Welfare implications of the Bankruptcy Reform Act of 1999

Journal of Monetary Economics 49 (2002) 1567–1595

Welfare implications of the Bankruptcy ReformAct of 1999$

Kartik B. Athreya*

Research Department, Federal Reserve Bank of Richmond, 701 E. Byrd Street, Richmond, VA 23261, USA

Received 15 June 1999; received in revised form 30 October 2001; accepted 6 December 2001

Abstract

In recent years personal bankruptcy has become an important issue to consumers, creditors,

and legislators alike. Over 40 billion dollars of unsecured debt were discharged in 1998 by 1.44

million households. These losses have led legislators to propose a variety of changes in

bankruptcy law, the most important and recent of which is the Bankruptcy Reform Act of

1999 (BA99). I develop a dynamic, stochastic, general equilibrium model of personal

bankruptcy to investigate the trade-off between the consumption smoothing role of

bankruptcy and the interest rate and deadweight costs it imposes. I find that stringent

means-tests would reduce filing rates only slightly, and would have only modest welfare

consequences. On the other hand, the elimination of bankruptcy altogether is found to have

substantial benefits. This result is robust to income shock persistence, and to stringency in the

application of means-tests.

r 2002 Elsevier Science B.V. All rights reserved.

JEL classification: D52; D58; G33

Keywords: Personal bankruptcy; Incomplete markets

$I thank Steve Williamson, colleagues at the Richmond Fed and University of Iowa, and the editor

Richard Rogerson. I am particularly grateful to the anonymous referee for very detailed comments which

have improved this paper substantially. Any errors are mine alone. The views expressed are those of the

author and are not necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve

System.

*Corresponding author. Tel.: +1-804-697-8225; fax: +1-804-697-8255.

E-mail address: [email protected] (K.B. Athreya).

0304-3932/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 3 9 3 2 ( 0 2 ) 0 0 1 7 6 - 9

1. Introduction

Personal bankruptcy can serve a role in completing markets. Under fullinformation, repayments from a risk-averse borrower to a risk-neutral lender couldbe made contingent on all possible outcomes, and insurance would be perfect.However, as Townsend (1979) shows, informational asymmetries and costly stateverification justify debt contracts that have a version of bankruptcy, i.e., there arestates where the borrower will make state-contingent payments to the lender, andthese states will be ones with verification of outcomes. Similarly, personalbankruptcy law as we know it is likely to have originated as a way to facilitaterisk sharing in the presence of informational asymmetries, costs of state verification,and costs of security design. Its spirit is one where society at large believes that mostborrowers face some uninsurable idiosyncratic risk, and therefore may facecontingencies where the repayment of debts would lead to great welfare loss fromtemporarily low consumption. It is in this way that bankruptcy helps householdssmooth consumption. However, the provision of such state-contingent insurance iscostly. In particular, interest rates on unsecured (and even secured) credit mustreflect the risk that some borrowers will exercise their bankruptcy option. Theseinterest rate costs of default in turn hurt the ability of households to smoothconsumption, all else equal. Secondly, ex post penalties that fall directly on thedefaulting household, both economic and non-economic, represent deadweightlosses.1 Therefore, two questions arise immediately. First, does current bankruptcylaw improve or hinder risk sharing and welfare relative to an environment with nobankruptcy? Second, what are the implications of recent congressional bankruptcyreform proposals for welfare, consumption, and interest rates?In this paper, I take a first step in answering the questions just posed by building a

dynamic, stochastic general equilibrium model of default. The model developed hereis constructed to be representative of the section of American households who relyon unsecured debt, primarily credit cards, to smooth consumption. To this end, Irestrict attention to unsecured credit, and do not consider collateralized debt. I usethe model to provide a quantitative and qualitative assessment of the effects of recentbankruptcy reform proposals.2 Specifically, the model allows me to assess the impactof proposed ‘‘means-testing’’ regulations as embodied in the Bankruptcy ReformAct of 1999. I assess the impact of these means-tests for bankruptcy rates, welfare,interest rates, consumption volatility, the average amount of debt discharged inbankruptcy, the average indebtedness of households, and overall consumptioninequality.The central findings of this paper are two-fold. First, current bankruptcy reform

efforts appear to be misdirected, as increasingly stringent means-tests will have only

1Unless they involve transfers of resources back to creditors, which is certainly counterfactual in

unsecured credit markets.2The analysis here takes observed and proposed default rules and lending practices and as given, and

examines their welfare implications. It does not address the question of what the first-best contract would

be.

K.B. Athreya / Journal of Monetary Economics 49 (2002) 1567–15951568

minimal impact on filing rates, interest rates, and welfare. Second, it is found that theelimination of the bankruptcy option altogether provides large welfare gains.Specifically, I find that as long as bankruptcy is allowed at all, households arebroadly indifferent to the stringency of bankruptcy reform, as filing rates, interestrates, and welfare respond only modestly to such regulations, with an upperbound of $80 per household annually. When bankruptcy is prohibited, however,the welfare gains are substantial, and are on the order of $280 annually perhousehold. The latter result obtains as interest rates on savings rise substantiallywhen bankruptcy is not allowed, while the interest rate on loans falls to match therate on savings plus transactions costs. These changes ensure that consumptionsmoothing is not adversely affected by the removal of the bankruptcy option, whilethe resource costs of running a bankruptcy system and the deadweight costs ofpunishing filers ex post are both avoided. These deadweight costs, as measured here,appear substantial.The quantitative evaluation of bankruptcy law is currently very pertinent. In the

past 20 years, the number of Americans who have used personal bankruptcy todischarge their debts has rapidly increased to unprecedented levels. Bankruptcyfilings have grown from less than three hundred thousand in 1981 to nearly one anda half million in each of 1997 and 1998 (Administrative Office of the U.S. Courts,1999). In terms of losses, according to 1998 WEFA estimates (WEFA, Group, 1998),personal bankruptcy resulted in the discharge of 42 billion dollars in consumer debtin 1997, roughly 7% of the 568 billion dollars in total consumer revolving debt(Source: Federal Reserve Statistical Release G.19, February 1999, U.S. FederalReserve Board of Governors). Further, the WEFA report estimated that lenderswould lose at least 200 hundred billion dollars from bankruptcy in the 4 year periodfrom 1997 through the year 2000. In the credit card industry alone, the annual lossesfrom bankruptcy filings are over 6% of 400 billion dollars in receivables,approximately 25 billion dollars annually.The losses above arise primarily from what are known as Chapter 7 bankruptcies.

A Chapter 7 filing removes all unsecured debt from the debtor’s balance sheet, inexchange for all ‘‘non-exempt’’ assets that may be held. Of the 1.4 millionbankruptcies in 1997, over 70%, nearly 1 million filings, were Chapter 7 filings. Theaverage debtor in a Chapter 7 bankruptcy defaulted on an average of 36,000 dollarsin 1997 (Source: Culhane and White, 1999).The rapid increase in the incidence of bankruptcy filing and the associated losses

have led to increasing scrutiny of bankruptcy law in general and to the introductionin congress of several bills aimed at making it more difficult to qualify forbankruptcy protection. Two of these bills are of particular interest. The first isHR3150, The Bankruptcy Reform Act of 1998 (BA98), introduced into the 105thcongress in June, 1998. This bill is an attempt to define a formula for ‘‘needs-based’’testing for bankruptcy eligibility. It requires both that an individuals’s income bebelow a regional median, and that their debts be at least 20% of their expected ‘‘net’’income over the next five years, where ‘‘net’’ income is defined as gross income lessappropriate expenses. The second bill is a very slightly modified version of BA98 thatwas reintroduced into the 106th congress as HR833 in May 1999. In this paper, I will

K.B. Athreya / Journal of Monetary Economics 49 (2002) 1567–1595 1569

focus exclusively on the implications of these proposed means-tests for consumption,interest rates, and welfare.As noted earlier, bankruptcy can provide insurance to debtors by helping them

keep consumption smooth when their wealth falls. Consumer groups, legal scholars,and others have argued that the proposed legislation, by restricting the availability ofa ‘‘fresh start’’, will harm debtors who use unsecured credit to smooth consumptionbut are simply unlucky.3 Credit issuers, especially unsecured creditors, argue insteadthat many debtors use bankruptcy irresponsibly, and force high interest rate andadministrative costs on responsible borrowers.The lack of consensus on bankruptcy regulation stems in part from the lack of a

simple framework within which to evaluate policy prescriptions. To this end, Idevelop a model that is closely related both to the incomplete markets models ofHuggett (1993), Aiyagari (1994), and also to the canonical models of competitiveequilibrium with default of Dubey et al. (2000), Zame (1993), and Zha (2001).Aiyagari (1994) and Huggett (1993) study whether uninsured idiosyncratic risks arehelpful in quantifying precautionary savings and in explaining the low observed risk-free rate, respectively, in a class of calibrated general equilibrium models. Dubeyet al. (2000) and Zame (1993) develop the pure theory of default in a two-period,stochastic, competitive equilibrium setting. I follow these antecedents and develop acompetitive, dynamic, stochastic model of bankruptcy. In order to understand thelong-run consequences of default, I abstract from business cycle risk, and restrictattention to the interaction of two factors: individual-level uninsured risk, and therules governing the exercise of the bankruptcy option. I develop a stylizedenvironment with three features. First, the environment has a large number ofindividuals with cross-sectionally independent but serially dependent stochasticallyfluctuating incomes. Second, there is a market for unsecured credit. Third, eachborrower is endowed with a bankruptcy option that allows them to discharge theirdebts subject to some penalties and conditions. I then calibrate the model such that itproduces observed default rates and interest rate spreads under current bankruptcylaw.I turn now to a brief review of the growing literature on bankruptcy. The work of

Gropp et al. (1997) is to date the most complete empirical study of how inter-statevariation in bankruptcy legislation affects bankruptcy incidence and interest rates.They find that states with very lenient rules regarding the exemption of assets fromseizure in a bankruptcy filing experience both higher bankruptcy incidence andgenerally higher interest rates on both unsecured and secured credit.4 Several studieshave also studied whether BA78, which made it easier for borrowers to file,contributed to an increased rate of filing. Shepard (1984), Peterson and Aoki (1984),and Boyes and Faith (1986) all find that BA78 contributed to an increased rate offiling. Domowitz and Eovaldi (1993) find, however, that it did not significantly

3Legal scholars have long appealed to idea of the ‘‘honest but unfortunate debtor’’ (see Jackson, 1985).4Bankruptcy rules may affect interest rates on secured credit because even when equity is largely, but

not completely, exempt from creditors. People sometimes use their credit cards to convert secured debt

into unsecured debt, which they then default on.


change filing rates. Other work includes Dye (1986), and White (1987). In an optiontheoretic framework, White (1998) finds that at least 15% of U.S. households wouldfind it financially advantageous to declare bankruptcy, while only about one-and-a-half percent do so. This suggests a large non-pecuniary cost of filing for bankruptcy,which I will use the model to estimate.Interestingly, almost all current research on bankruptcy is empirical, and does not

address issues of welfare and optimal regulation.5 This precludes economists fromusing empirical work on bankruptcy from making policy recommendations. In fact,a recent CBO review of personal bankruptcy literature states that: ‘‘y(CBO) foundthat those sources offered only limited guidance. Although economic reasoning canidentify the direction of borrowers and lenders responses, empirical research hadmade only a little progress in estimating the magnitude, and hence the significance ofthose responses.’’.The approach taken here will allow precisely this sort of measurement. To my

knowledge, this is the first study to address the welfare implications of currentbankruptcy means-testing proposals. Perhaps most importantly, while most of thebankruptcy research above embodies some sort of underlying optimization on thepart of consumers, it does not do so in an environment where quantities (bankruptcyrates, consumption volatility, etc.) and prices (interest rates) are endogenous. Thismay be a critical omission for welfare. The feedback of any given bankruptcy lawinto interest rates is exactly the way in which default is paid for, thereby affecting itsdesirability. A dynamic model is also crucial because bankruptcy penalties areinherently intertemporal; households are allowed to discharge debt, but aresubsequently penalized by being restricted from borrowing and re-filing forbankruptcy. With this background in place, I turn now to Section 2, which containsa precise description of the model. In Section 3, I present results and analysis ofBA99, and in Section 4, I provide some conclusions.

2. The model

The market for privately issued unsecured credit in the U.S. is characterized by alarge, competitive marketplace where price-taking lenders issue credit through thepurchase of securities backed by repayments from those who borrow. Thesetransactions are intermediated principally by credit card issuers. These issuers maybe viewed as technologies that pool risks, facilitate transactions, and providedelegated monitoring of borrowers. In terms of monitoring, credit card issuers arefaced with significant hurdles in assessing the likelihood that any single borrower willdefault, but hold large enough portfolios to allow fairly precise prediction about

5An important exception is the work of Zha (2001), who is apparently the first to address bankruptcy

law in a dynamic, stochastic, incomplete-markets setting. He studies, in a model similar to the one here, the

role of exemptions on capital formation, and finds that lax exemptions can be welfare improving. My focus

is on the role of means-tests.


aggregate bankruptcy rates and total losses in any given period.6 Therefore, theinterest rates charged by credit card issuers are better viewed as being set to coverthis aggregate default rate, rather than being individually tailored for each account.Clearly, this is descriptively accurate, as the typical credit card contract is describedby a fixed interest rate and credit line. Further, interest rates do not appear to varysystematically with individual debt levels, even though the marginal likelihood ofdefault may change.7

Consumers in this market, namely U.S. households, are small, risk-averse, pricetakers. They face stochastically fluctuating labor incomes and uninsurableidiosyncratic risk. The vast majority of U.S. households are also endowed with aline of unsecured credit, which they may use for transactions and consumptionsmoothing.8 I focus here on the consumption smoothing roles of unsecured creditand bankruptcy.

2.1. Agents, preferences and endowments

To capture the features of the real-world unsecured loan market discussed above, Iproceed as follows. The economy is composed of a continuum of infinitely livedhouseholds with unit mass. Time is discrete, and at the beginning of each period, allhouseholds receive a random endowment of the single, perishable good. There aretwo assets in the model. Agents have access to a competitive, unsecured creditmarket where they may lend, borrow subject to a liquidity constraint, or default onpreviously acquired debt. In addition to private risk-free debt, there is stock of publicdebt D; issued by the government. This debt is financed by lump-sum taxes Z ¼ rdD;on all households, where rd is the (endogenous) interest rate on risk-free savingsdeposits.The household’s beginning-of-period wealth is the sum of its (after-tax)

endowment *Y; and asset holdings a: The endowments of households are cross-sectionally independent but are serially dependent. Agents are identical ex ante interms of expected income, assets, and consumption. The random endowment inperiod t can take two values, *Y ¼ yl; and *Y ¼ yh; where yloyh: There is a transitionfunction over income whereby Pðy0 ¼ yljy ¼ ylÞ ¼ yll; and Pðy0 ¼ yhjy ¼ yhÞ ¼ yhh:The assumption of serially dependent income introduces anticipation effects in assetholdings and default behavior, and determines the effectiveness of using assets tosmooth consumption.Agents have standard additively separable CRRA utility functions over

stochastic processes for consumption. Therefore, the period utility function is uðctÞ ¼

6Well known difficulties in determining default probabilities, and more importantly, in assessing the

expected present value of a relationship with a card-holder, stem from poor information from credit

bureaus. This includes the absence of regularly updated, verifiable labor income data, a crucial indicator of

risk.7On the existence of competitive equilibrium in a model where interest rates on loans cover average

repayment rates, see Dubey et al. (2000).8See Jappelli et al. (1998) for evidence that credit cards are used for consumption smoothing.


ðc1�at � 1Þ=ð1� aÞ: Agents maximize

E0XNt¼0

bt c1�at � 1

1� a; ð1Þ

where bAð0; 1Þ: A full description of the household’s optimization problem is givenafter introducing more notation.While the use of a continuum of households is very natural, given the size of the

credit market, the use of infinitely lived households deserves justification. First, myconcern in this paper is not with matching the recent increase in bankruptcy filings,but rather with the longer term consequences of bankruptcy law on risk sharing.Changes in bankruptcy rates at frequencies as low as a decade may best be explainedby changes in bankruptcy law, ‘‘stigma’’, and changes in credit card issuer behavior.9

That is, there is no definitive evidence that age distributions are crucial in understandingbankruptcy rates. I therefore employ the simpler infinite-horizon framework.

2.2. Markets, assets, and financial intermediaries

The markets for risk-free bonds and public debt are competitive. There will be twoprices quoted for these assets, a loan rate rl; for those who borrow (hold shortpositions in the asset), and a deposit rate rd; for those who save (hold long positions).This arises because with the bankruptcy option, a certain fraction of households willdefault in equilibrium, and in order to break even, financial intermediaries will haveto charge higher interest rates on loans than they pay for deposits. To model thebehavior of large unsecured credit card lenders, I posit a costly intermediationtechnology whereby deposits are collected and loans are made to a large number ofhouseholds, thus allowing complete diversification. This will allow the use of fixedinterest rates that are common to all households. The cost of this intermediation willbe defined by a spread between borrowing and lending rates, as in Heaton and Lucas(1997), but will be explicitly denoted as a cost of t units per unit of loan issued by theintermediary.As mentioned above, households will be liquidity constrained in the model. The

existence of such constraints in credit card markets has been documented by Grossand Souleles (2000). If it is the case that the supply side response to changing default,delinquency and bankruptcy rates is to tighten these credit limits, among otherthings, then the welfare computations presented may be affected. However, evencasual empiricism shows that credit availability has not decreased along withbankruptcy rates over the past several years. The average amount of unsecured debtdischarged in a bankruptcy is, and has been over the last decade, of the order of$30,000. If the highest-risk borrowers are still able to obtain credit on this scale, theexistence of highly time- and state-dependent credit limits is questionable.10

9See Gross and Souleles (2000).10Furthermore, it is precisely the fact that lenders have been arguing loudly for legal recourse that

suggests that they face difficulties in managing their risks through purely economic incentives, such as

credit limits. Therefore, the fixed limits employed here are likely to be without loss of generality.


Lastly, the assumption that all debt is unsecured is made for a specific purpose,but is also less restrictive than it may seem. The model is designed to represent thesection of American households who have little or no collateral and rely onunsecured debt to smooth consumption. Therefore, the welfare implicationsdeveloped here apply directly to a population most affected by bankruptcy reform.Additionally, Gropp et al. (1997) argue that in many cases those considering filinguse unsecured credit to transform secured debts into unsecured credit, and thendischarge this debt in bankruptcy, thereby making the distinction between thesetypes of debt less clear, even in practice.

2.3. Bankruptcy

Bankruptcy in the model will most closely resemble Chapter 7 ‘‘total liquidation’’bankruptcy. If a household files for bankruptcy, their income and assets becomeknown to the credit market, and if they qualify, their unsecured debt is discharged,and they are constrained for a stochastic period of time from borrowing. They maysave during this time, however, and are therefore not fully in autarky. This is incontrast to the autarky that households are faced with in the literature on optimalcontracts with repudiation (e.g. Eaton and Gersovitz, 1981). Permanent autarky isclearly counterfactual in U.S. consumer credit markets. At the very least, householdsretain a storage technology after bankruptcy, namely, the ability to save.According to the proposals under study, qualification for bankruptcy requires

meeting two conditions. The first is a necessary, but not sufficient, condition. Itrequires that households only be allowed to file when their income is below theregional median. The second condition is what will be referred to as the debtthreshold, denoted Tn: If a household’s expected future income, net of ‘‘livingexpenses’’ during the 5 year period following bankruptcy is less than 20% of theirdebts, households are allowed to file, otherwise they cannot.11

Court determined expenses are likely to be subject to at least some subjectivejudgement of the bankruptcy court.12 Therefore, I denote by dA½0; 1Þ; the fraction ofgross household income designated as expenses. As d approaches 1, all householdswith below-median income qualify, and as d approaches 0, no one qualifies.However, in describing the results, I do not describe the results in terms of d directly.Instead, it will be convenient to define the threshold level of debt, TnðdÞ; such that,given d; only households with debts greater than this threshold qualify forbankruptcy protection.13 This is easier to interpret, and is the most pertinent

11HR3150 requires 20%, whereas HR833 requires 25%. However, given that the way in which expenses

are defined is the key determinant of qualification, we follow HR3150, and then vary strictness in the

definition of expenses.12These expenses include payments owed to secured creditors for auto and mortgage loans, food and

shelter expenses, etc. Note that these allowances would allow all but the poorest to retain their homes and

cars. Also, as Wedoff (2000) points out, this makes the law hard to define, and to defend, since perverse

outcomes may result. For example, a debtor with relatively new car on which debt is owed, will be given a

greater expense allowance (to meet car loan payments) than a debtor with a old car that is paid off.13From here on, I suppress explicitly denoting the dependence of Tn on d; but it is implicit.


information for a household considering bankruptcy. Given the finite-state markovstructure on income, it is trivial to compute the conditional expectation of the sum ofincome over the next 5 years. Denote this expectation by EðY5jytÞ: Given d; the debtrequirement a for eligibility (for households that have current income below themedian) is then given by

Tn �EðY5jytÞd

0:2: ð2Þ

If ap� Tn; the household qualifies, and if a > �Tn; the household does not.Bankruptcy is modeled here as a within-period event. It will not be a state variable

at any time. When a household files for bankruptcy, it pays the cost of filing, its debtsare completely erased, and it is then restricted from future borrowing.

2.3.1. The cost of bankruptcy and deadweight loss

Bankruptcy involves three types of costs. First, bankruptcy results in at least someexclusion from credit markets. Second, there are explicit time costs arising fromcourt dates, and other legal proceedings. Finally, societal disapproval or ‘‘stigma’’may play a role (see Dubey et al., 2000; Fay et al., 2002; Gross and Souleles, 2000).14

An important drawback of using bankruptcy to provide insurance is that thepenalties listed above typically do not involve any transfer of wealth from debtors toanyone, let alone creditors. For example, over 95% of Chapter 7 bankruptcies are‘‘no-asset’’ cases (Sullivan et al., 1989, pp. 201–218). Bankruptcy penalties thereforeimpose deadweight losses on society. Nevertheless, deadweight penalties are stillwidely used for two main reasons. First, even when debtors have wealth at the timeof filing, it is often difficult to seize this in the presence of various exemptions andprotections, arising from the ‘‘Fresh Start’’ reasoning behind current bankruptcylaw. Second, although wage garnishing transfers resources, it induces moral hazardby interfering with the ‘‘yincentive to earn’’, and has therefore been severelyrestricted by law in many states (Sullivan et al., 1989).It is clear from the preceding that beyond credit market exclusion, all remaining

costs of bankruptcy can be well represented as direct reductions in the value of filing.Furthermore, the precise composition of these various costs is not necessary forunderstanding how changes in means-tests affect outcomes. Following Dubey et al.(2000) and Zame (1993), I denote by l; all costs of bankruptcy beyond credit marketexclusion. I will calibrate l to match observed bankruptcy filing rates, given thecurrent average length of credit market exclusion.15

14 I find in experiments that in order to match the data, penalties that are ex ante restricted to only

exclusion from credit markets imply penalty periods in excess of 25 years under reasonable

parameterizations of preferences, market incompleteness, and idiosyncratic risk. This is not sensible as,

among other things, bankruptcy disappears entirely from one’s credit record after 10 years. This indicates

that the other costs above play an important role.15This nests the model in the class: GEðA; l;QÞ of Dubey et al. (2000), where A describes bankruptcy

law and endogenous asset payoffs (due to the strategic exercise of the bankruptcy option), l denotes thecost of bankruptcy, and Q denotes the credit limits.


I model the exclusion from borrowing with the use of a lottery that determinesboth the average length of time a household is borrowing constrained and restrictedfrom default. Specifically, in each period following a bankruptcy, a borrowingconstrained household is subject to a lottery, whereby it may be returned to solvency,or remain in the borrowing constrained state according to the outcome of a Bernoullitrial, with parameter r: The waiting time to return to full credit market access istherefore Geometrically distributed, with the average time that a household isborrowing constrained and prohibited from filing again given by 1=ð1� rÞ: Thisdevice allows us to avoid keeping track of how many periods have elapsed since agiven household’s bankruptcy, and thereby shrinks the dimension of the state vectordescribing a household.16

2.4. The consumer’s problem

At any point in time, households belong to one of two mutually exclusive classesof credit market status: solvent (S), or borrowing constrained (BC). Solventhouseholds are those who have full access to credit markets and have the option offiling for bankruptcy. Borrowing constrained households are those who have filedfor bankruptcy in the past and are restricted in their ability to borrow. Lastly,bankrupt households are those who have filed for bankruptcy in the current period.They pay the cost, have their debts discharged according to the rules, keep theircurrent income, and go to the borrowing constrained state.The assumption that households keep current income after filing for bankruptcy

deserves explanation. First, there is currently no formal ‘‘means-test’’ to determineeligibility for bankruptcy filing.17 Secondly, the large share of contractual write-offsall get to keep their current income, making the assumption more realistic inpractice. In terms of credit market participation, these households are restricted to atighter credit limit than solvent households but face the same lottery as the newlybankrupt households regarding their return to the solvent state. A solvent householdchooses a consumption/savings strategy knowing that if their debt tomorrow isbelow the threshold, and if their labor income is no greater than the median, they canfile for bankruptcy and enter the lottery determining their time in the borrowingconstrained state. Borrowing constrained households choose consumption andnonnegative asset holdings, and hope to be returned to solvency before they hit aperiod of low-income draws.

16As the referee has pointed out, being borrowing constrained and denied the option to file for

bankruptcy are not exactly the same thing. However, the repeat filing rate is rather low (8%, as

documented in Gropp et al., 1997). I therefore, do not appear to lose anything pivotal by the assumption,

but benefit by reducing the state vector by one dimension.17However, there is a strong likelihood that the bankruptcy court may turn down a Chapter 7 petition if

an individual has substantial labor income at the time of filing. Therefore, throughout the paper, we

enforce the requirement that only agents with income less than the mean qualify for bankruptcy and also

keep all their labor income. Allowing agents to keep all their labor income regardless of its level would

likely lead to mismeasurement (by overestimating) of the non-pecuniary costs of filing.


The value to a household of having a given level of current income, asset holdings,and credit market status (solvent, or borrowing constrained) can be expressed interms of utility from choices over current consumption/savings and credit marketstatus (if solvent), and the expected future value of those choices. I restrict assetlevels according to a household’s credit status as follows. For solvent households,assets must lie in the set AS; and for borrowing constrained households, ABC: Thesesets represent increasingly strict restrictions on asset holdings, with borrowingconstrained households being potentially allowed to take on some debt and solventhouseholds being allowed to incur larger debts.Each period, given their current income and beginning-of-period assets, house-

holds must choose consumption, c; and asset holdings to carry forward into the nextperiod, denoted a0: From the individual’s point-of-view, all savings is risk-free, andearns the same rate of return. Therefore, the household makes no distinctionbetween government debt and private bonds when choosing savings. Depending onwhether they choose to be net borrowers or lenders, they face either the net rate ofinterest on loans, rl; or deposits rd; where rl > rd; where a0 belongs to AS or ABC

respectively.When a household is solvent and qualifies for bankruptcy protection, they must

first choose whether or not to file. They then choose assets subject to the constraintsfor solvent or borrowing constrained households, depending on their defaultdecision. I now introduce two pieces of notation. First, the current period statevector conditional on credit status is denoted ða; yÞ; indicating assets and currentincome respectively. Let CðdÞ denote the set of ða; yÞ combinations which, given d;satisfy the bankruptcy eligibility criteria described above. With this notation, wehave the value of being solvent VS; given as follows:

VSða; yÞ ¼max½WSða; yÞ;WBða; yÞ if ða; yÞACðdÞ;

WSða; yÞ otherwise;

(ð3Þ

where WS denotes the value of not filing for bankruptcy in the current period, andsatisfies

WSða; yÞ ¼ maxfuðcÞ þ bEVSða0; y0Þg ð4Þ

s.t.

c þa0

1þ rd;lpy þ a ð5Þ

s.t.

a0AAS: ð6Þ

When the household qualifies for bankruptcy (i.e., ða; yÞACðdÞ), and chooses tofile, it has its debt removed, pays the non-pecuniary cost, l; and then is automaticallysent to the borrowing constrained state, where it obtains value VBC: Therefore, thevalue of filing for bankruptcy, denoted WB; satisfies

WBða; yÞ ¼ maxfuðcÞ � lþ bEVBCða0; y0Þg ð7Þ


s.t.

c þa0

1þ rdpy ð8Þ

s.t.

a0AABC: ð9Þ

To define VBC above, note that households in the borrowing constrained state facea lottery, whereby with probability r; they are returned to solvency (i.e., they are freeto borrow and default in the following period), and with probability ð1� rÞ; they arestill restricted from borrowing or defaulting. Thus, we have

VBCða; yÞ ¼ maxfuðcÞ þ rbEVSða0; y0Þ þ ð1� rÞbEVBCða0; y0Þg ð10Þ

s.t.

c þa0

1þ rdpy þ a ð11Þ

s.t.

a0AABC: ð12Þ

I turn now to the definition of equilibrium in the model.

2.5. Equilibrium

I closely follow Huggett(1993) to define a stochastic stationary equilibrium asfollows. Let X ¼ A *Y CS denote the state space for households, where CS ¼fS;BCg: Let wB be the Borel s-algebra on X : The household’s asset decision rule isdenoted aðxÞ: The decision rule and the uncertainty of income together imply astochastic process for consumption and asset holdings with an associated transitionfunction Qðx;ZÞ;8ZAwB on the measurable space ðX ; wBÞ: This transition functionimplies a stationary probability measure mðZÞ for all ZAwB: This is a measure onsubsets of X that describes the joint distribution of households on asset holdings,current income, and credit market status. For a measure to be stationary, it mustsatisfy the following fixed-point condition

mðZÞ ¼Z

X

Qðx;ZÞ dm: ð13Þ

This implies fixed interest rates on loans and deposits and a constant fraction ofbankrupt households. Not every stationary probability measure, however, qualifiesas part of an equilibrium. Since the private bond market must clear, aggregateholdings of private bonds must be zero. Additionally, all public debt must be held inequilibrium. Therefore, market clearing requires that the aggregate supply of bondsequals the stock of public debt, D:Next, as the banking sector is competitive, profits also must be zero. The zero-

profit constraint is motivated as follows. First, let Xpos ¼ fxAX ja > 0g denote thesubset of the state space X ; such that households hold positive asset balances, and let


Xneg denote those with negative asset balances. In the stationary state, there is a time-invariant mass of households, whose total borrowing is given by

RXneg

aðxÞ dm: Giventhe per-unit cost of intermediation, t; the total revenue for the intermediary willtherefore be ð1þ rl � tÞ ðj

RXneg

aðxÞ dmjÞ: Analogously, the total cost of funds for theintermediary is determined by total savings net of public debt times the gross depositinterest rate, ð1þ rdÞð

RXpos

aðxÞ dm� DÞ: The losses from default are on both interestand principal from those who borrow. Define pðxÞ to be the probability that ahousehold in state x will default. Total principal losses are therefore j

RX

aðxÞpðxÞ dmj:The zero profit condition on intermediaries is then: ð1þ rl � tÞ ððj

RXneg

aðxÞ dmjÞ �ðjR

XnegaðxÞpðxÞ dmjÞÞ � ð1þ rdÞð

RXpos

aðxÞ dm� DÞ ¼ 0: Lastly, the preceding impliesthat the aggregate default rate is given by P �

RXpðxÞ dm: The following four

equations will therefore define equilibrium.

Definition 1. A stationary equilibrium of the model is a four-tuplefaðxÞ;pðxÞ;mðZÞ; ðrl; rdÞg; that satisfies four conditions.

(1) The decision rule, aðxÞ; is optimal, given rd and rl:(2) mðZÞ is stationary: mðZÞ ¼

RX

Qðx;ZÞ dm for all ZAwB:(3) Asset market clearing:

RX

aðxÞ dm ¼ D:(4) Zero profits

ð1þ rl � tÞZ

Xneg

aðxÞ dm

��

!�

ZXneg

aðxÞpðxÞ dm

��

! !

� ð1þ rdÞZ

Xpos

aðxÞ dm� D

!¼ 0:

The computation of equilibrium in incomplete markets models has been madestandard by a series of papers including Imrohoroglu (1989), Huggett (1993),Aiyagari (1994), and others.18 The dimensionality of the state vector and non-trivialzero profit condition make computation somewhat more involved than theabove work. I use orthogonal polynomial approximations to the value func-tions, conditional on income and credit market status, and then use MonteCarlo integration with antithetic variates to compute all integrals. I then bisect onboth rl; and rd; until I simultaneously clear markets and satisfy the zero-profitcondition.

2.6. Parameterization

The following parameters will now be fixed. These are risk aversion, a; thediscount rate, b; the transition probabilities, yll and yhh; the average time spent in theborrowing constrained state, 1=ð1� rÞ; the debt threshold Tn; transactions costs t;

18Rios-Rull (1995) contains an excellent overview of techniques for solving heterogeneous-agent

models.


the per-capita public debt/income ratio, D; and credit limits for solvent, bankruptand borrowing constrained households, As; AB; and ABC; respectively.The risk aversion level and discount factor are standard parameters in this class of

models. I follow Aiyagari (1994) and Huggett (1993) and study cases where riskaversion is set at a ¼ 3:0: The model period is equivalent to one year, and followingCooley and Prescott (1995), I fix the discount factor b=0.947. A 1-year period isuseful because of the availability of income process estimates at this frequency, andbecause the actual process of bankruptcy is unlikely to take more than one model.The limits AB and ABC are set to zero and As is set at the average endowment for oneyear. In setting the debt threshold, Tn; for households who already meet the laborincome criterion, I vary this requirement and study five threshold levels, rangingfrom a zero debt threshold, whereby all households with below-median incomequalify, to a threshold where no household qualifies.To generate labor income risk, I use the two-state markov process estimated by

Heaton and Lucas (1997), estimated on annual PSID data. Income in the high state,denoted yh; is set at 1.25 units, and income in the low state, yl; is set at 0.75 units.Given the symmetry of the transition function, unconditional mean labor income istherefore normalized at one unit, and yhh ¼ yll ¼ 0:75 in the benchmark case.19 Thisimplies a coefficient of variation of 0.25, and a serial persistence parameter of 0.5.Income volatility under this process is also consistent with estimates by Kydland(1984), and Abowd and Card (1987, 1989). However, holding the coefficient ofvariation fixed, it is the persistence of income which determines the usefulness ofassets, and thereby bankruptcy, to smooth consumption. Serial persistence estimateshowever vary more substantially, but in addition to Heaton and Lucas (1997),Abowd and Card (1987, 1989) find an implied serial correlation of 0.3, and Heatonand Lucas (1996) find that a plausible range for serial persistence is between 0.3 and0.53. Lastly, recent work incorporating fixed effects by Quadrini (1999), finds a serialcorrelation coefficient of 0.43. This set of estimates is the basis for the benchmarkparameterization of yhh ¼ yll ¼ 0:75: However, I will also explore the implications ofmore persistent income processes by setting yhh ¼ yll ¼ 0:85; which implies asubstantially higher serial correlation of 0.7.The values for the parameter governing the mean length of the borrowing

constrained penalty period, r; are more difficult to pin down definitively. Creditpolicies are highly proprietary and there is no law governing the granting or denial ofcredit to those with bankruptcy on their credit record. However, bankruptcy remainson an individual’s credit report for 10 years, and is therefore information available tolenders for that period. Based on conversations with credit analysts at two of thelargest issuers of credit cards, I learned that each had ‘‘disaster’’ checks built intocredit risk assessments. In one case, credit would automatically be denied if there waseither a delinquency (late payment) in the past 6 months, or a bankruptcy on theircredit record any time in the past 7 years. In the other case, the disaster check

19The work of Storesletten et al. (1998), and others suggests that labor income is a near unit-root

process, in a life-cycle setting. Such persistence in a infinite-horizon setting (i.e., for a whole dynasty) is less

plausible, however.


automatically rejected applicants who had filed for bankruptcy within the past fouryears.20 However, the availability of sub-prime lending and the absence of a debtorsprison imply that the effective time spent credit constrained is as low as 1 year. Thesepolicies are used to set the benchmark mean length of time spent in the borrowingconstrained state at the intermediate value of four years, and therefore set r ¼ 0:75in all cases.21, 22

The model developed here is intended to capture the behavior of households thatfreely choose debt levels in response to income shocks. The model is less well suitedto describing the behavior of households who incur expenses in attempts to save thelives of its members. Similarly, circumstances leading to a large lawsuit brought on ahousehold may not represent unsecured debts that are freely chosen, and so are notexplicitly addressed in the present environment.23 My focus therefore will be onbankruptcies involving households with large credit card debts not driven by large‘‘expenditure’’ shocks involving either uninsured medical expenses or lawsuits. Ofthe approximately 1% of households filing for bankruptcy on average between 1990and 1998, roughly 70% have been Chapter 7 filings. Chakravarty and Rhee (2001)show that roughly one-third of filings are attributable to catastrophic health eventsand lawsuits.24 Therefore, the incidence of Chapter 7 bankruptcies, after removingthe preceding, is currently approximately 0.5%, and will be the filing rate target forthe benchmark environment.Given the preceding, the natural interest rate to compare the model with is the

interest rate on credit cards. Over the 5 years since the last major change inbankruptcy law, the Bankruptcy Reform Act of 1994, this rate has averaged roughly13%.25 The deposit rate in the model is closest in interpretation to the interest rateon treasury bills, as it represents a risk-free claim on consumption. Therefore, Icompare the deposit rate with the average annualized post-WWII real returnavailable on t-bills, which I estimate at 2.57%.26

The transactions cost t is parameterized according to Evans and Schmalensee(1999), who find that the cost of servicing accounts is roughly 5.3%. This cost isoffset however, by the interchange fee earned by credit card issuers. Evans and

20Although this seems more lax than the other issuer, this issuer specialized in department store credit

cards, and so had some ability to repossess charged merchandise.21Defending periods longer than this is difficult (e.g. see American Bankruptcy Institute’s bankruptcy

FAQ’s. Website: abiworld.org.). Also, varying this parameter would simply result in imputing relatively

more or less to non-pecuniary costs. However, given that the sum of these penalties results, by

construction, in the same equilibrium bankruptcy rate, I fix r at a plausible intermediate value and

proceed.22Recall also the low re-filing rate documented by White (1997). This occurs in part precisely because

debtors have a hard time obtaining unsecured credit after a bankruptcy. This makes the assumption that

agents are simultaneously restricted from borrowing and defaulting a reasonable one.23Debt incurred in these cases is perhaps better addressed in a model with large expenditure shocks-

driving income to deeply negative levels for a period, rather than as income shocks.24See also Domowitz and Sartain (1999).25Source: http://www.federalreserve.gov/boarddocs/RptCongress/creditcard/1999/.26CPI Source: http://www.stls.frb.org/fred/data/cpi.html.

3-Month T-Bill Rate Source: http://www.stls.frb.org/fred/data/irates/tb3ms.


http://www.federalreserve.gov/boarddocs/RptCongress/creditcard/1999/

http://www.stls.frb.org/fred/data/cpi.html

http://www.stls.frb.org/fred/data/irates/tb3ms

Schmalensee (1999) estimate these revenues to be approximately 1.9%. I thereforeset the net-of-interchange transactions cost, t; at 3.4%. The ratio of public debt toaggregate income D is set in accord with Aiyagari and McGrattan (1998) at 2

3; and is

the post-war average of the ratio of the sum of U.S. federal and state debt to GDP.An important feature of the model is that it will allow an indirect estimate of the

non-pecuniary costs of bankruptcy, beyond the costs imposed by credit marketexclusion (which are likely to be at least partially deadweight), and loan interestpremium. These additional costs must play a role in deterring default becauseexisting financial penalties alone appear inadequate to explain the observed filingrate (see White, 1998).27 In order to measure these costs, I fix explicit credit marketpenalties, given by the parameter r; at the empirically plausible value discussedabove, and then set non-pecuniary penalty such that I match the observed filing rate,under current law. Therefore, this cost, denoted l; will be re-calibrated for eachparameterization of the income process.28 The consumption (and dollar) equivalentof this penalty is imputed by finding the reduction in the current-period consumptionof a household in the low income state, with the average debt level held by bankrupthouseholds, that would result in a utility loss of l units.

2.7. Welfare

In terms of welfare analysis, the desirability of outcomes will be evaluatedaccording to the following expression:

L ¼Z

X

V ðxÞ dm; ð14Þ

where L is the expected value function of households over assets, income, and credit

status. This is a utilitarian social welfare function that weights all householdsequally. It measures ex ante welfare. I use this measure to estimate the increment/decrement to consumption under a given bankruptcy policy, at all dates and states,that makes households indifferent between the economy defined by the proposedbankruptcy policy and the benchmark economy. I denote this increment/decrementf: Let Lbench denote benchmark welfare, and Lpolicy denote welfare under a proposedpolicy. Given CRRA preferences, f will satisfy the following:

f ¼Lpolicy þ 1=ð1� aÞð1� bÞ

Lbench þ 1=ð1� aÞð1� bÞ

� 1=ð1�aÞ

�1: ð15Þ

Under this criterion, f > 0 implies that households are better off under a proposedpolicy than in the benchmark case, and fo0 implies the reverse.29 I turn now toresults.

27 In the model studied here, I experimented with ‘‘borrowing constrained’’ periods of varying length,

and found that exclusion for an average of at least 25 years were required to match observed filing rates

under different income processes. This is counterfactual, and implies that significant non-pecuniary costs

must be borne by bankrupt households, as the referee has pointed out.28 It will, of course, remain fixed, as I vary the strictness of the threshold, Tn:29Further details, and support for the use of this criterion, are found in Aiyagari and McGrattan (1998).


3. Results

The findings reported here demonstrate first that bankruptcy protection doesappear to improve risk-sharing marginally. With respect to the proposed means-testsunder study, I find that even substantial increases in the stringency of means-tests, asenvisioned in the Bankruptcy Reform Act of 1999, will have only modest welfareimpact. Under benchmark income persistence, welfare gains are bounded above ingeneral equilibrium by $80 dollars per household annually. In the setting with higherincome shock persistence, means-tests are essentially irrelevant.A more interesting finding, however, is that while means-tests may be improve

welfare non-trivially, eliminating personal bankruptcy altogether improves welfareby far more, by up to $280 per-household annually. This, in turn, suggests thatcurrent debate on means-testing misses the mark, as even strict means-tests fall farshort of capturing the much larger welfare gains available from eliminatingbankruptcy.In terms of filing rates, the results suggest that moving to a very strict form of

means-testing would reduce the filing rate by a maximum of 0.00064 percentagepoints relative to its current level. Additionally, interest rates are typically insensitiveto means-tests, but do fall more substantially in the case where strict means-tests arecombined with benchmark income persistence. I also find that a move to very strictmeans-tests would reduce the filing rate slightly, but would increase the averageamount of debt discharged per bankruptcy filing by approximately $800. Lastly, thepeople who file for bankruptcy are only those who have received a string of badshocks, and are at, or very close to, their borrowing constraint.

3.1. The Bankruptcy Reform Act of 1999

The benchmark case is presented below in Table 1. In all cases, a solventhousehold’s borrowing limit is set at current median annual household income, thatis, As ¼ �1: This corresponds to approximately $40,000.30 This limit is plausible,and will turn out in equilibrium to help produce nearly the observed average level ofdebt discharged in a bankruptcy, given a reasonable income process, transactionscost, and credit market penalty. As discussed earlier, the transactions cost parametert is set in accordance with the evidence of Evans and Schmalensee (1999) at 3.4%.Benchmark labor income is set as yll ¼ yhh ¼ y ¼ 0:75: The welfare, price, anddistributional implications of bankruptcy reform under the benchmark incomeprocess are given in Tables 1, 3 and 5. Tables 2, 4, and 6 report analogous results forthe case of increased income shock persistence.Under the benchmark parameterization, I find that the model performs well in

matching the data along several dimensions. First, under current law there is noqualifying threshold, i.e., Tn ¼ 0: To begin, let dBk denote the average debtdischarged in a bankruptcy, as a percentage of annual median income. In thebenchmark case, dBk ¼ 97:73%; approximately $39,000. This benchmark outcome is

30Source: 1999 dollars, U.S. Census Bureau, http://www.census.gov.


http://www.census.gov

broadly consistent with the recent estimates of Culhane and White (1999), who findan average debt discharge of $36,000 per filing (1999 dollars), roughly 92% ofannual median income. The model is also broadly consistent with the average debt/income ratio of households, denoted d=y: In the benchmark case, d=y is 6.16%, onlyslightly lower than the 8.5% debt-income ratio among U.S. households (Source:CBO, 2000 estimates). In terms of interest rates, the benchmark deposit rate of2.54% is almost exactly the real post-WWII risk-free rate, which I estimate at 2.57%,while the loan rate of roughly 15% is slightly higher than the observed credit cardinterest rate.With respect to the non-pecuniary costs of bankruptcy proceedings, I find that in

both cases, these costs are large. When y ¼ 0:75; the imputed cost is approximately$8900. When y ¼ 0:85; the cost rises to $10,400. The increase in non-pecuniarycosts with the increase in persistence occurs because exclusion from credit markets isless costly when incomes are highly persistent, implying greater non-pecuniarycosts. These high imputed costs are consistent with observed evidence on the rateof aggregate filings, given purely financial incentives to file. White (1998)documents the puzzle of why so few households file, even when financial incentivesimply nationwide filing rates in excess of 15%. Furthermore, Sullivan et al. (1989)provide detailed discussions of the typically desperate financial circumstances ofmost bankruptcy filers, arguing that few take the option lightly. As will be shownlater, the model delivers outcomes consistent with high bankruptcy costs, asonly those very close to their borrowing limit turn to bankruptcy. I turn now tospecifics.

Table 1

Bankruptcy rates, prices, debt and welfare ðy ¼ 0:75Þ

Tn P rl rd dbk d=y Welfare ¼ f $40; 000

Data 0.500% 13.0% 2.57% 92% �0.0850 —

0 0.500% 15.0% 2.54% 97.73% �0.0616 —

0.90 0.500% 15.0% 2.54% 98.75% �0.0618 $0

0.95 0.471% 14.7% 2.59% 98.85% �0.0640 +$5

0.99 0.436% 11.8% 3.08% 99.73% �0.0837 +$80

No BK NA 7.6% 4.21% NA �0.1634 +$280

Table 2

Bankruptcy rates, prices, debt and welfare ðy ¼ 0:85Þ

Tn P rl rd dbk d=y Welfare ¼ f $40; 000

Data 0.500% 13.0% 2.57% 92% �0.0850 —

0 0.500% 11.1% 2.01% 99.33% �0.0976 —

0.90 0.500% 11.1% 2.01% 99.33% �0.0977 $0

0.95 0.500% 11.1% 2.01% 99.33% �0.0976 $0

0.99 0.492% 11.1% 2.02% 99.33% �0.0987 +$2

No BK NA 6.8% 3.39% NA �0.2061 +$264


3.1.1. Welfare, bankruptcy rates, and interest rates

Tables 1 and 2 display the results from general equilibrium experiments wherebyboth the persistence of income shocks and the stringency of means-tests are varied.31

Row 1 of Table 1 is the benchmark economy. Table 2 displays the outcomes whichemerge from increasing income shock persistence to y ¼ 0:85: This increases theimplied AR(1) persistence parameter to 0.7, from an implied serial correlation of 0.5when y ¼ 0:75:32

In terms of welfare, means-tests do appear to improve welfare nontrivially underbenchmark income shock persistence, denoted (BP), while they appear irrelevant inthe experiment with high income shock persistence, hereafter (HP). In both Tables 1and 2 note first that as the qualifying threshold Tn is increased from 0 in thebenchmark case, to 0.9, 0.95, and then 0.99 respectively, welfare remains essentiallyunchanged, with only one notable exception. Under the (BP) income process, whenTn ¼ 0:99; welfare improves noticeably, by roughly $80 per-household annually.In terms of bankruptcy rates, we see in Table 1 that the bankruptcy rate,P; falls to

0.486% when Tn ¼ 0:90: When Tn is raised to 0.95, P falls to 0.471%, and whenTn ¼ 0:99; P falls further to 0.436%. When y ¼ 0:85; Tn does not affect bankruptcyrates until it is raised to 0.99, where P falls marginally to 0.492%.With respect to interest rates, In Table 1, we see that in the (BP) case, as means-

tests are made more stringent, the interest rate on loans falls from 15.0% whenTn ¼ 0; to 11.8% when Tn ¼ 0:90: The fall in interest rates arising from strictermeans-tests occurs for two reasons. First, bankruptcy rates fall, implying a smallerspread between loan and deposit rates. Second, the fall in bankruptcy rates has asmaller impact on prices than the effect of increased borrowing associated with morestringent means-tests. As Tn increases from 0 to 0.99, average debt/income ratios risefrom 6.16% to 8.30%. As income are fixed, this implies that more debt, in absolutevalue, is being held by the household. The amount of debt increases with thethreshold Tn because it takes a greater level of debt to keep the bankruptcy option‘‘in the money’’. However, a strict means-test prevents this increase in debt fromgenerating a proportional, offsetting, increase in bankruptcy rates. Thus, the volumeof loans rises, while net credit loss, ‘‘NCL’’, does not rise in proportion, implyinglower equilibrium loan rates. This in turn is why welfare rises nontrivially in the (BP)case when Tn ¼ 0:99:Additionally, in order convince households to lend amounts sufficient to satisfy

the shift in demand for borrowing arising from strict means-tests, the interest onsavings must rise. Indeed, in the (BP) case, we see that rd rises substantially, from2.54% to 3.08%, as Tn rises from 0 to 0.99.

31Asset holdings (and hence default rates) are more sensitive to deposit rates than loan rates. Due to the

transactions cost, default premium, and stock of public debt, changes in the loan rate only affect a small

measure of households. This is why only the first three significant digits are reported for loan rates, while

four significant digits are reported for deposit rates.32Other recent work has found even higher persistence, notably Storesletten et al. (1999). Very high

income shock persistence seems less plausible in an infinite horizon setting than in a life-cycle setting. I

therefore restrict attention to the moderately persistent processes of Heaton and Lucas (1997), and

Quadrini (2000), but still allow for a substantial increase in persistence, as shown in Tables 2, 4 and 6.


3.1.1.1. Increased income persistence. Under higher income persistence, prices,quantities and welfare are nearly invariant to means-tests. Increased persistence ofshocks increases the likelihood that a given level of savings will be depleted, and willinduce the household to borrow. This increased desire for borrowing is seen in Table2, where the debt/income ratio is nearly 10%, relative to the roughly 6% level underthe (BP) process. However, given that I calibrate bankruptcy rates to be the samegiven current law (i.e., Tn ¼ 0) under both income processes, and given that filersalmost always exhaust all available credit, total credit losses are constant. Thus, theNCL rate falls, and with it, the interest rate of loans. In the (BP) case, the loaninterest rate rl ranged from 15.0% to 11.8%, while in the (HP) case, the loan rate is aconstant 11.1%, as long as bankruptcy is allowed.The increases in both savings in good times, and borrowing in bad times, are

reflected in the coefficient of variation for assets, denoted ‘‘C.V.-A’’, which risesfrom 1.17 in the benchmark to 1.35 when yll ¼ yhh ¼ 0:85: Note also that thedeposit rate, rd; falls from approximately 2.5% under benchmark persistence to2.0% in the (HP) case. The intuition for this is that when income shocks are highlypersistent, the precautionary savings motive induces households to hold largeramounts of savings in order to smooth consumption than under benchmarkpersistence.Means-tests affect welfare materially under benchmark income persistence.

However, in the (HP) case, the welfare improvements emerging from increasinglystrict means-tests disappear. The increase in average debt holdings relative to the(BP) case is seen in Table 2. These estimates imply that households are likely toqualify for bankruptcy regardless of the stringency of means tests. Therefore, asmeans-tests do not materially affect asset holdings, consumption, and prices, theyalso do not affect welfare.

3.1.2. Bankruptcy filers and their debts

I turn now to the profile of a bankruptcy filer, and to the level of debt dischargedin a typical bankruptcy. I find that in all cases, households file for bankruptcy onlywhen they have received a string of bad shocks, and have nearly reached theborrowing constraint. This is seen by noting that in all cases, the minimum debt levelin a bankruptcy exceeded 97% of average annual income. This is precisely whymeans-tests have little effect on the level of debt discharged in an averagebankruptcy. Ironically, while helping reduce the unconditional probability ofbankruptcy, stringent means-tests imply that households must hold more debt onaverage in order to keep their bankruptcy option ‘‘in the money’’. I denote by dbk theaverage amount of debt discharged as a percentage of average annual income. FromTables 1 and 2, we see that average debt discharged rises with Tn; from 97.73% ofaverage income to 99.73% when y ¼ 0:75: When y ¼ 0:85; dbk rises from 99.33% to99.62% of average annual income. These increases imply an increase in per-bankruptcy discharge by approximately $800 when y ¼ 0:75; and $120 when y ¼0:85: I turn now to discussing what is special about eliminating bankruptcyaltogether.


3.1.3. Eliminating bankruptcy

As can quickly be seen in Tables 1 and 2, the welfare consequences of means-tests,so long as bankruptcy is allowed, pale in magnitude to the gains available from theelimination of bankruptcy and default altogether. The welfare gains fromeliminating bankruptcy are roughly $280 when y ¼ 0:75; and $260 when y ¼ 0:85:These gains emerge for three reasons. First, disallowing bankruptcy immediatelysuspends the use of wasteful ex post deadweight costs, such as court costs, lawyer’sfees, the time costs of preparing a clear case, and the entire legal apparatus necessaryto support personal bankruptcy proceedings. Second, to the extent that both stigmaand credit market restrictions are imposed and do not involve resource transfers,such deadweight losses are also avoided. Third, an important and easily observedbenefit is that the interest rate on loans would fall dramatically, while the rate ofreturn on savings would rise substantially. The change in interest rates is, ceterisparibus, unambiguously welfare improving, as it makes asset accumulation anddecumulation more effective in smoothing consumption.In both Tables 1 and 2, the interest rate on savings rises by a large amount; from

2.54% to 4.21% when y ¼ 0:75; and from 2.01% to 3.39% when y ¼ 0:85: Thesegains in the interest rate on savings are crucial factors in improving the ability ofsavings and dissaving to smooth consumption. Correspondingly, borrowing is muchcheaper in the absence of bankruptcy, with loan rates of 7.6% and 6.8% in the (BP)and (HP) cases respectively. Despite the removal of the bankruptcy option,consumption smoothing, as measured by the Gini-coefficient and coefficient ofvariation, denoted ‘‘Gini-C’’, and ‘‘C.V.-C’’, respectively, remains essentiallyunchanged. This is seen in Tables 3 and 4. I next address the distributionalimplications of means-tests for both consumption and asset-holdings.

3.1.4. The distributional implications of means-tests

The small welfare consequences reported above, and the fact that the ex antewelfare criterion used here takes into account all moments of the steady-statedistribution, suggests that the distributional impact of means-tests is also small.Indeed, distributional changes are typically small for both consumption and assetholdings. Tables 3 and 4 record the distributional effects of means-tests forconsumption in the (BP) case, and then the (HP) case, respectively. Tables 5 and 6consider changes in the distribution of assets for the (BP) and (HP) casesrespectively.In both Tables 3 and 4 it can be seen that the distribution of consumption remains

nearly fixed as means-tests become more stringent. In Table 5, when y ¼ 0:75; theGini-coefficient on consumption, denoted Gini-C, remains constant at up to foursignificant digits, at 0.0691 in the benchmark case, and rises to 0.0725 when thebankruptcy option is eliminated altogether. Analogous results for consumptionoccur when y ¼ 0:85: In this case, Gini-C remains fixed at roughly 0.867 regardless ofTn; and rises to 0.0892 when the option is removed. On a more disaggregated level,observe that in the (BP) case, as means-tests become stricter, consumption of the top1%, and top 5%, denoted ‘‘Top 1%’’ and ‘‘Top 5%’’, respectively, both risemonotonically with Tn; whereas the fraction of consumption accounted for by the


Table3

Distributionalmeasuresforcons.ðy

¼0:75Þ

Tn

Gini-C

C.V.-C

Top1%

Top5%

Top10%

Top20%

Top40%

Bott.1%

Bott.5%

Bott.10%

Bott.20%

Bott.40%

00.0691

0.1219

1.24%

5.98%

11.77%

23.01%

44.56%

0.73%

3.82%

7.75%

16.12%

34.92%

0.90

0.0690

0.1217

1.24%

5.98%

11.77%

23.01%

44.56%

0.73%

3.81%

7.77%

16.13%

34.94%

0.95

0.0692

0.1220

1.24%

5.99%

11.78%

23.02%

44.56%

0.73%

3.81%

7.77%

16.12%

34.93%

0.99

0.0689

0.1220

1.25%

6.00%

11.78%

23.00%

44.95%

0.71%

3.76%

7.71%

16.10%

34.99%

NoBk.

0.0725

0.1305

1.30%

6.13%

11.93%

23.16%

44.61%

0.67%

3.49%

7.40%

15.86%

34.79%

Table4

Distributionalmeasuresforcons.ðy

¼0:85Þ

Tn

Gini-C

C.V.-C

Top1%

Top5%

Top10%

Top20%

Top40%

Bott.1%

Bott.5%

Bott.10%

Bott.20%

Bott.40%

00.0866

0.1515

1.27%

6.16%

12.15%

23.78%

45.90%

0.72%

3.70%

7.49%

14.40%

33.47%

0.90

0.0867

0.1516

1.27%

6.16%

12.15%

23.78%

45.90%

0.72%

3.70%

7.49%

14.40%

33.47%

0.95

0.0867

0.1516

1.27%

6.16%

12.15%

23.78%

45.90%

0.72%

3.70%

7.49%

14.40%

33.47%

0.99

0.0867

0.1516

1.27%

6.16%

12.15%

23.77%

45.90%

0.71%

3.69%

7.48%

14.39%

33.47%

NoBk.

0.0892

0.1578

1.30%

6.26%

12.25%

23.85%

45.86%

0.67%

3.39%

7.04%

15.00%

33.46%


Table5

Distributionalmeasuresforassetsðy

¼0:75Þ

Tn

Gini-A

C.V.-A

Top1%

Top5%

Top10%

Top20%

Top40%

Bott.1%

Bott.5%

Bott.10%

Bott.20%

Bott.40%

00.6600

1.174

4.54%

18.51%

32.86%

55.78%

87.06%

�1.40%

�4.90%

�7.41%

�9.23%

�4.13%

0.90

0.6610

1.175

4.54%

18.53%

32.88%

55.80%

87.09%

�1.42%

�4.91%

�7.43%

�9.26%

�4.17%

0.95

0.6670

1.188

4.60%

18.71%

33.16%

56.20%

87.58%

�1.43%

�5.02%

�7.63%

�9.59%

�4.62%

0.99

0.7377

1.320

5.19%

20.74%

36.33%

60.61%

92.66%

�1.47%

�5.70%

�9.08%

�12.27%

�8.92%

NoBk.

0.9837

1.792

6.95%

28.10%

48.09%

77.18%

110.90%

�1.50%

�7.34%

�13.14%

�20.74%

�23.85%

Table6

Distributionalmeasuresforassetsðy

¼0:85Þ

Tn

Gini-A

C.V.-A

Top1%

Top5%

Top10%

Top20%

Top40%

Bott.1%

Bott.5%

Bott.10%

Bott.20%

Bott.40%

00.7654

1.349

3.66%

16.38%

30.18%

52.99%

84.85%

�1.39%

�4.31%

�6.75%

�7.78%

�2.60%

0.90

0.7654

1.349

3.66%

16.37%

30.17%

52.95%

84.80%

�1.38%

�4.27%

�6.22%

�7.74%

�2.54%

0.95

0.7654

1.349

3.70%

16.48%

30.35%

53.27%

85.29%

�1.40%

�4.37%

�6.40%

�8.44%

�3.04%

0.99

0.7673

1.352

4.61%

19.81%

35.67%

61.21%

95.19%

�1.48%

�5.94%

�9.76%

�13.99%

�11.95%

NoBk.

1.0570

1.889

6.81%

27.38%

47.95%

79.20%

117.85%

�1.50%

�7.48%

�14.61%

�24.73%

�30.61%


relatively poor, especially the bottom 1%, denoted ‘‘Bott. 1%’’, falls from 0.73% to0.67% as Tn rises from 0 to the case where bankruptcy is prohibited. When y ¼ 0:85;the top of the distribution changes little, and the fraction of consumption accountedfor by the bottom 1% experiences a drop from 0.72 when Tn ¼ 0; to 0.67, whenbankruptcy is not allowed. This indicates that bankruptcy is performing a veryminor risk-sharing function in the economy.In the benchmark case, asset markets show increased concentration at the upper

quantiles as means-tests become more stringent, while in the (HP) case, they do not.The results are displayed in Tables 5 and 6.When y ¼ 0:75; the top 40% of the population hold 87.06% of all assets when

Tn ¼ 0; and hold 92.66% when Tn ¼ 0:99: Conversely, the bottom 40% increasetheir debts. In all of the cases displayed here, the asset distribution shows a level ofinequality that is quite high, with a wealth (i.e. asset) Gini, denoted Gini-A, ofapproximately 0.66 in the (BP) case, and 0.76 in the (HP) case. Both of thesemeasures are close to the observed U.S. wealth Gini of 0.78 (see Quadrini and Rios-Rull, 1997). This indicates that with empirically justified income shock persistence,stringent means-tests tend to concentrate wealth. Therefore, although it is inefficientoverall, lax bankruptcy law does appear to play a risk-sharing role. Thus far, asteady state general equilibrium perspective has been maintained. I turn now to twopartial equilibrium experiments.

3.1.5. Partial equilibrium

3.1.5.1. Fixed prices. In order to assess the role of general equilibrium price effects,the first experiment varies policies while holding interest rates fixed. Table 7 reportsthe differences between the general equilibrium and partial equilibrium welfareestimates, and also reports the aggregate bankruptcy rate for each case.As in all prior experiments, the welfare effects are generally small. As long as

bankruptcy is allowed, there are only small deviations between the generalequilibrium and partial equilibrium measures. For example, the welfare differenceis zero in the (HP) case when Tn ¼ 0:95:When equilibrium interest rates do change,the partial equilibrium measure will, of course, misstate welfare moresubstantially. In the (BP) case where the Tn ¼ 0:99; equilibrium rates fall from15% in the benchmark to 11.8%, while the deposit rate rises from 2.54%to 3.08%. Holding prices fixed involves understating the welfare gain by $80per-household annually. Additionally, partial equilibrium estimates overstate the fallin bankruptcy rate as well. In the (BP) case, when Tn ¼ 0:99; partial equilibriumfiling rates fall to 0.336% while general equilibrium estimates indicate a fall to0.436%.When bankruptcy is eliminated, prices change even more than before. Therefore,

partial equilibrium estimates grossly mismeasure the gains to eliminating bank-ruptcy. In the (BP) case, the deviation is 0.64%, or roughly $260 dollars annuallyper-capita. Similarly, in the (HP) case, the deviations are very small until bankruptcyis eliminated, with the partial equilibrium measure understating the gain by $340 per-capita.


3.1.5.2. Fixed assets. Turning now to a second partial equilibrium exercise, in Table8. I document the results from the experiment where a household with a given assetlevel is placed in a new economy defined by a proposed means-testing policy, wherethey face the equilibrium prices that would result from that policy. This will allow meto measure the welfare change arising from placing households who hold assets a

into a setting with a new policy and new equilibrium prices, relative to their utilityfrom being in the old economy.To proceed, let Ybench denote a benchmark mean-test policy, and let Ypolicy denote

a proposed policy. Next, let a denote assets and x�a denote all elements in the statespace other than assets, such as credit market status, income shock, etc. Associatedwith each policy are equilibrium stationary distributions, mn

bench and mnpolicy; and value

functions, Vbenchða;x�aÞ and Vpolicyða;x�aÞ: Given these items, I compute welfare ineach case as before. Let Lbench denote benchmark welfare, and let Lpolicy

partial denotewelfare under a proposed policy, given the benchmark distribution. That is: Lbench ¼R

Vbenchða; x�aÞ dmnbench and Lpolicy

partial ¼R

Vpolicyða;x�aÞ dmnbench:

This implies, as in (15), that the equivalent variation implied by a move from thebenchmark environment to the policy, holding assets fixed, is given by

x ¼Lpolicypartial þ 1=ð1� aÞð1� bÞ

Lbench þ 1=ð1� aÞð1� bÞ

!1=ð1�aÞ

�1: ð16Þ

In Table 8, the most noticeable results are for the cases under the benchmark incomeprocess. If households were moved, with their benchmark asset holding into themeans-testing policy defined by either Tn ¼ 0:95; or 0.99, we see that welfare fallssharply. In the former case, welfare falls by a full 1.08%, completely negating thesteady-state gains available. In the latter case, fixed assets do not matter for welfare.The intuition is straightforward. Households have accumulated savings, and more

importantly, debt, that reflects benchmark bankruptcy law. However, they are nowin a setting where some will no longer qualify for bankruptcy, but must insteadservice their debts, for at least a full model period. Additionally, when Tn ¼ 0:95;

Table 7

Partial equilibrium: fixed interest rates

Tn ¼ 0:95 Tn ¼ 0:99 No Bk.

Low ðy ¼ 0:75Þ �$5, P ¼ 0:471% �$80, P ¼ 0:356% �$260High ðy ¼ 0:85Þ $0, P ¼ 0:500% $0, P ¼ 0:493% �$340

Table 8

Partial equilibrium: fixed assets

Tn ¼ 0:95 Tn ¼ 0:99

Low ðy ¼ 0:75Þ �$400 �$32High ðy ¼ 0:85Þ $0 $0


interest rates do not change substantially in the move from Tn ¼ 0 (rl falls from15.0% to 14.7%). Therefore, households do not benefit much from the newequilibrium prices. This intuition then helps demonstrate why, in the experimentmoving agents from the benchmark to Tn ¼ 0:99; the welfare loss is zero. In thiscase, interest rates on loans do fall substantially, from 15% to 11.8%, therebyoffsetting the impact of strict means-testing, especially for those households who willno longer qualify for bankruptcy in the current period. The impact of changing assetdistribution is less interesting for the (HP) case, as is quickly seen in bottom row ofTable 8. In this case, dbk is close to the borrowing limit and, like interest rates, do notvary with means-tests. Therefore, welfare remains constant.This experiment indicates that under benchmark income persistence, a sudden

transition to strict means-testing policy may create nontrivial welfare loss. Themodel therefore sheds some light on why so many consumer groups and legalscholars have chosen to vehemently oppose stringent means-tests. Further research isrequired on this point, but the preliminary results indicate that care must be taken inthe transition to new, stricter, bankruptcy law. There is, however, a mitigatingfactor. If income processes are more highly persistent than the benchmark, then thetransition losses will not be great, as nearly all filers will be at the borrowing limitregardless of means-testing policy.

4. Summary and conclusions

In this paper I developed the first dynamic, stochastic general equilibrium modelof means-testing in personal bankruptcy. The model allowed me to study the effectsof income variability, risk aversion, bankruptcy law, and consumer welfaresimultaneously. The results here imply that under current law, the bankruptcyoption reduces welfare. In particular, making the law much more strict than it isnow, leads to only modest welfare changes, as long as default is still allowed undersome circumstances. What is very interesting, and surprising, though, is how muchdamage even a strict bankruptcy law can do. That is, when default is completelyprohibited, welfare improves markedly, on the order of 1% of consumption,depending on the credit limit and the persistence of income. The key tounderstanding the findings presented here is that households can smooth wellenough without bankruptcy in this environment such that ex post bankruptcypenalties must be rather large in order to match observed filing rates. These penaltiesdo not transfer resources, and therefore induce deadweight loss. Thus, even thoughonly a small set of households file, average welfare falls. Justifying bankruptcyprotection, given the harshness of existing penalties, requires demonstrating thatexisting market incompleteness matters much more than is implied by existingevidence on income risk and credit market access.Despite the large welfare gains arising from eliminating bankruptcy, the model

may actually understate how beneficial in the steady state it may be to eliminatedefault. First, in a world with no default, private insurance mechanisms may becomemore prevalent. For example, it is known from the work of Kreuger and Perri


(1999), and Attanasio and Rios-Rull (1999) that the existence of public insurance candestroy private insurance arrangements. I have ignored here the role of lax defaultlaw in destroying private familial insurance. Additionally, note that even though Idid not include cases involving catastrophic health shocks in this model, allowingbankruptcy in these cases still involves non-trivial resource costs and generates allthe deadweight loss that a bankruptcy due to income interruption does. Therefore,while health shock driven bankruptcies are not accounted for here, it is by no meansself-evident that the bankruptcy system should be used to deliver to ‘‘last-resort’’health insurance to the general public.Despite the preceding steady-state implications, the experiments indicate that a

sudden transition to strict means-testing policy may engender serious welfare loss.The model therefore sheds some light on why so many consumer groups and legalscholars have chosen to vehemently oppose stringent means-tests. There is, however,a mitigating factor. It is found here that if income processes are highly persistent,then the transition losses will not be great, as nearly all filers will be at the borrowinglimit regardless of bankruptcy policy.Finally, the results here indicate that bankruptcy cannot be defended as

unequivocally desirable for reasons of equity. The reason is that, even if we were(only) concerned about a subset of U.S. households who hold little or no collateral,the interest rate and deadweight costs of bankruptcy and bankruptcy penalties willhurt them even more than a wider cross-section of society. For example, wealthierhouseholds will and do currently use secured lending of various types to smoothconsumption of goods and services. These households are not affected directly byincreases in unsecured lending rates. Rather than having the interest rate costs ofdefault spread over a large population, the smaller subset of ‘‘poor’’ households willthen pay for all default. In this sense, the model developed here is representative ofthe section of American households who rely on unsecured debt to smoothconsumption, as it restricts attention to unsecured credit and no collateral.Therefore, the welfare implications reported here directly challenge those who insistthat equity considerations alone justify lax bankruptcy law.

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Welfare implications of the Bankruptcy Reform Act of 1999