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
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(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 hellenzsx@gmail.com
Sabarwal: Department of Economics, University of Kansas, Lawrence,
KS 66045, Phone 785-864-2847, Fax 785-864-5270, E-mail sabarwal@ku.edu
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
gan@econmail.tamu.edu
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
