The Impact of Personal Bankruptcy on Labor Supply Decisions Daphne Chen and Jake Zhao Econ One Research and Peking University HSBC Business School

Abstract The Chapter 7 bankruptcy code was motivated by the notion of a ‘‘fresh start,’’ which was justified in part by the Supreme Court on the grounds that it would encourage work incentives. We ask the question, ‘‘how does a fresh start affect labor supply?’’ This question is explored in the context of a model with job search and bankruptcy choices. The model takes into account both the endogeneity and interdependence of decisions in labor and credit markets. The structural approach allows direct assessment of individuals’ labor supply responses given their bankruptcy decisions. We find that Chapter 7 filers on average increase labor supply by 12.3%. 1. Introduction There are two bankruptcy provisions in the United States, Chapter 7 and Chapter 13. Under Chapter 7 bankruptcy, filers have the ability to protect future income due to the ‘‘fresh start’’ provision where all unsecured debt is eliminated. In contrast, Chapter 13 bankruptcy filers are required to forgo a fraction of their incomes in order to repay creditors. This is one reason why the majority of filings fall under Chapter 7. Out of the total 1.56 million bankruptcy filings in 2004, 1.12 million were filed under Chapter 7 according I

We are indebted to Dean Corbae for his guidance and encouragement. We also like to thank Satyajit Chatterjee, Wenli Li, Burhan Kuruscu, Shi Qi, Erwan Quintin, Pierre-Daniel Sarte, Don Schlagenhauf, the editor, the referees, as well as numerous seminar participants for valuable suggestions. The Texas Advanced Computing Center (TACC) generously provided computational resources for this paper. Email address: [email protected] and [email protected] (Daphne Chen and Jake Zhao) Preprint submitted to Elsevier

February 3, 2017

to the Administrative Office of the U.S. Courts. Chapter 7 bankruptcies however remain on credit reports longer than Chapter 13 bankruptcies - 10 years versus 7 years respectively. What motivated the creation of a fresh start bankruptcy system in the U.S.? The Supreme Court justified a ‘‘fresh start’’ on the grounds that it would encourage work incentives. In the 1934 ruling involving the Local Loan Company and Hunt (See 292 U.S. 234), the court stated: ‘‘From the viewpoint of the wage earner, there is little difference between not earning at all and earning wholly for a creditor.’’ The above quote takes on an extreme view that without releasing debtors from personal liability and without prohibiting creditors from collecting on those debts, the burden of debt repayment would destroy all incentives to work. This paper asks the question, ‘‘how much does a fresh start change labor supply?’’ The answer to this question is non-trivial because there are two competing effects - ‘‘wealth effects’’ and ‘‘borrowing constraint effects’’ which cause the benefits from the fresh start provision for work incentives to be unclear. These effects are experienced by both Chapter 7 and Chapter 13 bankruptcy filers. We focus on the work incentives of Chapter 7 bankruptcy filers in comparison to nonfiling, but we also discuss Chapter 7 work incentives in comparison to Chapter 13. The wealth effect makes debtors reduce work effort after bankruptcy. Once individuals file for bankruptcy, they no longer need to work to service their debt. In addition, individuals can be more selective in their job search. On the other hand, in terms of the borrowing constraint effect, individuals with bankruptcy records have limited access to borrowing because of the change in their credit scores. Such individuals may have to work more in order to self insure against unexpected expenses. Since the effect of bankruptcy on labor supply is ambiguous, this paper builds a structural model and provides a quantitative answer. We seek a deeper understanding of the interdependence of labor and credit market decisions. This is important because labor supply has been an important component of policy discussions. Prior to any discussion of bankruptcy reform, the labor supply response of individuals facing bankruptcy must be understood, which is a major focus of this study. Because bankruptcy choices are endogenous, Chapter 7 bankruptcy filers tend to have less earnings and more debt on average in both our model and in the data. Moreover, they are more likely to have experienced job loss, and 2

hence Chapter 7 bankruptcy filers may behave differently than the average person in the economy. The self-selection for a fresh start must be considered when evaluating the labor supply implications. Without controlling for endogeneity, the change in work incentives might be underestimated simply because Chapter 7 bankruptcy filers are more likely to have fewer working hours due to job market disruptions, and therefore appear as if their incentives to work are low. The endogeneity issue is difficult to resolve. One of the popular solutions is to introduce instrumental variables in a regression analysis. This paper takes an alternative approach. Instead of evaluating the effect through regression analysis, we construct a dynamic job search model where individuals are able to both file and choose the form of bankruptcy. This allows us to deal with the endogeneity issues directly since agents’ decision rules are explicitly modeled. In the credit market, consumers in our model can save or borrow. For those who are in debt, they can discharge their debt through bankruptcy. Furthermore, they can choose to file under either Chapter 7 or Chapter 13. Since the majority of the bankruptcy filers choose to receive a fresh start, most papers only consider Chapter 7 bankruptcy. However, because Chapter 13 bankruptcy is an alternative to Chapter 7, the income garnishment associated with a Chapter 13 bankruptcy can potentially result in changes in labor supply responses. It is therefore essential to allow for both bankruptcy chapter choices in the model. In the labor market, model agents can choose whether or not to work on the extensive margin and how much to work on the intensive margin. It is essential here that individuals can make labor supply decisions on both margins, because if we compare bankruptcy filers with average people, bankruptcy filers are more likely to experience job loss, so they work less on the extensive margin. If filers have a job, they are more likely to work more on the intensive margin because they have low wealth and are borrowing constrained. Hence the effect of bankruptcy on the two margins of labor supply can be very different. To measure the effect of a fresh start on work incentives, we adopt the concept of the ‘‘average treatment effect on the treated’’ (ATET) from econometrics (a detailed description of ATET is discussed in the next section). Considering a fresh start as a ‘‘treatment,’’ the ATET calculates the difference in average labor supply for Chapter 7 bankruptcy filers under filing and repayment. A positive ATET suggests that a fresh start improves work 3

incentives, while a negative ATET indicates that a fresh start reduces labor supply. The computation of ATET requires the knowledge of what we observe and what we do not observe. We observe the equilibrium labor supply decision for every filer. However, for the exact same people, we also need to know their labor supply decision if they were instead forced to repay creditors, which is unobservable in the data. To deduce the unobserved labor supply decisions, we therefore run a counterfactual experiment for each filer where we disallow them to make their optimal choices. With the model calibrated to match labor and credit market statistics, the ATET can be calculated directly because we can solve for each filer’s optimal labor supply decisions under all possible bankruptcy choices. We find that a fresh start mainly increases labor supply for Chapter 7 bankruptcy filers through changes in the intensive margin. Chapter 7 bankruptcy filers provide 12.3% more labor supply than they would have if they were disallowed to file. In contrast, the labor supply increase is only 0.3% if Chapter 7 filers were instead compelled to file for Chapter 13 bankruptcy. These results can be viewed as strong supporting evidence that a fresh start does improve overall work incentives. This is one of the first papers that introduces labor supply decisions into a model with unsecured consumer credit that incorporates the main characteristics of U.S. consumer bankruptcy law. Most papers in the literature, such as Athreya (2002), Livshits et al. (2007), and Chatterjee et al. (2007), do not account for the possible interaction between credit and labor markets by assuming inelastic labor supply. However, it is difficult to answer the question of interest without endogenizing agents’ decisions in both markets. Hence in our model, consumers can participate in both the credit market and the labor market. This is also the first paper to our knowledge that allows the type of bankruptcy to be determined in an equilibrium setting as in Chatterjee et al. (2007). In this type of equilibrium, financial intermediaries offer a menu of loan contracts to borrowers. If borrowers default on their debt under Chapter 13 bankruptcy, financial intermediaries can minimize losses by using income garnishment. The availability of Chapter 13 bankruptcy makes loan interest rates prior to bankruptcy dependent on the labor supply decisions after bankruptcy. By allowing the loan prices to be risk based, the equilibrium generates endogenous borrowing limits given individuals’ characteristics. In contrast, Li and Sarte (2006) adopt the equilibrium concept employed in Athreya (2002) where every person in the economy faces the same loan interest 4

rate and the same borrowing constraint which is set exogenously to match the average debt-to-income ratio. Recently, the slow recovery in the labor market during the Great Recession has motivated researchers to look closer at the interaction between labor and credit markets. Herkenhoff (2015) evaluated the impact of consumer credit access on unemployment. He found that when borrowing opportunities are easy to find, households would optimally search for better-paying but harder-to-find jobs. The reason is that in the event where the job search fails, households can smooth their consumption with easy access to credit. Athreya et al. (2015), on the other hand, measured how much changes in labor market risk along with recent bankruptcy reform affect unsecured credit use. In particular, they evaluate the transitional dynamics during the Great Recession. However, few papers have investigated how bankruptcy decisions affect the work incentives of debtors. Han and Li (2007) made the first attempt to address this question, and they estimated the effect from a static treatment model using data from the Panel Study of Income Dynamics (PSID). They found that a fresh start reduces labor supply, which is the opposite of the stated goal, although the effect is not statistically significant. To reconcile the positive results from our structural model with their negative but insignificant results, we run a treatment regression using a pseudo dataset. The pseudo dataset is simulated from the equilibrium model distribution, and we show that time aggregation can reverse the result from positive to negative. Time aggregation is important because labor market activities occur more frequently than credit market activities, and bankruptcy filers are more likely to go in and out of employment within a year. We question the use of the ‘‘financial benefit’’ of default as an instrument since it is endogenously related to net wealth, and we show that low frequency data can easily downward bias the regression results even if perfect instruments could be found. The rest of the paper is organized as follows. We start by introducing the ATET methodology in Section 2. The model environment is formulated in Section 3. Section 4 describes the equilibrium, and the model is parameterized in Section 5. We then analyze equilibrium behavior in Section 6, while Section 7 presents the benchmark model results. In Section 8, we reconcile the benchmark results with reduced-form estimation results by running treatment regressions on simulated data. Finally, Section 9 concludes.

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2. ATET Methodology

Table 1: Labor Supply Response Table

d∗ \ d 0 7 13

0 (0,0) (7,0)

7

13

(7,7)

A labor supply response table can help us understand how to correctly measure the average treatment effect on the treated. The ultimate goal of this paper is to first fill Table 1 up through a model and then evaluate the ATET from it. Each individual first has to assess the value of choosing each bankruptcy action d = {0, 7, 13} listed as the columns of Table 1 where d = 0 means an individual does not file for bankruptcy, d = 7 means he files for Chapter 7 bankruptcy, and d = 13 means he files for Chapter 13 bankruptcy. The actual choice d∗ is the maximum of these possible values. Each individual belongs to one of the three rows according to his actual bankruptcy decision. For instance, a Chapter 7 bankruptcy filer chooses d∗ = 7 and thus is assigned to the second row. The diagonals are observable since the individual has revealed d∗ = d is his optimal choice. On the other hand, the off-diagonal elements are not observable - we only know that those values of d are not as high as d∗ . Specifically, for a Chapter 7 bankruptcy filer, we observe his labor supply response in cell (7,7) of the table when he is under Chapter 7 bankruptcy, but we do not observe his labor supply response in (7,0) if the filer were instead to choose to repay the creditors.1 1

We can calculate the average annual working hours conditional on bankruptcy decisions using a combined cross-sectional dataset from the 1984-1995 PSID. There are 28,893 nonfilers versus only 58 Chapter 7 filers and 41 Chapter 13 filers in the dataset. Chapter 7 bankruptcy filers on average work for 1890.60 hours, which is lower than nonfilers who on average work for 2114.20 hours in a year. The small sample size of bankruptcy filers induces imprecise estimates with large standard errors. We are not able to calculate any off-diagonal value directly from data.

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From Table 1, the effect of a fresh start on labor supply for each Chapter 7 bankruptcy filer is the difference between the values in (7,7) and those in (7,0). Therefore, the impact of a fresh start on labor supply can be measured by taking the average effect among all Chapter 7 bankruptcy filers. Formally, ATET = L(7, 7) − L(7, 0)

(1)

where L(d∗ , d) is average labor supply response given equilibrium and counterfactual bankruptcy decisions respectively. If the ATET is positive, this implies that a fresh start increases labor supply. This comparison requires knowledge of what we do not observe, i.e., the value in (7,0). We therefore directly evaluate the counterfactual outcomes for bankruptcy filers within our model. The reason why we cannot simply replace the value in (7,0) with the observable value in (0,0) is because bankruptcy events are endogenous instead of randomly assigned. If we do not consider the possibility that Chapter 7 bankruptcy filers are more likely to suffer from unemployment and have lower wealth than others, that is, if we ignore the endogeneity of bankruptcy decisions, the estimates could be biased. There are two possible ways to deal with the endogenous bankruptcy treatment if we were to estimate the ATET from micro-level data. The first situation is where we can include in the regression the factors which determine bankruptcy decisions. Therefore, given the covariates, the bankruptcy decision is independent of labor supply responses. We can then estimate the effect of endogenous bankruptcy on labor supply via a ‘‘kitchen sink’’ regression. The problem is that bankruptcy decisions can also be affected by labor market outcomes. For instance, a person having undergone a period of prolonged unemployment is more likely to default. The reverse causality thus would bias the estimates since it is not taken into account in the regression. The second possible method is through instrumental variables, which have effects on bankruptcy decisions but not directly on labor supply decisions, except through bankruptcy filings. Han and Li (2007) use two instruments, social stigma and potential financial benefit from bankruptcy, in their analyses. Because personal preferences are not directly observable, they use lagged U.S. state-level bankruptcy rate as a proxy for social stigma. To control for the possibility that the proxy may be correlated with labor-market conditions, they also include lagged state unemployment rate and lagged state incomegrowth rate in the regression. The potential financial benefit from bankruptcy, 7

defined as the amount of unsecured debts net of non-exempted assets, is calculated from wealth information. Because the PSID surveys wealth every five years, they assume that individuals have the same wealth over every five year interval, introducing possible measurement error. In addition, since the financial benefit of default is the amount of debt being discharged, the financial benefit is highly negatively correlated with net wealth for individuals who are in debt. Labor supply is then negatively affected by wealth, according to findings in the economics literature. These issues cast doubt on the validity of the instruments. Given that it would be difficult to correctly estimate the impact of personal bankruptcy on labor supply decisions due to the interdependence of labor and credit market behaviors, we take an alternative approach to estimate the ATET from a model that allows individuals to make endogenous bankruptcy and labor supply decisions. The difference between the equilibrium and counterfactual labor market outcomes can then be assessed through the model. In the next section, we begin describing the model environment. 3. The Model Time is discrete and infinite. There is a unit measure of agents who survive to next period with a constant probability ρ. Newborns replace those who do not survive. All agents are endowed with one unit of time that they can allocate between work h and leisure 1 − h. Competitive financial intermediaries take deposits from and give loans to agents. There exists a government that collects labor income taxes and runs social welfare programs. 3.1. Preferences Agents value non-negative consumption c ≥ 0 and dislike work h. The utility function u(c, h) is strictly increasing and concave in consumption c and strictly decreasing and convex in hours worked h. Agents discount the future at rate β ∈ [0, 1]. 3.2. Bankruptcy An agent enters a period with assets a ∈ IR and expense shocks ζ ∈ Z. The expense ζ occurs with probability z(ζ) independent of time, interpreted as unanticipated medical bills or lawsuits. Therefore, the net worth of an agent in the beginning of the period is defined as a − ζ. A person can, in addition, borrow from or lend to competitive financial intermediaries who 8

take the risk-free rate r as given. The asset choice decision made by the individual is denoted as a0 , and the individual saves if a0 ≥ 0 or borrows if a0 < 0. Let b ∈ {0, 7, 13} denote the bankruptcy flag status, where b = 0 means the agent has no bankruptcy record, b = 7 means he has a Chapter 7 bankruptcy record, and b = 13 means he has a Chapter 13 bankruptcy record. While an agent has a bankruptcy flag on his credit record, he is excluded from the credit market (i.e., a0 ≥ 0). The assumption that a person has limited access to the credit market after bankruptcy follows Chatterjee et al. (2007) and is consistent with the empirical findings in Musto (2004) and Han and Li (2011). The theory behind the reason why a bankrupt individual is restricted from the credit market is discussed in Chatterjee et al. (2015), where default decisions signal an agent’s unobservable type. An individual might have no bankruptcy record even if he has filed for bankruptcy in the past, because a bankruptcy filer may remove his bankruptcy record b ∈ {7, 13} with probability γ b in each period provided that he does not default in that period. The removal of the bankruptcy flag is modeled as an i.i.d. probabilistic event to avoid having to keep track of the number of periods the flag is already on a person’s credit record. This is also a simple way of modeling the fact that a bankruptcy flag only remains on the credit history for a finite number of years. Specifically, the average duration of carrying a bankruptcy flag b (not counting the period of default) is 1/γ b − 1. For instance, if γ b = 1, the flag is immediately removed in the period after default. If γ b = 0, an individual carries the bankruptcy flag forever. We also assume that γ 13 > γ 7 so that a person considering default may prefer Chapter 13 bankruptcy even though his income would be subject to garnishment because the flag would be removed earlier on average. An agent without a bankruptcy flag b = 0 can exercise the default option if a − ζ < 0. Any person in debt is eligible for Chapter 7 bankruptcy. Chapter 13 bankruptcy enables an individual with regular income to develop a plan to repay all or part of his debt. Although any individual is eligible for Chapter 13 subject to debt thresholds, a repayment plan filed with the court with a schedule of current income must be approved in the real world. 2 For 2

A person never reaches the debt thresholds for Chapter 13 bankruptcy in our model because we consider net debt (after consolidating all assets and debts). However, the real world eligibility requirements for Chapter 13 consider assets and debts separately without consolidation. In other words, it is possible that an agent has unsecured debt that exceeds

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simplicity, we abstract from the approval decisions of the proposed repayment plan, and our model allows Chapter 13 bankruptcy for all agents except for those who are collecting floor benefits to meet their basic consumption need. In the calibration, food stamps are used to proxy for floor benefits. Finally, an agent with a bankruptcy flag b ∈ {7, 13} on the credit record can only default if repayment results in negative consumption. If an agent files for bankruptcy, he continues into the next period with a bankruptcy flag associated with his bankruptcy choice. For instance, if he files under Chapter 7 (d = 7), his bankruptcy flag next period will be b0 = 7. Depending on bankruptcy chapter choices, the timing of debt discharge would vary. Under a Chapter 7 case, the discharge is usually granted promptly in the U.S., while under a Chapter 13 case, the discharge generally is granted after a debtor completes the repayment plan. Since the constraints of his asset market activities would be governed by the bankruptcy flag status within our model, the timing of the discharge would not affect the agent’s decisions. For this reason, we assume that all debt is discharged when a person files for bankruptcy. This allows us to avoid tracking the unpaid debt amount over time for a debtor who files for Chapter 13 bankruptcy. We can alternatively and equivalently assume that the debts are discharged once agents have their Chapter 13 bankruptcy flag removed. The actions of the agents would be the same in either case. We assume that an agent cannot save or borrow (i.e., a0 = 0) in the period of default. This is to capture the fact that whatever he saves will be confiscated by the court and given back to creditors, so an individual does not have incentives to save. He is also not able to get loans in the period of default, because he will default on loans altogether, so no financial intermediary will be willing to extend loans.3 The income garnishment associated with Chapter 13 bankruptcy is modeled as a proportional tax as in Li and Sarte (2006).4 Denote δ b as the the Chapter 13 debt threshold requirement, but after taking into account his assets, his net debt is lower than the debt threshold. We are unable to take into account this specific Chapter 13 eligibility requirement unless we allow assets and debt to be separate and distinct control variables in our model. 3 Some defaulters in reality have access to the credit card market after bankruptcy although the access is very limited. By allowing agents to regain credit access probabilistically, we are able to mimic reality without modeling the deep theory using signaling theory as in Chatterjee et al. (2015). 4 The rationale behind this assumption is that households could claim expenses which

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fraction of income garnished for an agent with bankruptcy flag status b. Because a Chapter 7 bankruptcy filer starts afresh, he has all his current and future incomes exempted, so δ 7 = 0. A Chapter 13 filer has a fraction δ 13 > 0 of his income garnished as long as he has the bankruptcy flag attached. In practice, Chapter 13 bankruptcy requires that a debtor repays creditors using earnings net of necessary expenses. This paper follows Li and Sarte (2006) to assume that the amount of necessary expenses is proportional to income. Furthermore, income from food stamps is assumed to be exempted from Chapter 13 garnishment, since all food stamp income is interpreted as necessary to meet basic consumption needs. Lastly, for a consumer without a bankruptcy flag, δ 0 = 0. 3.3. Employment The employment status for an agent is binary e ∈ {0, 1}, where e = 1 indicates the agent is employed and e = 0 indicates the agent is either unemployed or out of the labor force. An employed agent enters a period with wage rate w. He may receive an exogenous separation shock with probability κ and become non-employed involuntarily. Otherwise, given his wage rate w, he can decide whether to continue or quit his job. Denote the job-continuation decision as l ∈ {0, 1}. If l = 1, the agent continues with his current job. If l = 0, the agent quits and becomes non-employed. An individual who stays employed decides how much to work h ∈ [0, 1]. His earnings wh are taxed at rate τ by the government. Creditors receive δ b (1 − τ )wh, while the government collects τ wh. For simplicity, this model does not allow on-the-job search. Since we are interested in the counterfactual outcomes on the individual level, a partial equilibrium with an exogenous wage-rate offer distribution is sufficient to answer our question. Hence, we assume that any non-employed person may receive a wage rate offer w from a known distribution G(w) upon the receipt of a job offer. However, we understand that if the bankruptcy law changes for everyone, the wage-rate offer distribution could be affected and should be endogenized. were ”reasonably necessary” such as private school tuition. Insofar as higher income households likely had more diverse and larger expenditures, they would have had more opportunities and greater expenditures to claim as necessary. In addition, federal law prohibits creditors from taking more than 25 percent of the debtor’s income. Necessary expenses were therefore often tied to a fixed proportion of household income.

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The likelihood of getting an offer is allowed to depend on an agent’s bankruptcy flag status. Specifically, agents receive a wage-rate offer with probability φb . This feature is motivated by the fact that, based on a Survey by the Society for Human Resource Management (2010), sixty percent of companies use credit information (especially bankruptcy records) when making employment decisions. Herkenhoff et al. (2016) similarly find credit checks to have adverse effects on employment opportunities. They use a dataset which merges employment data from the Census Bureau and credit data from TransUnion. The theory behind why credit information is used by employers in the labor market is being explored in Chen et al. (2013) with a labor matching model with credit information as endogenous signals. We take a parsimonious approach here by allowing the job arrival rates to depend on the bankruptcy flag status, which is a simple way to capture the fact that agents may have adverse outcomes from having bad credit. Finally, a non-employed agent makes a job-acceptance decision lw if he receives a wage rate offer w. If lw = 1, the agent accepts the job offer and then makes work-leisure decisions. But if lw = 0, the agent rejects the job offer and stays non-employed. 3.4. Loan Pricing The price schedule q(a0 , ˜s) depends on the agent’s asset choice a0 , given that he is in state ˜s when he makes the asset choice. In the event of Chapter 13 bankruptcy, the creditors’ right to repayment is proportional to their share of total defaulted loans. For instance, for an individual who defaults on unsecured debt a0 and expenses shock ζ, financial intermediaries receive a fraction −a0 /(−a0 + ζ) of the total repayment. 3.5. Welfare Benefits The government runs a balanced budget by taxing earnings at rate τ to finance welfare benefits, which can take on three levels, y ∈ {0, y, y} where 0 < y < y. When an agent makes a transition from employment to non-employment, he receives unemployment insurance y. In subsequent periods while he remains non-employed, he loses the benefits with probability ν (calibrated to match the average duration people are eligible for unemployment insurance). Once he loses unemployment insurance, he does not regain eligibility before he takes on a new job. A non-employed agent who is ineligible for unemployment insurance receives floor benefits y, providing a

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lower bound of consumption. An employed worker does not receive any type of government transfer, i.e. y = 0. 3.6. Timing of the Events There are two subperiods in one period. Agents enter a period in state s = (e, b, a, w, y, ζ). Newborns are assumed to enter with no job, no bankruptcy flag, and no assets. They receive floor benefits y and experience the unanticipated expense shock ζ with probability p(ζ). In other words, they enter in state s = (0, 0, 0, 0, y, ζ). Agents make employment decisions as in a sequential job search model with exogenous separation in the first subperiod. In the second subperiod, they make bankruptcy and asset choice decisions. 3.6.1. Subperiod 1 • Agents enter subperiod 1 in state s = (e, b, a, w, y, ζ). • Employed agents (e = 1) receive separation shocks. If not separated from jobs, agents make job continuation decisions l ∈ {0, 1}. • Non-employed agents (e = 0) receive a wage offer w from G(w) with probability φb and make job acceptance decisions lw ∈ {0, 1}. • Non-employed agents learn their eligibility for unemployment insurance benefits. • Employment status ˜e with associated wage rate w ˜ and eligible welfare benefits y˜ are updated. 3.6.2. Subperiod 2 • Agents enter subperiod 2 with updated state ˜s = (˜e, b, a, w, ˜ y˜, ζ) according to labor market activities in subperiod 1. • Agents make bankruptcy decisions d ∈ {0, 7, 13}. • Workers (˜e = 1) make work-leisure decisions h ∈ [0, 1] and receive earnings. Non-workers (˜e = 0) receive social benefits y˜ from the government. • Agents consume c and make asset choice decisions a0 . • Agents learn their death shocks. If they survive, the bankruptcy flags b0 and expense shocks ζ 0 for next period are updated. 13

Because there is no uncertainty between the two subperiods, the model is equivalent if we combine the subperiods and allow agents to make labor and asset market decisions simultaneously. In other words, the optimal decisions in subperiod 1 take into account the optimal decisions in subperiod 2 and vice versa. The reason we formulate the agent’s problem with two subperiods is that it allows us to write out the labor and credit market decisions in separate equations. 4. Equilibrium 4.1. Agent’s Problem Let V (s) be the value function of agents who enter subperiod 1 in state s = (e, b, a, w, y, ζ) and W (˜s) be the value function of agents when they enter subperiod 2 with updated state ˜s = (˜e, b, a, w, ˜ y˜, ζ). 4.1.1. Subperiod 1 For employed agents, their value function in subperiod 1 is given by V (1, b, a, w, 0, ζ) =κW (0, b, a, 0, y, ζ)   (2) +(1 − κ) max W (1, b, a, w, 0, ζ), W (0, b, a, 0, y, ζ) . If employed agents are separated exogenously from their jobs with probability κ, they continue to subperiod 2 with the value of being non-employed W (0, b, a, 0, y, ζ). Also, they are eligible for unemployment insurance when they just become unemployed. For agents who do not receive the separation shock, they remain employed if the value of continuing with the current job W (1, b, a, w, 0, ζ) is greater than the value of quitting W (0, b, a, 0, y, ζ). For non-employed agents, their value function in subperiod 1 is given by   Z b V (0, b, a, 0, y, ζ) =φ max W (1, b, a, w, 0, ζ), Ey˜|y W (0, b, a, 0, y˜, ζ) G(dw) w

+(1 − φb )Ey˜|y W (0, b, a, 0, y˜, ζ). (3) Non-employed agents receive a wage-rate offer w from a distribution G(w) with probability φb and make the job-acceptance decision. They take the new job if the value of accepting W (1, b, a, w, 0, ζ) is greater than the value of 14

rejecting Ey˜|y W (0, b, a, 0, y˜, ζ), taking into account the probability of losing unemployment insurance while staying non-employed. With probability 1−φb , they do not receive a new job offer. In this case, they continue non-employed into subperiod 2 with a value of Ey˜|y W (0, b, a, 0, y˜, ζ). 4.1.2. Subperiod 2 Agents make bankruptcy decisions d ∈ {0, 7, 13} in subperiod 2. Agents without a bankruptcy record, b = 0, can default if a − ζ < 0. On the other hand, default is available to agents with a bankruptcy flag, b ∈ {7, 13}, if repayment results in negative consumption. Since Chapter 13 bankruptcy is available for agents with regular incomes, we assume that everyone can file for Chapter 13 except those who are collecting floor benefits. To maintain consistency, the labor earnings or unemployment insurance of Chapter 13 bankruptcy filers are subject to garnishment, while food stamps are exempted. We define θ(˜ y ) as the amount of government transfer that is subject to garnishment under a Chapter 13 repayment plan. Specifically, ( y if y˜ = y θ(˜ y) = (4) 0 if y˜ 6= y. The value function of agents in subperiod 2 is given by  W (˜e, b, a, w, ˜ y˜, ζ) = max W 0 (˜e, b, a, w, ˜ y˜, ζ),  W (˜e, b, a, w, ˜ y˜, ζ), W (˜e, b, a, w, ˜ y˜, ζ) . 7

(5)

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Given bankruptcy decisions of individuals, their values are determined as follows: 1. If agents do not exercise the option of default, they can make asset choice decision a0 . If they do not have a bankruptcy flag (b = 0), they can save or borrow (a0 ∈ IR). Otherwise, they cannot borrow (a0 ≥ 0) and a fraction δ b of their earnings or unemployment insurance is garnished. We therefore have W 0 (˜e, b, a, w, ˜ y˜, ζ) = max u(c, h) + βρE(b0 ,ζ 0 )|b V (˜e, b0 , a0 , w, ˜ y˜, ζ 0 ) 0 (h,a )

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where ( (1 − τ )wh ˜ + y˜ + a − ζ − q(a0 , ˜s)a0 c= (1 − δ 13 )(1 − τ )wh ˜ + y˜ − δ 13 θ(˜ y ) + a − ζ − q(a0 , ˜s)a0

if b = {0, 7} if b = 13.

Note that δ 13 θ(˜ y ) is the amount which is garnished in a Chapter 13 bankruptcy. 2. If agents file for Chapter 7 bankruptcy to discharge their debt, they enter next period with zero assets but with a Chapter 7 bankruptcy flag. In the period of default, they consume after-tax earnings. We have W 7 (˜e, b, a, w, ˜ y˜, ζ) = max u(c, h) + βρEζ 0 V (˜e, 7, 0, w, ˜ y˜, ζ 0 ) h

where c = (1 − τ )wh ˜ + y˜. 3. If agents choose to file for Chapter 13 bankruptcy to discharge their debt, they enter next period with zero assets but with a Chapter 13 bankruptcy flag. Starting from the period of default, their after-tax earnings or unemployment insurance are subject to garnishment. Recall that the bankruptcy flag is removed with a higher probability under Chapter 13 bankruptcy so it may be preferred despite being more costly in the short-term. Finally, we have W 13 (˜e, b, a, w, ˜ y˜, ζ) = max u(c, h) + βρEζ 0 V (˜e, 13, 0, w, ˜ y˜, ζ 0 ) h

where c = (1 − δ 13 )(1 − τ )wh ˜ + y˜ − δ 13 θ(˜ y ). The solution to the agent’s problem generates job continuation decision l(s) and job acceptance decision lw (s) in subperiod 1, and default decision d(˜s), asset choice decision a0 (˜s), and work-leisure decision h(˜s) in subperiod 2. 4.1.3. Reservation Wages Denote the reservation wages as wr (s) for agents in state s. For employed agents, the reservation wage wr satisfies the following condition: W (1, b, a, wr , 0, ζ) = W (0, b, a, 0, y, ζ). At the reservation wage rate wr , workers feel indifferent between continuing and quitting their current jobs. 16

For non-employed agents, the reservation wage wr satisfies the following condition: W (0, b, a, wr , 0, ζ) = Ey˜|y W (0, b, a, 0, y˜, ζ). If they receive a wage rate offer w = wr (s), they are indifferent between accepting and rejecting the new job offer. The reservation wage wr (s) determines the labor supply decisions on the extensive margin. Consumers are more likely to take on employment if their reservation wages are low. 4.2. Financial Intermediary’s Problem Competitive financial intermediaries take the risk-free rate r as given and provide a menu of deposit and loan contracts with interest rates that make zero profit at equilibrium. The risk-based menu of prices is motivated by the empirical findings in Edelberg (2006) and is consistent with the modeling assumption in Chatterjee et al. (2007), Livshits et al. (2007), and Athreya et al. (2015). In equilibrium, the price function does not depend on the current asset position a and the expense shock ζ, because the current asset position a is irrelevant once people make next period asset choice a0 , while the expense shock ζ is not persistent and thus provides no information about default risk in the next period. The prices take into account that some individuals may not survive to collect their savings or repay their debt. First, the deposit price is ρ/(1 + r). The loan prices additionally depend on the default probability and are given by ρR(a0 , ˜s) q(a0 , ˜s) = (6) 1+r where R(a0 , ˜s) is the expected recovery rate for loan amount a0 given that agents are in state ˜s when they borrow. Debtors face higher prices (lower interest rates) for loans when the expected recovery rate is higher.5 The financial intermediaries receive full repayment (recovery rate equals 1) if agents do not default next period. When agents default, the amount that the financial intermediaries can recover depends on agents’ bankruptcy 5

Loan prices can be conditioned on income, expenses, and debts in the real world according to the Federal Trade Commission (FTC). However, much of this information is also encapsulated in credit scores. Credit scoring is considered in Chatterjee et al. (2015) but it is beyond the scope of our model.

17

chapter choices. The recovery rate is 0 under Chapter 7 bankruptcy because they are not obliged to repay using any current and future earnings. The recovery rate however is between 0 and 1 under Chapter 13 bankruptcy depending on the amount of expected income garnishment. Let Γ(˜s0 ) be the total expected discounted repayments from Chapter 13 bankruptcy filers who default in state ˜s0 . The expectation is given by Γ(˜s0 ) = δ 13 (1 − τ )w(˜s0 )h(˜s0 ) + δ 13 θ(y(˜s0 )) + E˜s00 |˜s0 Λ(˜s00 ),

(7)

which includes the total amount garnished in the period of default δ 13 (1 − τ )w(˜s0 )h(˜s0 ) + δ 13 θ(y(˜s0 )). Note that w(˜s0 ) and y(˜s0 ) represent the element values of wage w and government transfer y in state ˜s0 . The expected discounted future repayment is E˜s00 |˜s0 Λ(˜s00 ), which can be defined recursively as follows:   0 0 |˜ 0 )=13,d(˜ 0 )=0} Λ(˜ E 1 s ) ˜ s s {b(˜ s s Λ(˜s) = δ 13 (1 − τ )w(˜s)h(˜s) + δ 13 θ(y(˜s)) + . (8) 1+r Income garnishment terminates when agents have Chapter 13 bankruptcy flags removed or file for bankruptcy again. However, although financial intermediaries do not receive repayment while agents are collecting floor benefits, as long as they carry a Chapter 13 bankruptcy flag, their earnings or unemployment benefits are subject to garnishment, which potentially makes the reservation wages of agents with a Chapter 13 bankruptcy flag different from others. Because there is no specific priority order among unsecured debts such as credit card debt or medical bills, we assume financial intermediaries split the repayment based on their share. Financial intermediaries collect a fraction −a/(−a + ζ) out of the total repayment from debtors who default on unsecured debt −a and expense shock ζ through Chapter 13 bankruptcy filings. Therefore, for a loan size a0 that is defaulted under Chapter 13 bankruptcy by agents in state ˜s0 , the financial intermediaries recover (−a/(−a + ζ))Λ(˜s0 ). As a result, the recovery rate for a Chapter 13 bankruptcy Φ(˜s0 ) when agents default in state ˜s0 can be calculated by taking the total partial repayment received by financial intermediaries divided by the loan size, i.e. Φ(˜s0 ) =

Λ(˜s0 ) . −a0 + ζ(˜s0 )

The expected recovery rate can be then calculated as follows:   R(a0 , ˜s) = E˜s0 |(a0 ,˜s) 1{d(˜s0 )=0} · 1 + 1{d(˜s0 )=7} · 0 + 1{d(˜s0 )=13} · Φ(˜s0 ) . 18

(9)

(10)

4.3. Distribution Let m(s) and m(˜ ˜ s) denote the invariant cross-sectional distribution measures of agents in state s in subperiod 1 and in state ˜s in subperiod 2 respectively. In subperiod 1, the population includes both agents who survive from the previous period and newborns. Surviving agents enter a period with asset position and bankruptcy flag status that depend on their default and asset choice decisions made in the previous period. Let B(b0 , b, d) be the probability that agents have updated bankruptcy status b0 given previous bankruptcy flag status b and default decision d in the last period. The distribution for agents with a current job is given by XZ 0 0 0 m(1, b , A, W, 0, ζ ) = ρz(ζ ) 1a0 (˜s)∈A B(b0 , b, d(˜s))m(1, ˜ b, da, dw, ˜ 0, ζ) ζ

a,w∈W ˜

(11) where the differentials da and dw ˜ indicate that the integral is taken over the asset and wage rate dimensions of the distribution. The distribution for non-employed agents includes newborns and is given by XZ 0 0 0 m(0, b , A, 0, y˜, ζ ) =ρz(ζ ) 1a0 (˜s)∈A B(b0 , b, d(˜s))m(0, ˜ b, da, 0, y˜, ζ) a (12) ζ + (1 − ρ)z(ζ 0 )1{b0 =0,{0}∈A,˜y=0} . In subperiod 2, employed agents include those who continue their old jobs and those who accept new jobs, which can be written as Z m(1, ˜ b, A, W, 0, ζ) = l(1, b, a, w, 0, ζ)m(1, b, da, dw, 0, ζ) a∈A,w∈W XZ + lw (0, b, a, 0, y, ζ)φb G(dw)m(0, b, da, 0, y, ζ). y

a∈A,w∈W

(13) Non-employed agents include those who are separated from jobs voluntarily or involuntarily and those who do not receive or do not accept new job offers,

19

which can be written as Z κ + (1 − κ)(1 − l(1, b, a, w, 0, ζ))m(1, b, da, dw, 0, ζ)

m(0, ˜ b, A, 0, y˜, ζ) =1{˜y=y} a∈A,w

+

X y

Z p(˜ y |y)

(1 − lw (0, b, a, 0, y, ζ)) φb G(dw)m(0, b, da, 0, y, ζ).

a∈A,w

(14) 4.4. Government The government taxes earnings at rate τ from employed agents and provides social welfare benefits to non-employed agents in subperiod 2. The government runs a balanced-budget such that the total tax revenue equals the total benefit payout,6 i.e. XZ XZ τ wh(1, ˜ b, a, w, ˜ 0, ζ)m(1, ˜ b, da, dw, ˜ 0, ζ) = y˜m(0, ˜ b, da, 0, y˜, ζ). b,ζ

a,w ˜

b,˜ y ,ζ

a

(15) 4.5. Definition of a stationary equilibrium The stationary equilibrium consists of a set of value functions V (s) and W (˜s), agents’ decision rules {l(s), lw (s), h(˜s), d(˜s), a0 (˜s)}, a price function q(a0 , ˜s), a distribution {m(s), m(˜ ˜ s)}, and a tax rate τ such that 1. Agents make job continuation decisions l(s) and job acceptance decisions lw (s) to maximize V (s) in subperiod 1; 2. Agents make hours-worked h(˜s), bankruptcy d(˜s), and asset choice decisions a0 (˜s) to maximize W (˜s) in subperiod 2; 3. The price function q(a0 , ˜s) satisfies the zero-profit condition; 4. The distributions {m(s), m(˜ ˜ s)} reproduce themselves; and 5. The government runs a balanced-budget. 6

The outstanding government debt as a percentage of GDP was relatively stable prior to 2005. It increased rapidly after the Great Recession and has gradually slowed down in recent years. Since our model focuses on the steady state equilibrium and is calibrated to the time period prior to 2005, the government budget is assumed to be balanced every period. Also, because our paper is not about the wealthiest households, we assume a proportional tax rate in the model for simplicity.

20

5. Parameterization Most papers in the bankruptcy literature set the model period to be a year, because bankruptcy filings are not frequent events within a year. In this paper, the model period is set to one quarter in order to study the interaction between credit and labor markets, because the labor market status can and often will change within a year. Specifically, when an individual loses his job, the average duration of unemployment is two quarters. We will not be able to capture this if we have an annual model. The model is calibrated to before 2005.7 The utility function is assumed to take the following form: (c1−η (1 − h)η ) u(c, h) = 1−α

1−α

−1

The wage-rate offers follow a lognormal distribution G(w) with mean µw and standard deviation σw . The expense shocks take on two possible levels ζ ∈ ¯ where 0 < ζ. ¯ We set the job-arrival rates for agents with bankruptcy {0, ζ}, flags to be the same, i.e. φ7 = φ13 . Therefore, the benchmark model has a total of 19 parameters, among which 9 are determined independently of all other parameters (see Table 2) and 10 are determined jointly in equilibrium to match target statistics (see Table 3). 5.0.1. Parameters Determined Independently The survival probability ρ is set to be 0.9938 to match an average duration of a working life of 40 years. The constant relative risk aversion coefficient α is set to 2.5, as in Hansen and Imrohoroglu (1992), who use the same form of utility for agents. The risk-free rate r is set to be one percent per quarter or four percent annually.8 The mean of the log wage-rate offer is normalized to 0. The exogenous job-separation rate κ is set to be 6 percent which is consistent with the 7

Debtors of all incomes could file for bankruptcy under Chapter 7 before the Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA) amendment was effective in 2005. But after BAPCPA was enacted, Chapter 7 bankruptcy became only available for debtors with incomes above the median income amount of the debtors’ state of residence. This resulted in a historic rush to file for Chapter 7 bankruptcy right before 2005. The model is therefore calibrated to prior to the BAPCPA amendment, as it focuses on a stationary equilibrium. 8 The average 3-month treasury yield between 1995 and 2004 inclusive was 3.93%.

21

Table 2: Benchmark Parameters Determined Independently

Description

Parameter

Value

Target

ρ α r µw κ ν γ7 γ 13 δ7

0.9938 2.5000 0.0100 0.0000 0.0600 0.5000 0.0250 0.0500 0.0000

40 years (age 25-64) Hansen et al. (1992) 0.04 annually Normalization JOLTS (2004) 6 months 10 years (FCRA) 5 years (FCRA) Fresh Start

Survival rate CRRA coefficient Risk-free interest rate Mean of log wage-rate offer Job-separation rate Probability of losing UI eligibility Chapter 7 flag removal rate Chapter 13 flag removal rate Chapter 7 income-garnishment rate

layoff and discharge rates from the Job Openings and Labor Turnover Survey (JOLTS). The probability of losing unemployment insurance ν is set to 0.5 to match the average duration of two quarters for unemployment insurance eligibility. We follow Chatterjee et al. (2007) to calibrate the average length of exclusion from access to credit according to the legal system prescribed by the Fair Credit Reporting Act (FCRA). The FCRA prescribes that Chapter 7 bankruptcy history stays in one’s credit report for ten years. The probability of removing a Chapter 7 bankruptcy flag γ 7 is set to 0.025, such that the average duration of ten years (40 quarters) is consistent with the FCRA. The length of repayment plans for Chapter 13 bankruptcy typically ranges between three and five years. Therefore, the probability of removing a Chapter 13 bankruptcy flag γ 13 is set to 0.05, so agents are on their repayment plans for five years (20 quarters) on average. 5.0.2. Parameters Determined Jointly Parameters which are not calibrated independently of the model are chosen to match key statistics in the labor and credit markets. To begin, we discuss the labor market statistics. According to the Bureau of Labor Statistics (BLS), the average fraction of civilians who were over age 20 and employed between 2000 and 2004 was 67 percent, as reported in the

22

Table 3: Benchmark Parameters Determined in Equilibrium

Description Discount rate Utility share of leisure Job-offer arrival rate with good credit Job-offer arrival rate with bad credit Standard deviation of log wage-rate offer Unemployment insurance Food stamps Level of expense shock Probability of expense shock Chapter 13 income-garnishment rate Target Statistics Employment rate Income Gini Mean-to-median wage rate UI replacement ratio Food stamps to average earnings ratio Bankruptcy rate Bankruptcy due to expense shock Debt-to-income ratio Chapter 7 fraction Chapter 13 recovery rate

Parameter

Value

β η

δ 13

0.9687 0.5649 0.3060 0.0941 0.2719 0.2689 0.0060 9.4796 0.0006 0.0993

Data

Model

0.67 0.44 1.30 0.50 0.015 0.0016 0.0006 0.023 0.72 0.57

0.68 0.32 1.09 0.48 0.016 0.0018 0.0006 0.019 0.71 0.56

φb=0 φb6=0 σw y y ζ¯ ¯ z(ζ)

Labor Force Statistics of the Current Population Survey. The income Gini index is determined to be 0.44 by Quadrini (2000) by taking an average of the 1984, 1989, and 1994 PSID dataset. The mean-to-median wage rate ratio is 1.30 on average from the 1968-1996 PSID dataset according to Heathcote et al. (2010). We choose the utility share of leisure η, standard deviation of the wage-offer distribution σw , and the job-arrival rate for agents with good credit φ0 to match the employment rate, income Gini, and mean-to-median wage rate ratio. The unemployment insurance y is chosen to match the average replacement ratio of 0.50. The average monthly Supplemental Nutrition Assistance Program (SNAP) food stamp benefit is about $101 per person, according 23

to the U.S. Department of Agriculture, which amounts to $303 per quarter. We then choose y such that the food stamp benefit amount is 1.5 percent of average earnings.9 For the asset market, it is important to match bankruptcy and debt statistics. According to the Administrative Office of the U.S. Courts, there were 1.56 million personal-bankruptcy filings in 2004. The Census Bureau reported that the total population above age 20 in 2004 was 211 million. Therefore, the percentage of bankruptcy in the population over 20 was 0.74 percent. The PSID furthermore classified the reasons for bankruptcy filings into five categories, and Chatterjee et al. (2007) associate job loss and credit misuse with earnings shocks, marital disruption with preference shocks, and health-care bills and lawsuits/harassment with expense shocks. According to Chakravarty and Rhee (1999), among all the bankruptcy filings, including both Chapter 7 and Chapter 13, 52.1 percent are related to earnings shocks and 33.8 percent are related to liability shocks. Following the adjustment method of Chatterjee et al. (2007), the target percentage of quarterly bankruptcy is 0.16 percent (0.74%×85.9%/4=0.16%), as the model only covers 85.9 percent of the reasons for bankruptcy filings. Similarly, the bankruptcy rate due to expense shocks is targeted at 0.06 percent (0.16%×33.8/(33.8+52.1)=0.06%). The annual estimate of the debt-to-income ratio is 0.0067, taken from Chatterjee et al. (2007). They obtain the consolidated asset position of households from the 2001 Survey of Consumer Finances (SCF). Only people with negative net worth are considered to be debtors. It is possible that agents have some unsecured debt on hand, but as long as the net asset position is positive, these agents are not regarded as debtors in the model. The average net negative wealth of the remaining households is $631.46 after excluding households with negative net worth larger than 120% of average income. To ensure that the model produces a reasonable size of defaults, we use a similar calibration strategy where the debt-to-income ratio is included in the moment 9

We can compare this consumption floor value to the literature as follows. Low et al. (2010) include unemployment insurance, disability insurance, and food stamps in their model. The food stamp benefit we computed from the data is about half as much as the amount from their calibration. We ran a robustness test where the food stamp benefit is set to their calibrated value and the qualitative results for the ATET do not change. On the other hand, Hubbard et al. (1994) set the household consumption floor to be $7,000 in 1984 dollars. This consumption floor however is not directly comparable to ours and implicitly includes unemployment insurance.

24

matching exercise and debt is defined as the negative net asset position after consolidation. The annual debt-to-income ratio is then 0.0067 by taking $631.46 divided by the per household GDP of $94,077. This gives us the adjusted quarterly target of 0.023 here (0.0067×4×85.9%=0.023). We choose the discount rate β, the expense shock amount ζ¯ and associated probability ¯ to match the bankruptcy rate, bankruptcy due to expense shocks, and z(ζ) debt-to-income ratio. Out of the total 1.56 million bankruptcy filings in 2004, 1.12 million are filed under Chapter 7 according to the Administrative Office of the U.S. Courts. The percentage of Chapter 7 filings is therefore targeted at 72 percent and the corresponding percentage of Chapter 13 filings is 28 percent. An earlier Government Accountability Office (GAO) study in 1983 reports that the amount scheduled to be repaid under Chapter 13 bankruptcy filings is about 57 percent of the unsecured debt owed. The Chapter 13 incomegarnishment rate δ 13 and probability of receiving a wage offer with bad credit φb6=0 are chosen to match the Chapter 7 bankruptcy fraction and expected recovery rate for Chapter 13 bankruptcy. We are also able to compare several unmatched moments to their data counterparts. The model produces an average tax rate of 9.9% and this value is very similar to the Congressional Budget Office’s 9.0% effective average individual income tax rate estimate for 2005. Next, 3.4% of those receiving food stamps are newborns and 96.6% are non-newborns. Although we do not have direct data to compare these statistics, the USDA reports that the percentage of nonelderly, nondisabled, and childless adults accounts for 7.7 percent of the SNAP program participants in 2005. Given that our newborns would be included, but not exclusively so, in this group of participants, we believe that our model moments should not be too far off. 6. Results 6.1. Bankruptcy Choices The default decisions for workers who do not experience expense shocks are plotted in Figure 1. It is clear from the graph that agents tend to default when they have more debt. When individuals file for bankruptcy, they discharge their debt. The financial benefit of bankruptcy is therefore higher when agents have more debt, which makes default more likely. Secondly, as we can see from Figure 1, agents with higher wage rates (above 1.6) file for Chapter 7 bankruptcy, while agents with lower wage 25

2.6 2.4 2.2

Chapter 7 Bankruptcy (d=7)

Repayment (d=0)

Wage Rate (w)

2 1.8 1.6 1.4 1.2

Chapter 13 Bankruptcy (d=13) 1 0.8

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Asset (a)

Figure 1: Equilibrium Default Choices for Workers

rates (below 1.6) file for Chapter 13 bankruptcy. This is because agents are not subject to income garnishment at the cost of longer exclusion from borrowing under Chapter 7. Since consumers with higher wages can better insure themselves against future income disruptions by saving more, they prefer avoiding income garnishment even if they will not be able to borrow for longer periods on average. Furthermore, the income garnishment they can avoid by not filing for Chapter 13 is higher if their wage rate is higher, and this adds on even more incentives for agents with higher wages to file under Chapter 7 instead of Chapter 13. On the other hand, income-poor people are more likely to experience consumption fluctuations without access to the credit market. Therefore, they prefer a shorter exclusion from borrowing even if a fraction of income is garnished. This model implication that the choice between Chapter 7 and Chapter 13 is dependent on wages but independent of debt when debt is beyond a certain level is empirically testable with detailed data. Finally, the bankruptcy choices for non-employed individuals depend on the government transfers they receive. Individuals who receive more government transfers are less likely to default.

26

6.2. Price Schedules Given agents’ decision rules, financial intermediaries price loans such that the zero profit condition is satisfied. With the availability of Chapter 13 bankruptcy, loan pricing requires the knowledge of individuals’ labor supply decisions, because how much Chapter 13 bankruptcy filers work can affect how much creditors expect to recover from income garnishment. 1.4 1.3 1.2

Γ(1,b,a,w,0,ζ)

1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Wage Rate (w)

Figure 2: Equilibrium Repayment from Chapter 13 Bankruptcy

When there is no default risk for a given loan, financial intermediaries charge the risk-free rate because the recovery rate is 100 percent from full repayment. When agents file for Chapter 7 bankruptcy, the recovery rate is 0 because agents have incomes fully exempted, and financial intermediaries receive nothing. If agents file for Chapter 13 bankruptcy, the expected present discounted value of total repayment through income garnishment determines the recovery rate. The equilibrium repayment from workers who file for Chapter 13 bankruptcy is graphed in Figure 2. We can see that agents with higher wages at the time of default make more repayments. The recovery rate is therefore higher for debtors with higher wages, although what really matters for the recovery rate is earnings, which is the product of wage and hours worked. Figure 3 graphs the equilibrium price functions for workers. First of all, agents face higher interest rates (lower q) for larger loans because agents are more likely to default when they have more debt. Furthermore, the price functions can be separated into two parts. The first part is for agents with 27

1 0.9 0.8

w = 0.6 w = 0.9 w = 1.6 w = 2.7

q(a′ , (1, 0, a, w, 0, ζ))

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Asset Choice (a′ )

Figure 3: Equilibrium Price Functions for Workers

higher wage rates. The price functions for these agents are initially high because they are less likely to default but drop to 0 when their debt levels are large enough to trigger default actions. This is because in the event of default, high wage earners prefer Chapter 7 bankruptcy to avoid income garnishment, as evident in Figure 1, and the recovery rate of a Chapter 7 bankruptcy is zero. On the other hand, for agents with lower wage rates, in the event of default, they would like to take advantage of shorter borrowing exclusion periods from Chapter 13 bankruptcy, even if they need to have part of their incomes garnished. Their credit limits are therefore extended because financial intermediaries can partially recover from the income garnishment associated with a Chapter 13 bankruptcy. Figure 4 graphs the price functions for non-workers. Like the price functions for workers, prices decrease (interest rates increase) with loan sizes. The loan prices also depend on the social welfare benefits that the people receive. People who receive unemployment insurance face lower interest rates than people who receive floor benefits because they are less likely to default. Although Chapter 13 bankruptcy is not available for agents who receive floor benefits, the price function still has a long left tail because it is possible that

28

1

0.9

y=y y=y

0.8

q(a′ , (0, 0, a, 0, y, ζ))

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 -3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Asset Choice (a′ )

Figure 4: Equilibrium Price Functions for Non-Workers

agents will accept a new job offer and file for Chapter 13 bankruptcy in the next period. 6.3. Reservation Wages In this section, we discuss how reservation wages are impacted by the characteristics of people such as employment and bankruptcy flag status. While presenting the reservation wages over the possible assets individuals can have, we specifically expand the asset axis in order to provide a complete picture of how reservation wages are affected by all possible asset levels, including the very high asset points. However, in equilibrium, it is likely that individuals may not reach a certain asset level, and in order to highlight the area where we do see action in equilibrium, we also include the distribution in each of the graphs to provide a comprehensive picture. Figure 5 graphs the reservation wages for workers. If their current wage rates equal their reservation wages, they feel indifferent between continuing and leaving their jobs. Therefore, they have to receive at least their reservation wages from their jobs to remain employed. Without on-the-job search, the only way for workers to receive better wages is through quitting, because only non-employed agents can receive new wage offers. Since the number of periods before accepting a new job is uncertain, agents with more assets can better smooth their consumption while being unemployed and hence have lower costs of income disruption. Therefore, employed agents have higher reservation wages when they are wealthier. 29

wr (1, b, a, w, 0, 0)

2.5 2

b=0 b=7 b = 13

1.5 1 0.5 0 0

5

10

15

20

25

30

20

25

30

Asset (a) Distribution for Workers

0.25 0.2 0.15 0.1 0.05 0 0

5

10

15

Asset (a)

Figure 5: Equilibrium Reservation Wages for Workers

When workers with bankruptcy flags quit, they can only use their savings to smooth consumption before they receive a better wage-rate offer, because they are constrained from borrowing. Moreover, given their bad credit, they are less likely to receive a job offer than agents with good credit due to their lower job arrival rate. If they quit, they have longer waiting periods before a new job offer arrives and this lowers their incentives for leaving current jobs. Therefore, individuals with bad credit have reservation wages lower than individuals with good credit ratings, given the same asset position. Among those who are borrowing constrained, the reservation wages further depend on the types of bankruptcy flags they carry. Agents with Chapter 13 bankruptcy flags expect to be excluded for fewer periods than agents with Chapter 7 bankruptcy flags. This can raise their reservation wages, because they are more likely to regain the privilege of borrowing, which helps them smooth consumption while searching for jobs. However, while individuals carry a Chapter 13 bankruptcy flag, they lose a fraction of their earnings. This may reduce their incentives to take on a job because they receive less income due to income garnishment. The net effect on reservation wages depends on which force dominates. We can see from Figure 5 that given the same asset position, employed

30

wr (0, b, a, 0, y, 0)

workers with a Chapter 7 bankruptcy flag are more likely to accept an offer than people with a Chapter 13 bankruptcy flag. This is because agents on a repayment plan take into account that part of their earnings will be garnished. Employed workers without a bankruptcy flag, in contrast, have the highest reservation wages. 1 b=0 b=7 b = 13

0.5 0 0

5

10

15

20

25

30

35

40

45

50

30

35

40

45

50

30

35

40

45

50

Distribution for Non-Workers

wr (0, b, a, 0, y, 0)

Asset (a) 2 b=0 b=7 b = 13

1 0 0

5

10

15

20

25

Asset (a) 0.2

0.1

0 0

5

10

15

20

25

Asset (a)

Figure 6: Equilibrium Reservation Wages for Non-Workers

Figure 6 graphs the reservation wages for non-employed agents. Again, when job offers arrive at their reservation wages, they feel indifferent between accepting or rejecting the new job. Reservation wages for the non-employed increase with their assets and social benefits. For agents who collect food stamps, they would take any job offer when it arrives. For agents who collect unemployment, their reservation wages are higher if they do not have a bankruptcy flag. Reservation wages are positively affected by wealth and negatively affected by borrowing constraints, consistent with the empirical findings of Rendon (2006). We observe the same pattern as before where individuals with no bankruptcy flag have the highest reservation wages followed by people with Chapter 13 and Chapter 7 flags respectively. The reservation wages generate the difference between the exogenous wageoffer distribution and the endogenous equilibrium wage distribution. Figure 31

1

b=0 b=7 b = 13

0.9

Cumulative Distributional Measure

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.5

1

1.5

2

2.5

3

Wage Rate (w)

Figure 7: Wage Offer and Equilibrium Wage Distributions

7 graphs the wage-offer distribution and the equilibrium wage distribution conditional on agents’ bankruptcy flag status. The wage distribution for agents without a bankruptcy flag first-order stochastically dominates the wage distribution for agents with a bankruptcy flag. The b = 0 line is meant to represent the equilibrium wage distribution for agents who don’t have any bankruptcy flag on their credit record. It is both a function of the exogenous wage offer distribution and the endogenous wage offer acceptance decision. The fact that the b = 7 and b = 13 lines are both above the b = 0 line indicates that agents with bankruptcy flags are more likely to accept the wage offer regardless of the wage rate. 6.4. Hours Worked While all agents make labor participation decisions on the extensive margin based on their reservation wages, workers also make labor supply decisions on the intensive margin by choosing the time allocation between work and leisure. Figure 8 graphs the equilibrium hours worked decisions for workers with wage rate w = 1 and no expense shocks. When workers choose to default, their labor supply decisions become a static problem because they discharge their debt and they can not borrow or save during the period of default. Their 32

0.7

0.7

b=7 b = 13

0.65

0.65

0.6

0.6

h(1,b,a,w=1,0,0)

h(1,b,a,w=1,0,0)

b=0

0.55

0.5

0.45

0.55

0.5

0.45

0.4

0.4

0.35

0.35

0.3

0.3 -2

0

2

4

6

8

0

Asset (a)

2

4

6

8

Asset (a)

Figure 8: Equilibrium Hours Worked Decisions

equilibrium hours worked lie flat around 0.44. However, when agents repay, their hours worked can affect consumption and savings. Therefore, labor supply decisions on the intensive margin can depend on agents’ characteristics. We can see from the figure that agents work less when they have more assets because leisure is a normal good and they would like to enjoy more leisure when they are wealthier. Given the same asset level, agents with Chapter 7 bankruptcy flags work more than agents with Chapter 13 bankruptcy flags. This indicates that the sum of the borrowing constraint effect (from expecting to be excluded longer from the credit market) and the substitution effect (because leisure is more expensive) dominates the income effect (from avoiding income garnishment). Figure 9 graphs the histogram of equilibrium hours worked. There is a large spike at zero that consists of non-workers who devote all of their time to leisure. Most workers choose hours worked around 0.45 (standard full-time jobs) and hours worked quickly tails off to the left or right. 7. ATET Measure In this section, we analyze the impact of bankruptcy on the labor supply decisions within the parameterized model. Since agents’ bankruptcy status 33

Figure 9: Histogram of Equilibrium Hours Worked

would affect the job offer arrival rates, in order to properly study work incentives, we measure the labor supply decisions assuming that the job offer rates stay the same. This allows us to isolate the changes in labor supply decisions. The average labor supply for a potential bankruptcy decision d given that ∗ d is the optimal bankruptcy decision can be measured by ATET(d∗ , d) = E[e0 · h0 |d∗ , d],

(16)

which depends on labor supply decisions for both extensive and intensive margins. First, we summarize the extensive margin of the labor supply in Table 4 by calculating the average employment rate, E(d∗ , d) = E[e0 |d∗ , d].

(17)

Using agents’ equilibrium labor supply decisions, we can calculate the values of E(d∗ , d∗ ) on the diagonal of Table 4. To fill in off-diagonal values, specifically E(d∗ , d) where d∗ 6= d, we solve for the optimal labor supply decisions 34

Table 4: Employment Rates

d∗ \ d 0 7 13

0 0.6923 0.1306 0.7574

7 0.7419 0.1303 0.8538

13 0.7423 0.1304 0.8543

given counterfactual bankruptcy choices. Conditional on individuals who file for Chapter 7 bankruptcy, the ATET on the extensive margin is -0.0003. Specifically, E(7, 7) − E(7, 0) = 0.1303 − 0.1306 = −0.0003. Therefore, a fresh start does not have significant effects on the extensive margin for Chapter 7 filers. The employment rate for Chapter 7 filers (0.1303) is lower than repaying individuals (0.6923) in equilibrium because they are more likely to suffer from job loss. This reflects the downward bias if we estimate the change in the extensive margin without taking into account the endogeneity of bankruptcy decisions. Moreover, in comparing labor supply decisions on the extensive margin when agents file for bankruptcy under different chapters, it is evident from Table 4 that employment rates are nearly identical across bankruptcy chapter choices. The fact that a fresh start does not significantly affect the labor supply decisions on the extensive margin is consistent with the low reservation wages for non-employed agents regardless of their bankruptcy status if they are asset poor (see Figure 5 and Figure 6). However, if we take into account that bankruptcy flags would have an adverse effect on bankruptcy filers’ labor market outcomes due to the lower job offer probability, then the employment rate would be higher if Chapter 7 filers chose to repay their creditors instead. This highlights the importance of potential policy implications from prohibiting the practice of credit checks on the labor market. Second, we measure the intensive margin of labor supply, shown in Table 5, by calculating the hours worked conditional on being employed, which is 35

Table 5: Hours Worked Conditional on Employment

d∗ \ d 0 7 13

0 0.4411 0.5315 0.4743

7 0.5992 0.5979 0.5961

13 0.5984 0.5960 0.5924

defined as H(d∗ , d) = E[h0 |d∗ , d, e0 = 1].

(18)

The average hours worked conditional on being employed for Chapter 7 bankruptcy filers is 0.5315 under repayment and 0.5979 under a fresh start, which suggests that the ATET on the intensive margin is 0.0664. Specifically, H(7, 7) − H(7, 0) = 0.5979 − 0.5315 = 0.0664. This implies that a fresh start increases labor supply on the intensive margin by 12.5 percent over repayment. Chapter 7 bankruptcy filers, on average, work a lot more (0.5979) than repaying agents (0.4411) in equilibrium because they have less assets and are borrowing constrained. This again reflects the fact that the estimated change in labor supply on the intensive margin can be upward biased if we ignore bankruptcy endogeneity. Like the extensive margin, workers provide similar labor supply intensities for different bankruptcy chapter choices. Chapter 7 bankruptcy filers work a bit more under a fresh start than under Chapter 13 bankruptcy. The average labor supply for any bankruptcy decision d given that d∗ is the optimal bankruptcy decision can be measured with ATET(d∗ , d) = E[e0 · h0 |d∗ , d]

(19)

by taking into account both the extensive and intensive margins of labor supply. Chapter 7 filers on average supply less labor (0.0779) than repaying agents (0.3054) and Chapter 13 filers (0.5060). It is however clear from Table 6 that Chapter 7 bankruptcy filers on average would work even less if they were compelled to repay (0.0694). A fresh start increases the labor supply by 12.3 36

Table 6: Average Labor Supply

d∗ \ d 0 7 13

0 0.3054 0.0694 0.3592

7 0.4446 0.0779 0.5089

13 0.4442 0.0777 0.5060

percent over repayment. Specifically, L(7, 7) − L(7, 0) = 0.0779 − 0.0694 = 0.0085. Furthermore, Chapter 7 bankruptcy filers on average also work less if they were forced to file for Chapter 13 bankruptcy instead (0.0777). A fresh start therefore increases the labor supply by 0.3 percent over Chapter 13 bankruptcy. It is worth noting that this paper measures the effect of bankruptcy on work incentives by considering a one-period deviation from optimal decisions. The focus on the short-term effect allows us to compare and reconcile our results with reduced form estimation and thus have a better understanding of how endogeneity issues might arise from answering the question of interest. The long-term impact of bankruptcy on labor supply is possibly an interesting and important question. However, to evaluate the long-term effect, the entire off-equilibrium paths of agents’ decisions in the counterfactual need to be computed. 8. Reduced-Form Estimation from Simulated Data The impact of bankruptcy on labor supply decisions is positive from the calculations within our structural model but negative from an earlier reducedform estimation by Han and Li (2007). To reconcile the opposite results, we estimate a treatment effect model as in Han and Li (2007) using simulated data generated from the structural model. In particular, we estimate how much a fresh start affects the log working hours. The estimation is done in a two-step procedure in order to control for the endogeneity of bankruptcy. In the first step, we run a probit regression of Chapter 7 bankruptcy filing decisions. Formally, the Chapter 7 bankruptcy

37

decision is determined by the following equation, d˜i = zi γ + i where

( 1 di = 0

(20)

if d˜i > 0 otherwise

(21)

such that individual i files for a fresh start when di = 1 and does not file when di = 0. The covariates must include factors (‘‘instrumental variables’’) that do not directly affect labor supply except through bankruptcy. From the estimates, we can compute the inverse Mills ratio mi for each observation i as −φ(zi γˆ ) φ(zi γˆ ) mi = di + (1 − di ) (22) Φ(zi γˆ ) 1 − Φ(zi γˆ ) where φ and Φ are the standard normal probability and cumulative density functions respectively. The log working hours hi is determined according to the following equation, hi = xi β + αdi + υi

(23)

where the pair (υi , i ) is assumed to be drawn from a bivariate normal distribution with mean (0, 0) and covariance matrix   1 ρσ . ρσ σ 2 Therefore, the expectation of log working hours given bankruptcy decisions can be written as   φ(zi γˆ ) −φ(zi γˆ ) E [hi |di ] = xi β + αdi + ρσ di + (1 − di ) . (24) Φ(zi γˆ ) 1 − Φ(zi γˆ ) | {z } mi

The equation directly above suggests an augmented linear regression in the second step by adding the inverse Mills ratio mi calculated from the first step as part of the covariates. Under this model specification, the difference in expected log working hours between bankruptcy filing and nonfiling for individual i is given by the coefficient of the Chapter 7 bankruptcy filing α. 38

We first create a dataset which consists of nearly 50,000 individuals, starting with the invariant cross-sectional distribution for agents without bankruptcy flags. Each individual is tracked over time for five model periods. It is assumed that there is no individual entry and exit in the dataset. That is, individuals are assumed not to receive death shocks over time, and no newborn is added into the sample. Observations are dropped from the combined crosssectional dataset after they file for bankruptcy. Furthermore, Chapter 13 bankruptcy filers are excluded from the sample. In the first step, Han and Li (2007) include ‘‘social stigma’’ and ‘‘financial benefit’’ as instruments, which are supposed to have direct effects on bankruptcy decisions but not labor supply decisions. Because personal preferences are unobservable, they use lagged U.S. state-level bankruptcy rate as a proxy for social stigma. They further include state unemployment rate to control for any possible correlation between social stigma and work ethics. Individuals do not have a stigma cost associated with bankruptcy from our model, and we thereby only use ‘‘financial benefit’’ as the instrument. In the second step, the inverse Mills ratio calculated from the first step is added into the regression to control for the selection effect. In both steps, wage, income, and change in income are included as covariates. Note that these variables can have effects on both bankruptcy and labor supply decisions. The results from the probit regression are presented in the top-left panel of Table 7. Similar to the findings in Han and Li (2007), the potential financial benefits have positive effects on the probability of filings for a fresh start. In other words, the more unsecured debt individuals can discharge through bankruptcy, the more likely they are going to file for Chapter 7. The significance of the financial benefits regressor indicates its strong explanatory power in predicting the probability of bankruptcy. Because the model period is a quarter, there is no in-and-out of employment using data from a quarterly model. Therefore, the estimation from a treatment effect model with log working hours as the response variable fully captures the effect of a fresh start on the intensive margin. The bottom part of Table 7 shows the second-step estimation results (even though we cast some doubts on the validity of the instrument). The positive coefficient of the bankruptcy filing regressor implies a positive effect of a fresh start on log working hours. In order to emphasize the difficulty of controlling for endogeneity, we also run an ordinary least squares (OLS) regression without any instrumental variables. The results of the OLS regression is shown in the right panel of Table 39

Table 7: Estimates of Treatment Effect Model (Quarterly Data)

Endogenous Treatment Ch7 Filing

Coeff.

Wage Income Income Change Financial Benefit

2.723∗∗∗ −5.956∗∗∗ −3.203∗∗∗ 6.930∗∗∗

Log Working Hours

Coeff.

Ch7 Filing Inverse Mills Ratio Wage Income Income Change

0.695∗∗∗ −0.007∗ −0.114∗∗∗ 0.359∗∗∗ 0.122∗∗∗

Std. Err. 0.547 1.211 0.633 0.443 Std. Err. 0.101 0.003 0.001 0.004 0.002

OLS Coeff. − − − − Coeff. 0.049∗∗∗ − −0.114∗∗∗ 0.358∗∗∗ 0.122∗∗∗

Std. Err. − − − − Std. Err. 0.004 − 0.001 0.004 0.002

# Observations = 125,407; ∗∗∗ significant at 1%; ∗∗ significant at 5%; ∗ significant at 10%

7. We can first see that all coefficients do not change much when comparing regressions with or without the instrument. This is consistent with the findings in Han and Li (2007) (see Table 7 in their paper). Importantly, the inverse Mills ratio is shown to be only significant at the 10% level, implying that the endogeneity issues might not be resolved by using instrumental variables, therefore leading to similar coefficients in these two regressions. Under this context, our results highlight the advantages of estimating the effect with a structural framework in which endogeneity is directly modeled. If we are restricted to annual datasets, the changes in annual working hours can be a combination of both extensive and intensive margins of labor supply. In particular, Chapter 7 bankruptcy filers can appear to work for less hours because they are more likely to be unemployed during part of the year. Time aggregation might prevent us from disentangling the labor supply in extensive or intensive margins and affect our estimation results. Thus the difficulties associated with empirical estimation of labor market activities in the presence of bankruptcy go beyond the task of finding valid instruments. 40

Table 8: Estimates of Treatment Effect Model (Annual Data)

Ch7 Filing

Coeff.

Wage Income Income Change Financial Benefit

−0.501∗∗∗ −0.337∗∗∗ −0.036 3.402∗∗∗

Log Working Hours

Coeff.

Ch7 Filing Inverse Mills Ratio Wage Income Income Change

−0.160 0.110 0.012∗∗ 0.228∗∗∗ 0.133∗∗∗

Std. Err. 0.117 0.076 0.047 0.611 Std. Err. 0.608 0.176 0.005 0.003 0.004

# Observations =160,418; ∗∗∗ significant at 1%; ∗∗ significant at 5%; ∗ significant at 10%

To show this, we create a combined cross-sectional annual dataset by combining model periods. The asset position and bankruptcy flag status are recorded at the beginning of each year. Annual working hours are the sum of working hours in all four quarters and annual incomes are likewise a sum of the quarters. Bankruptcy can occur at any time of a year. The estimation results are shown in Table 8. Interestingly, the coefficient of the Chapter 7 bankruptcy filing regressor turns from positive to negative and insignificant, which is consistent with the results in Han and Li (2007). The reason is because Chapter 7 bankruptcy filers are more likely to experience job loss, and given the difficulty to control for endogeneity in this framework, the estimated effect of a fresh start on labor supply is easily biased downward. In an effort to reconcile the different results from reduced-form estimation and structural analysis, we have identified the potential challenges. First, it is difficult to find valid instrumental variables to control for endogeneity given the interdependence of labor and credit market behavior. And second, there may be a lack of detailed data which allows researchers to disentangle changes on the intensive and extensive margins without worrying about time aggregation.

41

9. Conclusions According to the PSID, job loss has been cited as one of the most important reasons individuals file for bankruptcy. However, labor market activities not only affect bankruptcy decisions, bankruptcy decisions also affect labor market activities. While most papers in the literature assume inelastic labor supply regardless of bankruptcy decisions, this paper expands our understanding of how the labor market interacts with the credit market by allowing endogenous decisions in both labor supply and bankruptcy. Specifically, we are interested in answering the question, ‘‘how much does a fresh start increase labor supply?’’ The question is important because one of the justifications for a fresh start bankruptcy system in the U.S. is to improve work incentives. To answer this question quantitatively, we evaluate the labor supply responses for both equilibrium and counterfactual bankruptcy decisions by constructing a dynamic job search model with bankruptcy options. We find that a fresh start increases the work incentives of Chapter 7 bankruptcy filers primarily on the intensive margin over either repayment or Chapter 13 bankruptcy. Chapter 7 filers on average increase labor supply by 12.3% over counterfactual repayment and 0.3% over counterfactual Chapter 13 filing. Since the counterfactual experiment is done on an individual level, it is sufficient to have a partial equilibrium where the wage offer distribution is held fixed. Although, it might be of interest to evaluate the effect of bankruptcy policy reforms on the aggregate labor supply. This expanded question requires a general equilibrium model where the wage offer distribution can endogenously respond to policy changes. For future research, it may be worthwhile to study how the interaction between labor and credit markets might change due to aggregate policy changes, such as an elimination of bankruptcy, a reduction of bankruptcy chapter choices, or an implementation of a means test which prohibits Chapter 7 bankruptcy filings for individuals who earn more than the median income. To answer these questions, it is necessary that the wage offer distribution be endogenized, as the equilibrium labor market tightness will be affected. In this paper, we also investigate the endogeneity pitfalls and time aggregation issues associated with reduced-form estimates of labor supply on bankruptcy decisions. In particular, the financial benefit of default as an instrument is negatively correlated with net wealth, and wealth also impacts labor supply. Perhaps more worryingly, data limitations such as infrequent annual measures of labor supply can bias the results even if perfect instruments 42

can be found. References Kartik Athreya, Xuan S. Tam, and Eric R. Young. A quantitative theory of information and unsecured credit. American Economic Journal: Macroeconomics, 4(3):153--83, July 2012. Kartik Athreya, Juan M S´anchez, Xuan S Tam, and Eric R Young. Labor market upheaval, default regulations, and consumer debt. Review of Economic Dynamics, 18(1):32--52, 2015. Kartik B. Athreya. Welfare implications of the bankruptcy reform act of 1999. Journal of Monetary Economics, 49(8):1567--1595, November 2002. Kartik B. Athreya and Hubert P. Janicki. Credit exclusion in quantitative models of bankruptcy: does it matter? FRB Richmond Economic Quarterly, 92(1):17--49, 2006. Kartik B. Athreya and Nicole B. Simpson. Unsecured debt with public insurance: From bad to worse. Journal of Monetary Economics, 53(4): 797--825, May 2006. Sugato Chakravarty and Eun-Young Rhee. Factors affecting an individual’s bankruptcy filing decision. 1999. Satyajit Chatterjee, Dean Corbae, Makoto Nakajima, and Jose-Victor RiosRull. A quantitative theory of unsecured consumer credit with risk of default. Econometrica, 75(6):1525--1589, November 2007. Satyajit Chatterjee, Dean Corbae, and Jose-Victor Rios-Rull. A finite-life private-information theory of unsecured consumer debt. Journal of Economic Theory, 142(1):149--177, September 2008. Satyajit Chatterjee, Dean Corbae, Kyle Dempsey, and Jose-Victor Rios-Rull. Credit scoring and the competitive pricing of default risk. 2015. Daphne Chen, Dean Corbae, and Andrew Glover. Can employer credit checks create poverty traps? theory and policy evaluation. 2013. Ian Domowitz and Robert L. Sartain. Determinants of the consumer bankruptcy decision. Journal of Finance, 54(1):403--420, February 1999. 43

Wendy Edelberg. Risk-based pricing of interest rates for consumer loans. Journal of Monetary Economics, 53(8):2283--2298, November 2006. Scott Fay, Erik Hurst, and Michelle J. White. The household bankruptcy decision. American Economic Review, 92(3):706--718, June 2002. Song Han and Geng Li. Household borrowing after personal bankruptcy. Journal of Money, Credit and Banking, 43(2-3):491--517, 2011. Song Han and Wenli Li. Fresh start or head start? the effects of filing for personal bankruptcy on work effort. Journal of Financial Services Research, 31(2):123--152, June 2007. Gary D Hansen and Ayse Imrohoroglu. The role of unemployment insurance in an economy with liquidity constraints and moral hazard. Journal of Political Economy, 100(1):118--142, February 1992. Jonathan Heathcote, Kjetil Storesletten, and Giovanni L. Violante. The macroeconomic implications of rising wage inequality in the united states. Journal of Political Economy, 118(4):681--722, August 2010. Kyle Herkenhoff. Informal unemployment insurance and labor market dynamics. Working Papers 2012-057, Federal Reserve Bank of St. Louis, 2012. Kyle Herkenhoff. The impact of consumer credit access on unemployment. 2015. Kyle Herkenhoff, Gordon Phillips, and Ethan Cohen-Cole. The impact of consumer credit access on employment, earnings and entrepreneurship. 2016. R. Glenn Hubbard, Jonathan Skinner, and Stephen P. Zeldes. Expanding the life-cycle model: Precautionary saving and public policy. American Economic Review Papers and Proceedings, 84(2):174--179, May 1994. Wenli Li Hulya Eraslan, Gizem Kosar and Pierre-Daniel Sarte. An anatomy of u.s. personal bankruptcy under chapter 13. October 2014. Julapa Jagtiani and Wenli Li. Credit access after consumer bankruptcy filing: New evidence. American Bankruptcy Law Journal, forthcoming. 44

Dirk Krueger and Fabrizio Perri. Does income inequality lead to consumption inequality? evidence and theory. Review of Economic Studies, 73(1): 163--193, January 2006. Robert M. Lawless, Angela K. Littwin, Katherine M. Porter, John A.E. Pottow, Deborah K. Thorne, and Elizabeth Warren. Did bankruptcy reform fail? an empirical study of consumer debtors. American Bankruptcy Law Journal, 82(3):349--406, 2008. Rasmus Lentz and Torben Tranas. Job search and savings: Wealth effects and duration dependence. Journal of Labor Economics, 23(3):467--489, July 2005. Wenli Li and Pierre-Daniel Sarte. U.s. consumer bankruptcy choice: The importance of general equilibrium effects. Journal of Monetary Economics, 53(3):613--631, April 2006. Igor Livshits, James MacGee, and Michele Tertilt. Consumer bankruptcy: A fresh start. American Economic Review, 97:402--418, 2007. Igor Livshits, James MacGee, and Michele Tertilt. Accounting for the rise in consumer bankruptcies. American Economic Journal: Macroeconomics, 2 (2):165--93, April 2010. Hamish Low, Costas Meghir, and Luigi Pistaferri. Wage risk and employment risk over the life cycle. American Economic Review, 100(4):1432--1467, September 2010. Gangadharrao Soundalyarao Maddala. Limited Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press, 1983. David K. Musto. What happens when information leaves a market? evidence from postbankruptcy consumers. Journal of Business, 77(4):725--748, October 2004. Borghan Nezami Narajabad. Information technology and the rise of household bankruptcy. Review of Economic Dynamics, 15(4):526--550, October 2012. Vincenzo Quadrini. Entrepreneurship, Saving and Social Mobility. Review of Economic Dynamics, 3(1):1--40, January 2000.

45

Silvio Rendon. Job search and asset accumulation under borrowing constraints. International Economic Review, 47(1):233--263, February 2006. Juan Sanchez. The it revolution and the unsecured credit market. 2010. Michelle White. Personal bankruptcy: Insurance, work effort, opportunism and the efficiency of the ”fresh start”. 2005. Michelle White. Bankruptcy Law, volume 2 of Handbook of Law and Economics, chapter 14, pages 1013--1072. Elsevier, December 2007.

10. Appendix In Table 9, we summarize how robust the main results are to parameter perturbations. All parameters are increased by 5% and then decreased by 5% from the calibrated values. The only exception is that β is increased by 2.5% in order to keep it under 1. For every perturbation in the table, the ATET remains positive. Even with parameter perturbations of 25% up and down, the ATET is always positive. This suggests that our results are qualitatively robust. However, we should emphasize that the model is not recalibrated for the robustness checks so we cannot compare the numbers in Table 9 to our main results quantitatively.

46

47

φb=0 φb6=0 σw y y ζ¯ ¯ z(ζ) δ 13

β η

Parameter

32.4 8.4 19.8 3.6 16.3 17.1 12.8 12.3 12.1 7.0

ATET(7,0) 2.8 0.0 0.4 0.9 0.2 0.5 0.6 0.3 0.3 0.4

ATET(7,13)

Decrease

2.6 40.8 7.1 20.3 9.9 14.6 29.3 12.3 17.3 19.9

ATET(7,0)

0.1 0.4 0.4 0.2 0.3 0.2 0.0 0.3 0.2 0.1

ATET(7,13)

Increase

This table shows the robustness of the percent ATET(7,0)= L(7, 7)/L(7, 0) × 100 and ATET(7,13)= L(7, 7)/L(7, 13) × 100 estimates to perturbations of the parameters. All parameters are increased by 5% and then decreased by 5% from the calibrated values. The only exception is that β is increased by 2.5% in order to keep it under 1.

Discount rate Utility share of leisure Job-offer arrival rate with good credit Job-offer arrival rate with bad credit Standard deviation of log wage-rate offer Unemployment insurance Food stamps Level of expense shock Probability of expense shock Chapter 13 income-garnishment rate

Description

Table 9: ATET Robustness

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