A major question facing policymakers in most western economies is how best to guarantee a minimum level of support to their growing elderly population. Adverse demographic prospects and recent slowdowns in economic growth have prompted the reevaluation of the viability of public pension programs and the distribution of their financing burden across generations. In addition, as unfunded pension schemes approach maturity, the issue of how this burden is distributed across individuals of the same age cohort has received increased attention. Models that quantitatively explore the implications of government social security policy, however, have almost exclusively focused on issues of intergenerational redistribution, disregarding altogether the intragenerational transfers that arise from large differences in life expectancy and labor productivity between individuals.
This paper aims to quantify the extent of intragenerational redistribution in the U.S. social security system.1 In particular, it determines how social security policy affects the well-being of individuals who differ by gender, race, and education. For this purpose, a general equilibrium-overlapping generations economy is developed, where individuals face uncertain lifetimes. Within the same age cohort individuals with different life expectancy and labor productivity coexist. Individuals decide how much to work and how much to save in private assets for old-age consumption. Retirement is mandatory and individuals are not altruistic. The return to private saving and wages is determined by profit maximizing firms with standard neoclassical production technology. The government is responsible for administering the social security program. The program is pay-as-you-go and balanced budget, and incorporates many features of the U.S. old-age insurance program.
Related literature includes Auerbach and Kotlikoff (1987), who in an overlapping generations-general equilibrium simulation model study the short-run and long-run implications of changes in social security policy. Imrohoroglu, Imrohoroglu, and Joines (1995) extend their model by assuming credit and insurance market imperfections and find that unfunded pension schemes may in certain cases enhance the steady-state welfare of a dynamically efficient economy. Both works disregard ex ante differences in mortality risk and labor productivity between individuals belonging to the same age cohort, and therefore are unable to quantify the extent of intragenerational redistribution inherent in unfunded pension schemes.2 The paper is closer in spirit to that of Fullerton and Rogers (1993), who quantify the distribution of the burden of the U.S. tax system across 12 different lifetime income groups. Instead, in this paper individuals are categorized into eight different lifetime groups that differ in terms of their labor productivity and life expectancy. By focusing solely on the U.S. social security system, the model is capable of addressing in more detail certain features of the system.
In dynamically efficient economies, the return to unfunded pension schemes is less than the return to private saving. By essentially forcing individuals to substitute private assets for social security tax contributions, unfunded pension schemes in the presence of perfect insurance markets are welfare reducing. The magnitude of the loss increases with the expected present value of the difference between the future income that could have been guaranteed by the displaced saving and the social security benefits. Since unfunded pension schemes are designed not to discriminate on the basis of an individual’s probability of dying early, the expected rate of return to contributions increases with an individual’s life expectancy. In addition, unfunded schemes with progressive tax-benefit links reward individuals with lower-than-average lifetime earnings, at the expense of those with higher-than-average lifetime earnings. The higher the return to social security, the lower the observed welfare loss. However, differences in the expected return to an unfunded pension scheme can explain only part of the observed intracohort variability in welfare.
Differences in workers’ productivity-age profiles are also responsible for differences in capital accumulation and labor supply distortions.3 Assuming a closed economy, the introduction of pay-as-you-go social security crowds out capital formation, causing interest rates to rise and wages to fall. The change in relative factor prices will encourage workers to increase labor supply and saving early in life, so as to enjoy consumption and leisure later in life. Workers with later productivity peaks will not only observe a greater drop in the present value of their labor endowment, but will also find changes in their saving and labor supply behavior more distortionary.
The benchmark economy, which attempts to approximate certain features of the U.S. social security system, has an average replacement rate to labor earnings of 40 percent, a legal retirement age of 65, and a progressive tax-benefit formula. The paper simulates the steady-state effects of eliminating social security on macroeconomic aggregates as well as the lifetime welfare of cohorts that differ in their gender, race, and education. Results indicate that the steady-state welfare gains from privatizing (eliminating) social security are lower for females, whites, and noncollege graduates than for males, nonwhites, and college graduates. They are on average 40 percent greater for males than females, 4 percent greater for nonwhites than whites, and 9 percent greater for college graduates than noncollege graduates. The results are robust regardless of whether private annuity markets are assumed absent or present. Findings imply that the current system is lifetime progressive across gender and education, yet lifetime regressive across race. The latter result is very sensitive to the model’s calibration.
Appendix I. Computation of Equilibrium
The solution methodology, the Gauss-Seidel method, is borrowed from Auerbach and Kotlikoff (1987). It involves solving a complicated set of nonlinear equations that specify households’ and firms’ optimization behavior and the government’s budget constraint. The algorithm starts with guesses for the capital to labor ratio, the age-specific shadow wages, and the social security tax rate. When the social security benefit formula is progressive it also requires a guess for the economy’s average labor earnings. The capital to labor guess determines the relative factor prices that when combined with the shadow wage, social security tax rate, and benefit formula solve for the optimal behavior of individuals. The standard procedure in lifecycle models is to go to the last period of an individual’s life, where the future is no longer relevant, and solve for the behavior of the individual. In turn, this behavior would describe the nature of the future for individuals of the previous age. The recursive nature of the problem allows for the determination of the behavior for individuals of all ages.
From the derived labor supply decisions, new guesses for shadow wages are obtained. Aggregation of labor supply and saving decisions across all population subgroups in turn provide a new guess for the capital to labor ratio. From the labor supply decisions the earnings of each type of individual are determined, as well as the new social security tax guess that follows from the government’s budget constraint. Typically, 10 to 20 iterations are required to achieve convergence to a steady-state equilibrium. The introduction of heterogeneity in age-cohort labor productivity and mortality risk only adds to the size and dimension of the problem in hand, but fundamentally does not alter the solution algorithm.
The computational algorithm for the no-annuity-case differs only slightly. Besides providing starting guesses for the capital to labor ratio, the age-specific shadow wages, the social security tax rate, and the economy’s average labor earnings, a guess for the lump-sum transfer of accidental bequests must also be specified. In this case, the aggregation of labor supply and saving decisions provide new guesses for the capital to labor ratio and the lump-sum transfer of accidental bequests.
Appendix II. The Welfare Function
Welfare for type j individuals, who face a social security policy
The benchmark economy approximates the current social security program, where the average replacement rate to income is 40 percent, legal retirement age is 65, and the benefit formula is progressive. The welfare loss or gain for an individual of type j of departing from the benchmark economy is defined as the proportional increase or decrease in full lifetime resources required to make an individual of type j indifferent between the benchmark economy and an alternative economy. Because the utility function is homothetic, a change in an individual’s lifetime wealth, provided factor prices are fixed, is associated with a proportional change in an individual’s lifetime consumption and leisure. Therefore, the resources required to make an individual of type j indifferent between the benchmark economy
The product of ωj(x*) and the expected present value of labor endowment in the benchmark economy represents the additional resources necessary to make individuals of type j indifferent between the benchmark and alternative economy. Social security is considered “lifetime progressive” if resources required to make individuals indifferent between the benchmark economy and an alternative economy without social security increase with the present expected value of their labor endowment in the benchmark economy. The aim of this exercise is not to make pareto-like statements, but rather statements of the sort: “an individual is better or worse off in an economy with social security policy x* than if he or she were to live in an economy with social security policy
To compare the overall welfare gains or losses associated with alternative social security arrangements, a social welfare function is defined where the lifetime resources of each type of individual is given a weight equivalent to its measure at birth. The increase or decrease in the present value of labor endowment required to make all lifetime cohorts indifferent between the benchmark economy
Tables 3 and 7 in the main text show Ω(x*) expressed as both relative to output and relative to the present value of lifetime resources.
Appendix III. Sensitivity Analysis
This section examines the robustness of the policy experiments. In particular, it determines the extent to which results change with values for the risk aversion coefficient, γ, and the subjective discount factor, β.
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Luis Cubeddu is an Economist in the Fiscal Affairs Department of the IMF. He thanks Andrew Abel, Alan Auerbach, Richard Hemming, José-Víctor Ríos-Rull, and the participants at seminars at the University of Pennsylvania and the Latin American Econometric Society Meeting for helpful discussions and comments on a previous draft.
In this paper, social security is treated purely as an old-age insurance program. Survivor, disability, and hospital insurance features are disregarded.
In Imrohoroglu, Imrohoroglu, and Joines (1995), since individuals cannot fully insure against unemployment risk, individuals of the same age group may differ ex post not only in their labor income but also in their asset holdings.
Social security is financed through a payroll tax that 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 its 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 shorter life expectancy must have higher birth rates.
This condition is empirically verified. The data show that females, whites, and the college educated outlive males, nonwhites, and the noncollege educated, but that the latter group observes higher birth rates.
Although 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 fraction of PIA allowed per unit of AIME is calculated by multiplying the average replacement by π, where, π1 = 2.0; π2 = 0.71; π3 = 0.33; and π4 = 0.0. The bend points are as follows:
Obviously, changes in social security for an initial transition period will affect the young and old very differently. Appendix I describes the algorithm used in computing the model’s equilibrium.
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 resources.
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 is found in Feldstein and Samwick (1992), who document social security net marginal tax rates across age, gender, marital status, and income class.
Appendix II provides a detailed discussion on the measurement and comparison of steady-state welfare.
One may also argue that social security makes the lifetime distribution of wealth more equal, by taking larger amounts away from lifetime rich groups (male, college graduates) than from lifetime poor groups (female, noncollege graduates).
Studies show that only about 2 percent of the elderly own individual annuities. Not only do insurance companies lack information about an insurer’s survival probabilities, but regulatory constraints may force them to offer the same contract to males and females. See Warshawsky (1988) and Mitchell and others (1998) for evidence on why individual annuity markets are thin.
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 Imrohoroglu, Imrohoroglu, and Joines (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. Imrohoroglu, Imrohoroglu, and Joines (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 and mortality histories translate into intra-age wealth heterogeneity. Further research and sensitivity analysis on the subject is warranted, yet outside the scope of this paper.
In the absence of annuities, the equilibrium tax rate and the expected difference between the return to private capital and that of social security are lower, resulting in lower capital accumulation and labor supply distortions.
The long-run welfare gains of eliminating social security are on average 52.2 percent greater for males than females, 0.8 percent greater for nonwhites than whites, and 6.3 percent greater for college than noncollege graduates.
Cubeddu and Ríos-Rull (1997), in a similar framework, study how changes in the patterns of household formation and dissolution affect saving decisions at the household and aggregate level.
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.