Bulletin, Division of Research and Statistics, Federal Reserve Board, 2000.

Li, W., M. J. White, and N. Zhu. "Did Bankruptcy Reform Cause Mortgage Defaults to Rise?" American Economic Journal: Economic Policy, 3(4), 2011, 123-47.

Livshits, I., J. Macgee, and M. Tertilt. "Consumer Bankruptcy: A Fresh Start." American Economic Review, 97(1), 2007, 402-18.

--. "Accounting for the Rise in Consumer Bankruptcies." American Economic Journal: Macroeconomics, 2(2), 2010, 165-93.

Mansi, S. A., W. F. Maxwell, and J. K. Wald. "Creditor Protection Laws and the Cost of Debt." Journal of Law and Economics, 52(4), 2009, 701-17.

Modica, M., A. Rustichini, and J. M. Tallon. "Unawareness and Bankruptcy: A General Equilibrium Model." Economic Theory, 12(2), 1999, 259-92.

Musto, D. K. "What Happens When Information Leaves a Market? Evidence from Post Bankruptcy Consumers." Journal of Business, 77(4), 2004, 1-24.

Powell, J. "Least Absolute Deviations Estimation for the Censored Regression Model." Journal of Econometrics, 25, 1984. 303-25.

Sabarwal, T. "Competitive Equilibria with Incomplete Markets and Endogenous Bankruptcy." Contributions in Theoretical Economics, 3(1), 2003, Art. 1.

Stanley, D. T., and M. Girth. Bankruptcy: Problem. Process, Reform. Washington, DC: Brookings Institution, 1971.

Sullivan. T. A., E. Warren, and J. L. Westbrook. As We Forgive Our Debtors. New York: Oxford University Press, 1989.

--. "Consumer Debtors Ten Years Later: A Financial Comparison of Consumer Bankrupts, 1981-1991." The American Bankruptcy Law Journal, 68, 1994, 121-54.

--. The Fragile Middle Class. New Haven, CT: Yale University Press, 2000.

Traczynski. J. "Divorce Rates and Bankruptcy Exemption Levels in the United States." Journal of Law and Economics, 54(3), 2011, 751-79.

Warren, C. Bankruptcy in United States History. Cambridge, MA: Harvard University Press, 1935.

White, M. J. "Personal Bankruptcy under the 1978 Bankruptcy Code: An Economic Analysis." Indiana Law Journal, 63(1), 1987, 1-53.

--. "Why Don't More Households File for Bankruptcy?" Journal of Law, Economics, and Organization, 14(2), 1998, 205-31.

Zame, W. "Efficiency and the Role of Default When Security Markets Are Incomplete." American Economic Review, 83(5), 1993. 1142-64.

(1.) Using SCF data, we document a similar relationship for financial benefit, but a strongly significant and positive effect of divorce. With the FHW interpretation, the PSID data provide some support for strategic behavior while the SCF data provide some support for both strategic and the nonstrategic behavior.

(2.) The literature on consumer bankruptcy is very large. A partial list includes the following: Warren (1935), Stanley and Girth (1971), and Eaton and Gersovitz (1981) present early work in this area. Additional work includes Sullivan, Warren, and Westbrook (1989, 1994, 2000). White (1987, 1998), Ausubel (1991, 1997), Domowitz and Eovaldi (1993). Gropp, Scholz, and White (1997), Domowitz and Sartain (1999), Gross and Souleles (2002), Fay, Hurst, and White (2002), Fan and White (2003), Livshits, Macgee, and Tertilt (2007, 2010), Han and Li (2011), and Gross, Notowidigdo, and Wang (2012). Athreya (2005) provides a survey of equilibrium models of default. Additional theoretical contributions include Zame (1993), Modica, Rustichini, and Tallon (1999), Araujo and Pascoa (2002), Sabarwal (2003), Dubey, Geanakoplos, and Shubik (2005), and Geanakoplos and Zame (2007), among others.

(3.) This point may be made more generally: we show that in the standard random utility model underlying the binary choice of filing and not filing, the coefficient on unsecured debt (and hence, on financial benefit from filing) is positive, regardless of how debt is accumulated.

(4.) Although both PSID and SCF are among the best publicly available datasets of their kind, they have well-known limitations for bankruptcy research. Using two datasets provides some robustness to these results, but better bankruptcy data would help to arrive at stronger conclusions.

(5.) Before BAPCPA, consumers had more freedom in choosing the chapter in which to file. After BAPCPA, choice is restricted by a "means" test ([section] 707(b)(2)). Given the high rate of failures of chapter 13 plans, it is as yet unclear how many consumers required to file under chapter 13 eventually end up with a discharge under chapter 7. The analysis here and the dataset used are for filings before BAPCPA.

(6.) Sullivan, Warren, and Westbrook (2000, 14) estimate this to be about two-thirds of chapter 13 filings.

(7.) A chapter 13 filing may be viewed as a reduced form chapter 7 filing, where debt recovery is the total amount repaid over the course of the proposed plan. We do not force such an interpretation.

(8.) This is a simple model of individual decision-making, not general equilibrium. We take the risk-adjusted interest rate (price of debt) as given.

(9). Using standard assumptions, it is easy to show that both problems have an interior solution, and optimal debt for a strategic consumer is (weakly) greater than that for a nonstrategic consumer.

(10.) Notice that all we used here was that u is strictly increasing and continuously differentiable. No additional restriction is imposed on utility.

(11.) SCF asks the respondents about their bankruptcy history, but the region/state in which they stay is not revealed to the public after 1998. To match the two datasets, we choose the data of the most recent year.

(12.) See Kennickell et al. (2000).

(13.) See Berkowitz and Hynes (1999) and Musto (2004).

(14.) Data on unsecured debt and nonhousing wealth are subject to measurement error and, therefore, financial benefit is subject to measurement error, but as reported in FHW, this does not significantly affect the results.

(15.) Credit card debt includes not only the traditional Visa/Mastercard/Discover/Optima cards, but also revolving debts at stores, including store cards, gasoline cards, airline cards, and diner club cards. Installment loans refer to those for purposes other than purchasing houses or real estates.

(16.) Financial assets are the sum of all types of transactions accounts (checking accounts, saving accounts, money market accounts, and call accounts), certificates of deposits, total directly held mutual funds, bonds, stocks, total quasiliquid (sum of IRAs, thrift accounts, and future pensions), saving bonds, cash value of whole life insurance, other managed assets (trusts, annuities, and managed investment accounts in which household has equity interest), other financial assets: includes loans from the household to someone else, future proceeds, royalties, futures, nonpublic stock, deferred compensation, oil/gas/mineral investments, and cash not elsewhere classified.

(17.) The exemption levels calculated using PSID and using SCF have different advantages and flaws, and thus are subject to measurement errors, but it does not significantly affect the results.

(18.) We uniformly recode the variable to be 52 if the spell of unemployment is more than 1 year.

(19.) The reported results in Table 4 and 6 are using the dummy variable for divorce during years of 1996-1998. but we have tried dummy variables for divorce of each year, which do not change the significance of the result/coefficient.

(20.) We also tried the dummy for either the head or the partner was in poor health status. The results remain robust.

(21.) For all estimates, * indicates significance at 90%, ** at 95%, and *** at 99%.

(22.) The pseudo R2 for the four columns of Table 2 are 0.1378, 0.1320, 0.1377. and 0.1524, respectively. The first two columns use the PSID family weights. Standard errors (in PSID) are corrected using the Huber/White procedure, which allows error terms for the same household to be correlated over time. We apply this procedure to Tables 3 and 5. too.

(23.) See Arabmazar and Schmidt (1982), Powell (1984), and Crow and Shimizu (1988).

(24.) We apply a log transformation to financial benefit, because this variable exhibits a distribution that is similar to log-normal but is left-censored at zero. In particular, we use log(financial benefit + $1). This is to capture the characteristics of censored data at zero. The transformed variable is also left-censored at zero. The result is also robust if the actual value of financial benefit is adopted.

(25.) As there is no available weak-IV test or Sargan test for the joint determination model, we run the regression with two-stage-least-square to show the related statistics. For PSID, the F-statistic is 18.34, which is greater than the critical value of 10, by rule of thumb. This rejects the null hypothesis that the instruments are weak. The Sargan score is 5.898, with p value of 0.21. So the over-identifying restriction is valid. For SCF, the Anderson-Rubin statistic ([chi square] = 22.8), Kleibergen-Moreira Lagrange multiplier test ([chi square] = 20.29), the conditional likelihood ratio test (statistic = 21.39) all pass the 5% significance, which rejects the null. The Sargan score is 6.53, which is 0.16 as of p value. So we do not reject the null hypothesis and the over-identifying restriction is valid.

(26.) According to Traczynski (2011), marriage is another kind of individual insurance against adverse shocks through income sharing between partners; when the exemption level is high enough, people will choose to file for bankruptcy instead of using marriage as their income protection.

(27.) If negative, set the value to be zero.

(28.) Notice that the PSID sample has an average financial benefit of $ 1411 (Table 1), and a $ 1,000 change is about 70% of this number. For the SCF a $1,000 change is about a 25% increase from the mean of $3,991.

(29.) See Mansi, Maxwell, and Wald (2009).

(30.) See Li, White, and Zhu (2011).

Zhang: Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, Xiamen, 361005, China. Phone 86-28-8735-5955, Fax 86-28-8735-6958, E-mail [email protected]

Sabarwal: Department of Economics, University of Kansas, Lawrence, KS 66045, Phone 785-864-2847, Fax 785-864-5270, E-mail [email protected]

Gan: Department of Economics, Texas A&M University, College Station, TX 77843; National Bureau of Economic Research (NBER), Cambridge, MA 02138. Phone 979-862-1667, Fax 979-847-8757, E-mail [email protected]
TABLE 1
Summary Statistics

                                                     PSID Data

                                                            Standard
Variables                                      Mean Value   Deviation

Number of bankruptcy filings                            254
Financial benefit                                $1,411      $10,523
Log(financial benefit + 1)                        1.64        3.24
  Those file for bankruptcy                       3.65        4.26
Log(unsecured debt+ 1)                            3.85        3.94
  Those file for bankruptcy                       5.74        3.96
Debts (if financial benefit > 0)                 9,329       31,800
Nonexempt assets (if financial benefit > 0)       585        15.000
Household labor income                          $26,552      $32,672
Age of household head                            44.19        15.96
Years of education of household head             12.43        5.10
Family size                                       2.90        1.55
Own home                                          0.59        0.49
Self employed/own business                        0.11        0.31
Head is divorced                                  0.03        0.18
Head is unemployed                                0.06        0.23
Weeks of unemployment of head                     6.76        2.01
Head has health problem                           0.07        0.26
In(income)
Total number of observations                           64,200

                                                      SCF Data

                                                            Standard
Variables                                      Mean Value   Deviation

Number of bankruptcy filings                             55
Financial benefit                                $3,991      $26,001
Log(financial benefit + 1)                        1.94        3.69
  Those file for bankruptcy                       6.78        4.38
Log(unsecured debt+ 1)                            4.35        4.45
  Those file for bankruptcy                       5.88        3.96
Debts (if financial benefit > 0)                 9,549       38,318
Nonexempt assets (if financial benefit > 0)      1,981       29.429
Household labor income                          $114,192    $602,833
Age of household head                            49.84        16.52
Years of education of household head             13.74        2.90
Family size                                       2.65        1.44
Own home                                          0.70        0.46
Self employed/own business                        0.25        0.44
Head is divorced                                 0.036        0.186
Head is unemployed                               0.097        0.295
Weeks of unemployment of head                     1.82        7.90
Head has health problem                           0.04        0.19
In(income)                                        8.17        4.76
Total number of observations                           4,305

TABLE 2
Simple Probit Model

                                   PSID Data

                                Without Adverse
                                     Event
                                   Variables

Financial benefit            0.00006 *** (0.00001)
Financial benefit squared   -1.04e-9 *** (4.04e-10)
Lagged bankruptcy rate       5.95905 ** (2.67377)
Household labor income      -4.98e-6 *** (1.41 e-6)
Reduction in income          -2.17e-6 ***(5.92e-7)
Age of household head         0.02917 ** (0.0137)
Age squared                 -0.00048 *** (0.00016)
Education                   -0.02981 *** (0.01155)
Family size                  0.03736 ** (0.01673)
Own business                   0.04037 (0.0918)
Own home                      -0.1371 * (0.07437)
Lawyers per capita             -0.7776 (0.74456)
County unemployment rate       0.09337 (0.10457)
State income growth          -2.39603 ** (1.19746)
State income deviation        -0.12465 (0.08725)
Divorce
Period of unemployment
Health problem
State fixed effects                   Yes
Year fixed effects                    Yes
Constant                     -2.3797 *** (0.71384)

                                   PSID Data

                                  With Adverse
                                     Event
                                   Variables

Financial benefit            0.00006 *** (0.00001)
Financial benefit squared   -1.03e-9 *** (3.99e-10)
Lagged bankruptcy rate        5.62294 ** (2.68448)
Household labor income
Reduction in income
Age of household head          0.01846 (0.01306)
Age squared                  -0.00036 ** (0.00015)
Education                    -0.03879 *** (0.01097)
Family size                   0.03228 * (0.01669)
Own business                   0.09489 (0.09147)
Own home                     -0.19982 *** (0.06757)
Lawyers per capita             -0.98042 (0.73636)
County unemployment rate        0.10714(0.11386)
State income growth           -2.23304 * (1.18386)
State income deviation         -0.12976 (0.08821)
Divorce                       0.23206 * (0.13196)
Period of unemployment          0.0134 (0.02435)
Health problem                 0.09265 (0.11733)
State fixed effects                   Yes
Year fixed effects                    Yes
Constant                     -2.23563 *** (0.75997)

                                   SCF Data

                               Without Adverse
                                    Event
                                  Variables

Financial benefit            0.00003 *** (6.9e-6)
Financial benefit squared   -1.55e-10 * (8.15e-11)
Lagged bankruptcy rate
Household labor income      -4.12e-6 ***(1.48e-6)
Reduction in income         -2.71e-7 *** (7.34e-8)
Age of household head          0.0486 (0.0339)
Age squared                   -0.00058 (0.00038)
Education                      0.0022 (0.0193)
Family size                   0.0618 * (0.0321)
Own business                   -0.3162 (0.1949)
Own home                       -0.1122 (0.1435)
Lawyers per capita
County unemployment rate
State income growth
State income deviation
Divorce
Period of unemployment
Health problem
State fixed effects                  Yes
Year fixed effects                    No
Constant                     -3.5272 *** (0.8701)

                                   SCF Data

                                 With Adverse
                                     Event
                                   Variables

Financial benefit             0.00003 *** (7e-6)
Financial benefit squared   -1.61 e-10 ** (8.2e-11)
Lagged bankruptcy rate
Household labor income
Reduction in income
Age of household head           0.0281 (0.0302)
Age squared                    -0.0003 (0.0003)
Education                      -0.0125 (0.0198)
Family size                    0.0631 * (0.0334)
Own business                  -0.3321 * (0.1858)
Own home                        -0.1759(0.1425)
Lawyers per capita
County unemployment rate
State income growth
State income deviation
Divorce                       0.7627 *** (0.1765)
Period of unemployment          0.0047 (0.0053)
Health problem                  0.0359 (0.2980)
State fixed effects                   Yes
Year fixed effects                    No
Constant                     -3.2664 *** (0.8059)

TABLE 3
Joint Determination Model (PSID Data)

                                                             Standard
Variables                                    Coefficient      Error

Correlation between the two                    -0.1402       0.1183
  error terms [theta]

Bankruptcy equation

Log financial benefit                           0.0786 ***   0.0291
Age                                             0.0146       0.0114
Age squared                                    -0.00026 **    .00013
Lagged bankruptcy filing rate                   5.8113 **    2.3557
Education                                      -0.0204 **    0.0083
Family size                                     0.0223       0.0145
Own business                                    0.0528       0.0804
Own home                                       -0.0839       0.0574
Lawyer per capita                              -0.0376       0.6017
Growth rate of income                          -1.9152 *     1.1194
State income deviation                         -0.1429 *     0.0764
State and time dummies                          yes
constant                                       -2.1588 ***   0.4615

Financial benefit equation

Excluded adverse event variables Health         1.9230 ***   0.2287
Divorce                                         0.3550       0.3391
Unemployed                                     -1.3573 ***   0.2645
Period of unemployment                          0.7437 ***   0.1970
Period of unemployment                         -0.0470 ***   0.0124
  squared

Other control variables

Age                                            -0.1338 ***   0.0263
Age squared                                    -0.00067 **   0.00028
Lagged bankruptcy filing rate                  -3.7895       8.5598
Education                                      -0.0306 *     0.0169
Family size                                     0.4164 ***   0.0401
Own business                                   -3.2056 ***   0.2267
Own home                                       -3.2106 ***   0.1331
Lawyer per capita                              -3.0452 *     1.7055
Growth rate of income                          -2.2850       3.4461
State income deviation                         -0.2774       0.2114
State and time dummies                          yes
Constant                                        0.4705       1.4079
Standard deviation of error                     3.2073 ***   0.0067
  term
Log-likelihood                             -61774.312

TABLE 4
Joint Determination Model (SCF Data)

                                               Standard
Variables                      Coefficient      Error

Correlation between the two      -0.2599        0.1746
  errors [theta]

Bankruptcy equation

Log financial benefit             0.1462 ***    0.0400
Age                               0.0471        0.0307
Age squared                      -0.00046       0.0003
Years of education                0.2266        0.1579
Years of education squared       -0.0091        0.0061
Family size                       0.0544 *      0.0331
Own business                     -0.1998        0.1910
Own home                          0.0605        0.1340
Region dummies                    Yes
Constant                         -5.7178 ***    1.2966

Financial benefit equation

Excluded adverse variables
Health                            0.0161        1.0442
Divorce                           3.0169 ***    0.8821
Unemployed                       -0.3506        1.1332
Period of unemployment            0.1937        0.1289
Period of unemployment           -0.0046 *      0.0024
  squared

Other control variables

Age                               0.0863        0.0848
Age squared                      -0.0033 ***    0.0009
Years of education                0.6088        0.3863
Years of education squared       -0.0519 ***    0.0158
Family size                       0.1311        0.1486
Own business                     -7.0680 ***    0.7049
Own home                         -5.1467 ***    0.4931
Region dummies                    yes
Constant                          4.4593        3.2282
Standard deviation of error       3.0730 ***    0.0294
  term
Log-likelihood                -4831.71

TABLE 5
Robustness Check with Different Combination of AE Variables (PSID
Data)

                                           (1)               (2)
Variables                                Divorce           Health

Correlation between the two error        -0.157            -0.1530
  terms [theta]

Bankruptcy equation

Log financial benefit                     0.0826 ***        0.0816 ***
Age                                       0.0148            0.0148
Age squared                              -0.0003 **        -0.0003 **
Lagged bankruptcy filing rate             5.8535 **         5.8598 **
Education                                -0.0205 **        -0.0203 **
Family size                               0.0219            0.0220
Own business                              0.0554            0.0551
Own home                                 -0.0806           -0.0815
Lawyer per capita                        -0.0377           -0.0395
Growth rate of income                    -1.9044 *         -1.9073 *
State income deviation                   -0.1410 *         -0.1413 *
State and time dummies                     yes               yes
Constant                                 -2.1774 ***       -2.1749 ***

Financial benefit equation

Excluded adverse event variables
Health                                                      1.9552 ***
Divorce                                   0.2930
Unemployed
Period of unemployment
Period of unemployment squared

Other control variables

Age                                      -0.1308 ***       -0.1309 ***
Age squared                              -0.0006 **        -0.0007 **
Lagged bankruptcy filing rate            -0.5250            1.1547
Education                                -0.0400 ***       -0.0290 *
Family size                               0.4238 ***        0.4124 ***
Own business                             -3.2845 ***       -3.2436 ***
Own home                                 -3.1842 ***       -3.1468 ***
Lawyer per capita                        -2.9152 *         -3.0434 *
Growth rate of income                    -0.9614           -0.9563
State income deviation                   -0.2875           -0.2829
State and time dummies                     yes               yes
Constant                                  2.8076 **         2.7932 **
Standard deviation of error term          3.2099 ***        3.2084 ***
Log-likelihood                       -62371.5          -62335.8

                                           (3)
Variables                              Unemployed

Correlation between the two error        -0.1288
  terms [theta]

Bankruptcy equation

Log financial benefit                     0.0758 **
Age                                       0.0144
Age squared                              -0.0003 **
Lagged bankruptcy filing rate             5.8147 **
Education                                -0.0204 **
Family size                               0.0226
Own business                              0.0512
Own home                                 -0.0855
Lawyer per capita                        -0.0377
Growth rate of income                    -1.9136 *
State income deviation                   -0.1434 *
State and time dummies                     yes
Constant                                 -2.1470 ***

Financial benefit equation

Excluded adverse event variables
Health
Divorce
Unemployed                               -1.3401 ***
Period of unemployment                    0.7541 ***
Period of unemployment squared           -0.0475 ***

Other control variables

Age                                      -0.1321 ***
Age squared                               0.0006 **
Lagged bankruptcy filing rate             3.5714
Education                                -0.0414 **
Family size                               0.4259 ***
Own business                             -3.2456 ***
Own home                                 -3.2498 ***
Lawyer per capita                        -2.9500 *
Growth rate of income                    -2.3346
State income deviation                   -0.2861
State and time dummies                     yes
Constant                                  0.4481
Standard deviation of error term          3.2089 ***
Log-likelihood                       -61809.4

TABLE 6
Robustness Check with Different Combination of AE Variables (SCF
Data)

                           (1)              (2)              (3)
Variables                Divorce         Unemployed         Health

Correlation between th   -0.2532          -0.0406          -0.0074
  [theta]

Bankruptcy
  equation
Log financial             0.1447 ***       0.0982 *         0.0911
  benefit
Age                       0.0471           0.0444           0.0440
Age squared              -0.0005          -0.0005          -0.0005
Years of education        0.2274           0.2446           0.2467
Years of education       -0.0092          -0.0101          -0.0103 *
  squared
Family size               0.0544           0.0591 *         0.0597 *
Own business             -0.2017          -0.2683          -0.2806
Own home                  0.0583           0.0054          -0.0040
Region dummies             Yes              Yes              Yes
Constant                 -5.7157 ***      -5.4954 ***      -5.4508 ***

Financial benefit
  equation
Excluded adverse
  variables
Health                                                     -0.0785
Divorce                   3.0112 ***
Unemployed                                -0.3793
Period of                                  0.1946
  unemployment
Period of                                 -0.0047 *
  unemployment
  squared

Other control variables

Age                       0.0751           0.1040           0.0929
Age squared              -0.0032 ***      -0.0036 ***      -0.0035 ***
Years of education        0.5873           0.6339 *         0.6118
Years of education       -0.0509 ***      -0.0534 ***      -0.0524 ***
  squared
Family size               0.1359           0.1039           0.1083
Own business             -7.0173 ***      -7.1141 ***      -7.0613 ***
Own home                 -5.1526 ***      -5.2125 ***      -5.2192 ***
Region dummies             yes              yes              yes
Constant                  4.9251           4.2912           4.7577
Standard deviation        3.0757 ***       3.0769 ***       3.0795 ***
  of error term
Log-likelihood        -4835.32         -4836.33         -4839.87

TABLE 7
PSID Predictions

                                      Mean Effect on Log
Hypothesized Variable Change        Financial Benefit (Std)

Financial benefit + $ 1000                    --
Age of household head + 10 years            -0.0433
Education + 1 year                          -0.0010
Family size + 1                              0.0156
Own home from 0 to 1                        -0.0997
Unemployed (from 1 to 0)                     0.0372
Period of unemployment - 1 week             -0.0051
Health problem (from 1 to 0)                -0.0937
Divorce (from 1 to 0)                       -0.0130

                                      Percentage Point
Hypothesized Variable Change        Marginal Effect (Std)

Financial benefit + $ 1000             0.216 (0.0007)
Age of household head + 10 years      -0.053 (3.87e-5)
Education + 1 year                    -0.014 (7.2e-6)
Family size + 1                        0.018 (1.65e-4)
Own home from 0 to 1                  -0.071 (0.0036)
Unemployed (from 1 to 0)               0.004 (3.le-5)
Period of unemployment - 1 week       -0.007 (3.le-6)
Health problem (from 1 to 0)          -0.011 (1.2e-4)
Divorce (from 1 to 0)                 -0.0015 (2.97e-6)

                                    Percentage Change
Hypothesized Variable Change        in the Filing Rate

Financial benefit + $ 1000                71.59
Age of household head + 10 years         -18
Education + 1 year                        -4.7
Family size + 1                            6
Own home from 0 to 1                     -24
Unemployed (from 1 to 0)                   1.3
Period of unemployment - 1 week           -0.23
Health problem (from 1 to 0)              -3.7
Divorce (from 1 to 0)                     -0.5

Notes: We compute each household's estimated probability of
bankruptcy under the hypothesized change, holding all other household
characteristics at their mean. The marginal effect is the change in
the probability of bankruptcy for that household. The last column
translates the marginal effects into the corresponding percentage
change in the filing rate, as follows: divide the marginal effect by
the filing probability, which is 0.3017% in the sample. Figures in
parentheses are standard errors, computed using delta method.

TABLE 8
SCF Predictions
                                               t
                                      Mean Effect on Log
Hypothesized Variable Change        Financial Benefit (Std)

Financial benefit+ $1000                      --
Age of household head + 10 years            -0.0102
Education + 1 year                          -0.1041
Family size + 1                              0.0177
Own home from 0 to 1                        -0.0079
Unemployed (from 1 to 0)                     0.0749
Period of unemployment - 1 week             -0.0194
Health problem (from 1 to 0)                -0.0733
Divorce (from 1 to 0)                       -0.6065

                                      Percentage Point
Hypothesized Variable Change        Marginal Effect (Std)

Financial benefit+ $1000                0.56 (0.0006)
Age of household head + 10 years       -0.06 (4.9e-4)
Education + 1 year                     -0.08 (0.0063)
Family size + 1                         0.10 (5.37e-4)
Own home from 0 to 1                  -0.0038 (9.89e-4)
Unemployed (from 1 to 0)               0.045 (2.67e-4)
Period of unemployment - 1 week        -0.012 (0.0017)
Health problem (from 1 to 0)          -0.046 (2.43e-4)
Divorce (from 1 to 0)                   -0.44 (0.015)

                                    Percentage Change
Hypothesized Variable Change        in the Filing Rate

Financial benefit+ $1000                  43.75
Age of household head + 10 years          -4.7
Education + 1 year                        -6.25
Family size + 1                            7.8
Own home from 0 to 1                      -0.3
Unemployed (from 1 to 0)                   3.5
Period of unemployment - 1 week           -0.94
Health problem (from 1 to 0)              -3.6
Divorce (from 1 to 0)                    -34.38

Notes: We compute each household's estimated probability of
bankruptcy under the hypothesized change, holding all other household
characteristics at their mean. The marginal effect is the change in
the probability of bankruptcy for that household. The last column
translates the marginal effects into the corresponding percentage
change in the filing rate, as follows: divide the marginal effect by
the filing probability, which is 1.28% in the sample. Figures in
parentheses are standard errors, computed using delta method.

FIGURE 1
Timeline

Period 0

* Receive signal
* Update belief

Period 1

* Choose debt

--Strategic: with
conditioning on signal

--Non-strategic: without
conditioning on signal

Intermediate
Period

* Shock realized

Period 2

* Filing Decision
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