محدودیت های بدهی های درونی در مدل چرخه زندگی با یک برنامه امنیت اجتماعی

This paper develops a simple life-cycle model that embeds a theory of debt restrictions based on the existence of inalienable property rights à la Kehoe and Levine [1993. Debt constrained asset markets. Review of Economic Studies 60(4), 865–888; 2001. Liquidity constrained markets versus debt constrained markets. Econometrica 69(3), 575–598]. In our environment, net debtors have the option of defaulting on unsecured debt at the cost of being subjected to wage garnishment and/or having some or all of their future assets seized by creditors. One advantage of our framework is that it encompasses two standard versions of the life-cycle model: one with perfect capital markets and one with a non-negative net-worth restriction. We study the impact of a payroll financed social security system to illustrate the role of endogenous debt constraints and compare our results to a model with exogenous debt constraints. Whereas the aggregate effects are similar under both types of constraints, the distributional consequences are found to be significantly different across debt regimes.

This paper develops a simple life-cycle model that embeds a theory of debt restrictions based on the existence of inalienable property rights (Kehoe and Levine, 1993 and Kehoe and Levine, 2001). In our environment, net debtors (typically young individuals with bright futures) have the option of defaulting on unsecured debt at the cost of being subjected to wage garnishment and/or having some or all of their future assets seized by creditors. One advantage of our framework is that it encompasses two standard versions of the life-cycle model: one with perfect capital markets and one with a non-negative net-worth restriction. Our environment differs in two important ways from typical models with ‘endogenous debt constraints’, such as Kehoe and Levine, 1993 and Kehoe and Levine, 2001, Kocherlakota (1996), Alvarez and Jermann (2000), and Krueger and Perri (2005). First, the income fluctuations which give rise to our debt constraint emanate purely from life-cycle considerations. Since these papers use the infinitely lived agent abstraction, individuals need to face other kinds of fluctuations in order for the default option to be meaningful. In our framework, debt constraints arise from the simple fact that young individuals with bright futures want to smooth their life-cycle consumption. But doing so potentially entails contracting large amounts of unsecured loans. Once in their peak earning years, these individuals may find defaulting on their loans an attractive option. Since rational creditors take these incentives into account in their supply of loans, individuals may find themselves debt constrained early in their life-cycle. Second, whereas debt constraints in our environment arise from a default option, the default option does not correspond to autarky.1 The default option in our framework is meant to capture in a crude way the main aspects of the bankruptcy law.2 In essence, bankruptcy laws restrict the extent to which creditors can garnishee wage income and seize an individual's assets (current and future). Upon default—which does not occur in equilibrium in the model—the rights to a fraction of an individual's current and future assets and/or wage income that can be legally garnisheed are transferred to the creditors. The permanent nature of the punishment implies that creditors will refrain from lending to individuals with a history of default. A by-product of our theory, then, is that individuals face a non-negative net-worth restriction conditional on default—a familiar problem—rather than a lending constraint, which obtains when autarky is assumed following loan default. In our framework, the garnishment limits naturally translate into debt limits at the individual level: the more creditors can garnishee, the more credit is extended to individuals. In other words, harsher punishment upon default imply higher levels of debt, consistent with the work of Mateos-Planas and Seccia (2006). Following the work of Bulow and Rogoff (1989) on sovereign debt, it is well known that the possibility of savings upon default in standard models implies that no credit will ever be extended. In other words, ‘merely denying credit is not a sufficient threat to create a loan market’ as Kehoe and Levine (2001) put it. The reason is simple: since no individual would ever pay back a loan during their last period of life, no credit will be extended to such an individual. But since it is known that default would occur in the last period of life, there is no point in extending credit the period before since individuals would default there as well, and so on. The reason why this does not occur in our economy is because of the long lasting effect of default: when an individual defaults, there is always some resources that creditors can garnishee in future periods. This feature is what makes credit markets operational from the first periods of individuals’ life. Our framework offers a simple way of modeling debt constraints which respond endogenously to exogenous changes in the environment. As an application of our setup, we illustrate the role of endogenous debt constraints by studying the impact of introducing a payroll-tax financed social security system. We compare our results to those of the Hubbard and Judd (1987), who were among the first to examine the welfare implications of a social security system in the context of a life-cycle model with exogenous debt constraints. Because the U.S. social security system is financed primarily through a payroll tax, the burden of finance falls disproportionately on the young and middle-aged members of the population who are approaching, or are in, their peak earning years. The provision of social security is likely to reduce the desired private saving (increase desired borrowing) among individuals in these younger cohorts. But to the extent that individuals in this subgroup are debt constrained, a proportional payroll tax reduces consumption expenditures dollar for dollar, and as a consequence, increases the welfare cost (reduces the benefit) of the government program. Hubbard and Judd (1987) demonstrate that these effects can be quantitatively important. Through a parameterized version of our model, we show that the introduction of a redistributive fiscal policy such as a pay-as-you-go social security system does affect the functioning of private credit markets by tightening individuals’ debt constraints (as the supply of private loans contracts). Thus, in contrast to exogenous non-negative net-worth constraints, the consumption of debt constrained individuals may respond more than one for one in the face of a payroll tax. Our findings indicate that whereas the aggregate effect of introducing a social security system is similar whether the debt constraint is endogenous or exogenous, its distributional effects are significantly different. Rojas and Urrutia (2008) extend our analysis and show that our aggregate results are robust to the introduction of idiosyncratic uncertainty. Furthermore, they show that the transition following the elimination of social security is monotonic and that while individuals alive at the time of the announcement suffer significant losses, these losses are invariant to whether the debt constraint is endogenous or exogenous. The rest of the paper is organized as follows. The next section lays down the economic environment and studies the consumer's problem under endogenous debt constraints. In Section 3 we parameterize the model and investigate its behavior under different parameters governing the bankruptcy code. The impact of a payroll financed social security system under endogenous and exogenous debt constraints is the subject of Section 4. Finally, concluding remarks are offered in Section 5.

This paper investigates whether the welfare calculations usually found in the literature with regard to the introduction of a social security system (e.g., Hubbard and Judd, 1987) are sensitive to the specification of the borrowing constraint. We develop an overlapping generations model in which, in the spirit of Kehoe and Levine (1993), debt restrictions arise endogenously due to the existence of inalienable property rights. The legal structure we consider is one in which creditors lay claims to a fraction of a defaulter's assets (either current or future). Although an improvement in the ability of creditors to seize assets helps debt constrained individuals to obtain credit, it also lowers the level of the capital stock as well as the wage rate, leading to lower aggregate welfare. This is in contrast to pure exchange economies, as in Mateos-Planas and Seccia (2006), where the effect on wages does not arise. The results of this paper suggest that if one is only interested in the aggregate impact of social security, then an exogenous specification of the borrowing constraint is not a bad approximation. Indeed, results in Rojas and Urrutia (2008) suggest that our results generalize to economies where individuals face uninsurable idiosyncratic uncertainty, not only in steady state but also during the transition. These aggregate results, however, mask important heterogeneous effects at the individual level.