Personal Bankruptcy and Incentives in aDynamic Model of Entrepreneurship 1

Ronel Elul2 and Piero Gottardi3

October 2002Highly Preliminary — Do not Circulate

Abstract

We develop a model of personal bankruptcy and debt overhang. Inour model an entrepreneur must repeatedly borrow in order to financea sequence of risky projects under conditions of moral hazard whichlimit the possibility of being financed. We assume that only short-termcontracts can be written; the role of the bankruptcy code in this modelis thus to provide a long-term element to these contracts. This codedictates the degree to which debts are discharged, or equivalently, thedebt overhang. While too generous a discharge makes it difficult foragents to obtain financing, having too little can interfere with futureincentives. Furthermore, the code allows us to endogenize exclusionfrom future credit-markets without requiring it be written explicitlyinto contracts.

The key result of the paper is to provide a characterization of theoptimal bankruptcy code as a function of individual characteristicsand the parameters of the economy. We then apply this characteriza-tion to obtain some insight into cross-country differences in personalbankruptcy codes, particularly between Europe and the U.S.

1The authors thank Franklin Allen, Leonardo Felli, Armando Gomes, Gary Gorton,Bengt Holmstrom, Ronen Israel, Tom Krebs, Nicholas Souleles, Paul Willen, and semi-nar participants at Accounting and Finance in Tel Aviv, Ben-Gurion University, Brown,ESSFM (Gerzensee), EUI, FRB, Hebrew University, Iowa State, Penn, Stanford (SITE),Stony Brook and York University.

2Finance Department, Wharton School, University of Pennsylvania, Philadelphia, PA19104, USA. E-mail: ronel@elul.org.

3Dipartimento di Scienze Economiche, Universita Ca’ Foscari di Venezia, FondamentaSan Giobbe, Cannaregio 873, 30121 Venezia, Italy. Email: gottardi@unive.it. Tel: +39-041-234 9192. Fax: +39-041-234 9176/7.

I Introduction

One of the foundations of the U.S. personal bankruptcy system is the ideaof the “Fresh Start”. Personal bankruptcy in the U.S. is characterized bya discharge of all debts which cannot be met either immediately, after aliquidation of the debtor’s nonexempt assets (for a chapter-7 bankruptcy) orunder the auspices of a 3–5 year payment plan (chapter-13)1

By contrast, most European countries traditionally did not permit sucha broad-based discharge. In fact, until the late 1980’s, the only Europeancountries who even had consumer bankruptcy laws on their books were theUnited Kingdom and Denmark,2 and only in the British law was there aprovision for discharge of debts.3 In France, for example, consumers hadno possibility of any sort of debt relief until a new Act went into force in1990; moreover this new law does not even provide for the discharge of debts.Similarly, until the German reforms went into effect in 1999, debtors remainedliable for unpaid debts for thirty years. Details of these and other countries’laws can be found in Huls (1992), Niemi-Kiesilainen (1997), Alexopoulosand Domowitz (1998) and Fletcher (1999). The 1990’s saw the reform ofbankruptcy laws in many of these countries (Germany’s came into force in1999). Even after these reforms, however, the U.S. laws remain far morefavorable to debtors in general, and to the discharge of debts in particular.

The goal of this paper is to develop a model of the discharge of debts inbankruptcy and to use this model to gain some insight into the internationaldifferences in these bankruptcy laws. The key insight of our model is thata bankruptcy code which governs the extent to which debts are discharged(or, conversely, the debt overhang) represents a tradeoff between current andfuture incentives. Too generous a discharge makes it difficult for agents toobtain financing today; having too little can interfere with future incentives.We are not the first in recognizing this tradeoff, of course. In particular, ithas played an important role in the development of U.S. bankruptcy law, assuggested by the following statement (on the Bankruptcy Act of 1898) bythe U.S. Supreme Court in Local Loan v. Hunt (1934).

1The debtor may choose the chapter of filing and in fact 70% opt for chapter 7. Thefigure is even higher if one takes into account the fact that half of all chapter 13 plans failand subsequently “convert” to chapter 7.

2See also Niemi-Kiesilainen (1997).3This provision was in any case rarely used before its revision in 1987, because of its

stringent requirements — see Niemi-Kiesilainen (1997).

2

“The Act gives to the honest but unfortunate debtor ... a newopportunity in life and a clear field for future effort, unhamperedby the pressure and discouragement of pre-existing debts.”

In our model of personal bankruptcy and debt overhang an entrepreneurmust repeatedly borrow in order to finance a sequence of risky projects;moral hazard is present, which limits the funds which lenders are willing tooffer. We assume that the only avenue open to agents for enforcing long-term contracts is the bankruptcy code. This code dictates the degree towhich debts are discharged, or conversely, the debt overhang. While toogenerous a discharge makes it difficult for agents to obtain financing, havingtoo little can interfere with future incentives. We should also point out thatthe distinguishing factor which makes this a model of personal bankruptcy isthat the legal code can dictate claims to any projects the entrepreneur mightundertake in the future, as well as to his nonentrepreneurial income.

We derive the optimal level of discharge in our model as a function ofthe parameters of the economy and individual’s characteristics. We thenuse the model to try to gain some insight into why differences exist betweenU.S. and European bankruptcy laws and also why they have diminished inrecent years. The approach we take is to view these observed differencesin personal bankruptcy laws as an optimal response to differences in othereconomic factors which impinge on incentives. In particular, we suggest thatthe more generous social insurance policies in place in Europe interfere withincentives and aggravate the moral-hazard problem faced by entrepreneurs infinancing their investment — stricter bankruptcy laws offer a way to restoreincentives and thereby mitigate these incentive problems. Our model willalso shed light on why the European tax and welfare reforms which havetaken place in the past two decades have also been contemporaneous withan “Americanization” of the bankruptcy code.

We should begin by pointing out that this approach stands in contrast tothose who prefer to take differences in legal codes as given (by longstandinghistorical precedent) and instead explore the economic implications of thesedifferences; see La Porta, Lopez-de-Silanes, Shleifer and Vishny (1998) andalso Franks and Sussman (1999). It is certainly the case that the U.S. hasa long history as a debtor’s haven, and even within America, the West hastraditionally treated bankruptcy more leniently. Furthermore, it is also thefact that the roots of the bankruptcy discharge are in late 17th-early 18th

3

century English Law (Defoe was an early proponent)4 — and it is still thecase that the English and Canadian systems are closest to that of the UnitedStates, although of course they continue to treat debtors more harshly. Butwe feel that it is still important to understand the economic determinants ofthese laws; since they have such a strong impact on financial contracting itis somewhat extreme to assume that there is no feedback from the economicenvironment back onto the legal system. Furthermore, our approach alsoallows us to understand the more recent evolution of bankruptcy codes and,in particular, why the European codes have converged towards the Americanmodel in recent years.

It is interesting to compare our results, which suggest the optimalityof full discharge of debts when incentives are sufficiently strong, with theconclusions of other work. Both Wang and White (2000) and Adler, Polakand Schwartz (2000) propose that any discharge of debt is suboptimal, unlessthere is an insurance motive due to borrowers’ risk aversion. The reason forthis, however, is that their models allow for only a single investment, andso there is no question of debt overhang impacting on future investmentdecisions. By contrast, this tradeoff between current and future incentives isa key feature of our model and, as we argued above, of the legal debate aswell.

The efficiency of debt overhang is also explored by the literature on inter-national debt reduction. The paper which is perhaps closest to ours, in thatit is concerned with the long-term effect of a debt overhang, is Fernandez-Ruiz (1996).5 In contrast to our work, however, the focus of this literature ismore ex-post,6 in that it typically begins with the existence of a debt largerthan the country’s repayment capability and investigates the policy whichmaximizes the repayment to the lenders.

Two other interesting papers which also focus on the ex-post effects offorgiving a debt overhang (and like us in the context of the design of le-gal institutions) are Bolton and Rosenthal (1999), who model the politicaleconomy of debt moratoria and bailouts, and Kroszner (1999), who brings ahistorical example of a beneficial repudiation.

The focus of this paper is the effect of bankruptcy laws on investment. Wethus have in mind a world of small entrepreneurs (or potential entrepreneurs)

4See McCoid (1996)5See also the references cited therein.6As opposed to ex-ante in our paper.

4

who finance their business ventures with loans for which they are person-ally liable; this is also the setting of Alexopoulos and Domowitz (1998) andmany others. Data from the 1993 National Survey of Small Business Finance(NSSBF) suggests that a significant proportion (over one half) of U.S. smallbusinesses do indeed finance themselves with some sort of personal loan orguarantee; similar evidence is found by Franks and Sussman (2000) for theU.K. These entrepreneurs are also three times as likely to file for personalbankruptcy as their counterparts in the general population, and constitute20% of all filers — see Sullivan, Warren and Westbrook (1989).7 In such asetting we are then naturally led to explore the incentive effects of bankruptcylaws; this seems to be where the greatest economic impact should be foundand also the most fertile field for explaining cross–jurisdictional differences.Another approach, however, might be to focus on the risk-sharing and redis-tributive impact of these laws on consumers; see for example Athreya (2001),Chatterjee, Corbae, Nakajima, and Rios-Rull (2000) and also Lehnert andMaki (2002).

The bankruptcy code plays a role in our model because we assumedthat agents cannot privately enforce long-term commitments, which maybe needed for agents to obtain financing. This paper is thus related to theliterature on long-term contracts in a repeated principal-agent setting (albeitin a very particular way), for example Allen (1985), Chiappori et al (1994)and Fudenberg, Holmstrom and Milgrom (1990).

In our model bankruptcy is costly because of the effect that debt over-hang has on future investment opportunities. A different approach is takenby some of the earlier literature — beginning with Dubey, Geanakoplos andShubik (1989) — which introduces a utility penalty for defaulting. Dubey,Geanakoplos and Shubik (1989) then argue that there is a role for defaultin spanning incomplete securities markets and thus it should be penalizedneither too harshly nor leniently. Using a similar notion of utility penalties,Rampini (1998) considers an economy with asymmetric information and ex-plores the role default penalties play in the optimal contract by facilitatingseparation of types.8

Another approach, first taken by Allen (1981), is to penalize default bythe denial of credit, without reference to borrowers’ ability to repay (see also

7The effect of state exemptions on an entrepreneur’s likelihood of being denied entryinto this market is studied empirically by Berkowitz and White (1999).

8See also Santos and Scheinkman (1998).

5

Kehoe and Levine (1993)). Our approach is different, in that borrowers areonly denied credit when their incentives are so bad that they will not repay;we choose this because we believe that having a competitive credit marketmakes it more difficult to enforce arbitrary denial of credit.

This paper is also related to the literature on corporate bankruptcy. Theclosest work is that of Berkovitch and Israel (1999), who derive optimalbankruptcy laws as a function of a country’s financial system (e.g. undevel-oped, bank-based, or reliant on security markets). This approach – of basinga difference in bankruptcy laws on some other divergence in the economicsystems which is taken as exogenous – parallels ours.

Finally, we have yet to justify the need for a bankruptcy code — ratherthan simply having private contracts to specify payments in all contingencies.We take the simplest approach to this problem — appealing to the notionthat borrowers find it difficult to commit returns from future projects topay off current loans and so must rely on a government-enforced bankruptcylaw. Another approach is that of Aghion and Hermalin (1990), who showhow agents might refrain from proposing bankruptcy clauses when borrowingfor fear sending a bad signal, and thereby leave themselves underinsured; agovernment-mandated bankruptcy law can thus enhance welfare.9 Otherexplanations which have been proposed focus on the role that a (lenient)bankruptcy law can have in forcing lenders to internalize the full impactof project default. For example, Manove, Padilla and Pagano (1999) arguethat laws which provide strong protection for creditors in bankruptcy mightmake banks too “lazy” in screening projects. Posner and Hynes (1999) alsotouch on a somewhat similar idea, suggesting that too strict a code leads tohigher bankruptcy rates (since lenders have little incentive to take care inwhom they lend to) and hence imposes a burden on the social welfare system,which must support these bankrupt individuals.

The plan of the paper is as follows. We first discuss the empirical ev-idence which motivates and supports our investigation. Next, we presentour model of default, discharge and investment. In section IV we derive theoptimal contract for a single agent in such a setting and ins section VII showthat it indeed has the property that increasing the tax rate leads to lessdischarge. We also demonstrate that the average level of entrepreneurshipis lower in a “European” system, not because taxes hurt incentives directly— since the entrepreneurs are always financed — but rather because the

9See also Rea (1984).

6

stricter bankrupty laws which are needed to finance agents in a high-taxenvironment also shorten agents’ entrepreneurial tenure. This is consistentwith recent studies which have found that the level of entrepreneurship inthe U.S. is over three times that in Germany and France, and twice that ofthe U.K. (see Reynolds, Hay and Camp (1999)).

Finally, in the appendix we present evidence on the differences in bankruptcylaws across U.S. states and use this to motivate a model of bankruptcy ex-emptions which also exhibits a correlation between taxes and the “toughness”of the bankruptcy code.

II Empirical Underpinnings

In this section we present some empirical evidence which motivates and sup-ports our basic model.

We first begin by documenting several facts concerning European bankruptcylaws. Our primary focus will be the Northern European countries, becausethe similarities between these countries. By contrast, the economic systemsof the Southern European countries, especially with regard to taxation, differenough to make comparisons with the other European countries difficult.

Firstly, as we have already pointed out, the discharge of debts has beena central feature of American personal bankruptcy law since its inception.By contrast, European countries have adopted such laws only rather recentlyand much more modestly. The first to do so was Denmark, which enacteda new bankruptcy code in 1984 permitting discharge of consumer debts incases where the debtor was “hopeless indebted”.10. The next was the UnitedKingdom, which in the Insolvency Act of 1986 removed the social and eco-nomic barriers which had prevented most bankrupts from taking advantageof provisions for debt discharge which were already extant. The 1990’s sawan increase in the number of countries enacting laws with provisions forconsumer debt discharge. In 1993-94 discharge of consumer debts was intro-duced in Austria, Finland, Norway, and Sweden. In 1994 Germany enacteda consumer bankruptcy code which finally came into force in 1999.11 Yetthese laws continue to remain quite a bit tougher than the U.S. bankruptcycode: they generally require repayment out of income, give courts and cred-

10See Graver (1997).11See Grossman (1996) and European Commission (1995) for details of these new

statutes.

7

itors more power in vetoing a discharge, and place strict limits on repeatdischarges (or prohibit them altogether).

There are, however, several Northern European countries which have notadopted such provisions. The most notable is France, which only allows fordischarge of mortgages in excess of the proceeds from the sale of the home.In addition, Belgium, the Netherlands and Luxembourg all have drafts ofproposed legislation (with varying provisions for discharge), but have yet toadopt them. The Southern European countries (Greece, Italy, Spain andPortugal), tend to either have no personal bankruptcy law whatsoever, orwhen they do have a law (in the case of Portugal), have no provision for debtdischarge.

III The Model (Incomplete)

A Introduction

We consider an economy with an infinitely-lived agents and a single consump-tion good. An agent have identical risk-neutral preferences and discounts thefuture at a rate β < 1, and is restricted to non-negative consumption in everyperiod. In every period, the agent is endowed with one project. This projecthas a fixed scale and requires one unit of the consumption good as input inthe beginning of the period in order to be operated; at the end of this sameperiod the project yields either R > 0 units in case of success or 0 in the caseof failure. The probability of success is endogenous in that it depends on theagent’s effort level: it is πh if the agent exerts high effort and πl if low effortis exerted. High effort is costly, however; to simplify the notation we assumethat this cost appears as a leisure benefit c ∈ �+ accruing to the agent whenlow effort is exerted.

Project outcomes are independently and identically distributed over time.Agents have no resources of their own and the commodity is assumed to

be nonstorable; thus an agent needs to obtain one unit of external financingin each period in order to operate the project. We make this assumption inorder to focus attention on the impact of the bankruptcy code on incentives;were the agent able to store a sufficient amount of his output, he could self-finance and thereby avoid all incentives problems associated with externalfinancing.

We assume that agents seek this financing on a competitive market in

8

which the expected one-period gross interest rate is exogenously given andequals one, so that the total expected repayment per unit of financing mustbe precisely 1.

We consider the case where the parameter values are such that the projectis viable if and only if high effort is exerted, i.e. we assume:

Assumption 1: πh > 1/R > πl.In addition, we assume that the level of effort actually exerted is not

observable, so that external financing takes place under conditions of moralhazard and thus can only be obtained if an incentive compatibility condi-tion, ensuring that the agent will choose to exert high effort, is also satisfied.Clearly, the incentive problem will be most severe, and financing most diffi-cult to obtain, the higher the effort cost c, and agents with high costs c maynot be able to obtain any financing at all in the presence of such moral haz-ard. Were the agents’ effort levels observable, or more precisely contractible,then such problem would not exist, since the repayment could be made con-tingent on an agent’s effort, and all agents would be able to obtain financingin every period. On the other hand, we assume here that lenders can observethe cost c, so that there is no adverse selection.

If at any point an agent is unable to obtain financing at all future dates(because the moral hazard problem he faces is too severe) then we assumethat he leaves the entrepreneurial market and accrues L ∈ (0,∞). This maybe thought of as the present value of his income from working at some otherjob which is not subject to moral hazard; alternatively this may be viewedas the liqudiation value of his entrepreneural assets and indeed we will referto this event loosely as “liquidation”. We will see below that having somepositive future income L > 0 which is not subject to moral hazard and whichmay pledged as part of a personal guarantee is critical for enabling agents toimprove their incentives (and thereby obtain some financing) by using debtcontracts with long-term features.

We will restrict attention to the case in which entrepreneurship is prefer-able to liquidation — this may be viewed as an entrepreneurial participationconstraint.

More formally, we have:Assumption 2: L < πhR−1

1−β

Note that this is equivalent to assuming that the expected utility gainedby being financed for one more period is higher than that lost by the depre-ciation this would induce in the present value of L. Also note that the leisure

9

benefit c is absent from this expression, because we are assuming that it onlyaccrues if the agent is engaged in entrepreneurial activity while exerting loweffort — this assumption be relaxed without affecting any of our results andit is maintained only to simplify the notation.

Although we have assumed that the project has a negative NPV when loweffort is exerted, it is also useful to exclude the uninteresting case where loweffort nevertheless yields the agent higher utility than the non-entrepreneurialactivity (due to a high disutility of effort). That is, we also assume:

Assumption 3: L > c+(πlR−1)1−β

for each c in question.Lastly, note that this discussion assumes that once an agent leaves the

entrepreneurial market he cannot return; however, we later show that ourresults are in fact robust to temporary exclusion.

B Contracts and Codes

The structure of the contracts whereby an agent obtains financing is as fol-lows. Contracts can take the form of either equity or debt, but we assume thatprivate long-term contracts, which make explicit claims on future projects orwealth, cannot be enforced. So the agent can choose to finance his currentproject by issuing equity on this project, thus promising to repay a fraction ofthe project’s payoff at the end of the period. Alternatively, he can issue one-period debt, which promises to repay a fixed amount next period. Of course,if this project fails then he will be unable to repay anything and will haveto default on his debt and file for bankruptcy. In this event, the bankruptcycode specifies the extent to which this debt is discharged in bankruptcy, andhence the payments which the agent will have to make in the future as aconsequence of his current default.

In our model, then, the principal role of the bankruptcy code is to intro-duce a government-enforced long-term feature which would otherwise be ab-sent in purely private contracts. As we will see, such long-term features maybe needed to overcome the moral hazard problem and ensure that the agentcan obtain outside financing (i.e. that high effort is incentive-compatible).In particular, while agents with a lower value of c (the “better types”) canensure an expected return of one to lenders with single-period contracts, thesame is not true for the agents with high c (the “worse” types). Hence whilethe former may obtain financing by issuing one-period equity (and therebycompletely circumventing the bankruptcy process), the other agents can onlybe financed with debt — and, as we will see, only if this debt has a sufficiently

10

long-term character (or, in our context, if the bankruptcy code prescribes asufficiently low level of discharge).

The reason why we view this model as one of personal bankruptcy is thatthese long-term claims induced by the bankruptcy code are on the agent’sfuture projects as well as his non-entrepreneurial income; as such they aremeant to be seen as representative of the “personal guarantees” which havebeen found to be used by the majority of small businesses.

Although a “strict” bankruptcy code can enhance incentives and mayallow “worse” types to obtain some financing by postponing some paymentsto the future, the cost of this is that incentives in the future may be weakenedby this “debt overhang”, as the agent’s required payments out of futureproject revenues will be larger. As a consequence, the net effect on incentivesdepends on the interplay between the positive effect of future payments onaccount of failure in the current period, and the negative effect of paymentswhich must be made on account of past failures (the “debt overhang”). Sincethe latter increases as failures accumulate over time, we will see that agentswho must resort to debt contracts in order to finance their projects will onlybe able to obtain financing up to a finite number of failures.

The bankruptcy code will be formally identified by the payments whichthe agent is mandated to make out of his future income after he files forbankruptcy, which determine the extent of the discharge he is granted. Agentsmay file for bankruptcy many times,12 and thus the required payments mustbe made contingent on the number of times the agent has defaulted in thepast, as well as on the current period.

IV Optimal Bankruptcy Codes

In this section we derive the optimal bankruptcy code for an agent as afunction of the parameters of the model and the agent’s characteristics. Thiswill be the code which maximizes the agent’s discounted expected utility,subject to incentive-compatibility and feasibility (nonegativity) constraints.

12While many countries restrict such “serial filing” (for example, in the U.S. a Chapter-7discharge may be obtained only once every seven years, in the U.K. the interval is 15 years,and in Norway it is a once-in-a-lifetime opportunity — see Alexopoulos and Domowitz)we will show that in our context (in which agents cannot completely eliminate the risk offailure) the optimal code may well dictate allowing agents to file more than once.

11

A Full Discharge

We begin with the simplest case — contracts which have no long-term fea-tures. As mentioned, these can be viewed as short-term equity contracts or,alternatively, debt contracts in an environment in which all unpaid liabili-ties are discharged in bankruptcy. We view the latter characteristic as thebankruptcy code; this is determined by the government.

Given this code, at each stage the agent must decide the the level of effort(high or low) which he exerts. Conversely, the lenders must decide whetheror not to lend to the agent. Since the project is only viable when high effort isexerted, this leads to an incentive-compatibility constraint which this agentmust satisfy in order to obtain financing. In particular, it must be the casethat an agent’s utility from high effort exceeds that accruing to low effort.

Since their contracts are completely static, in each period they must repaythe funds used to finance that investment solely out of the proceeds of thatperiod’s investment (if successful) — that is, they pay r = 1/πh in case ofsuccess in each period.

So if we let uS denote the continuation utility which the agent receives(next period) in case this current project succeeds, and uF that followingfrom failure of the current project, then the incentive compatibility conditionensuring high effort in the current period must be:

πl(R − r) + πlβuS + (1 − πl)βuF + c ≤ πh(R − r) + πhβuS + (1 − πh)βuF

orc ≤ (πh − πl)

[R − 1/πh + β(uS − uF )

].

Given the stationary nature of this bankruptcy code, it is natural to focusattention on stationary equilibria — that is equilibria in which the agent istreated the same whether or not his project fails. In particular, we considerthe equilibrium in which the agent is financed forever whether or not hisproject succeeds. Such an equilibrium, if it exists, will clearly be optimal.

In this case uS = uF and the incentive compatibility constraint becomes

c ≤ (πh − πl) [R − 1/πh] . (1)

We term the agents who satisfy this condition, and hence can be financedforever with purely short-term contracts, the natural-born entrepreneurs.

12

Notice that the agent receives R− 1/πh every period; this is always non-negative when incentive compatibility is satisfied, and so this code is alsofeasible.

B General Case

Those agents who do not satisfy this condition may nevertheless be able toobtain some financing if they are able to rely on the bankruptcy code tointroduce some long-term features to their contract. We now consider thisextension.

V The Optimal Code

A Introduction

Let σt ∈ Σt (t = 1, 2, . . .) denote a particular realization of the exogenousproject uncertainty up through time t (for example, a string of t consecutivefailures). Given any node σt, it is also useful to introduce notation to rep-resent the two immediate successors of this node: σS

t if the agent’s projectsucceeds in this period, and σF

t if it fails; both of these are elements of Σt+1.A bankruptcy code δ is an assignment of debt overhang to every possible

history; that is, a mapping δ : Σ∞ → R∞+ . When this can be done without

confusion, we write δt ≡ δ(σt). As above, it will also be convenient tointroduce the following notation for next period’s debt overhang: δS

t ≡ δ(σSt )

and δFt ≡ δ(σF

t ) for the debt overhang in the next period, following thesuccess and failure, respectively, of the current period’s project. It is notdifficult to see that writing the code in this manner also in effect specifieshow much of an agent’s debt — whether incurred on account of past failuresor the current one — has been forgiven, and how much he is required to payin the future. As such, it also determines how much an agent must pay fromhis current earnings.

For a given bankruptcy code, the entrepreneur must decide on the level ofeffort he will extert in any given period. Since the project is only viable underhigh effort, this will lead to incentive compatibility condition which must besatisfied by the code in order for the agent to obtain financing. In addition,the code must also be feasible in the sense that it leaves the entrepreneur withnon-negative wealth in every period. On the other hand, the lenders must

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decide whether or not they wish to offer financing in a given node, conditionalon both the bankruptcy code and on the behavior they anticipate from theentrepreneur.

Now, if the agent begins period t with debt overhang δ(σt), and if the debtoverhang he inherits in the two successors of this node are δ(σS

t ) and δ(σFt )

in case of success and failure, respectively, then the amount of inherited debtoverhang which is not postponed to the future (and hence must be paid-offfrom the current project) is simply

δ(σt) − β[πhδ(σ

St ) + (1 − πh)δ(σ

Ft )

].

To this we must also add the repayment for the loan financing this period’sproject, which must have an expected present value of 1, so the value ofliabilities which must be repaid in this period — in expected terms — is

1 + δ(σt) − β[πhδ(σ

St ) + (1 − πh)δ(σ

Ft )

].

Now, the entrepreneur can make a payment in this period only when hesucceeds, which occurs with probability πh (since he will obtain financingtoday only when it is certain that he puts in high effort).

As a result, the code implies that his total payment in case of success is:

1/πh + δ(σt)/πh − β[δ(σS

t ) +1 − πh

πhδ(σF

t )].

So when the project succeeds, the agent actually receives (net of all re-payments)

R − 1/πh − δ(σt)/πh + βδ(σSt ) +

1 − πh

πhβδ(σF

t ).

Therefore, given a bankruptcy code δ, and the lender’s decisions F , theexpected continuation utility u(σt) conditional on being in state σt can bespecified recursively as:

u(σt) = F(σt){πh

[R − 1/πh − δ(σt)/πh + βδ(σS

t ) +1 − πh

πhβδ(σF

t )]

+ πhβu(σSt ) + (1 − πh)βu(σF

t )}

14

+(1 − F(σt))(1 − β)[L − δ(σt)],

where we have simplified this expression by making use of the fact thatthe agent will only be financed when it is known that he will exert higheffort today. The last term in the above expression is the one-period non-entrepreneurial utility; we will show below that the optimal code does notrequire temporary exclusion from financing, but only permanent.

It is now easy to derive the incentive compatibility and feasibility cond-tions which the code must satisfy.

First of all, feasibility is the requirement that the utility received bythe entrepreneur be non-negative in every state. When the entrepreneur isfinanced, this is simply the requirement that the return from the project, netof all repayments, be non-negative, or that:

0 ≤ R − 1/πh − δ(σt)/πh + βδ(σSt ) +

1 − πh

πhβδ(σF

t )

When he is not financed, then he accrues non-entrepreneurial wealth L; forthe code to be feasible in this case we must have δ(σt) ≤ L.

Next we have incentive compatibility. Since the agent’s utility when higheffort is exerted is

πh

[R − 1/πh − δ(σt)/πh + βδ(σS

t ) +1 − πh

πhβδ(σF

t ) + βu(σSt )

]+(1−πh)

[0 + βu(σF

t )],

and low effort yields

c+πl

[R − 1/πh − δ(σt)/πh + βδ(σS

t ) +1 − πh

πh

βδ(σFt ) + βu(σS

t )]+(1−πl)

[0 + βu(σF

t )],

the following must hold whenever the agent is financed:

c ≤ (πh−πl){R − 1/πh − δ(σt)/πh + βδ(σS

t ) +1 − πh

πhβδ(σF

t ) + β[u(σS

t ) − u(σFt )

]}

More formally, the optimal code is the one which maximizes the expectedutility at time 0, subject to the following constraints:

• 0 ≤ δ(σt) ≤ πhR−11−β

for all σt (the upper bound requires δ(σt) to be lessthan the total lifetime resources accruing to an agent who is financedforever — this restriction will not bind at the optimum and is onlyincluded to ensure compactness)

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• Feasibility (F):

– 0 ≤ F(σt)[R − 1/πh − δ(σt)/πh + βδ(σS

t ) + 1−πh

πhβδ(σF

t )]

for allσt

– 0 ≤ (1 −F(σt))[L − δ(σt)] for all σt

Feasibility is simply the requirement that the agent cannot pay morethan his total resources in any period.

• Incentive Compatibility (IC):

– 0 ≤ F(σt)(−c + (πh − πl)

{[R − 1/πh − δ(σt) + βδ(σS

t ) + 1−πh

πhβδ(σF

t )]

+

β[u(σS

t ) − u(σFt )

]})for all σt

As above, incentive compatibility is the requirement that high effort yieldmore utility than low for the entrepreneur whenever he is financed.

B Results

We get the following characterization of the agents’ optimal code:Proposition: The optimal code has the following characteristics:

1. Natural-Born Entrepreneurs: If c ≤ cN ≡ (πh−πl)(R−1/πh), then theagent can be financed forever without accumulating any debt overhang(δ(σt) = 0 ∀σt, t).

2. Pariahs: If c > cP ≡ πh−πl

1−πhβ

[R − 1/πh + (1−πh)β

πhL

]then the agent can-

not be financed at all.

3. Potential Entrepreneurs: An agent who falls in this region can be fi-nanced for a finite number of consecutive failures. Moreover, his op-timal code is characterized by setting δS(δ) = 0 ∀δ (full repayment ofall liabilities in case of success) and determining δF (δ) by satisfying ICwith equality, until we reach the final feasibility condition δ = L.

16

C Proof

We first point out that the characterization of the natural-born entrepreneursfollows directly from our determination of those agents who can be financedwith static contracts.

To demonstrate the remainder of the characterization we derive the fol-lowing properties of the optimal contract.

As far as the pariahs, we will show that they can be bounded below byfinding the marginal agent for whom the IC constraint given δ = 0 wouldbe binding when he can be financed for precisely one failure. So what prin-cipally remains to be demonstrated is our characterization of the potentialentrepreneurs. The following results will ultimately give us our characteriza-tion.

Consider a generalization of the utility-maximization problem describedabove. Suppose that at time 0 the agent begins with debt δ(0) = δ. Thedesigner of the code would like to maximize

u(0) = πhR−1−δ(0)+πhβδS(0)+(1−πh)βδF (0)+πhβu(σS(0))+(1−πh)βu(σF (0))

= −δ(0) + πhR − 1 + πhβ[u(σS(0)) + δS(0)] + (1 − πh)β[u(σF (0)) + δF (0)]

subject to the incentive-compatibility and feasibility constraints.Consider the set U which is defined to be the set of all pairs (δ, u(δ) + δ)

where u is the utility achieved by some bankruptcy code (not necessarilyoptimal), when the agent begins with utility δ, and is constrained by theincentive-compatibility and feasibility constraints described above. For anyδ, let v(δ) denote the maximal value when the agent begins with δ(0) = δ,i.e. the utility-maximizing value, and let v0(δ) ≡ v(δ) + δ. Observe that(δ, v0(δ)) determines the upper boundary of U .

Our first result is that whenever δF (σt) < L, then it is optimal to chooseu(σS) and u(σF

t ) to be maximal. That is, until we reach δF = L, it is neveroptimal to use a pure “utility punishment”. This allows us to compute theoptimal code recursively.Property 1: Wherever δ < L then u(σS

t ) = v(δS). Moreover, when δF (σt) <L, then u(σF

t ) = v(δF ) as well.Proof: The proof follows by induction on δ(σt)

First note that our goal is to maximize u(σ0) (where δ(σ0) = 0).Next, we claim that where δ < L, u(σ) is always maximized by choosing

u(σSt ) to be maximal. Moreover, when δF < L, then we also want u(σF

t ) tobe maximal.

17

First suppose that δ < L and that u(σSt ) were not maximal. Then con-

sider raising u(σSt ) without changing δS. This would certainly raise u(σ),

while leaving feasibility unaffected. Now, since u(σSt ) enters positively into

the IC constraints, such a change is compatible with IC and, indeed, ICpermits raising u(σS

t ) as much as possible.Next suppose that u(σF

t ) is not maximal and that δF < L. Since rais-ing u(σF ) hurts IC, we now consider an improvement which respects IC,namely raising u(σF

t ) by an amount ∆ while simultaneously also raising δF

by ∆× πh

1−πh. This corresponds to traveling up the IC constraint towards the

frontier of the utility possibility set. Notice first of all that this also respectsfeasibility. Now, since δF < L and u(σF

t ) is not maximal by assumption, thisis admissible. Finally, it is easy to see that it constitutes an improvement,since the net effect on utility is in fact 2∆, and so we can conclude that theoriginal choices of debt overhang did not maximize u(σ). �

Property 2: Whenever δ(σ) < L, then δF > δ (for the non-natural born).Proof:

Suppose this property did not hold. That is, suppose we had δ ≥ δF .Since this would also imply δF < L, from property 1 we would have

u(σ) = v(δ) and u(σF ) = v(δF ).We now demonstrate the montonicity of v(·).

Lemma 1: Monotonicity of v: v0(δ) ≡ v(δ) + δ is weakly decreasing in δand v(·) is strictly decreasing.Proof:First rewrite the recursive optimization problem as follows: v(δ) = −δ+v0(δ),where v0(δ) = sup(δS ,δF )∈Γ(δ) πh[R−1/πh +βδS + 1−πh

πhβδF ]+β[πhv(δS)+(1−

πh)v(δF )]. The result then follows if we note that Γ(δ′) ⊇ Γ(δ) for δ′ < δ; thatis, any (δS, δF ) which satisfy F and IC given δ also satisfy these constraintsfor any δ′ < δ.

The result on v(δ) = v0(δ) − δ is immediate once we have the weakmonotonicity of v0(·). �

Having established that v(·) is strictly decreasing, δ ≥ δF implies thatv(δ) ≤ v(δF ).

We now show that the IC constraints can be written in a more compactform:Claim: The IC constraints at σ can be written as: cπh

πh−πl≤ u(σ) − βu(σF ).

18

Proof: Recall the IC constraints:

c ≤ (πh−πl)[R−1/πh− δ(σ)

πh+βδ(σS)+

(1 − πh)

πhβδ(σF )+β(u(σS)−u(σF ))]

The result then follows simply by using the recursive definition of u(·)given above to substitute for β(u(σS) − u(σF )).�

Now, in our case, where we have argued that the utilities are maximalsince δF < δ < L, the IC constraint which must be satisfied at σ is thus

cπh

πh − πl≤ v(δ) − βv(δF ).

Since we have shown that v(δ) ≤ v(δF ), this would imply that

cπh

πh − πl

≤ v(δF ) × (1 − β).

But v(δF ) is bounded above (weakly) by the utility accruing from beingfinanced forever, which is πhR−1

1−β. That is, we would have

cπh

πh − πl≤ πhR − 1,

orc ≤ (πh − πl) × (R − 1/πh).

But this is precisely the condition defining the natural-born, so if an agentis not natural-born then we obtain a contradiction.�

The following result will also be useful, as it tells us that it is alwaysoptimal for at least one of the constraints (F or IC) to bind when δ < L.Property 3: Whenever δ(σ) < L, then either IC and/or F bind.Proof: Suppose that both IC and feasibility are slack. We will show thatin this case it is possible to improve v(δ) by raising u(σF ).13 This wouldcontradict property 1, which asserts that for δ < L we have u(σ) maximal.

Note that with feasibility and IC slack, such an improvement would re-spect both of these constraints (in fact it does not even affect feasibility).

First suppose that u(σF ) < v(δF ), i.e. that u(σF ) is not maximal; fromProperty 1 this can only occur when δF = L. In this case it is straightforward

13Note that since δ < L, from Property 1 we can assume without loss of generality thatthe utility at σ is maximal.

19

to increase u(σF ) and thereby improve v(δ(σ)) (note δF is being held fixed),showing that v(δ) could not have been maximal.

Next, consider the case where u(σF ) = v(δF ), that is maximal. Considerlowering δF ; note that this will necessarily bring it below L. So from Property2 it will be optimal to keep the utility at σF maximal, i.e. to preserveu(σF ) = v(δF ). But since v(·) is strictly monotonic, this will increase v(δF ).

Now, although this change may well tighten both F and IC, since theseconstraints are slack they are not violated. Moreover, by raising v(δF ) andlowering δF we are raising raising v0(δ

F ), and hence v(δ), so this indeedconstitutes an improvement.Observation: The non-natural born cannot be financed at every node

Proof: Consider a non-natural-born agent. By definition, such an agenthas

c > (πh − πl)(R − 1/πh)

That is,cπh

πh − πl

> πhR − 1

Now, recalling the IC constraints for such an agent at some generic node σ,we know that we must have

cπh

πh − πl

≤ u(σ) − βu(σF )

Now, if this agent could be financed everywhere, we would have u(σ) =u(σF ) = πhR−1

1−β.

In this case, the IC constraints would become:

cπh

πh − πl≤ (1 − β) × πhR − 1

1 − β= (πR − 1)

That is, for this agent to be financed everywhere we would need:

cπh

πh − πl

≤ πhR − 1,

which cannot hold for the non-natural born.�Having derived the most general properties of the recursive problem and

its solution, we can now begin to characterize the optimal code more ex-plicitly. We first show that when feasibility does not bind in the optimalcontract, then we must have δS = 0.

20

Property 4: Whenever the optimal code at δ(σt) < L is characterized byfeasibility slack, then δS(δ) = 0 is (weakly) optimal.Proof: Suppose that feasibility is slack but that δS > 0. Then we show thatutility can be improved by lowering δS while keeping v(δS) maximal. Firstnote that from Property 1 it is always optimal to have u(σS) maximal (i.e.equal to v(δS)). In addition, note that, if this change is possible, then it willindeed constitute an improvement, since we know from above that v0(δ

S) is(weakly) monotonic in δS.

Now, since feasibility is slack, lowering δS does not violate this constraint.Furthermore, since the IC constraint is increasing in v(δS), this change willalso respect IC. �

Finally, we impose an additional assumption which guarantees that fea-sibility is indeed be everywhere slack and thus ensures that the previousproperties fully characterize the optimal code; lemma 2 shows that this con-dition is sufficient.

The intuition behind this condition — and the lemma that follows — canbe summarized as follows. Feasibility requires that the difference between thecurrent liabilities due (δ) and the present value of expected future liabilities(πhβδS + (1 − πh)βδF ) be no greater than the expected net revenues fromthe project, which are πhR − 1. Thus the “worst case” for feasibility occurswhen both δ = L and δF = L, since then δ is maximal and liabilities cannotbe shifted into the future failure state to help satisfy feasibility while stillmaintaining δS = 0. By requiring that L be sufficiently small, however, weensure that the revenues from the current project will suffice.Assumption 4: L < πhR−1

1−(1−πh)β

Lemma 2: When L < πhR−11−(1−πh)β

then feasibility is everywhere slack.Proof:

To demonstrate this, we first note that Property 2 asserts that δ is mono-tonically increasing, i.e. δ < δF . So the “worst case” for feasibility beingslack occurs when δS = 0 and δ is maximal — i.e. when δ = L = δF .

In this case for feasiblity to be satisfied we need

0 ≤ (πhR − 1) − δ + πhβδS + (1 − πh)βδF = (πhR − 1) − L + (1 − πh)βL

Solving for L immediately gives us the above condition. �

We now conclude by addressing the issue of the optimal contract whenδ(σ) = L.

21

Remark (insert here):

VI Temporary Exclusion

In this section we show that the equilibrium we describe above is robust totemporary exclusion, i.e. to a one-shot deviation in which the agent worksat his non-entrepreneurial job for k < ∞ periods and applies the proceedsto paying down his liabilities.14 In particular, without loss of generality weexamine the case when he works until his debt goes from δF < L down to δ.

Now, for every period the agent works at his non-entrepreurial job, hereceives income w = L × (1 − β). So working for k periods would generate

income with a present value of w× (1−βk)1−β

, where the final term is the k-period

annuity factor; this simplifies to L(1 − βk).Now suppose that the agent begins with a liability of δF . In order to

work his liability down to δ, k must satisfy

δ =δF − L(1 − βk)

βk. (2)

This then yields him a utility of βkv(δ), where the term βk simply ac-counts for the fact that he only returns to entrepreneurship after k periods.

We will show that βkv(δ) ≤ v(δF ), as long as δF < L. That is, that theentrepreneur cannot increase his utility via temporary exclusion.

Now, from equation (2) we have βk = L−δF

L−δ, so we must show that

v(δ)

[L − δF

L − δ

]≤ v(δF )

Now, we can write L − δF as (L − δ) + (δ − δF ), so this is equivalent toshowing that

v(δ) −[δF − δ

L − δ

]v(δ) ≤ v(δF )

or

− v(δ)

L − δ≤ v(δF ) − v(δ)

δF − δ

14From Assumption 2 and Property 1 it is certainly not optimal to consume (or waste!)this w rather than using it to pay down the debt.

22

Now, since v(L) ≥ 0, v(L)−v(δ)L−δ

≥ − v(δ)L−δ

and so it suffices to show that

v(L) − v(δ)

L − δ≤ v(δF ) − v(δ)

δF − δ(3)

To show this consider the piecewise linear function v which is constructedso that v(δ′) = v(δ′) at δ and all successor nodes of δ (e.g. δF (δ), δF (δF (δ)), . . . , L).

We also define ˜v(δ′) = v(δ′) −(v(δ) + v(L)−v(δ)

L−δ(δ′ − δ)

).

Notice that ˜v(δ) = 0 = ˜v(L), by construction.Moreover, from Lemma 3 below, v(·), and hence ˜v(·), are concave.So in this case ˜v(δ) = 0 = ˜v(L) implies that we must have ˜v(δF ) ≥ 0

That is, v(δF ) −(v(δ) + v(L)−v(δ)

L−δ(δF − δ)

)≥ 0.

By the construction of v, v(δF ) = v(δF ), and so this implies

v(δF ) − v(δ) ≥ v(L) − v(δ)

L − δ(δF − δ),

which gives us (3).�

Lemma 3: v(δF )−v(δ)δF −δ

≥ v(δF F )−v(δF )δF F−δF whenever δFF < L.

Proof:First note that it suffices to demonstrate this result for v0(δ) ≡ v(δ) + δRecall the recursive definition of v0, making use of the fact that the op-

timal contract is everywhere characterized by δ(σS) = 0 since feasibility isalways slack (Property 4):

v0(δ) = (πhR − 1) + πhβv0(0) + (1 − πh)βv0(δF )

Similarly, for δF , we have

v0(δF ) = (πhR − 1) + πhβv0(0) + (1 − πh)βv0(δ

FF )

Subtracting the first from the second, we obtain:

v0(δF ) − v0(δ) = (1 − πh)β[v0(δ

FF ) − v0(δF )] (4)

Next, recall the IC constraint for δ, again using the fact that δS = 0.

c/(πh − πl) = R − 1/πh − δ/πh +1 − πh

πh

βδF + β[v(0) − v(δF )],

23

where we have also made use of the fact that IC binds at δ.This can be rewritten as

δ = −cπh/(πh − πl) + (πhR − 1) + βδF (δ) + βπh[v0(0) − v0(δF )],

where recall that v0(δ) ≡ v(δ) + δ.The expression for the IC constraint at δF is completely analogous.Subtracting the IC constraint for δ from that for δF and simplifying we

get:δF − δ = β(δFF − δF ) − πhβ[v0(δ

FF ) − v0(δF )] (5)

Dividing (4) by (5), we obtain:

v0(δF ) − v0(δ)

δF − δ= (1 − πh)

v0(δFF ) − v0(δ

F )

(δFF − δF ) − πh[v0(δFF ) − v0(δF )]

Now recall that v0(·) is (weakly) decreasing. Since we know that δFF >δF , this means that 0 ≥ v0(δ

FF ) − v0(δF ) and hence

v0(δF ) − v0(δ)

δF − δ= (1−πh)

v0(δFF ) − v0(δ

F )

(δFF − δF ) − πh[v0(δFF ) − v0(δF )]≥ (1−πh)

v0(δFF ) − v0(δ

F )

δFF − δF

Since these fractions are all strictly negative, and since πh ∈ [0, 1], thisimplies that in fact

v0(δF ) − v0(δ)

δF − δ≥ v0(δ

FF ) − v0(δF )

δFF − δF,

as desired.

VII Debt Overhang and Taxes

A In our Model (Incomplete)

The model of this paper can be used to suggest a possible correlation betweenredistributive taxation and bankruptcy laws. In the context of our model,a redistributive tax could be easily introduced with a lump-sum tax t tobe paid in case of an entrepreneur’s success. This would have the effect oflowering the return received by the entrepreneur — that is, we would replaceR by R − t.

24

We will show that the primary message is that introducing such a taxmakes the optimal bankruptcy code “‘tougher” — i.e. it raises the optimaldebt overhang δ.

Introducing a tax would first of all have the effect of shrinking the setof natural-born entrepreneurs, from c ≤ (πh − πl)(R − 1/πh) to c ≤ (πh −πl)(R − 1/πh). That is, the set of agents whose optimal code was uniformlyzero would be smaller.

Moreover, it is not difficult to see that increasing t makes incentives worsefor the non-natural-born, so that for a given debt overhang δ, the expectedfuture debt overhang πhδ

S(δ) + (1 − πh)δF (δ) which would be needed to

sustain incentive-compatibility is higher.

B Empirical Evidence

As we have shown above, the model of this paper suggests that reforms inbankruptcy laws should be somewhat correlated with reforms in the welfarestate which strengthen entrepreneurial incentives; in this section we discussthe evidence supporting this hypothesis. The following table gives the datesof the main changes in these tax laws, as well as of the introduction orsubstantive reform of bankruptcy codes concerning the discharge of personaldebts in these countries (in cases when such a reform occurred). The dates ofchange in the tax laws should be taken as indicative of reforms in the welfarestate; although these countires also experienced associated changes in thebenefit side of the welfare state, we focus on taxes, firstly because benefitsare obviously related and, more importantly, because for most entrepreneursthey are probably not an important factor.

Country 1978 1985 1992 BankruptcyReform

Belgium 48.8 59 57.7 —Denmark 66.7 73.2 68.7 1984Finland 57.9 59 57.8 1993France 30.1 32.7 34.2 —Germany 48.6 52 43.8 1999Netherlands 50 52 60 —Norway 70.7 68.2 48 1993Sweden 81.8 75.4 51.0 1994UK 33.0 30.0 40.0 1987

25

Table 1: Marginal Personal Income Tax Rates15

Several features of this table are of interest as they are broadly supportiveof our model. Firstly, note that in addition to being one of the early adoptersof a bankruptcy discharge, the UK (under Thatcher) was among the first ofthese countries to reform its tax code. Also note the radical tax reformsundertaken in Germany, Norway and Sweden prior to their bankruptcy re-forms. Finally, it is interesting to note that three countries which appearnot to have made significant changes to their tax codes — France, Belgiumand the Netherlands — have also enacted no provisions for debt discharge todate.

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A.1: Introduction

In this section we shift our focus to examine bankruptcy exemptions, and inparticular the differences one observes in these exemptions across the UnitedStates. As discussed above, bankruptcy exemptions refer to the propertywhich a household may retain in a bankruptcy filing. Although the lawsgoverning the “fresh start” are part of the Federal Bankruptcy Code and areuniform across the United States,16 there is a substantial amount of variation

16Although some have suggested that there are differences in their practical application— see Sullivan, Warren and Westbrook (1997).

29

Figure 1: State Tax Rates and Bankruptcy Exemptions (1983)

across U.S. states in their bankruptcy exemptions, ranging from $6,000 inMaryland and West Virginia, to unlimited exemptions in Florida, Texas andseveral other states.

As discussed above, the seizure of property serves as another way to bothcompensate lenders and punish defaulters; in this regard exemptions, whichprotect debtor’s property, play role which is analogous to the laws dischargingdebt in bankruptcy and should thus have an analogous effect on incentives.This is modeled more explicitly below, but it is not difficult to see that lowexemptions both reduce interest rates and serve as a punishment in the caseof failure.17 The same argument as we made for discharge thus suggeststhat high exemptions should be associated with low tax rates. Moreover,because the basic structure of bankruptcy law is fixed at the federal level,and since there are far more similarities in tax codes across U.S. states thanEuropean countries, interstate differences in fact give us a better laboratoryfor examining our hypothesis. In addition, the fifty states also give us far

17The effect of exemptions on credit constraints has been verified empirically by Gropp,Scholz and White (1997).

30

more data with which we can confront our theory.

A.2: Empirical Evidence

The plot of state tax rates and bankruptcy exemptions from 1983 in figure 1suggests that bankruptcy laws are indeed “tougher” in states with generousexemptions; the correlation between the two is approximately 25% (and issignificantly different from zero at the 7% level). This plot was constructedby using using data on state tax rates from Feldstein and Wrobel (1998),18

and bankruptcy exenmptions from Gropp, Scholz and White (1997);19 thedata is reported in full in table 2 below.

A.3: A Model of Bankruptcy Exemptions

It is not difficult to develop a model linking incentives and exemptions andshow that the optimal level of bankruptcy exemption is indeed positively re-lated to the strength of incentives. This suggests an explanation for this in-verse correlation between bankruptcy exemptions and tax rates. This modelbears some similarity to that of Fan and White (2000). The key differenceis that while they derive the optimal bankruptcy exemption by imposing anexogenous cost of bankruptcy of unspecified origin, in our model it is op-timal not to make the code too generous because of the effect this has onincentives. Another difference is the focus of our model on the interactionbetween bankruptcy laws and other policy variables which affect incentives.

We work with a variant of the model used throughout the paper. Considera single investment project with a possible return of either R (success) or 0(failure). Once again, suppose that this project requires one unit of financing,and that it is only viable if the entrepreneur exerts high effort, in which casethe success probability would be πh. If low effort is exerted then the successprobability would be πl, and the entrepreneur would accrue a leisure benefitof c, but the project would no longer be viable. Note that for simplicity weassume that the entrepreneur has access to only a single such project whichcannot be repeated.

In addition, suppose that the entrepreneur also has some assets A whichcan be pledged towards the repayment of the future debt. We assume that

18For households earning $100,000.19We attached a value of $100,000 to states with unlimited homestead exemptions, but

the results reported are robust to different specifications.

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that these assets are insufficient to guarantee the full repayment of the loanand thus moral hazard remains.

Assumption A1: A < 1

The bankruptcy code is now represented by the amount X which the lawallows the entrepreneur to retain in bankruptcy.

Thus given A and X, if the entrepreneur exerts high effort, the expectedrepayment is

πhr + (1 − πh)(A − X).

Setting this equal to 1, the loan size, yields an expression for the interestrate:

r = 1/πh − 1 − πh

πh(A − X).

Finally, in order to motivate the exemption, we now assume that theentrepreneur is risk-averse, with a von Neumann-Morgenstern utility functiongiven by v(·), with v′(·) > 0. Were the entrepreneur risk-neutral, there wouldbe no justification in this model for exempting any property from seizure.20

By contrast, if there were no moral-hazard problem the optimal outcomewould be one of full-insurance: i.e. the solution to:

maxX

πhv(A + R − t − r) + (1 − πh)v(X)

s.t. πhr + (1 − πh)(A − X) = 1

is to setA + R − t − r = X,

orX = πh (R − t − 1/πh − A/πh) .

We make the further assumption that full-insurance cannot be achievedeven when there is no moral hazard; since X < A this means:

A < πh (R − t − 1/πh − A/πh)

or

20Although it should be noted that in practice bankruptcy laws often exempt “tools oftrade” from seizure in order to facilitate future endeavors.

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Assumption A2: A < πh

2(R − t − 1/πh) .

We now derive the incentive-compatibility constraint in this context. Theutility the entrepreneur receives if he exerts high effort is

πhv(A + R − t − r) + (1 − πh)v(X),

which must exceed the utility from low effort:

πlv(A + R − t − r) + (1 − πl)v(X) + c.

That is, we get the constraint:

c ≤ (πh − πl) [v(A + R − t − r) − v(X)] . (6)

Because of assumption A2 — that full insurance cannot be achieved —the optimal contract X∗ sets the exemption level as high as is compatiblewith the incentive-compatibility constraint (6).21 That is, we want:

c = (πh − πl) [v(A + R − t − r) − v(X∗)] .

Substituting for r, this becomes

c = (πh − πl)[v

(R − t − 1/πh + A/πh − 1 − πh

πhX∗

)− v(X∗)

].

An application of the implicit function theorem to this equation immedi-ately shows that

∂X∗

∂t=

−v′(A + R − t − r)[(1−πh

πh

)v′(A + R − t − r) + v′(X)

] .

Since v′(·) > 0, we obtain the following:

Proposition: The optimal exemption level X∗ is monotonically decreasingin t.

21An analogous result can be found in Fan and White (2000).

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