Consumer Bankruptcy Behavior Over The Life Cycle

Consumer Bankruptcy Behavior Over The Life Cycle E Yang Stony Brook University February 18, 2014 Abstract US bankruptcy filing rate increased dramatically before 2004, and decreased after 2005, when the Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA) was enacted. What caused the U.S. bankruptcy filing rate to change? We argue that certain events, including job loss, medical bills and divorce can not explain bankruptcy filing very well. I also use log likelihood test to test the null hypothesis of savings and borrowing in bankruptcy filing in two sub-samples, and find that savings and borrowing have no predictive power. In the paper, a dynamic stochastic general equilibrium model is adopted in which households make their optimal decision, with uncertain income and consumption. We find that when interest rate increases, debt to earnings ratio decrease, bankruptcy filing decreases. We also find there is clear pattern for non-fresh bankruptcy filing rule, with relative high bankruptcy filing in middle 20s and late 40s, the peak bankruptcy filing time in 40s will be delayed to 50s if bankruptcy law is very friendly. This finding is very meaningful for policy makers. Keywords: bankruptcy law, garnishment, interest rate,income JEL Classification codes: K42,G02,G01 Department of Economics, Stony Brook University (State University of New York), stony brook, NY 11794-4384. Email:e.yang@stonybrook.edu 1

1 Introduction In 1980, the number of personal bankruptcy filings in the United States was 287,564, it doubled 1988 and tripled 1991. With some famous and rich people filed bankruptcy, it caused a wide public awareness that filing bankruptcy can be a good choice to avoid paying debt, and public awareness also decrease social embarrassment. From 2001 to 2004, there were more than 1.5 million personal bankruptcy every year. The banks spent more than 100 million in lobbying bankruptcy reform, but did not work until 2005. The Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA) was enacted in April 2005, it made sweeping changes to American bankruptcy laws, affecting both consumer and business bankruptcies. BAPCPA is less debtor friendly: increasing bankruptcy filing cost; not allowing debtors to choose between chapter 7 and chapter 13, and not allowing self-proposed repayment plan under chapter 13. As we expect, debtors rushed to file under the old law, personal bankruptcy filings increased to 2 million in 2005 and then fell dramatically to 0.5 million in 2006. After that, personal bankruptcy filings have been keeping increasing. In 2009, it is back to 1.4 million again. What determines bankruptcy filing? What cause bankruptcy increase? When the bankruptcy law changed, how bankruptcy behavior changed? How the strictness of bankruptcy law affect bankruptcy filing behavior? Many research has been done about bankruptcy filing. We will first look at papers focusing on adverse effect, and then discuss theoretical contributions. Adverse events, such as job loss, medical cost caused by health problems, and divorce are believed to be most common bankruptcy causes. Himmelstein et al. (2005) concluded that 55 percent of bankrupts filed because of illness, injury, or medical bills based on survey data. As we have mentioned, even if the medical expenditure is very modest, health problem is still treated as the cause of bankruptcy. Sullivan et al. (2000) argued that 67 percent of bankruptcy filed because of job loss. This study has also been criticized as exaggerated, because even if debtors quickly obtained new jobs, job loss is still treated as a cause of bankruptcy. Job loss, and medical bills do not provide a good explanation for the dramatic increase 2

in bankruptcy filings, because these events have not become much more frequent over time. According to Bureau of labor Statistics, the unemployment rate was 7.2 percent in 1980, and increased to 9.7 percent in 1981 and 1982, after that it has fluctuated between 4.0 and 7.5 percent. The divorce rate increase from 1960 to 1980, however decrease after that. Medical costs also can not explain the increase in bankruptcy filings. According to U.S. Census Bureau, the percentage of Americans not covered by health insurance has also remained fairly steady: about 15%. With regards to medical bill, White (2007) argue that the percentage of Americans not covered by health insurance has also remained about 15% from 1985 to 2004, and Out-of-pocket medical expenditures borne by households increased only slightly as a percent of median U.S. family income, from 3.5 percent in 1980 to 3.9 percent in 2005. Moss and Johnson (1999) claim that easy access to credit for lower income household can potentially explain the recent increase in bankruptcies. Domowitz and Sartain (1999) argue that that with homeownership playing an important role with respect to both the decision to declare bankruptcy and the choice of bankruptcy alternative, the potential effects of legal changes relating to property exemptions and dischargeable debt categories are found to encourage debt repayment through Chapter 13. Fay et al. (2002) analyze PSID data and conclude that households are more likely to file bankruptcy when their financial benefit from filing is higher, and also conclude that households are more likely to file for bankruptcy if they live in districts with higher aggregate filing rates. White (2007) claims that the main reason of personal bankruptcy rates is the growth of credit card debt. In this paper, we adopt life cycle model to understand individual s bankruptcy behavior choice over the time. It is different from the research by Shumway (2001),Hoynes (2000), Gross and Souleles (2002), in which a dynamic probit model is estimated for default. From the model perspective, there are four different levels of literature involved. First,the life cycle model is applied in this paper. The model is originally from Ghez and Becker (1975). Kotlikoff and Summers (1981) apply this model to analyze the integration transfers in aggregate capital accumulation. Deaton (1991) applied this techniques to analyze savings and liquidity constraint. 3

Second, to make the problem more realistic, we simulate life-cycle consumption models with both income and consumption uncertainty. Thus this paper is closely related to Gourinchas and Parker (2002) who calibrate a discount rate and relative risk aversion, and also find strikingly different consumption behavior for households at different ages. Palumbo (1999) analyze the uncertain medical expense and precautionary savings near the end of life cycle. Third, in this paper, consumers are assumed to borrow, and when borrowing is negative, savings substitute borrowing. There are many papers in which consumers are assumed to save each period, such as Gourinchas and Parker (2002) and Gakidis (1998). This techniques are also used in Carroll and Samwick (1997) and Kehoe and Levine (2006). However,when borrowing, not savings, is assumed, the constraint used in the model slightly changed. Finally, default choice is allowed in the model. Lopes (2008)quantify the effect of different factors on household decision to default,while interest rate is exogenous. Chatterjee et al. (2007) estimate a dynamical model of consumer bankruptcy considering uncertainty and inability to commit to future repayment. Athreya (2001) found that exemptions are strongly negatively associated with the availability of unsecured credit. Livshits et al. (2007) focus on the comparison between fresh start and non-fresh start. Since it is hard to quantify the effect of bankruptcy law on bankruptcy behavior, we have not seen many paper about this, especially with pure empirical data analysis. Borrowing the dynamic model help us to have a big picture of how households make their bankruptcy filing decision. The model we use is the classical model in this field, the model also can be seen in Livshits et al. (2007) and other papers. However, most current research either focus Chapter 7 bankruptcy rule or Chapter 13 bankruptcy rule. Livshits et al. (2007) discuss two bankruptcy rule, but only use fresh start model prediction to match empirical data, failing to consider there are 30% percent of Chapter 13 bankruptcy in the US. Livshits et al. (2007) also ignore the fact that the model is solved backward, the first time period we solved represents the end of the life cycle, and the last time period represents the beginning of the life cycle, which leads to the consumption is greater at retirement age than at middle 20s. 4

In this paper, besides null hypothesis tested on empirical data, we consider the existence of two bankruptcy rule, and make model prediction on both bankruptcy rules, and the proportion of each bankruptcy is based on the empirical data. We also adjust the order of result to reflect the life cycle correctly. One of the important finding in our paper is that under non fresh start bankruptcy law, the peak bankruptcy filing time will be delayed from 40s to 50s if bankruptcy law is very friendly. This finding is very meaningful for policy makers, especially for some countries only with non-bankruptcy rule, such as German 14 years ago and China in the near future. By adjusting the strictness of bankruptcy law, policy makers can have control over the distribution of bankruptcy filers. The paper is organized as follows. The second section gives the background of bankruptcy law. Models are discussed in section 3, section 4 covers the estimation method and parameters from empirical data, section 5 presents the results. 2 Bankruptcy type and change in bankruptcy law Bankruptcy law allows consumers to get away from their debts. Once bankruptcy is filed, most consumer debt is discharged. Some secured debt, such as mortgage and car loans, is not discharged; student loans, tax obligations, child support obligations and some credit card debt incurred shortly before filing are also not discharged. Consumers are only allowed to file bankruptcy every six years, bankruptcy record will keep in credit report for ten years. Chapter 7 and Chapter 13 are two basic forms of bankruptcy. Under both procedures, individuals are allowed to get rid of unsecured debts, creditors must immediately terminate all efforts to collect debt. Chapter 7 requires bankrupts to repay from their assets. Bankruptcy under chapter 7 is known as straight bankruptcy, or liquidation bankruptcy. A person filing bankruptcy under Chapter 7 can fully discharge debts. However most assets will be sold, except some property, such as cars, work-related tools and basic household furnishings. Chapter 13 requires bankrupts to repay from future income. Bankruptcy under Chapter 13 is more like a payment plan, under Chapter 13 some debt balances might be partially liquidated, and the filers agrees to a monthly payment plan for their debt. It stays on 5

credit report for seven years. The court typically approves a repayment plan that allows the bankruptcy filers under Chapter 13 to pay off their debts during a period of three to five years. For those consumers who do not want to lose their asset, bankruptcy under Chapter 13 might be preferred to Chapter 7. The Bankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA) of 2005 altered the conditions of bankruptcy. Prior to BAPCPA, bankruptcy law is relatively friendly to consumers, many bankruptcy filers ended up with credit debt fully discharged. The new bankruptcy legislation is less debtor-friendly. BAPCPA made several major changes. First, debtors are not allowed to choose between Chapters 7 and 13. Second, BAPCPA brought many more strict requirements for the debtors to file a bankruptcy. For example, debtors are required to attend credit counseling session six months before filing a bankruptcy. The debtors also should attend a financial education class from an approved provider before bankruptcy can be finished. In addition, to prevent people from abusing the bankruptcy system, two steps of means test were brought out. ( Under means test, first, multiply a filers net monthly income by 60,if it is at least $10,000, the debtor fails the means test; if it is less than $6000, the debtor passes the means test; if it is at least $6,000, but less than $10,000, then continue to the next step. In the second step, the net monthly income multiply 60 is compared with the maximum amount between 25% of the debt and $6000, if the net monthly income is less than the later one, then the debtor passes the means test, if not, fails the test.) If the debtors fails any step of means test, they will be restricted to file Chapter 7 bankruptcy. These requirement increases bankruptcy cost. 3 Models We start with the basic discrete-time, overlapping -generations model where households live for T periods, T is exogenous and fixed. All households are identical, they maximize their life time discounted utility, with discounted factor, β. 6

3.1 Households We start with the basic discrete-time, overlapping -generations model where households live for T periods, T is exogenous and fixed. All households are identical, they maximize their life time discounted utility, with discounted factor, β. We assume consumption is the only source of utility for each household. Consumer utility function is defined as: T β t 1 U(c t ) (1) t=1 In Equation 1, utility function is assumed to be increasing and concave, follows constant relative risk aversion form U(c) = (c 1 σ /1 σ). β is the discount factor of a household, c is consumption. The household labor income is from labor endowment and shock for each period. y i t = z i tη i te i t; (2) z i t represents persistent shock, η i trepresents transitory shock, which affects current time period only. The household labor income uncertainty is from the product of both parts. z i t is approximated with a finite-state Markov chain. Considering the cost of computation, we assume persistent shock follows a age-independent transition matrix. Household labor income are defined from both shocks and labor endowment, for household at different age t, labor endowment is different. We can calculate the logorithm of household labor income for age group, and assume one group as base group, calculate the ratio of logincome between other age group and this age group. Provided the price of the loan with simulated labor income, consumers decide how much to spend, how much to borrow(save), and whether they will file a bankruptcy for each period. Consumers are assumed not to be able to file a bankruptcy twice in six years. Considering the computation cost and the convenience of calculation, each time period is defined as three years, which means consumers are not allowed to file a bankruptcy in two continuous periods. First, for bankruptcy filing under Fresh start, consumers can fully discharge their debt. 7

Let V be the value function of consumers repay their debts; let V be the value function of filing a bankruptcy; Once a consumer files a bankruptcy in current period, he is not allowed to file a bankruptcy next time period, however, he still can default, which means that he choose not to pay in current period, but he is still responsible for it, debt will be cumulated in the next time period. Let W be the value function continuous with the period of bankruptcy filing. After shock is realized, consumers choose consumption in current period and debt in next period to maximize utility. V (d, z, η, κ) = max c,d [u(c) + βemax[v (d, z, η, κ ), V (z, η )]]; (3) c + d + κ ezη + q b (d, z, t)d Equation 3 is the value function when no default happening. State variables are : labor income persistent shock, transitory shock, and expenditure shock, and the debt level; Control variables are: consumption in current and debt in the next period. When V > V, consumers will choose to file a bankruptcy next period, otherwise, no bankruptcy next period. V (z, η) = max c,d [u(c) + βemax[v (d, z, η, κ ), W (z, η, κ)]]; (4) c = (1 γ)ēzη The above is the value function when bankruptcy is filed in current period, with similar state variable and control variables. Since consumers are only allowed to file bankruptcy once every six years ( it can be looked as two 3-year time periods). If they file bankruptcy in current period, they are not allowed to file bankruptcy next period, but he can choose to default, not paying debt right now, but be responsible for their rollover debt. When W > V in next period, they will choose to default, otherwise, choose not to default. W (z, η) = max c,d [u(c) + βemax[v (0, z, η, κ ), V (z, η )]]; (5) 8

c = (1 γ)ēzη, d = (κ γēzη)(1 + r) When consumers default(with debt rollover) in current period, they are allowed to file a bankruptcy next period, when V > V in next period, they choose to file a bankruptcy. For Non Fresh Start system, value function is defined as: V NF S (d, z, η, κ) = max c,d,i[u(c) + βev NF S (d, z η, κ )]; (6) s.t. c + d + κ ezη + q b (d, z, t)d, ifi = 0 c = (1 γ)ēzη, ifi = 1 d = max[(d + κ γēzη), 0](1 + r), ifi = 1 Equation 6 shows the objective function for non-fresh start bankruptcy filing. Similarly, state variables include d, z, η and κ, d is the debt level in the last period, z is the persistent shock, η is the transitory shock, κ is the expenditure shock. The control variables include consumption, debt level in next time period, and whether to file a bankruptcy. 3.2 Financial Institution Financial Institution offers both saving rate and loan rate in the market. Since there is no risk for the consumers, the saving rate is defined as exogenous. However, the price of the loan is decided by the market. To calculate the expected price of loan, we need to know the probability of default and probability of not default, if we also know the price of loan when default and price of loan and not default, it is easy to sum up to get the expected price of loan. Let q b be the price of bond with zero default probability, then q b 1 = 1+r s+τ. and τ is transaction cost. Assume θ is the probability of a household file a bankruptcy or default tomorrow, θ depends on total borrowing d and shock z, and age t, ie, default probability is 9

θ(d, z, t). Hence the bond price for loans with Fresh start: q b (d, z, t) = [1 θ(d, z, t)] q b + θ(d Γ, z, t)e( I = 1) q b (7) d + κ Here E( Γ )is the expected rate of recovery through garnishment. Garnishment is as- d +κ sumed to be proportionally to the money need to pay debt and expenditure shock. For Non-fresh Start, it is slightly different. Consumers are not fully discharged under Nonfresh Start, they are still responsible for the debt in the future, besides paying the garnishment in current defaulting period. Hence, q b (d, z, t) = [1 θ(d, z, t)] q b + θ(d, z, t)e( Γ + q(d, z, t + 1)d d + κ I = 1) q b (8) d = max[d + κ τ, 0](1 + r) 3.3 Equilibrium DEFINITION 1. Given a bankruptcy rule and risk-free bond prices (q s ), a recursive competitive equilibrium with FS is value functions V, V, W, policy functions c, d, I(d, z, η),a default probability θ(d, z, t), and a pricing function q b such that: (1) The value functions satisfy the functional equations 3, 4 and 5, and c, d, and I are the associated optimal policy functions. (2) The default probabilities are correct: θ(d, z, t) = E(I t+1 (d + K, Z, η )). (3) The bond prices q b are determined by zero profit equation 8. For NFS, a competitive equilibrium is defined analogously to above, only the value function and bond price are given by the NFS condition. Since the value of declaring bankruptcy 4 is independent of the debt level, and the value of repaying 3 is decreasing in the debt level, it makes the existence of equilibrium with FS straightforward. For any income realization at any time period, there is a unique level of debt d t (z, η) which solves V t (d, z, η, 0) = V (z, η). We solve the problem by backward induction. The equilibrium prices, value and policy 10

functions can be computed from the household s last period in their life to the next to the last period. The optimal choice will be made during each life period based on the function of state variables. 4 Data The data we use in this paper include Panel Study of Income Dynamics(PSID) 1996, and Survey of Consumer Finance (SCF)2004 and 2007. PSID 1996 provided a detail information about household bankruptcy filing. The survey covers many bankruptcy related questions, including: have you filed a bankruptcy, and if yes, how many times altogether have you filed for bankruptcy? Then more detail question about the most recent bankruptcy are asked: in what year, what state, under which Chapter? why you filed the most recent bankruptcy? Did the bankruptcy court take any of your property to pay your creditors? How much and how long did the court take from your earnings to repay your debts? What was the total value of that property? What was the total amount of your debt at the time you filed for bankruptcy? What is the debt remained after bankruptcy was filed? As a result of having filed for this bankruptcy, did you have an application for credit card or loan denied, have a credit card you had before the bankruptcy canceled, have credit denied when trying to buy a car or other large item, or receive financial support from family and friends? Then similar questions about the next to most recent bankruptcy for those filing bankruptcy more than twice. Table 1: Summary statistics for all observation variable summary mean standard deviation N hage age of household head 44.192 15.910 7372 ttinc total household income 42704.536 51378.576 7372 ttdebt total debt of household 4325.981 15424.019 7372 ttasset total asset of household 62155.956 253011.448 7372 Table 1 shows the statistics for all observation in the data, the average age is 44, and the average total income for each household is $42704, and the average debt level for each observation is $4325, and the average total asset is $62155. 11

Table 2: Summary statistics for bankruptcy filer variable summary mean standard deviation N hage age of household head 38.680 9.920 194 agebkrp age when bankruptcy filed 35.459 9.759 194 ttinc total household income 37988.943 29779.938 194 ttdebt total asset of household 6434.079 11765.763 194 ttasset total asset of household 20741.262 83511.320 194 totdebtbkrp1 debt when 1st bankruptcy filed 50985.959 159941.399 194 howlongy1 how long for 1st bankruptcy filing 0.804 1.692 194 earningstaken1 earnings taken by court 80.232 215.36 194 Table 2 shows the statistics for observations with bankruptcy filed before, the average age is 38, and the average bankruptcy was filed at 35 years old. For these who have filed a bankruptcy, the total income is $37988, about $5000 less than the average total income for all observations; the total debt amount is $6434, $2000 more than average debt level with all observations; the average total asset is $20741, about $40000 less than the average for all observations. When bankruptcy was filed, the average total debt for a bankruptcy want to discharge is $50985, which on average took 0.8 year for them to pay back. Table 3: Bankruptcy type distribution Race Frequency Percent Chapter 7 128 65.98 Chapter 13 59 30.41 Convert from 13 to7 7 3.61 Table 3 shows that according to PSID data, there are 65.98 percent of bankruptcy filed under chapter 7, and 30.41 percent bankruptcy filed under chapter 13, and 3.6 percent transfer from chapter 13 to chapter 7. The Survey of Consumer Finance include information on families balance sheets, pensions, income, and demographic characteristics. It not only asks respondent s bankruptcy history, but also collects respondents income, savings, and even include respondents spending habit, whether respondents spend more than their net income. In 2004 and 2007, after dropping the missing observation for family income and savings, we have 1079 bankruptcy filers out of 12

13505 observations in 2004, and 1066 bankruptcy filer out of 13617 observations in 2007. We use combine SCF 2004 and 2007 cross sectional data, and distinguish the families by the median family income, for those less than median income, we define them low income, and for those great than median income as high income, and find that high income group has a low bankruptcy filing rate. Table 4 shows the bankruptcy filing rate across groups with different income level. Table 4: Comparison between different income group Income Bankruptcy Rate Low Income 0.1111 High Income 0.0339 We also find that in SCF 2004 and 2007 survey, the bankruptcy filing rate is similar, around 7%. Table 5 shows different bankruptcy filing rate before and after BAPCPA. Table 5: Comparison between before and after BAPCPA (2005) Time Bankruptcy Rate Before BAPCPA (2004) 0.0740 After BAPCPA (2007) 0.0726 For the group of observations before the time when bankruptcy law changed, we analyze how income, savings and spending habit affect bankruptcy filing rate. Logit model(9) is applied to cross sectional data and then applied to SCF 2004 and 2007 separately. p log( 1 p ) = c 1 + β 1 Income + γ 1 Savings + θ 1 Spendingmorethanincome (9) Bankruptcy filing is the dependent variable in our logistic regression. The variables in the right hand side, such as income, savings, whether spending more than their net income are the independent variables. The coefficients are the values for the logistic regression equation for predicting the bankruptcy variable from the independent variable. They are in log-odds units.the results is shown in Table 6. The null hypothesis is that the coefficients of subsets are the same. Since the dependent 13

Table 6: regression result (1) (2) (3) bkrpt bkrpt bkrpt lnttfincome -0.0581*** -0.0601** -0.0592* (0.0217) (0.0306) (0.0308) lnsaving -0.254*** -0.263*** -0.245*** (0.00908) (0.0126) (0.0130) spendmore 0.310** 0.309 0.307* (0.125) (0.194) (0.163) cons 0.365* 0.426 0.336 (0.208) (0.294) (0.296) N 29267 14584 14683 R 2 Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01 variable is bankruptcy filing, it is between zero to one, we use log likelihood test to test whether these two sets of coefficients are the same. After running the logit model separately for two subset data, we sum the likelihood from two models and get the likelihood for the unrestricted models (Lur). Then we do the same to all the subset data and get the likelihood data for restricted models (Lr). The statistics can be calculated as through Lr - Lur, we calculated the difference of likelihood ratio, and get1451.84-(770.01+684.56)=-2.73, which is obviously less than the critical value from Chi squared table with degree of freedom of 6 (2*k) at 5% level. It implies that these sets of independent variable affect the bankruptcy filing the same across year. From the table, we see that income, savings and spending habit affect the bankruptcy filing consistently. There is negative relationship between income and bankruptcy filing, increase in savings also decrease the bankruptcy filing probability. It is also shown that when respondents spend more than their net income, the probability of filing bankruptcy increases significantly. To explain how bankruptcy behavior change over time, we adopt a life cycle model and consider the strictness of bankruptcy legislation and interest rate. 14

5 Parameters Calibrating This section explains all of the parameters we use in the paper. First, we discuss income simulation, since PSID is widely accepted as the best source for income-related data, we calibrate our model to match the characteristics of age profile earnings from PSID data. We assume earnings composed of age dependent endowment, persistent shocks, and transitory shocks. Based on age-dependent cross-sectional variances, we estimate the autocorrelation coefficient of the persistent shocks. According to the variance and AR(1) coefficient, approximate a finite state of Markov Chain to simulate a series of income data. y it = β i X it + z it + η it (10) where y it represents log of earnings, X it represents a vector of explanatory variables, η it represents transitory earnings, we assume all transitory earnings shock is from measurement error. z it = ρ z it 1 + ɛ it (11) z it represents persistent shock, ɛ it follows iid distribution. The data we use is from PSID on families during the years 1986-1990, which reports earnings in years 1985-1989. The total household earnings is defined as the sum of earnings of husband and wife, plus the total transfer income of husband and wife, plus unemployment insurance. The household with total earnings less than $3000 are excluded from the data. The households with head education undefined are also dropped. We can also estimate earnings regression for three different education level, the details are shown in Appendix. From the earnings regressions, we predict residuals from the regressions, and the residuals are used to estimate AR(1) process for the residuals. Table 16 in Appendix shows autocorrelation, persistent shock variance, and transitory shock variance for three different education level. We choose the average of each variable for all observations with different education level, it is shown in Table 7. We discretize the persistent income shock as a five-state Markov 15

Table 7: parameters Parameters value ρ 0.98 σɛ 2 0.0006 ση 2 0.07281 process, with age-independent transition matrix. Several other parameters are shown in Table 8. The annual discount rate is set to 0.94, since each time period in the model represents three years, β = 0.94 3. The annual saving interest rate is set to 4%, which is slightly greater than average real return on the bonds, but consistent with saving interest rate used in McGrattan and Prescott (2001) and Laibson (1998). The three year saving rate is 12.5%. The transaction cost is set to 4% too, which made Table 8: parameters Parameters value β 0.83058 r s 12.5% τ 4% σ 2 annual lending rate is lower than what credit card company offers, while it is consistent with most mortgage loans. Hence the period lending rate is 26%. We assume utility function follows constant relative risk aversion form U(c) = (c 1 σ /1 σ), where 1/σ represents intertemporal elasticity of substitution. σ is set to 2. Medical bills, divorces and unplanned pregnancies are three major reasons for filing bankruptcy, and these are beyond the control of the household. We consider these three different shock. Each expense shock takes one possible value k (k 1, k 2, 0), with probability π (π 1, π 2, 1 π 1 π 2 ) Table 9 shows the expenditure shock, which is abstracted from the Medical Expenditure Panel Survey(MEPS) and aggregate data on divorce. MEPS provides the detailed data on medical expense for a random sample of around 20,000 persons (about 7500 households) from 1996 to 2005. For each person in the sample, total medical charges, total expenditures and insurance information are reported. We analyze 16

Table 9: Expense shocks Shock Magnitude Fraction of income Probability k1 $33368 0.2648 7% k2 $69000 0.5476 2.07% MEPS data from 1996 to 1998. Table 10 shows that the median medical expenditure value across three years, 1% observe a medical expense shock of $40659, 2% with a medical expense shock of $28406, 3% with a medical expense of $21540, 5% with a shock of $14618, 7% with a shock of $11156, and 10% with a shock of $8142. Table 10: medical expenditure across years Percentage Median96 Median97 Median98 Average Median 1% 37703 40282 43991 40659 2% 26161 28933 30123 28406 3% 20584 22192 21844 21540 5% 13918 15165 14771 14618 7% 10513 11582 11374 11156 10% 7472 8428 8497 8132 Based on median medical expenditure across three years, we can simulate a series of medical expense shocks with a certain probability, such as $40659 shock with 1% probability, $28406 shock with 2% probability, $21540 shock with 3% probability, $14618 shock with 5% probability, and so on. In this paper, we simulate a medical expense shock of $11156 with 7% probability, for a three year period, shock size will be $33368, which is consistent with the medical expense shock in Livshits, MacGee, and Tertilt (2003). Our divorce shock comes from aggregate data, since most divorce shock is from the child support, when we measure annual divorce rate, divorces number with children under 15 is considered. According to U.S. Census Bureau (2000),there are 69,594,000 families in 1996. According to America s families and living arrangement (2000), there are 1,442,000 divorces with children under 15. The annual divorce rate is 2.07%. The divorce causes legal fee and child support fee, and also lose the economies of scale associated with breaking up a household. We estimate an average legal fee of $5000, the average annual cost of a young child is $8000, and annual economies of scale is $10000. Total 17

divorce cost is $23000.The high expense shock is based on divorce shock, $69000 for each period (three year), with probability of 2.07%. From 1996-1998, the average median income is $42000, three year income is $126000, Based on this, the fraction of average income is given in Table 9. 6 Results This part is organized as follows. First, benchmark model is briefly discussed. Then consumption and bankruptcy over the life cycle under two models are compared with each other, and weighted bankruptcy filing from both models are compared with data. In the last part, several policy experiments are done to show how bankruptcy filing change with garnishment rate, interest rate, income level, and shock. The benchmark parameters generate an annual borrowing interest is 9.86%, which is close to the borrowing interest during late 1990s. The benchmark also predicts that the mean earnings of defaulters is 0.56 of the average household earnings, in 1996 PSID data, the average s bankruptcy household s earning is the 0.53 of the average household earnings. Figure 1: Smooth consumption over time Figure 2: Smooth consumption across state A key aspect of the evaluation of bankruptcy is how it is sensitive to the uncertainty. Figure 1 shows the consumption smooth over the life under both bankruptcy rules, we notice that consumption increases and then decrease, and people consume more when they are young than when they are old. Non-fresh start model does a slightly better job in smoothing 18

consumption over the life cycle, however, the variance of log consumption is just opposite. As is shown in Figure 2, fresh start model does a better job in smoothing consumption across states. It is not hard to understand, when there is great uncertainty, fresh start can fully discharge debt, and have consumption smooth over the life. From the equivalent consumption variance perspective, we can see that fresh start does better than non-fresh start when there is great uncertainty, and non-fresh start dominates when there is no uncertainty. Therefore, we can argue that chapter 7 bankruptcy fully discharging debt in some sense improves welfare, by encourage people to work during the remaining life, while consumers are discouraged to work under chapter 13 because their future income is responsible for debt at earlier time. Figure 3: Two models comparison Figure 4: Model and data comparison Figure 3 shows the bankruptcy filing rate under both models, and Figure 4 shows the comparison of bankruptcy filing between data and weighted results from both models. The bankruptcy filing data is from 1996 PSID. From the figure, we can see that two models produce different bankruptcy filing pattern over the life. For fresh start, the bankruptcy filing is relatively stable over the life, while bankruptcy under non-fresh start is not stable all the time. There are two peak bankruptcy filing time periods, one is early 30s, and the other is late 50s. Table 11: Model results garnishment rate(+) interest rate(+) income(+) debt/earnings + - - bankruptcy rate - - - 19

Table 11 shows how the default rate and the debt to earnings ratio changes with garnishment rate, interest rate, and income level from the weighted results under both fresh and nonfresh models. When garnishment rate increase, bankruptcy legislation becomes less friendly, debt to earnings ratio increases, and bankruptcy rate decreases; when interest rate increases, debt to earnings ratio decrease, and bankruptcy rate decreases; when income increases, debt to earnings ratio decreases, and bankruptcy rate decreases. The detail is discussed as follows. 6.1 Change in Garnishment We took several experiments to understand the effect of environment factors. First, we look at the effect of bankruptcy legislation. When the punishment for bankruptcy increases, the amount that can be recovered from debtors increases, it means the garnishment increases. Figure 5shows how bankruptcy filing changes over the life cycle with three levels of garnishment rate under fresh start model, Figure 6 shows how bankruptcy changes with three levels of garnishment rate under non-fresh start model. Figure 5: different garnishment-fresh Figure 6: different garnishment-nonfresh Under fresh start, bankruptcy keeps increasing with two turnoff points at middle of 20s and 40s. Under non-fresh start model, we can see there are two peaks over the life when bankruptcy is very friendly to the debtors, one peak time is middle 20s, and the other peak time shows up at 60s. For a median strict level of bankruptcy, one peak time is in middle 20s, and the other peak time will be in late 40s. When bankruptcy law is very strict, we will 20

see a peak time in 20s, and then smooth down till the end of the life. Table 12: Results from the model with different garnishment rates - γ = 0.155 γ = 0.355 γ = 0.555 bankruptcy 0.04848 0.01964 0.00753 debt/earnings 0.01600 0.03449 0.04095 We find that bankruptcy filing rate decreases with the cost of bankruptcy increasing. It is consistent with intuition that when the bank can collect more from the debtors, they tend to offer more credit, hence relax the borrow constraint. With high garnishment rate, the debt will increase. Table 12 shows the weighted results from both models, and bankruptcy over the life cycle can also be seen in Figure 11 in Appendix. As shown in the table, when garnishment rate increases from 0.155 to 0.555, the bankruptcy decrease from 0.048 to 0.007, and the debt/earnings ratio increases from 0.016 to 0.041. 6.2 Change in interest rate Figure 7: different interest rate-fresh Figure 8: different interest rate-nonfresh The experiment policy of risk free saving rate is discussed, Figure 7 shows bankruptcy filing over the time under fresh start model, non-fresh start model results can be seen in Figure 8. The base model is the same as we have explained before. From the figure, we can see that bankruptcy rate is high for low interest, and is low for high interest rate. It is 21

consistent with our intuition, low interest rate implies a large money supply and easy access of borrowing, end up with high debt level and then high bankruptcy rate. Table 13: model prediction with different interest rates - 2% 4% 6% bankruptcy 0.02162 0.01964 0.01671 debt/earnings 0.03993 0.03449 0.02771 Table 13 shows the weighted results from both models. The weighted results for bankruptcy under both models can also be seen in Figure 12 in Appendix. When the risk free rate increases, which leads to a low debt level and fewer bankruptcy filing. The high interest rate decreases the benefits to young households of borrowing to smooth consumption intertemporally. From the table, we can see that when interest rate changes from 2% to 6%, default rate changes from 0.022 to 0.017, and debt to earnings ratio decreases from 0.040 to 0.028. 6.3 Change in income Figure 9: across income-fresh Figure 10: across income-nonfresh We also explored how income levels affect bankruptcy rate. Income parameters from empirical data is approximated as a five-state Markov chain, we can change income level by adjusting the probability of each state of income. when bad things happen, it is hard for households with low income live through the difficulty, so low income group will expect a high bankruptcy rate. Figure 9 and 10 show the bankruptcy filing over the time under two models separately. The results in the figures are consistent with what we expected. 22

Table 14: Results from the model with different income level - Low Income Median Income High Income bankruptcy 0.02354 0.01964 0.01574 debt/earning 0.01951 0.01583 0.01215 The low income group has higher debt level and higher default rate. As income increases, debt to earnings ratio decrease, and bankruptcy decreases too. As Table 14 shows, bankruptcy under low income group is 0.023, and decreases to 0.0158 under high income group. 7 Conclusion This paper asks what determines bankruptcy filing. We discuss why job loss, medical bills and divorce can not predict the bankruptcy well, we also do a hypothesis test of whether savings and borrowing affect bankruptcy across time, and conclude that these factors do not have predictive power either. We also ask how the strictness of bankruptcy law affect bankruptcy filing behavior. We adopt a dynamic model to analyze bankruptcy under different rules quantitatively, and model predicts that strict bankruptcy law leads bankruptcy filing decreases, and when interest rate increases, debt to earnings ratio decrease, bankruptcy filing decreases. We argue that bankruptcy is not simply determined by any of adverse events alone, the change of bankruptcy filing in the last decade is affected by many factors, not only income, but also legislation, interest rate and many other factors beyond bankruptcy filers. We also find that there is clear pattern for non-fresh bankruptcy filing rule, with relative high bankruptcy filing in middle 20s and late 40s, The peak bankruptcy filing time in late 40s will be delayed to late 50s if bankruptcy law is very friendly. This finding is very meaningful for policy makers, especially for some countries only with non-bankruptcy rule, such as German 14 years ago and China in the near future. It is common sense that no society would like a large proportion of elderly bankruptcy filers, these people have low earnings ability, and paying debt from limited earnings might cause it hard for them to maintain a reasonable standard of living. If there is a baby boom at certain range of time, then policy makers can 23

have control over the distribution of bankruptcy filers. An important caveat to our analysis involves utility preferences, which we have assumed to be identical for all consumers across time. If utility preference varies with consumers and changes with time, the consumption and bankruptcy decision over the life will be affected. We also simplify the strictness of bankruptcy law as one garnishment rate, and ignore other negative social effect it causes. These issues are left for future research. References Athreya, K. (2001). The growth of unsecured credit: are we better off? FRB Richmond Economic Quarterly, 87(3):11 34. Carroll, C. D. and Samwick, A. A. (1997). The nature of precautionary wealth. Journal of monetary Economics, 40(1):41 71. Chatterjee, S., Corbae, D., Nakajima, M., and Ros-Rull, J.-V. (2007). A quantitative theory of unsecured consumer credit with risk of default. Econometrica, 75:pp. 1525 1589. Deaton, A. (1991). Saving and liquidity constraints. Econometrica, 59(5):pp. 1221 1248. Domowitz, I. and Sartain, R. L. (1999). Determinants of the consumer bankruptcy decision. The Journal of Finance, 54:pp. 403 420. Fay, S., Hurst, E., and White, M. J. (2002). The household bankruptcy decision. The American Economic Review, 92(3):pp. 706 718. Gakidis, H. E. (1998). Portfolio choice with uninsurable labor earnings. PhD thesis, Massachusetts Institute of Technology. Ghez, G. and Becker, G. S. (1975). The allocation of goods over the life cycle. In The Allocation of Time and Goods over the Life Cycle, pages 46 82. NBER. Gourinchas, P.-O. and Parker, J. A. (2002). Consumption over the life cycle. Econometrica, 70(1):47 89. 24

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Appendices A Regression results and residual statistics Table 15: regression result (1) (2) (3) education<12 12=<education=<16 education>16 age 0.315*** 0.233** 0.393*** (0.0577) (0.0985) (0.130) age 2 /100-0.479*** -0.377** -0.562** (0.0954) (0.167) (0.223) age 3 /1000 0.0234*** 0.0195** 0.0263** (0.00498) (0.00919) (0.0128) y1986 0.00245 0.0176 0.00536 (0.0158) (0.0235) (0.0402) y1987 0.0113 0.0343 0.00334 (0.0243) (0.0343) (0.0695) y1988 0.0462 0.0776* 0.0200 (0.0338) (0.0470) (0.101) y1989 0.0613 0.0750 0.0207 (0.0439) (0.0600) (0.132) cons 3.068** 5.730*** 1.971 (1.235) (1.965) (2.850) N 4570 1950 1410 R 2 0.020 0.021 0.044 Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01 Table 16: Parameter estimates of earnings uncertainty (1) (2) (3) education<12 12=<education=<16 education>16 AR(1) term 0.955 0.9418 0.968 (0.000047) (0.000052) (0.00018) iidσɛ 2 0.0004 0.0005 0.0009 ση 2 0.0634 0.06917 0.08009 B Model prediction 27

Figure 11: Bankruptcy rate changes with different garnishment level Figure 12: Bankruptcy rate changes with different interest level 28

Figure 13: Bnakruptcy rate changes with different income level 29