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We analyze the welfare effects of an unfunded social security system. We do so using an overlapping generations economy wherein agents have self-control preferences, face mortality risk, individual income risk, and borrowing constraints. Given our specification of preferences, unfunded social security helps reduce the agents’ temptation to consume in every period; consequently, the welfare costs it otherwise entails are substantially mitigated. While both social security and self-control when considered separately reduce welfare, their combination renders this effect considerably less severe. Moreover, if the cost of resisting temptation is very high, the introduction of social security might even improve welfare.

The economic benefits of an unfunded social security system are largely summarized in providing intra- and intergenerational risk sharing. Still, this is accomplished at the significant cost of encouraging early retirement, while also entailing distortions in agents’ labor supply and private savings decisions. The latter can be readily shown in an overlapping generations model where consumers supply labor inelastically (Diamond, 1965). Since social security redistributes income from the young to the old generation, it lowers savings and consequently, the steady-state capital stock. In addition, Auerbach and Kotlikoff (1987), Imrohoroglu et al. (1995), and Hugget and Ventura (1999), using large-scale overlapping generations models, show that an unfunded social security system generates distortions in labor supply and capital accumulation, yielding a net reduction in aggregate welfare. Interestingly, the redistribution mechanism of social security and its induced between-and-within-generation allocation of risk is not the only factor that affects welfare: potential idiosyncrasies in agents’ preferences highlight yet another important source of ambivalence with regard to the welfare implications of social security. Many studies, both theoretical and empirical, have argued on the welfare gains that can be accrued thanks to social security when households lack the foresight to save adequately for their retirement.1 Two distinct research approaches have provided empirical support as well as theoretical machinery that could serve in explaining the observed anomalies. It is well documented in the experimental economics literature that subjects facing intertemporal choice problems often exhibit preference reversals, or that their preferences feature some kind of time inconsistency (e.g. see Gul and Pesendorfer, 2001, Gul and Pesendorfer, 2004a and Gul and Pesendorfer, 2004b). Furthermore, theoretical advances have elucidated underlying factors that induce these anomalies. In a seminal paper Phelps and Pollak (1968) introduce an intertemporal framework involving quasi-hyperbolic discounting (in lieu of exponential discounting) and utilize it in order to study intergenerational altruism (we shall henceforth refer to the preference structure developed by Phelps and Pollak, 1968 as “time-inconsistent preferences”).2 In a recent study that enhances considerably the insights found in Feldstein (1985), Imrohoroglu et al. (2003) investigate the welfare effects of unfunded social security in an economy populated by agents with time-inconsistent preferences who suffer from inability to commit to future actions and hence, save inadequately. In Imrohoroglu et al. (2003), there is a government that engages in savings on behalf of the quasi-hyperbolic discounters through the social security system. Their main findings are that (1) quasi-hyperbolic discounters incur substantial welfare costs due to their time-inconsistent behavior; (2) to maintain old-age consumption, social security is not a good substitute for a perfect commitment technology; and (3) there is little room for social security in a world of quasi-hyperbolic discounters. In spite of their theoretical appeal in providing an alternative that adequately explains observed patterns of behavior, quasi-hyperbolic discounting models entail a non-recursive structure that renders them computationally intractable. This is because quasi-hyperbolic discounting structure does not allow a desire for commitment to one's future actions. Gul and Pesendorfer (2004a) choose a different approach in their attempt to explain preference reversals. They develop self-control preferences that depend on what an agent actually consumes on one hand, and what would be the level of consumption that would explain the experimental phenomenon, on the other. To this purpose, they introduce self-control and temptation utilities, concepts that capture the trade-off between the temptation to consume on the one hand, and the long-run self interest of the agent on the other. Under certain rationality assumptions, preferences over sets of actions are consistent with experimental evidence. In stark contrast to time-inconsistent preferences however, self-control preferences are time-consistent. In particular, it is assumed that preferences governing behavior at time t differ from preferences over continuation plans implied by the agent's first period preferences and choices prior to period t. In contrast, self-control preferences may already exhibit a desire for commitment. 3 In this paper we explore the role of an unfunded social security system in a setting where agents have self-control preferences. To this purpose, we develop an overlapping generation model in which agents live up to the real age of 85. The economy consists of three sectors: agents, firms and a government. Agents have idiosyncratic income and face a mortality risk. They work up to the real age of 65 whenever they have an opportunity to work. When unemployed or retired, they are compensated by the government by unemployment insurance or retirement benefits, respectively. In addition, they maintain positive asset holdings in order to insure against idiosyncratic income risks and low old-age consumption. Moreover, we assume that private credit markets (including annuities’ markets) are closed. The government collects unemployment insurance and payroll taxes from workers to the purpose of financing its activities. We compute steady-state equilibria under different social security replacement rates by calibrating our model economy to the U.S. economy. From previous studies we know that if an economy is populated by agents with constant relative risk aversion (CRRA) preferences (thus facing neither a commitment nor a temptation problem), the introduction of an unfunded social security system reduces welfare (Imrohoroglu et al., 1995 and Imrohoroglu et al., 2003). The reason is that the insurance benefit of an unfunded social security system is dominated by its negative effect on agents’ savings decisions. We also know that if an economy is populated by agents with time-inconsistent preferences, the introduction of social security still reduces welfare, despite providing an additional benefit as a commitment apparatus. The reason is that the latter benefit, along with the insurance benefit, are dominated by a negative effect on agents’ savings decisions (Imrohoroglu et al., 2003). Several interesting insights obtain in our setting: social security indeed tends to reduce welfare. However, it is worth mentioning that social security is less detrimental to welfare under self-control preferences than it is under CRRA preferences. In addition, if the cost of resisting the temptation is very severe, the introduction of social security might even improve welfare. Controlling for all other factors, we infer that this is due to our specification of preferences: agents with self-control preferences face no commitment problem. Nonetheless, the cost of resisting the temptation associated with the exertion of self-control becomes severe as wealth increases. In turn, this may impair overall savings in an economy. In our environment, an unfunded social security system has no role as a commitment apparatus, but might play a role as a device to decrease available wealth when agents make their consumption–savings decisions. We identify the underpinnings of our results with the impact social security has on agents’ marginal propensity to consume. In the ‘traditional’ setting where agents have CRRA preferences, the young have a low marginal propensity to consume while the old have a high marginal propensity to consume. This relation preserves a high rate of capital accumulation through higher savings during the young age. In contrast, in our environment the young face temptations that operate as impediments to their propensity to (privately) save. Alternatively, the agents’ marginal propensity to consume is not as low as it is in the case of CRRA preferences. Accordingly, the cost of resisting temptation increases with the level of wealth. Inevitably, social security, by being a mechanism that deprives agents from early consumption, accomplishes a reduction in the cost associated with the exertion of self-control, thus partially offsetting its adverse effect on welfare. Note that this effect is absent in environments wherein preferences do not afford agents the option to exert self-control as in Imrohoroglu et al. (2003)

Expenses related to social security comprise one of the largest expenditure items in the U.S. government's budget. As a result, there is an extensive literature regarding social security related issues. The costs and benefits of social security are well analyzed by many authors in the context of standard preferences: all of the studies with the exception of Imrohoroglu et al. (2003) use CRRA preferences. Imrohoroglu et al. use quasi-hyperbolic preferences instead, and show that even in such a context where social security could be used as a commitment device, it turns out that social security does not improve welfare. In the present paper, we assume that consumers have self-control preferences. In our environment, agents do not have a commitment problem but they instead face a temptation to consume all of their available wealth at each point in time. Our methodology consists in implementing calibration techniques, similar to those used in the related literature, in order to simulate our economy and draw conclusions regarding the impact of social security on consumers’ lifetime welfare. In doing so, we consider several variations of our specification of the temptation utility function (different degrees of convexity/concavity of the temptation function), and assess their influence separately, while at the same time compare it with the standard (CRRA) preferences case. Finally, we verify the numerical validity of our results by administering various robustness tests. Our main findings can be summarized as follows: in a world in which agents have self-control preferences social security generally decreases lifetime welfare. Interestingly, however, we call attention to a noteworthy novelty arising from our specification of self-control preferences: the presence of temptation considerably reduces the cost of social security. That is, indeed social security penalizes welfare but when the economy features agents with self-control preferences the above cost is substantially mitigated. Moreover, should the cost of resisting temptation become very high, the introduction of social security may even improve welfare. Furthermore, in our calibrations we measure that the cost of temptation, namely, the amount of consumption that agents would be willing to relinquish in order to eliminate temptation is as high as 4.82% of their steady-state consumption. Since this percentage corresponds to an insignificant deviation (increasing λλ from 0 to 0.0010.001) from the CRRA preference specification, it underscores the welfare reducing role temptation (and the induced cost of self-control) plays in our model. Nonetheless, at the same time it validates our main intuition, namely, that social security may not be as detrimental to welfare as it has been generally argued in the literature. While both social security and self control, when considered separately, have detrimental effects on welfare, their combination yields a remarkable result: welfare reduction is considerably less severe. The intuition behind this result lies in the following fact: social security is a mechanism that deprives agents from early consumption. When agents face temptations, social security at the same time reduces the cost associated with the exertion of self-control and consequently partially offsets its adverse effect on welfare. It is worth noting that this effect is absent in environments wherein preferences do not allow agents the option to exert self-control, or in contexts wherein the impact of temptation on lifetime consumption is moderate.