وسوسه و امنیت اجتماعی در چارچوب سلسله

We investigate welfare and aggregate implications of a pay-as-you-go (PAYG) social security system in a dynastic framework in which individuals have self-control problems. The presence of self-control problems induces individuals to save less because of their urge for temptation towards current consumption. Individuals' efforts to balance between the short-term urge for temptation and the long-term commitment for consumption smoothing result in self-control costs. In this environment PAYG social security works as a self-control cost reducing device. In contrast, the presence of altruism induces individuals to save more. This in turn mitigates the adverse effects of self-control problems and PAYG social security on savings but magnifies the self-control costs. We find that in our environment the adverse welfare effects of a PAYG system are further mitigated relative to the environments that incorporate altruism and self control issues separately. However, the level of mitigation is quite modest.

Many countries including the US run a pay as you go (PAYG) social security system in which tax revenues collected from current workers pay current retirees' benefits. Because the PAYG system substantially affects individuals' fundamental economic decisions and it is one of the largest expenditure items in a government's budget, aggregate and welfare effects of it have been analyzed quite extensively in the public finance literature. In the standard models of social security it is assumed that individuals save to smooth their consumption and insure against idiosyncratic productivity shocks and a longevity risk. It has been known for a while that individuals' saving decisions are also be affected by their altruistic concerns and self-control problems. There is a number of studies that analyze the implications of the PAYG system in the settings in which individuals have either altruistic concerns or self-control problems but we do not yet know the implications of the PAYG system when altruism and temptation coexist. In this study, we develop a model economy that incorporates those factors and investigate the aggregate and welfare implications of the PAYG system accordingly. In particular, we address the following two questions. First, what are the effects of temptation and altruism together on individuals' inter-temporal allocations and welfare? Second, what are the role and effects of the PAYG system in that environment? The benefits and costs of the PAYG system are well documented in the literature: the PAYG system provides an insurance against longevity and income risks but, at the same time, distorts individuals' saving and labor supply decisions. Using a deterministic standard overlapping generations (OLG) model, Diamond (1965) shows that social security reduces the steady-state capital stock because it taxes workers who have a high propensity of saving in order to pay benefits of retirees who have a low propensity of saving. A decrease in the steady-state capital stock, in turn, reduces welfare when the economy is dynamically efficient. Auerbach and Kotlikoff (1987) assess the magnitude of welfare losses using a deterministic large-scale OLG model and find that social security always results in a welfare loss. Hubbard and Judd (1987) analyze the extent of insurance benefit of social security in an incomplete market setting where individuals have stochastic life-span. They show that even in the environment that social security provides insurance against longevity risk, it still decreases welfare. Imrohoroglu et al. (1999) extend Hubbard and Judd's study by incorporating individual earning uncertainties. They show that the PAYG's adverse effects dominate its insurance benefits. Individuals' altruistic concerns affect the extent of the PAYG system's costs and benefits. There is a strand of the literature that analyzes the effects of social security by using dynastic models. In a seminal work, Barro (1974) shows that if a bequest motive is operative then private transfers can neutralize the effects of public transfers and public debt i.e. Ricardian equivalence holds. Fuster (1999) demonstrates that when individuals have bequest and inter-vivos transfer motives (two-sided altruism), social security is less detrimental to the capital stock in an economy. Fuster et al. (2003) develop a dynastic OLG model with inelastic labor supply. They show that social security's insurance benefit dominates its crowding-out effects on saving and hence, the steady-state welfare increases with social security for most of the households. Potential idiosyncrasies in individuals' preferences are another important source of uncertainty regarding the welfare implications of social security.1Imrohoroglu et al. (2003) investigate the welfare effects of a PAYG system when individuals have time inconsistent preferences. Social security in that environment works as a commitment device i.e. social security saves on behalf of individuals who, otherwise, would not save enough for their retirement. They show that the existence of a PAYG social security is less detrimental to welfare when individuals have time-inconsistent preferences. Bucciol (2011) and Kumru and Thanopoulos (2008) incorporate self-control preferences into a model of social security. They show that social security mitigates individuals' self-control costs by reducing their available wealth and hence, it might improve welfare. There is sound empirical and experimental evidence that individuals suffer from self-control problems. Frederick et al. (2002) provide an overview of experimental studies documenting that individuals indeed exhibit bias toward immediate gratification. Huang et al. (2007) and Bucciol (2012) study the empirical relevance of self-control preferences using household-level data from the Consumer Expenditure Survey. Their estimates support the presence of temptation.2 There is also a number of studies that provide empirical evidence that individuals have altruistic concerns. Bernheim (1991) presents evidence in support of the view that a significant fraction of total savings is motivated by the desire to leave bequests. Kopczuk and Lupton (2007) find that roughly three-fourths of the elderly single population has a bequest motive and both the presence and the magnitude of the bequest motive are statistically and economically significant. Moreover they show that, on average, households with a bequest motive spend about 25% less on consumption expenditures.3 In this paper we analyze the macroeconomic and welfare effects of a PAYG system in a setting with both two sided altruism and temptation. To conduct our analysis we first develop a simple two period model similar to that of Krusell et al. (2009).4 Our simple model helps us to understand how the interaction between altruistic concerns and urge for temptation influences the effects of the PAYG system on individuals' saving decisions. We show that altruistic individuals with self-control problems face larger self-control costs when they are young because they save not only for their old age consumptions but also for to leave bequests. In such an environment, we show that the PAYG system provides an additional benefit: reducing self-control costs. In contrast to non-altruistic individuals, altruistic individuals face self-control costs when they are old too. Yet, the PAYG system does not provide any relief for old age self-control costs. Our simple model shows that the complex interaction between altruistic concerns, urge for temptation, and the PAYG system has substantial impacts on savings and self-control costs. This, in turn, raises the possibility that welfare implications of social security might differ from those of the previous studies, which incorporate altruistic concerns and self control issues separately to large-scale general equilibrium OLG models. Next, we develop a large-scale model economy that comprises altruistic individuals with self-control preferences, competitive firms and a fully committed government. In our model, parents and children form a decision unit called a household in which resources are pooled and decisions are made jointly. A sequence of households in a family line, which is linked together through skill transmission and a bequest motive, creates a household dynasty. Households face demographic and skill shocks. All insurance markets for longevity risk and labor income shocks are closed. The set up of the household sector is quite similar to that of Fuster et al. (2003) except the preference structure: we incorporate the self-control preference structure introduced by Gul and Pesendorfer (2004). Our model allows us to analyze the interaction between altruism, temptation, and PAYG social security first time. We calibrate the model economy to the US data. Our experiments deliver the following results: First, the same level of temptation reduces the aggregate capital stock relatively more in the dynastic framework. Second, although both altruism and temptation factors mitigate social security's adverse welfare effects, the existence of altruism mitigates relatively more. Third, a comparison of the setting with two sided altruism and temptation with the setting with two sided altruism only reveals that the introduction of the PAYG creates a similar effect on the aggregate capital stock. Fourth , the negative welfare effects of social security are mitigated most in the setting with two sided altruism and temptation. However, we find that the level of mitigation is quite modest i.e. the existence of the PAYG generates a small additional benefit even when the strength of temptation increases substantially. Another result is that the existence of temptation matters much less than the existence of altruism in evaluating the effect of the PAYG system on economic aggregates and welfare. The paper is organized as follows. Section 2 presents our two-period partial equilibrium model and analytical results. In Section 3 we present our large-scale model economy, describe the parameter values of it, present results of our policy experiments, and conduct sensitivity analysis. Section 4 concludes. The mathematical details of the solution to the simple model are delegated to Appendix A. Appendix B explains the computational techniques used in the paper. Remaining tables are delegated to Appendix C. Finally, Appendix D presents how macroeconomic aggregates are affected by a change in the strength of temptation keeping everything else constant.

In this paper, we analyze the welfare implications of a PAYG social security system in a dynastic framework in which individuals have self-control preferences. To conduct our analysis we first develop a simple two period model. Our simple model helps us to understand how the interaction between altruistic concerns and urge for temptation influences the effects of the PAYG system on individuals' saving decisions. We show that altruism and temptation factors affect individuals' saving decisions in the opposite directions. That is on the one hand individuals prefer to save more because of their altruistic concerns, on the other hand, they prefer to save less because of their urge for temptation towards current consumption. Furthermore, we show that altruistic individuals with self-control problems face larger self-control costs when they are young because they save not only for their old age consumptions but also for to leave bequests. In such environment, we show that the PAYG system offers an additional benefit: reducing self-control cost. Next, we develop a large-scale OLG model economy that comprises altruistic individuals with self-control preferences, competitive firms and a fully committed government. We calibrate our model to the US data. Our simulations deliver the following results: First, the same degree of temptation reduces the capital stock relatively more in the dynastic framework. Second, the existence of altruism mitigates social security's adverse effects on welfare more than the existence of temptation does. Third, the level of capital stock does not differ much across settings in which individuals have both altruistic concerns and temptation and they have altruistic concerns only. Fourth, the negative welfare effects of social security are mitigated more when individuals have self-control preferences in the dynastic framework. Notably, we find that the level of mitigation is quite modest. For instance, a substantial increase in the temptation strength parameter causes a very modest increase in the optimal replacement rate that maximizes HL type's utility. Fifth, welfare effects of social security vary across different types of households but there is no evidence that richer individuals demand more social security than the poorer households because of the higher self-control costs. In sum, this paper makes two major contributions. First, it analytically demonstrates how altruism and temptation together affect individuals' inter-temporal allocations and welfare in a simple model. Second, it quantifies aggregate and welfare effects of PAYG social security when temptation and altruism factors are present at the same time.