اصلاح امنیت اجتماعی با ریسک در آمد نامطمئن و محدودیت وام گیری درونی

We study the effects of a social security reform in a large overlapping generations model where markets are incomplete and households face uninsurable idiosyncratic income shocks. We depart from the previous literature by assuming that, because of lack of commitment in the credit market, the borrowing constraint in the unique asset is endogenously determined by individuals' incentives to default on previous debts. In our model, after the reform the incentives to default are lower and consequently households face more relaxed borrowing limits, leading to an increase in debt and a reduction in the size of precautionary savings. However, the quantitative impact of this mechanism on stationary aggregate savings is small. Computing the transitional dynamics for the basic model following the social security reform we obtain important welfare gains for workers at the bottom of the income distribution (equivalent to 1.3% of consumption each period) associated to the relaxation of the endogenous borrowing constraints, which are missed in an environment with fixed borrowing limits

In this paper, we address the following methodological question: Are endogenous borrowing constraints, arising from the lack of commitment in the credit market, important in order to understand the effects of reforming social security? Our answer is that, when idiosyncratic income risk is important and borrowing limits are endogenous, the magnitude of the increase in capital accumulation after a social security reform is reduced, although this effect is quantitatively small. Moreover, eliminating the public pay-as-you-go social security system has large effects on aggregate debt and the welfare of individuals at the bottom of the income distribution which are not accounted for by models with exogenous borrowing constraints.There is a well-established literature on social security reform using dynamic general equilibrium models. The seminal example of this tradition is the deterministic model by Auerbach and Kotlikoff (1987). More recently, some studies have addressed the aggregate effects of reforming social security in model economies with idiosyncratic in- come risk. The work of Imrohoroglu et al. (1995), Conesa and Krueger (1999) and Storesletten et al. (1999) are typical examples. With the probable exception of Fuster (1999), who works on a dynastic framework, these studies find that eliminating the pay-as-you-go system has large positive effects on capital accumulation and savings, as well as important welfare and distributional effects. One common feature in these models is that individuals face exogenous borrowing constraints, in fact, zero- borrowing limits. Consequently, they do not account for the possible effect that a change in the social security regime may have on the incentives to default on previous debts. With limited commitment, financial intermediaries take into account an individual rationality constraint from the borrower’s side, namely, that the value of paying back the debt is no less than the value of defaulting given an exogenous punishment, associated to some level of exclusion from financial markets in the future. Hence, a drastic change in the economic environment like a social security reform may affect the relative value of default and the endogenous debt constraints associated to it. If idiosyncratic risk is important, these changes in borrowing limits affect precautionary savings and household’s debt position. 1 To analyze (and quantify) this mechanism, we build a large overlapping generations model where households face uninsurable idiosyncratic earnings shocks. Agents live for a maximum number of periods and retire at an exogenous age. In addition to idiosyncratic income risk, agents face a life cycle profile of average earnings and mortality risk after retirement. All agents are ex-ante equal. Markets are incomplete by assumption, since we only allow for one asset. These features of the model are standard in the social security literature and correspond closely to the assumptions in Imrohoroglu et al. (1995). We depart from this literature by assuming that, because of lack of commitment, financial intermediaries are only willing to lend to a worker the maximum amount of resources that satisfies the rationality condition of no default for all possible values of the earnings shock tomorrow. A similar assumption has been used by Zhang (1997), Fernandez Villaverde and Krueger (2002), and Bai and Zhang (2005), among others. Consequently, individuals face age-specific borrowing limits and there is no default in equilibrium. Our choice of the financial structure requires some discussion. In the incomplete markets literature our structure lies somewhere in between two classes of models. On the one hand, precautionary savings models (as in Huggett, 1993 and Aiyagari, 1994) exogenously restrict the number of assets to one and assume a borrowing limit (often, zero borrowing). On the other hand, the seminal paper by Kehoe and Levine (1993), followed by Alvarez and Jermann (2000), assumes a full set of contingent assets but with an endogenous borrowing limit in each arising from the lack of commitment from the borrower’s side. In our model we do restrict the set of assets, as in the first framework, but we also endogenize the borrowing limit, as in the second. The main reason for not following Kehoe and Levine (1993) throughout and assume a complete set of contingent assets is because such a formulation would minimize the role of precautionary savings, which are key to our story. Moreover, the results would be less comparable to the current social security literature, which assumes one asset and exogenous limits. 2 We start from the steady state of our economy under a pay-as-you-go social security system with a generous re- placement rate. Each worker pays a social security tax proportional to her labor income when working, and collect benefits after retirement. We assume that the benefits are the same for all retirees, independently of the amount con- tributed to the social security fund. Hence, social security plays an insurance role against earnings shocks during the working life. The basic experiment is to compare this steady state, calibrated to reproduce some key statistics for the US economy, to one in which the replacement rate is zero so workers have also to build their own savings for retire ment. We also compute the transitional path between these two stationary equilibria assuming a gradual elimination of the pay-as-you go social security system. Our numerical results replicate previous findings in that a social security reform increases savings and fosters capital accumulation. Keeping fixed the initial borrowing constraints, the elimination of social security increases the capital to output ratio and the savings rate by 27% in the long run. When we allow for endogenous borrowing constraints to adjust to the change in default incentives, the increase is smaller, about 25%. The reason is that with the elimination of social security individuals have less incentives to default on debts. The relaxation of borrowing constraints associated to this fact implies that the agents need to save less for precautionary reasons, which goes in the opposite direction to the traditional increase in savings associated with the reform of public pensions. However, the difference between the two environments is quantitatively small. We obtain larger differences in the level of debt supported in equilibrium: With endogenous constraints, the relaxation of borrowing limits leads to a debt boom, which is missed in the model with fixed borrowing limits. 3 The transitional dynamics of the model features monotonic convergence between the initial steady state under a pay-as-you-go pension system and the final steady state without social security. We also obtain in the short-run small differences in savings rates between the models with endogenous and fixed borrowing constraints. More importantly, computing the transition allows us to do welfare comparisons. For individuals at the bottom of the income distribution, we find large welfare gains in the order of magnitude of 1.3% lifetime consumption associated to the relaxation of the borrowing limits after the social security reform. These gains are missed in a model with fixed constraints. The paper is organized as follows. Section 2 describes the main features of our economic environment and defines the equilibrium concept. Section 3 explains the calibration procedure and discuss some features of our benchmark quantitative model. In Section 4 we perform the main policy experiment, analyzing the long-run effects of eliminating social security on savings under fixed and endogenous borrowing limits. The transitional dynamics of the model is analyzed in Section 5, where we also perform the main welfare calculations. To assess the robustness of our results to different financial structures, Section 6 introduces risky loans with default in equilibrium. Finally, we conclude.

We have shown that when borrowing constraints are endogenous and idiosyncratic income risk is important the magnitude of the increase in the capital to output ratio and the savings rate due to a social security reform is reduced. The reason is that with the elimination of social security individuals have less incentives to default on debts. The relaxation of borrowing constraints associated to this fact implies that the agents need to save less for precautionary reasons. This effect goes in the opposite direction to the traditional increase in savings associated with the reform of public pensions. From a quantitative perspective, though, the aggregate effects are small, especially if we allow for risky loans with the default option.However, endogenizing the borrowing limits matters if we want to analyze the evolution of some financial variables after a social security reform. Ignoring the relaxation of borrowing limits underestimates the increase in total debt, as well as the reduction in default rates (when the default option is allowed). Moreover, we find significant welfare gains associated to the relaxation of borrowing limits after the reform for individuals at the bottom of the income distribution, mainly young workers with bad income realizations. There are two important directions for future research that we plan to pursue. One is to include additional sources of risk, as marital status or medical expenses. Chatterjee et al. (2004), among others, show that the uncertainty asso- ciated to such distresses are important for the borrowing decisions of households. Second, it seems relevant to add a third asset to the model (as durables or housing) which could be used as collateral for loans, in the direction of Fer- nandez Villaverde and Krueger (2002). Then changes in the social security system might have an additional impact on borrowing limits through the price of such an asset