تصمیم بازنشستگی در حضور یک سیستم تامین اجتماعی

We compare a retirement decision in the presence of a social security system with that in the first-best allocation, using an overlapping-generations model in which the labor supply of elderly agents is endogenous. We show that although the social security subsidizes a retirement decision, the retirement period may be shorter than in the first-best allocation. More importantly, such results occur even when the retirement decision (i.e., leisure demand) is not backward-bending. We also show that the levels of elasticity in decisions regarding retirement and consumption among both young and old agents play important roles.

In many countries, it has been observed that in a postwar period, the labor force participation rate of the elderly has dropped. On the other hand, social security benefits have increased sharply in the postwar period. Table 1 shows the historical trends of the these levels in the US economy. The second and the last columns of the table show the labor force participation rate (of civilians) for men aged 55–64, and the percentage of Old-Age and Survivors Insurance (OASI) benefit payments in comparison with the US gross domestic product (GDP), respectively. Although both the labor force participation rate of the elderly workers and the OASI/GDP ratio declined temporally in the 1980s (see Krueger and Pischke, 1992), in general, a negative correlation can be observed. (See Diamond and Gruber (1997). With regard to other industrialized countries, it is useful to see the National Bureau of Economic Research Conference Report, edited by Gruber and Wise (1999).)Many previous studies have investigated the extent to which social security affects the retirement behavior of the elderly. The results on this issue are divergent. Some studies––for example, Feldstein (1974), Boskin (1977), Sheshinski (1978), Hurd and Boskin (1984), Kahn (1988), Hurd (1990), and Yamada (1990)––maintain that social security systems exert enormous influence on retirement decisions and on declines in the labor force participation of the elderly; other studies––for example, Burtless (1986), Blau (1994), and Ruhm (1995)––argue that social security has large effects on retirement, but that the effects of an increase in social security benefits on a decline in labor force participation are not large. Ruhm (1995) notes that when the level of social security benefits increases, those who would otherwise leave the labor force at age 60 or 61 may delay retirement until they become eligible for social security benefits (at age 62). On the other hand, other studies––for example, Hu (1979), Blinder et al. (1980), and Krueger and Pischke (1992)––have cast doubt on the view that social security provides a significant work disincentive for the elderly. Krueger and Pischke (1992) argues that the relationship between social security benefits and retirement becomes insignificant by controlling for the effects of age and period, and thus that social security benefits cannot explain a large degree of decline in male labor supply. (It is useful to see Ruhm (1996) on this point.) These preceding studies follow one of the two following paths. Some studies compare the decision to retire in the presence of a social security system with that in the absence of such a system. Other studies investigate the effects of an increase in social security benefits on retirement decisions. When the issue is whether or not retirement age is lowered by the presence of a social security system, such approaches are appropriate. However, the issue is whether or not retirement decisions in the presence of a social security system are excessive from a social welfare viewpoint, the retirement decisions must be compared with the retirement decisions in a socially desirable allocation, rather than in the absence of a social security system, since it cannot be necessarily said that induced retirement per se is undesirable from the welfare viewpoint. Thus, the purpose of this paper is to compare retirement decisions in the presence of a social security system with those in a socially desirable allocation, and to examine whether or not the length of the retirement period in the presence of a social security system is excessive. In this paper, social security benefits are considered to be paid in proportion to the length of the retirement period of elderly agents. Preceding papers, for example Boskin (1977), maintain that social security benefits guarantee retired persons a certain income and that they implicitly tax continued work. We can interpret such a transfer scheme as an example of a social security system with earning tests; the earning tests can be observed in many countries today. Intuitively, the length of the retirement period chosen under a social security system may be expected to be longer than that attained under the first-best allocation, since the social security system provides a subsidy for retirement. It will be shown that this intuition is not true; that is, the length of the retirement period in the second-best allocation may be shorter than that in the first-best allocation. To generalize the results obtained from the present analysis, the following can be stated: although the government implements policies which distort relative prices among commodities and subsidizes a certain commodity, the consumption level of this commodity does not necessarily increase relative to the level attained under a policy which brings about no distortion and thus provides no subsidy for that commodity. It is of interest to point out that we can obtain such a counterintuitive result without resorting to the assumption that a retirement decision, which we treat as the leisure demand of elderly agents in the model, is backward-bending. As will be shown later, when the retirement decision is backward-bending, the length of the retirement chosen by elderly agents in equilibrium may decrease as the level of social security benefits (in other words, as the subsidy to a retirement decision) increases. In such a case, the result that the length of retirement period in the second-best allocation may be shorter than that of the first-best allocation seems to be obvious and not interesting. Hence, we confine our analysis to the case in which retirement behavior does not exhibit backward-bending. The rest of this paper is structured as follows. Section 2 introduces the model used in the analysis. In Section 3, we derive the first-best allocation, that is, the socially desirable allocation. This serves as the benchmark allocation. Section 4 examines the second-best allocation, that is, an optimal decision in the presence of a social security system. In Section 5, we compare the retirement decision in the second-best economy with that attained under the first-best allocation. We show that although the social security system subsidizes a retirement decision, the length of the retirement period may be shorter than that under the first-best allocation. It will be also shown that three kinds of elasticity play important roles when we interpret the results: the elasticity of (1) the retirement decision, (2) the young agent’s consumption, and (3) the elderly agent’s consumption with respect to social security benefits. Furthermore, we provide a numerical example in which the length of the retirement period becomes shorter than that attained under the first-best allocation. This example suggests that such a counterintuitive result may occur in a simple situation. Finally, Section 6 concludes the paper.

We have investigated retirement decision in the presence of a social security system, the benefits of which are paid proportionally to the length of the retirement period. We have obtained that the length of the retirement period in the presence of a social security system may be shorter than that attained under the first-best allocation even if the social security system provides a subsidy to the retirement decision. More importantly, we have shown that the present result holds even under conditions in which the leisure demand is not backward-bending. It has been argued that such a counterintuitive result tends to occur more often when the elasticity of the retirement with respect to social security benefits is low and when the elasticity of young agent’s consumption is lower than that of the old agent’s consumption. We have also suggested that even if the elasticity of the retirement with respect to the social security benefits is high, it is nevertheless possible that such a result may take place when the elasticity concerning a young agent’s consumption is higher than that concerning the old agent’s consumption.