Dealing with Consumer Default: Bankruptcy vs Garnishment
Satyajit Chatterjee
1
Federal Reserve Bank of Philadelphia Grey Gordon University of Pennsylvania September 1, 2010
1 Corresponding
Author: Satyajit Chatterjee, Research Department, Federal Reserve Bank of Philadelphia, 10 Independence Mall, Philadelphia, PA 19106. Tel: 215-574-3861. Email:
[email protected]. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Philadelphia or of the Federal Reserve System.
Abstract
The goal of this paper is to study, in a quantitative-theoretic fashion, the positive and normative implications of two different approaches to handling consumer default: bankruptcy and garnishment. We find that which of these two legal systems is in place makes a large difference to prices, allocations and welfare. Garnishment increases the level of commitment displayed by debtors toward meeting their obligations and with competition and free entry into intermediation, the added commitment translates into lower interest rates on debt. The result is a very large expansion in unsecured debt, a drop in capital per worker as the additional borrowing crowds out business fixed investment, a significant decrease in wages and a significant increase in interest rates. Nevertheless, despite these apparently adverse general equilibrium effects of credit expansion, every single individual in our baseline economy is better off without the bankruptcy option. The improved ability to borrow against future earnings and the improved risk-sharing afforded by a well-functioning consumer credit market underpin these welfare gains.
Key Words: Default, Bankruptcy, Garnishment, Unsecured Consumer Credit
1
Introduction
Since September 2008, the outstanding stock of revolving consumer debt has declined by $149 billion, or 15.3 percent. It declined largely because debtors stopped making payments on their obligations and, as required by regulation and law, the defaulted debt was charged off and removed from the balance sheets of the creditor banks. The staggering level of default on non-mortgage-related consumer debt raises questions about the efficacy of the institution of personal bankruptcy – the legal framework within which default on consumer debt is handled in the United States. Traditionally, US law is creditor friendly: creditors who have been defaulted upon have the legal right to seize any unencumbered property as well as some portion of the debtor’s earnings in satisfaction of their claims. This is the right of garnishment. Importantly, personal bankruptcy law provides protection to individual debtors against the right of garnishment. For instance, an individual who is under the threat of garnishment can appeal to a bankruptcy court to have his debt removed – the legal term is discharged – so that his creditors have no legal claim to pursue. The financial crisis has generated renewed policy interest in consumer default. For instance, based on the view that sudden increases in interest rates can be a trigger for default, legislators in the US have attempted to control how easily the terms of credit (such as interest rates and limits) can be changed by credit card banks. Given this general ferment and on-going re-thinking of the nature of regulation regarding consumer finance, it seems appropriate and valuable to step back from detailed questions about the operation of consumer credit markets and ask a “big picture” question: is the debtor protection offered by bankruptcy law a good thing? How would the consumer credit market, and the economy more generally, function if the option to declare bankruptcy was eliminated? The positive and normative implications of bankruptcy has received attention in the quantitative macro literature. However, a common assumption in this literature – and in our view a failing of it – is that it treats default and bankruptcy as synonymous. Thus, the elimination 1
of the option to declare bankruptcy has been uniformly interpreted to mean elimination of default on consumer debt. Examples are Athreya (2002, 2008), Li and Sarte (2006), Chatterjee, Corbae, Nakajima and Rios-Rull (2007) and Athreya, Tam and Young (2009). But, in reality, nothing prevents indebted households from stopping to make payments on their debts even if the bankruptcy option is absent. What elimination of the bankruptcy option really means is that default and delinquency will be handled by a different set of laws, ones that define the extent and scope of creditors rights to enforce repayment on defaulted debt. In the United States, these rights are constrained by federal law, which makes collecting on defaulted debt a time consuming process. The main contribution of this paper is to model a realistic alternative to bankruptcy law, one that is based on the actual garnishment laws in existence in the United States and then examine what might plausibly happen if bankruptcy – but not default, necessarily – is eliminated.1 This quantitative comparative institutional approach fits in well with the body of work within the law and economics tradition that has looked at the question of the efficacy of personal bankruptcy. This literature is discussed and reviewed in Jackson (1986). The focus of this literature is on the different kinds of moral hazard induced by different legal arrangements regarding the handling of consumer default. What the current paper brings to this analysis is an explicitly quantitative focus and a focus on the system-wide effects of legal changes in the treatment of consumer default. The research presented here is also complementary to the empirical research on bankruptcy as exemplified in Fay, Hurst and White (2002) and Gross and Souleles (2002). Among quantitative studies, one that comes closest in spirit to our study is Livshits, MacGee and Tertilt’s (2007) comparison of the discharge option (or, “Fresh Start”) with something akin to garnishment (which they label as the “European System”). In their “European System”, an individual cannot discharge his debt, so default leads to some portion of his future 1
There is ample historical evidence to suggest that there will be default even in the absence of a bankruptcy option. Historically, it was the plight of delinquent debtors caught in the grip of unrelenting creditors that provided the impetus and motivation for discharge. See, for instance, the discussion in Coleman (1999) and Warren (1935).
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wage earnings being taken in satisfaction of the creditors claim. But there are some important differences between their study and this one. First, the focus of our paper is on the role of bankruptcy in the US. If bankruptcy were to be eliminated, the legal framework to handle consumer default would be the law of garnishment. Therefore, we model the actual garnishment law in the US as closely as possible. Second, we model the production side of the economy whereas Livshits, MacGee and Tertilt work with an endowment economy. This difference is important because strong general equilibrium effects can emerge (and, in fact, will emerge) from elimination of the bankruptcy option which can change the earnings process for people. This point was stressed in Li and Sarte, who showed that taking into account general equilibrium effects can overturn welfare results obtained in partial equilibrium settings. In related work, Athreya (2008) presents a careful study of the implications of eliminating the bankruptcy option in a partial equilibrium life-cycle setting with earnings risk. Elimination is taken to mean that default becomes infinitely costly which, in turn, means that the maximum level of borrowing that can be supported in the no-bankruptcy equilibrium is determined by the lowest earnings an individual may receive (since he will not choose to borrow any more than the present discounted value of this level over of the person’s lifetime). This fact introduces a tight link between “default policy” and “social insurance provision” which the paper explores. In Athreya, Tam and Young (2009), the focus is on understanding (again, in a partial equilibrium context) the merits of harsh default penalties (in effect, making the cost of default infinite) versus keeping penalties low but providing loan guarantees to lenders so as to lower the price of credit to households. Currently, there are two quantitative-theoretic approaches to modeling consumer debt and default. The Livshits MacGee and Tertilt study mentioned above is calibrated to life-cycle facts regarding earnings. This introduces life-cycle reasons for borrowing, which play an important role in the analysis. Their approach is followed by Athreya (2008), and Athreya, Tam and Young (2009), among others. In contrast, Chatterjee, Corbae, Nakajima and
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Rios-Rull (henceforth CCNR) follow the “permanent income hypothesis (PIH)” tradition of Friedman (1957) and abstract from life-cycle elements. Although less realistic, the PIH approach makes it computationally easier to incorporate production and endogenize factor prices, as was done, for instance, in Aiyagari’s (1994) seminal contribution on the role of precautionary savings on interest rates and in CCNR and Li and Sarte (2006) (who also follow the PIH tradition). Furthermore, abstracting from life-cycle elements also makes it easier to compute the transition dynamics between steady states necessary for a proper evaluation of welfare implications of a change in the law. In this paper, we draw on CCNR and extend that environment in a computationally tractable way to handle labor-effort choice and a realistic garnishment regime. A compelling positive and normative analysis of US garnishment law requires that labor effort be a choice variable because the distortion in labor effort caused by creditors’ right to garnish wages is generally thought to be an important drawback of garnishment and a point in favor of discharge. We find that elimination of the bankruptcy option makes a large difference to prices and allocations and causes a substantial increase in welfare. Fundamentally, these effects stem from the fact that eliminating the bankruptcy option increases the level of commitment displayed by debtors toward meeting their obligations. With competition and free entry into intermediation, the added commitment on the part of debtors translates into lower interest rates on debt. The result is a very large expansion in unsecured debt, a drop in capital per worker as the additional borrowing crowds out business fixed investment, a significant decrease in wages and a significant increase in interest rates. Nevertheless, despite these apparently adverse general equilibrium effects of credit expansion, every single individual in the economy is better off in a world without the bankruptcy option. These welfare gains come from several sources. First, having more attractive interest rates on debt allow asset-poor individuals to borrow against their future income, which, given their impatience, they would like to do. Second, asset-rich individuals also gain from the elimination of the bankruptcy option because they experience an increase in the flow return 4
on their assets. Third, because of the improved efficiency of the unsecured consumer credit market in terms of providing a cushion against temporary fluctuations in earnings, there is better consumption smoothing among initially asset-poor people. And, finally, because of improved consumption smoothing via borrowing and lending there is less need for precautionary savings for self-insurance purposes. Thus, along the transition path, the economy de-accumulates capital and the additional consumption afforded by this de-accumulation increases consumption and welfare. These effects outweigh the adverse effects of a lower real wage for workers in the long run, the fact that more people spend time shut out of the credit market from being in garnishment, and the distortionary effects on labor supply due to garnishment. This last effect turns out to be small in our model because we calibrate the elasticity of labor supply to be consistent with the generally low elasticity of labor supply estimated in micro studies. The paper is organized as follows. Section 2 lays out the model economy. The layout mostly follows CCNR except with regard to the garnishment regime, which is new to this study. In section 3 we describe all of the decision problems. Because our analysis allows for transition dynamics, we introduce the current and future sequence of factor prices as an aggregate state variable and give the appropriate recursive formulation of the decision problems and of the competitive equilibrium. Section 4 presents the calibration of the model. We choose functional forms for utility in such a way as to keep the calibration of the model as close as possible to the calibration presented in CCNR. This has the advantage of comparability and allows us to make use of the insights in the earlier paper in terms of matching key data moments. Section 5 gives all of the results regarding bankruptcy versus garnishment. It first compares the (calibrated) bankruptcy equilibrium with the equilibrium that would result if garnishment becomes the law with regard to default and explains why the differences arise. Second, it presents estimates of the welfare gain of moving from the bankruptcy equilibrium to the garnishment equilibrium and explains why individuals are differentially affected by the change. Third, it attempts to better understand the source of the welfare gains by comparing mean consumption and dispersion of consumption across individuals under the 5
two regimes. Section 6 discusses the sensitivity of findings to alternative parametrizations. Section 7 summarizes the main findings of this study and collects some thoughts on future research topics of interest.
2
The Model Economy
We begin by specifying the physical environment in which people live. This is followed by a discussion of the two different ways default on consumer debt may be legally dealt with. The market arrangement is described next and then the decision problems of all the agents in the economy. The decision problems differ depending on the legal system in place regarding default.
2.1
Preferences and Technology
At any given time, there is a unit mass of people in the economy. Each person has probability of survival given by ρ ∈ (0, 1) so that a fraction 1 − ρ of the population dies each period and is replaced by newborns. Each person has one unit of time endowment. People differ in terms of the productive efficiency of their time endowment, which varies stochastically over time. These efficiencies are denoted by e. In any period, an individual’s e is drawn from a discrete probability distribution with compact support E ⊂ R++ and probability mass function φs (e).2 Here, s is a finite-state Markov chain taking values in the set S with transition probabilities πs,s0 . 2
In CCNR, these probability distributions were assumed to be continuous, not discrete. Continuous e is necessary to prove the existence of a competitive equilibrium. We will not provide any existence theorems in this paper. Computationally, a continuous e allows for a very accurate solution of equilibrium prices, but the algorithm to compute the solution is more complicated. These complications can be avoided if e is taken to be discrete. Provided the number of grid points on e is taken to be large, reasonably accurate solutions to equilibrium prices can be found. See Chatterjee and Eyigungor (2010) for discussion of the computational challenges involved in computing debt/default models of this type and their Appendix C for a comparison of the numerical accuracy of the solution when e is taken to be discrete vs continuous.
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Draws from this process, as well as from the φs (e), are independent across people. Thus, the efficiency process has a persistent component controlled by s and an idiosyncratic component controlled by φ. Conditional on survival (or birth), a person’s lifetime utility from a sequence {ct , nt , et } consumption, effort and efficiency levels is given by X∞ t=0
(βρ)t u(ct , nt , et )
where β is the discount factor of the person and the momentary utility function u(c, n, e) : [0, ∞) × [0, 1] × E → R is strictly increasing in c, strictly decreasing in n, differentiable and concave in the first two arguments. We permit current utility to be affected by the realization of the current efficiency level. There is an aggregate production function F (K, N ) : R+ × R+ → R+ , which gives the total quantity of the single good produced in this economy as a function of the aggregate capital stock K and aggregate efficiency units of labor N . We assume that F is CRS, differentiable and displays diminishing marginal products with respect to each input. The capital stock depreciates at the rate δ ∈ (0, 1).
2.2
Market Arrangement
In each period, there is a market for efficiency units of labor where people and the representative firm in charge of the (aggregate) production technology transact in labor services: people can sell any portion of their efficiency endowments to the firm at the wage wt per efficiency unit, where the wage is expressed in period-t consumption good. There is a market for the services of physical capital. The representative firm can rent physical capital from the intermediary sector at the rate of rt units of consumption good per
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unit of capital. Most crucially, there is a market in which people can borrow and lend. When a person borrows, the option to default implies that the interest rate at which he borrows will depend on his likelihood of default. The latter, in turn, will depend on all observable factors that potentially influence that likelihood. In the context of this model, these factors are (i) the size of the liability (or promise), (ii) the person’s current efficiency status and (iii) all current and future factor prices. It is notationally convenient to denote assets by positive numbers and liabilities by negative numbers. We use p to denote the sequence of current and future j=∞ factor prices {wj , rj }j=0 . Then, the unit price of a promise to deliver y (if y < 0) units
of consumption good next period by a person with current persistent efficiency level s is q(y, s, p) > 0.3 By making this promise, the person receives q(y, s, p)(−y) units of the consumption good in the current period. If y ≥ 0, the person obtains a promise to receive y next period and gives up q¯(p)y in the current period. Thus, people borrow at interest rates that vary with the loan size but lend at a (gross) interest rate that is independent of the amount lent or the person’s efficiency level. These prices depend on the current and future trajectory of factor prices because our analysis allows for transition dynamics. In addition to the market for new loans and deposits, there is also a market where intermediaries may trade debt that is in default. Depending on the legal environment, there may or may not be an active market for defaulted debt. In the event there is, the market price of unpaid obligation of the amount y < 0 belonging to an individual with current persistent efficiency level s is denoted x(y, s, p). We assume that the intermediary sector is the counterparty in all intertemporal trades entered into by people. One implication of this assumption is that if a person dies, his assets or liabilities are absorbed by the intermediary sector. 3
The price depends only the persistent component of efficiency because this is the component that helps predict future efficiency level e0 . In particular, current e does not affect the price because it is a purely transitory draw that does not predict future earnings.
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2.3
Garnishment and Bankruptcy Laws
As noted in the introduction, in order to understand the macroeconomic consequences of personal bankruptcy law, we need to be clear about the creditor and debtor remedies against default that would plausibly prevail if the legal institution of bankruptcy (i.e., the discharge of debt) were to be eliminated. In the United States, the law that would prevail (and against which personal bankruptcy currently provides protection) is the law governing garnishment. Under this law, creditors have the right to garnish the earnings of the delinquent debtor, as well as seize any unencumbered property, in satisfaction of their claims. But this right of garnishment is importantly constrained by federal law. Under this law, default would have the following consequences in reality and in the model:
1. As long as there is any unpaid obligation, assets accumulated by the defaulter can be seized by creditors to satisfy the obligation. In the model, this corresponds to the restriction that the delinquent debtor cannot accumulate assets until he pays off his debt. 2. As long as there is any unpaid obligation, creditors can seize up to 25 percent of disposable income in satisfaction of their claims. 25 percent is the federal limit (some states have lower limits). The notion of disposable income is income in excess of reasonable living expenses. There are federal guidelines regarding the calculation of “reasonable living expenses” which are discussed in the calibration section. In the model, this garnishment formula is modeled as the assumption that the defaulter must pay at least min{max{0, 0.25(wen − cmin )}, −a} toward reducing his obligation, where wen is current period earnings, −a is the size of the unpaid obligation in the current period, and cmin is “reasonable living expenses” mandated by law. Importantly, the choice of n is left to the defaulter and there is no compulsion to earn above cmin . Thus, creditors may not receive any payments at all or receive payments with considerable delay. The 9
defaulter is free to repay more than the amount stipulated by the garnishment formula. 3. The federal law prohibits the accumulation of interest on unpaid obligations. Thus, in the model, unpaid obligations do not accumulate any interest. 4. Default has adverse consequences on reputation and leads to pecuniary and nonpecuniary costs. In the model, these costs of default are modeled as a consumption loss that is a proportion χ of earnings. These costs are paid each period for as long as lenders know that the person defaulted sometime in the past (more on this below).
We now turn to personal bankruptcy. Under bankruptcy law, default would have the following consequences in reality and in the model (these assumptions follow the existing literature):
1. A defaulter is permitted by law to have his unpaid obligations discharged. Legally, discharge of debt gives the defaulter protection against the law of garnishment. Once a debt has been discharged, creditors must cease all efforts to collect on the debt. In the model, this is modeled as the disappearance of any unpaid obligation. 2. Bankruptcy law stipulates that in exchange for discharge of debt, the defaulter must give up any assets he possesses toward satisfaction of the obligation. The exception to this requirement are so-called exempt assets which the defaulter can keep even in bankruptcy. In the model, we assume that there are no exempt assets, so a defaulter must give up all of his assets in exchange for discharge. We assume that the process of getting discharge consumes the entire period. This means that in the period in which the defaulter invokes bankruptcy protection, he cannot accumulate assets. 3. Because bankruptcy is a form of default, the pecuniary and non-pecuniary costs of default mentioned earlier apply here as well. That is, we assume these costs result in the same loss of consumption equal to the proportion χ of earnings and these costs are paid for as long as lenders know that the person declared bankruptcy in the past. 10
The Fair Credit Reporting Act describes how long negative information, such as late payment, bankruptcies, garnishments, tax liens, etc., may stay on a person’s credit report. By law, bankruptcy information can stay on a credit report for ten years. Garnishments can stay on the report for twelve years from the date of entry or for seven years from the date they were satisfied. This aspect of US law is relevant for our study because negative information in a person’s credit report appears to impair the person’s access to credit.4 In what follows, we will make the following set of assumptions:
1. A person with a record of a past bankruptcy or a past garnishment that has been satisfied cannot borrow. 2. The record of a past bankruptcy or a past garnishment that has been satisfied may be permanently removed from a person’s credit history with probability λ.
As noted earlier, bankruptcy law provides protection against the law of garnishment. Thus, both laws exist simultaneously. This means that a debtor need not invoke bankruptcy upon default – i.e., he may choose to enter into garnishment instead. However, our assumption regarding the handling of negative information will imply that a person choosing to default will always avail himself of bankruptcy rather than permit garnishment. Thus, we will proceed under the assumption that when bankruptcy law is in place, it replaces the law of garnishment and the debtor chooses between repayment and bankruptcy only. 4
Musto (2004) provides compelling evidence in favor of this assumption. See Chatterjee, Corbae and Rios-Rull (2010) for the theoretical foundation for this finding.
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3
Decision Problems
3.1
People
Let A ⊂ R denote the set of asset positions. In the theory as well as in the computation, A is taken to be a finite set, which includes 0 and positive and negative elements. A−− is the set of strictly negative elements and A+ the set of non-negative elements. Given the sequence of factor prices p, w(p) and r(p) denote the current wage and rental rates implied 0 0 by p and let B denote the shift operator B(p) = {wj0 , rj0 }∞ j=0 , where wj = wj+1 , rj = rj+1 ,
j = 0, 1, 2, . . . , ∞. We first describe a person’s decision problem when the law governing default is garnishment.
3.1.1
Decision Problem Under Garnishment
In addition to the individual states a, e, and s, there is a state variable h ∈ {0, 1} that takes on the value 1 if the person is currently under garnishment (i.e., has some unpaid debt obligation) or if the person has satisfied the garnishment but the record of the garnishment has not yet been removed from the person’s credit history. We will denote the optimal lifetime utility of a person in state (a, e, s, h) by V (a, e, s, h; p). We index the value functions (and decision rules) by p to emphasize the fact that the value of these objects depends on the current and future trajectory of factor prices. A person under garnishment can be in one of four situations:
1. a < 0 and h = 0. In this case, the person has two options: he can repay his debt or, he can default on his debt and subject himself to garnishment. The value from repayment, which we denote as V R (a, e, s, h = 0, p) is given by the following dynamic
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program: V R (a < 0, e, s, h = 0; p) =
max
a0 ∈A,n∈[0,1],c≥0
u(c, n, e) + βE(s0 ,e0 )|s V (a0 , e0 , s0 , h = 0; p0 )
s.t. c = w(p)en + a − I{a0 <0} q(a0 , s; p)a0 − I{a0 ≥0} q¯(p)a0 p0 = B(p), where I{·} denotes an indicator function that takes on the value 1 if the expression in {·} is true and 0 otherwise. The value from default and garnishment, which we denote by V G (a, e, s, h; p) is given by the following dynamic program V G (a < 0, e, s, h = 0; p) = max
a0 ∈A,n∈[0,1],c≥0
u(c, n, e) + βE(s0 ,e0 )|s [I{a0 <0} V G (a0 , e0 , s0 , h = 1; p0 ) + I{a0 ≥0} V (a0 , e0 , s0 , h = 1; p0 )]
s.t. a0 − a ≥ min{max{0, 0.25(w(p)en − cmin )}, −a} c = (1 − χ)w(p)en − [a0 − a]I{a0 <0} − I{a0 ≥0} [¯ q (p)a0 − a] p0 = B(p). The person chooses the best of these options. Therefore, in this case, V (a < 0, e, s, h = 0; p) = max{V R (a < 0, e, s, h = 0; p), V G (a < 0, e, s, h = 0; p)}
2. a < 0 and h = 1. This is the case where the person defaulted in some previous period,
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hasn’t paid off his obligations and is under garnishment. V G (a < 0, e, s, h = 1, p) = max
a0 ∈A,n∈[0,1],c≥0
u(c, n, e) +
βE(s0 ,e0 )|s [I{a0 <0} V G (a0 , e0 , s0 , h = 1; p0 ) + I{a0 ≥0} V (a0 , e0 , s0 , h = 1; p0 )] s.t. a0 − a ≥ min{max{0, 0.25(w(p)en − cmin )}, −a} c = [1 − χ]w(p)en − [a0 − a]I{a0 <0} − I{a0 ≥0} [¯ q (p)a0 − a] p0 = B(p).
3. a ≥ 0 and h = 1. This is the case where the person defaulted in the past, is no longer in garnishment but the default flag has not yet been removed. V (a ≥ 0, e, s, h = 1; p) = max
a0 ∈A+ ,n∈[0,1],c≥0
u(c, n, e) + βE(s0 ,e0 )|s [(1 − λ)V (a0 , e0 , s0 , h = 1 : p0 ) + λV (a0 , e0 , s0 , h = 0; p0 )]
s.t. c = [1 − χ]w(p)en − q¯(p)a0 + a p0 = B(p).
4. a ≥ 0, h = 0. In this case, the person has no outstanding obligations and no record of past default. V (a ≥ 0, e, s, h = 0; p) =
max
a0 ∈A,n∈[0,1],c≥0
u(c, n, e) + βE(s0 ,e0 )|s V (a0 , e0 , s0 , h = 0; p0 )
s.t. c = w(p)en + a − I{a0 <0} q(a0 , s, p)a0 − I{a0 ≥0} q¯(p)a0 p0 = B(p).
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The solution to this individual problem implies decision rules a0 (a, e, s, h; p), n(a, e, s, h; p) and c(a, e, s, h; p). In addition, for a < 0 the solution also implies a default decision rule d(a, e, s, h; p), which takes the value of 1 if the person defaults (or continues in default) and subjects himself to garnishment and 0 otherwise.
3.1.2
Decision Problem Under Bankruptcy
Under bankruptcy, h ∈ {0, 1} encodes whether a past bankruptcy appears in the person’s credit record (h = 1) or not (h = 0). We will denote the optimal lifetime utility from being in state a, e, s, h by W (a, e, h, s; p). A person can be in one of three different situations:
1. a < 0 and h = 0. The person has some outstanding debt and has no record of past bankruptcy in his credit history. This person has two options. He can repay his debt or file for bankruptcy. Let W R (a < 0, e, s, h = 0; p) denote the value from repayment. Then, W R (a < 0, e, s, h = 0; p) =
max
a0 ∈A,n∈[0,1],c≥0
u(c, n, e) + βE(s0 ,e0 )|s W (a0 , e0 , s, h = 0; p0 )
s.t. c = w(p)en + a − I{a0 <0} q(a0 , s, p)a0 − I{a0 ≥0} q¯(p)a0 p0 = B(p),
The value from default and bankruptcy, which we denote by W B (a, e, s, h) is given by
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the following dynamic program W B (a < 0, e, s, h = 0; p) =
max
a0 ∈A,n∈[0,1],c≥0
u(c, n, e) + βE(s0 ,e0 )|s W (0, e0 , s0 , h = 1; p)]
s.t. c = w(p)en p0 = B(p). The person chooses the best of these options. Therefore, in this case, W (a < 0, e, s, h = 0; p) = max{W R (a < 0, e, s, h = 0; p), W B (a < 0, e, s, h = 0; p)} (1)
2. a ≥ 0 and h = 1. This is the case where the person defaulted in some previous period and the bankruptcy record has not yet been removed. W B (a ≥ 0, e, s, h = 1; p) = max
a0+ ,n∈[0,1],c≥0
u(c, n, e) + β ×
E(s0 ,e0 )|s [(1 − λ)W B (a0 , e0 , s0 , h = 1; p) + λW (a0 , e0 , s0 , h = 0; p)] s.t. c = [1 − χ]w(p)en − q¯(p)a0 + a p0 = B(p).
3. a ≥ 0, h = 0. In this case, the person has no outstanding obligations and no record of past default. W (a ≥ 0, e, s, h = 0; p) =
max
a0 ∈A,n∈[0,1]
u(c, n, e) + βE(s0 ,e0 |s) W (a0 , e0 , s0 , h = 0; p)
s.t. c = w(p)en + a − I{a0 <0} q(a0 , s, p)a0 − I{a0 ≥0} q¯(p)a0 p0 = B(p). 16
The solution to this individual problem implies decision rules a0 (a, e, s, h; p), n(a, e, s, h; p) and c(a, e, s, h; p). In addition, for a < 0 and h = 0, the solution also implies a default decision rule d(a, e, s, h; p), which takes the value 1 if the person defaults and invokes bankruptcy and 0 otherwise.
3.2
Decision Problem of the Representative Firm
The representative firm’s optimization problem is static: it rents K and hires N each period to maximize current period profits. This decision problem is the same regardless of the legal regime in place. max F (K, N ) − w(p)N − r(p)K
K≥0,N ≥0
3.3
Decision Problem of the Intermediary Sector
As noted earlier, intermediaries are the counterparty to every borrowing and lending contract entered into by consumers and are also the owners of capital stock in this economy. We will assume that there is one representative intermediary who takes prices as given and (i) chooses how much capital to purchase in the current period (for use in the following period), (ii) how many new borrowing or lending contracts of different types to enter into with consumers, and (iii) if there is a market for defaulted debt, how much of each different types of defaulted debt to purchase. The net return from the first activity (purchase of capital) is: −K 0 +
(1 − δ) + r(B(p)) 0 K 1 + i(p)
(2)
Let m0 (y, s, p) be the measure of newly issued contracts of type (y, s, p) held by the inter17
mediary sector at the end of the current period. Let θ(y, s, p) be the fraction of borrowers defaulting next period conditional on taking out a loan of size y and having current persistent efficiency level s. And, conditional on there being a default, let q D (y, s, p) be the expected (per unit) value of the defaulted debt. We will refer this as the expected recovery rate. In the bankruptcy regime, q D = 0 but it is generally positive in the garnishment regime. Then, the net return from the second activity (purchase of newly issued loans or deposits) is:
X ρ m (y, s, p)y q¯(p) − + m0 (y, s, p)y × 1 + i(p) y∈A+ ,e y∈A−− ,e ρ D [(1 − θ(y, s; p) + θ(y, s; p)q (y, s, p) . −q(y, s, p) + 1 + i(p) X
0
(3)
In the event garnishment law is in place, let z 0 (y, s, p) be the measure of defaulted debt of type (y < 0, s, p) held by the intermediary sector. Let η(˜ a, y, s0 ; p) be the fraction of delinquent debtors who choose choose a ˜ next period (by assumption, a ˜ must be greater than or equal to y), given an unpaid debt of y, a persistent efficiency level of s0 and next period’s aggregate state B(p). Then, the net return from the third activity is: X
z 0 (y, s, p)y ×
y∈A−− ,e
XX ρ η(˜ a, y, s0 ; B(p)) (min{(˜ a − y), −y})/(−y) + I{˜a<0} x(˜ a, s0 , B(p)) πs0 |s −x(y, s, p) + 1 + i(p) 0 s
! .
a ˜∈A
(4)
Let M 0 denote the distribution of newly issued contracts held by the intermediary sector and Z 0 the distribution of defaulted debt held by the intermediary sector.
18
If the law in place is garnishment, the decision problem is to choose K 0 , M 0 , Z 0 to maximize the sum of (2), (3) and (4). When the law in place is bankruptcy, the intermediary’s decision problem is to choose K 0 and M 0 to maximize the sum of (2) and (3), where in (3) the value of defaulted debt is zero.
3.4
Equilibrium
We focus on perfect foresight equilibrium. Let µ(a, e, s, h) denote the distribution of people over the individual states. Let Γ(µ, p) describe the law of motion of this distribution. That is, µ0 (a, e, s, h) = Γ(µ(a, e, s, h), p) is the distribution of people of individual states next period, given the current distribution µ and current and future sequence of factor prices p. The time evolution of the distribution is then given by the recursion µt+1 (a, e, s, h) = Γ(µt , B t (p)), where it is understood that µ0 = µ and B 0 (p) = p. A perfect foresight competitive equilibrium for an initial distribution of people over individual states µ(a, e, s, h) and an initial aggregate capital K is (i) a sequence of current and future factor prices p, (ii) a set of credit market prices q(a < 0, s, p), q¯(p), x(y < 0, s, p) and i(p), (iii) a set of individual decision rules a0 (a, e, s, h; p), n(a, e, s, h; p), c(a, e, s, h; p) and d(a, e, s, h; p), (iv) a set of production sector decision rules K(p) and N (p), (v) a set of intermediary sector decision rules K 0 (p), m0 (y, s, p) and (if applicable) z 0 (y, s, p) and (vi) a law of motion Γ(µ, p) such that:
1. The decision rules solve the individual dynamic optimization problem, given p and credit market prices q(y, s, p) and q¯(p). 2. K(p) and N (p) solve the production sector static optimization problem. 3. K 0 (p), m0 (y, s, p) and (if applicable) z 0 (y, s, p) solve the intermediary optimization problem.
19
4. The goods market clears: K 0 (p) − (1 − δ)K = X F (K(p), N (p)) − c(a, e, s, h; p) + I{h=1} χw(p)en(a, e, s, h; p) µ(a, e, s, h) a,e,s,h
(5)
5. The labor market clears: N (p) =
X
e n(a, e, s, h; p)µ(a, e, s, h).
(6)
a,e,s,h
6. The market for physical capital clears: K(p) = K.
(7)
7. The credit market for newly issued debt clears: ∀ (y, s) ∈ (A × S) X m0 (y, s, p) = I{a0 (a,e,s,h=0;p)=y} µ(a, e, s, h = 0)
(8)
a,e
8. If active, the market for defaulted debt clears: ∀ (y, s) ∈ (A−− × S) X z 0 (y, s, p) = I{a0 (a,e,s,h=1;p)=y} µ(a, e, s, h = 1)
(9)
a,e
9. The probabilities θ(y, s, p) and η(a0 , a, e, s; p) and the price q D (y, s, p)) that appear in the intermediary sector’s decision problem must be consistent with individual decision
20
rules and market prices. This requires: θ(y, s, p) =
XX s0
d(y, e0 , s0 , h = 0; B(p))φs0 (e0 )πs0 |s ,
(10)
e0
η(˜ a, y, s0 ; B(p)) =
X
I{a0 (y,e0 ,s0 ,h=1;B(p))=˜a} φs0 (e0 ),
(11)
e0
d(y, e0 , s0 , h = 0; B(p)) q (y, s, p) = E(e0 ,s0 )|s × θ(y, s, p) min{a0 (y, e0 , s0 , h0 = 0; B(p)) − y, −y} 0 0 0 0 + x(a (y, e , s , h = 0; B(p)), s , B(p))(12) −y D
In the expression for q D , if for some y d(y, e0 , s0 , h = 0; B(p)) = 0 for all (e0 , s0 ), the expectation term on the rhs becomes indeterminate (i.e., evaluates to 0/0). In this case, the recovery rate in default is irrelevant, we set the expectation to 1. 10. The law of motion for µ is consistent with individual decision rules. This requirement is easiest to describe in two parts. Γ(µ, s)(˜ a, e˜, s˜, h = 0) =
X a<0,e,s
.
I{a0 (a,e,s,h=0;p)=˜a and d(a,e,s,h=0;p)=0} µ(a, e, s, h = 0)πs˜|s φs˜(˜ e) X + I{a0 (a,e,s,h=1;p)=˜a} λµ(a, e, s, h = 1)πs˜|s φs˜(˜ e), a≥0,e,s
Γ(µ, s)(˜ a, e˜, s˜, h = 1) =
X
I{a0 (a,e,s,h=1;p)=˜a and d(a,e,s,h=1;p)=1} µ(a, e, s, h = 1)πs˜|s φs˜(˜ e) a<0,e,s X I{a0 (a,e,s,h=1;p)=˜a} (1 − λ)µ(a, e, s, h = 1)πs˜|s φs˜(˜ e). + a≥0,e,s
(13)
11. There is perfect foresight. That is, the sequence p is implied by the evolution of the economy starting from K and µ(a, e, s, h). Formally, this requires that for any t ≥ 1 conditions (1)-(9) are satisfied for K = K 0t−1 (p)) and µ(a, e, s, h) = µt (a, e, s, h), where µt satisfies the recursion µt (a, e, s, h) = Γ(µt−1 , B t−1 (p)), with µ0 = µ(a, e, s, h) and B 0 (p) = p.
21
The factor market clearing conditions and the two credit market clearing conditions impose restrictions on factor prices and on the price of loans and deposits which are used in computing the equilibrium of the model. If there is positive production in each period, then r(p) = FK (K(p), N (p)) and w(p) = FN (K(p), N (p)). If the intermediary sector holds positive quantity of capital each period, profit maximization requires that the net return from holding capital is exactly zero. From (2), this implies: i(p) = r(B(p)) − δ. If the intermediary sector holds positive amounts of deposits or loans of a given type, then the net return on the deposit or the loan must be zero. From (3) this implies that ρ and ˙ 1 + i(p) ρ q(y, s, p) = (1 − θ(y, s; p) + θ(y, s; p)q D (y, s, p) . 1 + i(p)
q¯(p) =
(14) (15)
Finally, in the garnishment regime, if the intermediary sector holds positive amounts of defaulted debt then the net return on these debts must be zero as well. From (4), this implies: x(y, s, p) = XX ρ η(˜ a, y, s0 ; B(p)) (min{(˜ a − y), −y})/(−y) + I{˜a<0} x(˜ a, s0 , B(p)) πs0 |s . 1 + i(p) s0 a˜∈A (16)
22
4
Calibration
To render the model quantitative, we will select parametric forms and parameter values in order to make the equilibrium with bankruptcy law come as close as possible to aggregate macroeconomic statistics as well as aggregate statistics on consumer debt and default. As discussed in CCNR, the calibration of a debt-default model can be challenging. Parameter values that deliver the level of indebtedness currently observed in the US economy, both in terms of the fraction of people in debt and the level of debt, typically imply default frequency that is lower than what is currently observed. Conversely, a default frequency that is consistent with the data seems to require a higher level of indebtedness than actually observed. Incorporating a labor-leisure choice further complicates the calibration of the model because additional statistics regarding effort choices have to be matched as well. In order to meet all these challenges, our strategy is to adopt functional forms that allow us to re-use the calibration in CCNR to a large extent.
4.1
Functional Forms
For u(·) we assume:
u(c, n, e) = (1 − σ)
−1
(1−σ) n1+ξ c−ζ , with σ > 0, ζ > 0, ξ > 0. + A(e) 1+ξ
Thus, we adopt the Greenwood, Hercowitz and Huffman (1988) specification for preferences, modified slightly as in Mehlkopf (2010), to allow for a state dependent constant term A(e). There are two advantages to this specification. First, the level of consumption c does not affect the MRS between consumption and effort, which is simply given by ζnξ . Second, for any feasible c, the requirement that c − ζn1+ξ /(1 + ξ) + A(e) ≥ 0 – which is needed for current utility to be well-defined – can be effectively reduced to the requirement that c ≥ 0 by an appropriate choice of A(e). By the first property, for a person in good standing the 23
unconstrained choice of n is given by n ¯ (e; p) = (ew(p)/ζ)1/ξ . In what follows, we set A(e) to be equal to ζ(¯ n(e; p))1+ξ /(1 + ξ). In steady state, when w is constant over time, this term will vary with e only and will generally offset the −ζ(n(a, e, h, s; p))1+ξ /(1 + ξ) term. Thus, the requirement that c − ζn1+ξ /(1 + ξ) + A(e) ≥ 0 will effectively become the requirement that c ≥ 0. Furthermore, when the offset is operative, utility is simply given by c1−σ /(1 − σ). Our efficiency process cannot be easily calibrated to match earnings processes estimated in say, Storesletten, Telmer and Yaron (2004) or Gourinchas and Parker (2002). This is because these processes build in life-cycle elements that are not part of our model. CCNR discipline the choice of the earnings process by requiring that it reproduce both the earnings and wealth distribution statistics observed for the US.5 In what follows, we will restrict the parameters of the efficiency process so our endogenous earnings process matches the exogenous one in CCNR. The GHH specification helps us to make this link because labor supply in any period simply depends on that period’s efficiency and real wage (and is independent of consumption). Following CCNR, we assume that the persistent component of efficiency can take one of three values. Loosely speaking, these correspond to people who have very high earnings (the super-rich) those who are middle to upper-middle class earners (white collar) and those who are lower-middle class or poor (blue collar). When s = i ∈ {1, 2, 3}, the efficiency e is drawn from a probability mass function with support [eimin , eimax ] and a discretized version of the CDF
e − eimin eimax − eimin
ϕ .
This functional form is the same as in CCNR, except that in their paper e referred to earnings rather than efficiencies. We assume that the aggregate production function is given by AK α N 1−α . 5
In doing so, they implicitly used consumption, debt and default implications of their model to discipline the choice of earnings processes. Recently, Guvenen and Smith (2010) have strongly advocated taking consumption information into account in estimating parameters of the earnings process.
24
4.2
Data Targets and Parameter Values
With these functional forms, aside from A(e), there are 19 parameter values to fix. These are: four preference parameters (β, σ, ζ, ξ); one demographic parameter (ρ); three technology parameters (α, δ, χ); one legal system parameter (λ); and 10 earnings parameters which include four transition probabilities for π (we assume that the probability of transiting from s = 1 to s = 3 and vice versa is 0) and five parameters for the upper and lower limits (since units do not matter, e3min is chosen arbitrarily, and, for numerical convenience, it was set to 1/60) and distribution parameter ϕ. We constrain the value of ξ by the requirement that the highest paid person works twice as long as the lowest paid person. Using the expression for unconstrained labor choice, this restriction requires that [e1max /e3min ] = 2ξ . We take the upper and lower limits for earnings for the three income groups to be the same as in CCNR. These limits were chosen to target various quintiles of earnings and wealth distributions. Given a value of ξ, these limits on earnings determine corresponding upper and lower limits of efficiencies e. Again, using the unconstrained choice of n, earnings when efficiency is e are ζ −1/ξ (w(p)e)(1+ξ)/ξ . Thus, if the ratio of earnings of two people is y1 /y2 , the ratio of their respective efficiencies must be (y1 /y2 )ξ/(1+ξ) . In CCNR (Table III, pp. 1550), the ratio of earnings of the highest paid to the lowest paid is 21, 264. Therefore, the restriction regarding ξ can expressed as 21, 264ξ/(1+ξ) = 2ξ . This implies ξ = 13.37. In terms of elasticity of hours worked with respect to wages, this implies an elasticity of 0.07, which is consistent with the generally low values of elasticities found in micro studies.6 Given this value of ξ, the ratio of the efficiency limits can be recovered from the earnings limits reported in CCNR. For instance, the ratio of the highest to the lowest 6 Domeij and Floden (2006) have noted that borrowing constraints could downwardly bias the estimate of labor supply elasticity for certain specifications of utility functions. Our GHH specification does not suffer from this bias because labor supply is is independent of consumption and therefore wealth. Nevertheless, we will investigate how our findings are altered by a lower choice of ξ (and, therefore, a higher choice of labor supply elasticity).
25
earnings implies that (e1max /e3min )ξ/1+ξ = 21, 264, which yields (e1max /e3min ) = 10, 632.7 Setting of ξ and the efficiency limits leaves 13 parameters to be determined. Of these, six are determined independently by appeal to micro facts and the remaining seven are set so as to make model moments come close to relevant data moments. Table 1 gives the values of the parameters and the data targets that determine them.
5
Bankruptcy vs Garnishment
In this section, we compare bankruptcy and garnishment as ways of dealing with default on consumer debt. We do this by considering what happens to allocations and prices if the right of discharge is eliminated. As noted earlier, eliminating discharge will not eliminate default on consumer loans. It will simply activate a different set of creditor rights in dealing with default, namely, a creditor’s right to garnish a delinquent debtor’s wages (and property). In order to implement this, we need to give a value to cmin . We use IRS Financial Collection Standards for allowable living expenses to estimate “reasonable cost of living”. We take into account the allowable costs of housing, utilities, food, personal care and services, and miscellaneous expenses for households of different sizes. We then use the distribution of household size in the US to arrive at an average estimate for reasonable living expenses. Normalizing this estimate by average household income gives a value of 0.6103. We set cmin such that the ratio of cmin to average earnings in the (bankruptcy) model is 0.6013. This 7
The first-order serial correlation of earnings implied by this process is 0.75. This is much lower than the 0.98 AR1 coefficient estimated by Storesletten, Telmer and Yaron based upon the near-linear increase in the dispersion of earnings with age. Ignoring the information contained in the link between dispersion and age, Floden and Linde (2001) report persistence parameters for US earnings between 0.88 and 0.96 and Aiyagari and McGrattan (1998) suggest that it is closer to 0.6. More recently, Guvenen (2009) has challenged high estimates of persistence of earnings shocks on the grounds that researchers have erroneously attributed heterogeneity in income profiles (in terms of the level and growth rate of earnings) to persistent earnings shocks. Karahan and Ozkan (2010) argue that the near-linear increase in dispersion need not be indicative of a persistent income process if age variation in the persistence parameter and in the volatility of shocks is taken into account.
26
Table 1: Model Statistics and Parameter Values
Statistic Targets determined independently Average years of life Coefficient of risk aversion Labor share of income Depreciation rate of capital Average years of punishment Ratio of hrs worked by highest paid and lowest paid Upper limit of top earnings distn as multiple of e3min Lower limit of top earnings distn as multiple of e3min Upper limit of middle earnings distn as multiple of e3min Lower limit of middle earnings distn as multiple of e3min Upper limit of bottom earnings distn as multiple of e3min Lower limit of bottom earnings distn Targets determined jointly Average hours worked Earnings Gini index Wealth Gini index Percentage of defaulters Percentage in debt Capital-output ratio Debt-output ratio × 100
27
Target
Model
Parameter
Value
40 2.0 0.64 0.10 10 2 21264 14336 116 39 31 -
40 2.0 0.64 0.10 10 2 21264 14336 116 39 31 -
ρ σ α δ λ ξ e1max /e3min e1min /e3min e2max /e3min e2min /e3min e3max /e3min e3min
0.975 2.000 0.640 0.100 0.100 13.38 10,632 7,367 83 30 24 1/60
0.33 0.61 0.80 0.29 3.6 3.08 0.36
0.33 0.60 0.74 0.26 4.5 3.19 0.41
ζ π2,3 π3,3 β χ π1,1 π2,1 ϕ
5 × 105 0.240 0.972 0.909 0.021 0.095 0.0008 0.521
value is held constant when we calculate equilibrium under garnishment. Thus, roughly speaking, if a person’s earnings is less than 60 percent of mean income in the economy, he will not be obligated to make any payments on his defaulted debt.
5.1
Allocations and Prices
Table 2 compares the bankruptcy steady state with the garnishment steady state. In the garnishment economy, all parameters that are common between bankruptcy and garnishment economies are set to the values determined for the bankruptcy economy. Table 2: Comparison of Bankruptcy and Garnishment Economies
Statistic
Bankruptcy
Average hours worked Percentage under garnishment Earnings Gini index Percentage in debt Debt-output ratio as percentage Percentage of defaulters Percentage of pop w/ impaired credit Capital-output ratio Wage per efficiency unit Rental rate on capital (MPK - δ) Wealth Gini index
0.33 0.60 4.53 0.41 0.26 2.10 3.19 1.23 0.013 0.74
Garnishment
0.33 2.82 0.60 44.43 49.06 0.15 3.33 2.76 1.13 0.031 1.11
Comparison reveals some similarities and also some very striking differences. First, we see that the average labor supply in the two steady states are basically the same – actually, aggregate labor supply is slightly lower in the garnishment economy. There are two reasons for this. First, labor supply is lower because wages are lower (as we will see below). Second, 28
garnishment distorts effort choices downwards because of the “tax” element. However, these effects do not amount to much because the elasticity of labor supply is low and the fraction of people who are in garnishment is only 2.82 percent of the population. Because labor supply is not that much affected by the garnishment regime, the earnings Gini remains essentially the same even though average real income is lower. The most striking difference between the two equilibria is in the debt measures. In the bankruptcy equilibrium the percentage in debt is 4.53 percent and in the garnishment economy it is higher by almost a factor of 10, at 44.43 percent. Additionally, the debt-to-output ratio goes from 0.41 percent to a little under 50 percent. We will examine the causes underlying this huge expansion in consumer credit in detail below, but the basic reason this happens is because garnishment makes default on small levels of debt very expensive and, consequently, small debtors do not have the incentive to default. Under competition, the reluctance to default results in lower interest rates (higher q(a, s; p)) which motivates people to borrow more. The expansion in debt continues until the default rate becomes significantly different from zero. The default rate in the garnishment equilibrium is 0.15 percent of population, compared to 0.26 percent in the bankruptcy equilibrium. Thus, elimination of the bankruptcy option does not eliminate default, although it does substantially lower the default frequency. Even though the default rate is lower in equilibrium in the garnishment economy, the fraction of people with impaired credit (i,e., in bad standing) is 3.33 percent, which is higher than in the bankruptcy equilibrium. The reason is that a person’s garnishment flag stays on longer, on average, than a person’s bankruptcy flag. The duration of garnishment may itself last several periods, and once the debt has been paid off, the garnishment flag remains, on average, for as long as a bankruptcy flag does. The big increase in consumer credit crowds out fixed capital. The capital to output ratio declines from 3.19 to 2.76. This decline then has consequences for the real return on capital, which rises from 1.3 percent to 3.1 percent, and for the real wage, which falls from 1.23 units 29
of consumption goods to 1.13 units (a decline of 8.13 percent). We computed the transition path from one steady state to the next. It takes about 40 years for the capital stock to essentially converge to the new lower steady-state value. The transition is monotonic: the capital stock and real wages decline monotonically, while the real return on capital and the interest rate on deposits rise monotonically. Figure 1 display these transition paths (note that there is a decline in labor supply, although the decline is very small). Finally, it appears that the institution of bankruptcy is a potent force keeping the lid on wealth inequality in the US. When the bankruptcy option is eliminated, there is a massive increase in wealth inequality. This comes about because so many individuals become indebted. Figure 2 show the steady-state cumulative distribution for asset holdings for the two economies and the Lorenz curves of wealth distribution for the two economies. The CDF for asset holdings show that there is considerable mass on negative asset positions in the garnishment economy, whereas there is virtually no mass on these positions in the bankruptcy economy. The Lorenz curves dip measurably below zero because the bottom 44 percent of the population have a large negative asset position. Because of this, the value of the Gini coefficient exceeds 1 in the garnishment economy. The differences in the two economies stem from the the fact that there is a large expansion in the competitive supply of credit under garnishment because debtors find it less attractive to default. Why exactly does the incentive to default change so drastically in the garnishment economy? There are two effects at work. One is the stick effect, which is that default is more costly to the individual, and the other is the carrot effect, which is that maintaining access to markets is more beneficial. Figure 3 shows that both effects are at work. The green line in the center of the figure shows the value function under the bankruptcy regime of a bluecollar individual with the mean level of (blue collar) income. The point at which the value function becomes horizontal is the debt level at which this individual is indifferent between declaring bankruptcy or repaying. This happens at a debt level of 0.041. The other two lines show this individual’s value function conditional upon repaying and upon default under the
30
Figure 1: Transition Paths
Aggregate Capital, Transition Bank−>Gar
Aggregate Labor Suppply, Transition Bank−>Gar
0.72
0.1129
0.7
0.1128
0.68 0.1127 0.66 0.1126
K
N
0.64 0.1125
0.62 0.1124 0.6 0.1123 0.58
0.1122
0.56
0.54
0
5
10
15 20 Periods (change occurs in t=1)
25
30
35
0.1121
0
5
10
15 20 Periods (change occurs in t=1)
25
30
35
30
35
Net Return to Capital, Transition Bank−>Gar
Wage, Transition Bank−>Gar 1.24
0.032
0.03 1.22 0.028
0.026 1.2
r−delta
w
0.024
1.18
0.022
0.02 1.16 0.018
0.016 1.14 0.014
0
5
10
15 20 Periods (change occurs in t=1)
25
30
35
31
0.012
0
5
10
15 20 Periods (change occurs in t=1)
25
Figure 2: Wealth Distributions
Wealth Distribution Comparison
Lorenz Curve Comparison
1
1.2 Equality Bnk Lorenz (Gini = 0.74) Gar Lorenz (Gini = 1.09)
Bankruptcy Garnishment 0.9 1 0.8 0.8
Fraction of Wealth
Fraction of Households
0.7
0.6
0.5
0.4
0.3
0.6
0.4
0.2
0.2 0 0.1
0 −15
−10
−5
0 5 10 Wealth as Fraction of Income
15
20
25
32
−0.2
0
0.1
0.2
0.3
0.4 0.5 0.6 Fraction of Households
0.7
0.8
0.9
1
Figure 3: Value Functions
Value Function Comparisons −5
−10
−15
Utility
−20
−25
−30
−35 Good Standing Bnk Repayment Gar PE Std Default Gar PE Std −40 −5
−4
−3
−2
−1 0 1 Wealth as Fraction of Income
33
2
3
4
5
garnishment regime, holding all factor prices constant at the bankruptcy equilibrium. The bottom blue line is the value function from default under garnishment. Observe that as the debt level rises, default under garnishment becomes increasingly worse relative to the value of default under bankruptcy. This is the stick effect of garnishment: default under garnishment is simply not as beneficial to the individual as default under bankruptcy (because there is no discharge, the value under default falls with higher levels of debt). The top red line shows the value function under garnishment conditional on repayment. Notice that this value function lies considerably above the middle green line. This is the carrot effect of garnishment: by lowering the costs of borrowing, garnishment improves the value of maintaining access to credit market. The lens shaped area trapped between the blue and red line left of zero is the area where repayment is better than default under garnishment. Thus, reluctance to default has both a carrot as well as a stick aspect to it. As we will see, this aspect will play an important role in the welfare gains and losses experienced by different people in moving from bankruptcy to garnishment. Another way to understand the sources underlying the expansion of credit is to approach the differences between the bankruptcy and garnishment regimes in two steps. The first difference is that once a debt has been incurred it must be paid off (no discharge). The debtor may delay repayment over many periods, but the obligation to repay never goes away. The second difference is the garnishment per se: namely, the requirement that once a person has delayed his payment, he must pay some pre-determined fraction of his disposable income (if any) to his creditors toward satisfaction of the unpaid debt. Both aspects introduce a form of commitment on the part of individual debtors and each is partly responsible for the expansion in credit supply.8 The left hand plot in Figure 4 shows the separate contributions of the two aspects of the garnishment regime to the expansion of credit supply. The three thickest blue lines toward 8
The first difference also introduces a form of state contingency that goes beyond the state contingency that is implicit in bankruptcy: instead of a choice between repaying fully and not repaying at all, the individual can choose to pay a portion of the debt and defer payment on the remaining portion to future periods.
34
Figure 4: Loan Supply Schedules under Bankruptcy and Garnishment
Price Schedules Gar PE Standard and Gar GE 1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
q
q
Price Schedules Bank GE, Gar PE Simple, and Gar PE Standard 1
0.4
0.4
0.3
0.3
0.2
0.2 Bank GE Gar PE Simple Gar PE Standard
0.1
0 −10
−9
−8
−7
−6 −5 −4 −3 Wealth as Fraction of Avg Income
−2
−1
0.1 Gar PE Standard Gar GE 0
0 −10
−9
−8
−7
−6 −5 −4 −3 Wealth as Fraction of Avg Income
−2
the right of the figure are the loan schedules facing the three income classes in the bankruptcy regime. As one would expect, the top income class is offered the best loan terms and the bottom income class the worst. But, regardless of income class, the loan schedules drop off steeply as loan size increases. The drop-off mirrors the sharp increase in default probability with increase in loan size. The three black lines of medium thickness show the loan supply schedule when only discharge is eliminated but there is no garnishment per se. Formally, this is the garnishment environment where, once the person defaults, he is restricted to choosing a0 − a ≥ 0 as long as he has unpaid obligations. We refer to this partial equilibrium (PE) as “simple garnish35
−1
0
ment” (the phraseology refers to the fact that the debtor is not permitted to save in default because any assets would be seized in satisfaction of the claim). These loan schedules have been computed assuming no change in factor prices (so, all factor prices are held fixed at their bankruptcy steady-state values). We can see that eliminating discharge alone shifts out (or up) the loan supply schedules. The set of loan sizes for which there is no default (i.e., the horizontal segments of these schedules) is considerably larger than in the loan schedules under bankruptcy and the schedules do not drop off as sharply. The thin red lines on the far left of the figure are the loan supply schedules when garnishment of wages is permitted (factor prices are still held fixed at their steady-state bankruptcy values). In this case, a0 − a ≥ min{max{0, 0.25(w(p)en − cmin )}, −a}. We call this the PE “standard garnishment” case. The additional commitment to repay further expands the competitive supply of credit. The right-hand figure shows how the schedules for standard garnishment change as factor prices are changed to the new garnishment steady-state values. In the new steady state interest rates are higher and we see this reflected in the small shift down in the horizontal segment of the loan supply schedules. The new steady state also has lower real wages, which has a substantial downward effect on the loan supply schedule. Because people have less income, they are less able to service their obligations, so repayment rates go down. An alternative way of seeing the same set of effects is to compare the expected recovery rate on defaulted loans in the two PE cases and the GE case. The expected recovery rate is the expected return on each unit of defaulted debt, namely, q D (a, s, p). Figure 5 shows both the PE recovery rates for the simple and standard garnishment cases as well as the recovery rate for the standard garnishment case in the new garnishment equilibrium. The first point to note is that the recovery rate for the super-rich is 1. Thus, if such a person were to default, he would repay the whole debt in the period of default. Obviously, such a person would never default. For the white collar and the blue collar workers, the recovery rates decline with the level of debt. Since there is no discharge under garnishment, these declines 36
Figure 5: Recovery Rates
Recovery Rates in PE and GE 1 PE simple PE std GE
0.9
0.8
Recovery Rate
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 −10
−9
−8
−7
−6 −5 −4 −3 Wealth as Fraction of Avg Income
37
−2
−1
0
reflect the fact that once an individual defaults, full repayment takes longer for larger debts than smaller debts. The delay in repayment results in lower recovery rates. Delays are longer under “simple garnishment” because the debtor is not obligated to make minimum payments when disposable income is positive. Under “standard garnishment” recovery rates are higher, especially for large debts – that is the situation in which the added commitment from garnishment per se really matters. As we move from PE to GE, the recovery rates fall and they do so mostly because earnings are lower for all individuals. People make smaller payments and any given level of unpaid debt takes longer to be fully repaid.
5.2
Welfare
We now turn to the welfare effects of the eliminating bankruptcy. We focus on two measures of welfare. In the first measure we compute how much flow consumption a person would give up to go from a regime in which there is bankruptcy to a regime in which bankruptcy is eliminated and garnishment becomes the way to deal with default. In the second measure, we simply count the fraction of people who would be in favor of eliminating bankruptcy. The latter measure provides some insight into the degree of political support in favor of or against the institution of bankruptcy. In both cases, we assume that the question is posed in an unanticipated manner after people have made their default decision but before they have chosen their new asset positions. This timing ensures that the contemplated switch in regime will not impose any unanticipated losses or gains on the intermediary sector.9 Panel A of Table 3 reports the consumption equivalent measure from eliminating bankruptcy when people do not take the general equilibrium effects on factor prices into account. In other words, they continue to expect that the interest rate on deposits and the wage rate will 9
We start with the steady state bankruptcy distribution in period 0. Then, all households who would default in steady state are transitioned to 0 assets and h = 1. This is the period 1 distribution. We then we let households make their c, n and a0 choices.
38
remain the same as in the bankruptcy steady state. Each cell gives the consumption flow averaged across the cell’s households. Thus, overall, there is a very large perceived welfare gain from eliminating bankruptcy – amounting to 13.3 percent of consumption in perpetuity. The gain is not uniform: the “blue-collar and in debt” group gains the most. The reason is easy to understand – this is the group that sees a large shift out in the loan supply schedule and, consequently, they can refinance their existing debt at a much lower interest rate and increase their borrowing if they so desire. The white collar groups also experience gains in welfare, with those in debt gaining more than those not in debt. The super-rich group see a small loss in welfare. Generally, these are people who are asset-rich and expect to borrow with a very small probability. Therefore, the change in regime is of little consequence for them. We do not have a compelling explanation for why the estimate is negative other than to believe that numerically, zero change in welfare could manifest itself as a small negative or positive number. Panel B of the table reports the fraction of people in each cell in favor of eliminating the bankruptcy option. The super-rich are unanimous in their opposition to the change but this could be a numerical artifact; a better interpretation would be that this group is indifferent between elimination or not. For the other two classes, those in debt are unanimous in their approval of eliminating the bankruptcy option. Table 4 gives the welfare numbers, taking into account all of the general equilibrium effects, including the transition from the bankruptcy steady state to the garnishment steady state. As noted earlier, the new garnishment steady state has lower capital per worker. During the transition, capital stock declines monotonically to the new steady state. Along the way, the interest rate facing the intermediary sector rises and the wage rate for efficiency units falls monotonically. As is evident, taking the general equilibrium effects into account improves welfare for all of the cells, relative to bankruptcy. In particular, even the rich are willing to pay to move to eliminate the bankruptcy option because they own assets and the interest rate on assets improves during the transition and in the steady state. As the bottom panel
39
Table 3: PE Welfare Gains From Elimination of Bankruptcy Panel A
All
Rich
White Collar
Blue Collar
All In Debt No Debt
13.3 41.1 12.3
-0.0 -0.0
3.4 6.6 3.3
15.0 42.2 13.3
Panel B
All
Rich
White Collar
Blue Collar
All In Debt No Debt
98.8 100 98.8
0.0 0.0
99.8 100 99.8
99.9 100 99.9
in the table shows, the elimination is unanimously preferred. It is somewhat surprising that elimination of bankruptcy is viewed favorably even after general equilibrium effects are taken into account. In the new steady state, people whose incomes flow mostly from labor earnings are going to be poorer because of the lower wage rate. We would expect these people to suffer some loss in utility. Indeed, if we simply compare the welfare gains from moving directly from the bankruptcy steady state to the garnishment steady state, the welfare estimates for some groups are negative. Table 5 displays these estimates. Observe first that the rich are now fully in favor of the elimination – this results from the fact that they see a higher interest rate on their assets. White collar workers, especially those in debt, see lower welfare gains. These declines reflect the shift back in the loan supply schedule resulting from the lower capacity to repay due to lower wages. There is also a similar decline for blue collar workers for the same reason. Panel B of the table shows that there is a lot more disagreement among people regarding the elimination of bankruptcy. The blue-collar workers in debt is now the only group that unanimously favors elimination. Evidently, it is important to take transition effects into account when performing experiments of this sort. 40
Table 4: GE Welfare Gains From Elimination of Bankruptcy Panel A
All
Rich
White Collar
Blue Collar
All In Debt No Debt
6.1 25.0 5.5
15.9 15.9
2.5 2.1 2.5
6.5 25.7 5.8
Panel B All In Debt No Debt
All 100 100 100
Rich 100 100
White Collar 100 100 100
Blue Collar 100 100 100
Table 5: SS Welfare Gains From Elimination of Bankruptcy Panel A
All
Rich
White Collar
Blue Collar
All In Debt No Debt
4.7 21.0 4.1
15.3 15.3
2.0 -0.3 2.0
4.9 21.7 4.3
Panel B All In Debt No Debt
All Rich 80.9 100 97.7 80.3 100
White Collar 58.9 23.9 59.2
Blue Collar 84.0 100 83.3
41
Although everyone is better off with elimination of the bankruptcy option it is not the case that elimination is preferable under all circumstances. Figure 6 shows the distribution of welfare gains taking account of transition for different levels of wealth and different levels of efficiency for each of the three income classes. It shows that there is a welfare loss from elimination for white and blue collar individuals with high levels of debt. Such individuals are indebted enough that default is a relatively likely event for them and, as discussed earlier, default is worse under garnishment than under bankruptcy. Of course, such highly indebted individuals do not exist in the bankruptcy equilibrium and so their their opposition to elimination is not recorded. More generally, the heterogeneity in welfare gains evident in the Figure 6 reflects the differential effects of the carrot and stick effects noted earlier. Garnishment makes borrowing cheaper but at the expense of making default more costly. Thus, the welfare gains tends to rise with the likelihood of the person borrowing in the current or some future period and it tends to decline with the likelihood of the person defaulting in some future period. To confirm this intuition we simulated a very large number of individuals under the garnishment regime for 80 periods (with prices held constant at the bankruptcy equilibrium) and computed the probability that an individual would eventually borrow or eventually default in this 80 year period. We then regressed the welfare gain measure for each individual against these probabilities. Table 6 summarizes the results. The regression shows that about 79 percent of the variation in welfare gains can be accounted for by these two probabilities. Furthermore, the welfare gain rises with the probability that the individual will borrow and decrease with the probability the individual will default.
5.3
Consumption Smoothing Under Garnishment
Garnishment increases the value of maintaining access to credit markets and allows for a vast expansion of credit. We may wish to understand exactly what this expansion allows
42
Figure 6: Distribution of Welfare Gains by Wealth
Consumption Equivalence Under Transition 120
100
Csn Equivalence (% Csn Incr)
80
60
40
20
0
−20
−40
−60 −5
Bl.Col. Wh.Col. S.Rich −4
−3
−2
−1 0 1 Wealth as Fraction of Income
43
2
3
4
5
Table 6: Welfare Gains, Borrowing and Default Constant
Probability of Borrowing
Probability of Default
R-Square
-2.436
0.332
-0.841
0.788
in terms of consumption profiles. With this in mind, we simulated a large number of blue collar individuals who “start life” with a = 0, h = 0 and e drawn independently conditional on being blue collar. We recorded their consumption and asset holdings for the next 80 periods (years) under both the bankruptcy steady state and the garnishment steady state. The following two figures display average consumption and average asset holdings across the two regimes for each of the 80 periods. Observe that mean asset holdings decline below zero in the garnishment economy, whereas they increase rapidly in the bankruptcy economy. In the latter, the high cost of loans forces individuals to accumulate assets in order to self-insure. In the garnishment economy, the need to accumulate precautionary savings is much less urgent, since the loan supply schedule is much more attractive. As a result, mean asset holdings are actually negative in the first few years of life. We see the effect on consumption in the adjacent figure. Mean consumption is higher in the garnishment economy because people are saving less. Mean consumption stays high for some time until the accumulated debt burden begins to lower consumption below that in the bankruptcy economy. We can see the effects of better consumption smoothing in Figure 8. The left hand panel displays the standard deviation of consumption. Observe that the standard deviation is initially lower in the garnishment economy but then eventually exceeds that of the bankruptcy economy. It is lower initially because of the superior consumption smoothing afforded by the generous loan supply schedules under garnishment. But the other side of the same coin is the increased dispersion of asset holdings resulting from enhanced borrowing and lend44
Figure 7: Mean Assets and Mean Consumption by “Age”
Sample Mean of Wealth
Sample Mean of Consumption 0.18
0.16 0.8 0.14
0.12
mean(c)
mean(a)
0.6
0.4
0.2
0.1
0.08
0.06
0.04 0 0.02 Mean(a) bankrupcty Mean(a) garnishment −0.2
0
10
20
30
40 Period
50
60
70
Mean(c) bankrupcty Mean(c) garnishment 80
45
0
0
10
20
30
40 Period
50
60
70
80
Figure 8: Dispersion of Consumption by “Age”
Sample Standard Deviation of Consumption
Sample Coefficient of Variation of Consumption
0.5
3
0.45 2.5 0.4
0.35 2
CV(c)
std(c)
0.3
0.25
1.5
0.2 1 0.15
0.1 0.5 0.05 Std(c) bankrupcty Std(c) garnishment 0
0
10
20
30
40 Period
50
60
70
CV(c) bankrupcty CV(c) garnishment 80
46
0
0
10
20
30
40 Period
50
60
70
80
ing. Higher wealth inequality eventually translates into higher consumption inequality. The right hand panel displays the coefficient of variation of consumption. The fall in the initial dispersion of consumption in the garnishment economy is even more evident in this panel.
6
Sensitivity Analysis
We perform two sensitivity analyses. In the first, we experiment with an estimate of elasticity of labor supply from the upper end of the range of estimates available. In the second, we pick an efficiency process that does not generate the kind of income and wealth inequality we see in the US but which better matches longitudinal data (PSID) on earnings.
6.1
The Effect of a Higher Labor Supply Elasticity
We consider a labor supply elasticity parameter of 0.33 as opposed to 0.07. This meant setting ξ = 1/0.33. To keep the earnings distribution the same as in the baseline model, we changed the upper and lower limits of the efficiency distributions for each income class so that relative earnings (the highest paid vs the lowest in each group) remained the same as in the baseline model. We also adjusted the value of ζ to keep the average hours worked under bankruptcy equal to 0.33 and the values of A(e) were adjusted as well to reflect the new unconstrained labor choices. All other parameter values were kept at their baseline values. Table 7 reports the operating characteristics of the bankruptcy and garnishment economies. The operating characteristics of either economy do not change much from their baseline counterparts. In particular, even though we did not attempt a full re-calibration of the bankruptcy model, the fit between the model and targets is about as good as in the baseline calibration. There is a bit more debt and default relative to the baseline model and the capital output ratio is slightly lower. The most significant change is in the Gini for wealth:
47
it drops from 0.74 in the baseline model to 0.69. For the garnishment economy there is a drop in average hours worked relative to bankruptcy (and the garnishment economy with lower elasticity of labor supply), from 0.33 to 0.32. The drop results from the downward distortion in labor supply for those in garnishment, which is now more pronounced. There is bit more debt and default relative to the baseline garnishment economy. Over all, the elimination of the bankruptcy option has the sorts of effects as in the baseline economies. Table 7: Comparison of Bankruptcy and Garnishment Economies with Higher Labor Supply Elasticity Statistic
Targets
Average hours worked Percentage under garnishment Earnings Gini index Percentage in debt Debt-output ratio as percentage Percentage of defaulters Percentage of pop w/ impaired credit Capital-output ratio Wage per efficiency unit Rental rate on capital (MPK - δ) Wealth Gini index
0.33 0.61 3.50 0.36 0.29 3.08 0.80
Bankruptcy
0.33 0.60 4.52 0.43 0.30 2.42 3.12 1.21 0.015 0.69
Garnishment
0.32 2.60 0.60 40.60 45.52 0.17 3.54 2.73 1.13 0.032 1.05
Table 8 display the welfare gains from moving from the bankruptcy steady state to the garnishment steady state, taking into account the transition. The pattern of gains is similar to the baseline model. The overall welfare gain is now 7.1 percent of flow consumption in perpetuity as compared to 6.1 percent in the baseline model. As before, all groups are unanimous in their support for eliminating the bankruptcy option.
48
Table 8: GE Welfare Gains From Elimination of Bankruptcy for Economy with Higher Elasticity of Labor Supply
6.2
sub Panel A
All
Rich
White Collar
Blue Collar
All In Debt No Debt
7.1 28.4 6.4
14.3 14.3
3.0 3.0 3.0
7.6 29.2 6.8
Panel B All In Debt No Debt
All 100 100 100
Rich 100 100
White Collar 100 100 100
Blue Collar 100 100 100
The Effect of Higher Persistence of Efficiency Shocks
Here we examine how our results change if keep all parameters the same but adopt an efficiency process that better matches the longitudinal data on earnings. Floden and Linde (1999) estimate a wage process implied by the observed earnings and hours dynamics in the PSID. They find that cross-sectional variation in wages come from three sources: permanent variation in wages (wage inequality) with an estimated variance of 0.1175, temporary but persistent variation estimated to have an AR1 representation with autocorrelation parameter of 0.91 and an innovation variance of 0.0426, and pure measurement error with estimated variance of 0.0421. Thus permanent wage inequality accounts for 28 percent of the variance in wages, temporary but persistent variation accounts for 62 percent, and the purely transitory measurement error accounts for 10 percent. We map this earnings process into our model in the following way. We model the permanent variation in efficiency by assuming that there are two types having mean efficiencies that 1
are 0.1175 2 above and below mean efficiency in the economy. For numerical convenience we assume that it is possible for one type to change into the other but the probability with which this happens (for either type) is 0.0001. Thus, the types are essentially permanent. 49
The (mean zero) AR1 process is modeled with a first-order Markov chain with 43 states. Thus, over all, the efficiency process now has 86 states which also means that the loan supply schedules need to distinguish between 86 states as well. Other than rescaling the efficiencies so that mean earnings with this new process is same as the mean earnings in the baseline bankruptcy economy, we left all other parameters the same as in the baseline calibration. Table 9 reports the operating characteristics of this economy under bankruptcy and garnishment. Looking first at the bankruptcy economy, observe that income and wealth inequality is seriously under-predicted with the new process. The degree of income inequality depends on the elasticity of labor supply, with higher elasticities implying more inequality. However, for the low elasticities generally estimated in the micro labor literature, the efficiency process implied by longitudinal data seem inconsistent with the degree of income inequality observed in the real world. Observe also that the debt-to-output ratio is now less than a third of the data and defaults are essentially non-existent. Basically, with the new parametrization of the efficiency process, the loan supply schedules under bankruptcy are such that people borrow very small amounts and default very rarely.10 Setting aside these issues, however, the effect of eliminating the bankruptcy option is similar. There is large expansion in debt as well as the percentage of individuals in debt. The default rate is higher and the steady state percentage of delinquent debtors under garnishment is almost 19 percent. There is a decline in the capital output ratio and increase in wealth inequality. Turning to welfare, Table 10 reports the average welfare gain for different segments of the population. Overall, eliminating the bankruptcy option leads to a gain in welfare of 0.8 10
It is possible to get more debt and default into the model by increasing the pecuniary costs of default (i.e., by increasing χ). See for instance Li and Sarte (2006) and Athreya (2008). We do not follow this approach because we are uncomfortable with assuming an efficiency process that seems so off with regard to income and wealths distribution statistics.
50
Table 9: Comparison of Bankruptcy and Garnishment Economies with a Different Efficiency Process Statistic
Targets
Average hours worked Percentage under garnishment Earnings Gini index Percentage in debt Debt-output ratio as percentage Percentage of defaulters Percentage of pop w/ impaired credit Capital-output ratio Wage per efficiency unit Rental rate on capital (MPK - δ) Wealth Gini index
0.33 0.61 3.50 0.36 0.29 3.08 0.80
Bankruptcy
0.32 0.39 8.10 0.10 0.0002 0.002 2.41 1.05 0.050 0.66
Garnishment
0.32 18.73 0.39 25.99 58.17 0.64 20.53 2.25 1.01 0.059 1.07
Table 10: GE Welfare Gains From Elimination of Bankruptcy for Economy with Different Income Process All
In Debt
No Debt
Average Consumption Equivalent
0.8
2.7
0.7
Percentage in Favor of Eliminating Bankruptcy
57.9
70.6
56.8
51
percent. This is a much smaller gain than the one calculated for the baseline economy. As one would expect, the gain is most for people who are already in debt since they see a lower interest rate. In terms of the percentage in favor of eliminating bankruptcy, a majority continues to be in favor of it.
7
Conclusion
This paper compared bankruptcy and garnishment as two different legal approaches to consumer default. The garnishment regime makes default on consumer loans more costly (but not impossible), which makes it possible for a competitive intermediary sector to expand the supply of consumer credit. The increased supply of credit, in turn, makes credit market access valuable and further reduces the incentive to default on loans. The combined effect of these changes is a very large expansion in the supply of credit to households. In the new equilibrium, consumer credit crowds out fixed investment and leads to higher interest rates and lower wages. Despite what might appear to be adverse general equilibrium effects from the perspective of indebted households, welfare is higher under garnishment than under bankruptcy. The ability to borrow cheaply against future income allows better intertemporal allocation of consumption. In conclusion, some caveats regarding the findings presented in the paper are in order. First, as demonstrated, the improvement in average and individual welfare under garnishment is accompanied by radical increase in wealth inequality. Our welfare analysis did not make any attempt to balance the efficiency gains stemming from garnishment against the potential social costs of greater wealth inequality. A more complete welfare comparison of bankruptcy and garnishment would require attention to be paid to the dramatic inequality implications of garnishment. Second, we ignored life-cycle features. As noted earlier, this was done so as to allow computa-
52
tion of equilibrium factor prices (steady state as well as transition ones) within a reasonable time frame. Presumably, this time constraint will get relaxed in the future, which would then allow life-cycle features to be taken into account in a fully general equilibrium analysis. However, incorporating age explicitly in the model would complicate the computation of equilibrium in a different way. US law prohibits lenders from discriminating on the basis of age in setting credit terms and it would be desirable to take this restriction into account in computing equilibrium prices. However, when lenders are forced to charge the same interest rate to people with different propensities to default, the computation of competitive (zero profits) prices will require knowledge of the distribution of loans: what fraction of a loan any given size is acquired by individuals of a given ages? This added informational requirement will increase the computational burden and would complicate the task of computing equilibrium factor prices. Finally, our analysis abstracted from aggregate shocks. It would be interesting to explore how aggregate variability in the efficiency of the economy (TFP shocks) might affect the cyclical variability of consumption under a garnishment regime. We know from the literature on sovereign debt (Aguiar and Gopinath (2006), Arellano (2008)) that cyclical variability in income can cause countercyclical variation in default risk premium on loans. In bad times the loan supply schedules shift right (or down) to reflect a higher probability of default on loans. This cyclical variation in the supply for loans can become an additional reason for cyclical fluctuations in consumption, provided indebtedness is pervasive and significant, as it is under garnishment. This could potentially detract from the welfare improvements associated with the garnishment regime.
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