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I would like to thank Andrew Abel, Alan Auerbach, Richard Hemming, Jose Victor Ríos-Rull, and participants at seminars at the University of Pennsylvania and the Latin American Econometric Society Meeting for helpful discussions and comments on a previous draft. The Boettner Institute provided financial support. The views expressed are those of the author and do not necessarily represent those of the International Monetary Fund.
In this paper, social security is treated purely as an old-age insurance program. Survivor, disability, and hospital insurance features are disregarded.
In Imrohoroğlu et al. (1995), since individuals cannot fully insure against unemployment risk, individuals of the same age group may differ expost not only in their labor income but also in their asset holdings.
Social security is financed through a payroll tax which distorts an individual’s labor supply decision. The magnitude of the distortion is a function of both the age-specific net marginal tax rate and the shape of a worker’s wage-age profile. Since workers in deciding how much to work perceive no linkage at the margin between social security benefits and taxes, marginal taxes will equal across types for all ages.
A population’s steady-state growth rate is determined by it’s age-specific mortality and fertility rates (assuming these remain constant over time) If different types of individuals have different survival probabilities, as is the case in this paper, then for all types to grow at the same rate, fertility rates must differ. Specifically, individuals with lower life expectancy must have higher birth rates.
This condition is empirically verified. The data shows that while females, whites and college educated outlive males, nonwhites, and noncollege educated, the latter observe higher birth rates.
While the current U.S. demographic structure is far from being stationary, as the proportion of nonwhites and college educated people in the population has been increasing over time, the assumption allows for the existence of a stable population where different lifetime cohorts coexist.
Craig and Batina (1991) use a two-period general equilibrium overlapping generations model to simulate the effect of spouse and retirement insurance on family labor supply. In their specification, they are able to use households as welfare measuring units by assuming that the marital status of the couple does not change over the lifecycle.
For the preferences used in this paper, the lower the degree of risk aversion, the less individuals care about consumption smoothing and the more willing they are to substitute labor from periods of low wages to periods of high wages. In the presence of uncertainty, the lower the degree of risk aversion, the smaller the fraction of resources devoted to precautionary savings.
Legislation passed in 1983 calls for a gradual increase in the age at which future retirees are able to receive full benefits. By 2022, the age will be 67.
In computing an individual’s AIME, the model considers labor earnings for all ages prior to retirement. Current legislation instead considers the highest 35 years of labor earnings.
The bend points are as follows:
Obviously, changes in social security for an initial transition period will affect the young and old very differently.
These results are similar to those found in Auerbach and Kotlikoff (1987), who show a replacement rate of 60 percent reduces steady-state capital by 24 percent, and that the welfare loss is about 6 percent of full-time resource.
The welfare loss increases with the expected present value of the difference between the future income guaranteed by the displaced saving and the social security benefits.
If workers were to perceive a tax-benefit link, labor supply distortions would be mitigated. Workers with higher life expectancy and lower lifetime earnings would observe lower net marginal taxes and in turn lower labor supply distortions. In addition, since net marginal taxes fall with age, workers would be encouraged to postpone their labor effort. Therefore, those with late productivity peaks will find changes in their labor supply less distortionary. A more elaborate discussion of these issues are found in Feldstein and Samwick (1992), who document social security net marginal tax rates across age, gender, marital status, and income class.
Precautionary saving in response to risk is associated with convexity of the marginal utility function or a positive third derivative. The model’s preferences guarantee a positive precautionary saving motive. See Kimball (1990), for more on this issue.
While recent work by Imrohoroğlu et al. (1995), and Valdivia (1997) show that under certain conditions the gains of social security can outstrip the costs; their economies differ in some very important dimensions to that of this paper. Imrohoroğlu et al. (1995), assume that individuals also face uninsured unemployment risk. The introduction of an additional source of uninsured risk increases the precautionary motives for saving, and increases the gains of introducing social security by reducing the size of unintended bequests. Valdivia (1997), assumes that bequests are operational and that preferences are of constant relative risk aversion. In this framework the costs of living longer than expected are greater, partly because precautionary motives are absent and partly because reduced bequests affect the welfare of future generations. In addition, both papers restrict individual labor supply decisions and hence underestimate the potential distortionary effects of a wage-tax financed social security system. Finally, the comparison of welfare results across these models is complicated because, unlike in this paper, different employment (Imrohoroğlu et al. (1995)) and mortality (Valdivia (1997)) histories translate into intra-age wealth heterogeneity. Further research and sensitivty analysis on the subject is warranted, yet outside the scope of this paper.
The expected difference between the return to private capital and the return to social pensions is smaller in the absence of private annuities, hence capital accumulation distortions are less severe. In addition, since the resulting marginal taxes are lower, so will the labor supply distortions in the absence of these markets.
In the absence of annuities, the expected return to private assets increases with an individual’s survival probability. Since the return to social security contributions increase with life expectancy, the expected difference between the return to private saving and social security need not fall with life expectancy, as is true in the case when private annuities are present.
For smaller discount factors, the increase in full lifetime resources required to make all individuals indifferent between the benchmark economy and one where social security is absent is larger relative to the economy’s present value of labor endowment.
One quarter of all Old Age and Survivor Insurance (OASI) payments goes to survivors.