تامین اجتماعی و رفتار دوران بازنشستگی و پس انداز از خانواده های کم درآمد

In this paper, we develop and estimate a model of retirement and savings incorporating limited borrowing, stochastic wage offers, health status and survival, social security benefits, Medicare and employer-provided health insurance coverage, and intentional bequests. The model is estimated on a sample of relatively poor households from the first three waves of the Health and Retirement Study (HRS), for whom we would expect social security income to be of particular importance. The estimated model is used to simulate the responses to changes in social security rules, including changes in benefit levels, in the payroll tax, in the social security earnings tax and in early and normal retirement ages. Welfare and budget consequences are estimated.

The literature on retirement behavior has grown rapidly during the last twenty years. Much of that growth has been due to recent methodological advances in the structural estimation of dynamic discrete choice models of behavior under uncertainty. Unlike earlier static lifetime models (e.g., Fields and Mitchell (1984)), dynamic models account for the sequential nature of the retirement process in which individuals adjust their behavior as events unfold. Structural estimation of the fundamental parameters of preferences and constraints as opposed to “reduced form” analyses permits the simulation of policy experiments that act directly on constraints and which may be outside of current or prior policy regimes. Much of the focus in the initial attempts to formulate and estimate a forward-looking model of retirement behavior has been on explaining the empirical regularities of a declining full-time employment rate with age (for males), with particularly large drops at ages 62 and 65, as well as the substantial heterogeneity in retirement behavior across individuals (see Gustman and Steinmeier (1986), Stock and Wise (1990), Berkovec and Stern (1991), Phelan and Rust (1991), Lumsdaine et al., 1992, Lumsdaine et al., 1994 and Lumsdaine et al., 1996, Rust and Phelan (1997) and Blau and Gilleskie, 2006 and Blau and Gilleskie, 2008). Besides establishing the importance of health, wealth and labor market opportunities in explaining retirement patterns, these studies also point to the significance of capital and health insurance market imperfections and social security and private pension rules. Social security rules may affect work decisions through the structure of the benefits schedule, the earnings tax and its actuarially unfair delayed retirement credit associated with postponing retirement beyond the normal retirement age. Private pensions often include substantial incentives to remain with a firm until a given age, combined with substantial incentives to leave the firm at an older age. Therefore, even in an economy with perfect capital markets where individuals can smooth consumption by borrowing against future pension and social security income, public and private pensions can produce delays in retirement and spikes in retirement rates at certain ages. However, their importance for labor supply decisions is likely to be substantially greater in the presence of borrowing constraints, which may prevent many low-wage individuals, who optimally accumulate relatively little tangible wealth, from retiring before reaching the age at which they first become eligible to receive benefits. A similar role can be attributed to the Medicare program when health insurance markets are imperfect. Limited private health insurance options could make it too risky for individuals who do not have access to employer-provided retiree health insurance to retire prior to being eligible for Medicare at 65. Rust and Phelan (1997) provide empirical evidence of the importance of market imperfections, attributing a large part of the drop in employment at age 62 to social security eligibility and at age 65 to Medicare eligibility. Blau and Gilleskie, 2006 and Blau and Gilleskie, 2008 also find significant, although more modest, employment effects of employer-provided health insurance. However, there is an important reason to believe that the roles attributed to social security and employer-provided health insurance in these studies may be overestimated. The models on which these results are based do not allow households to save, thereby removing an important instrument through which to smooth consumption (and facilitate early retirement) and to self-insure against future health expenditures. Gustman and Steinmeier, 1986 and Gustman and Steinmeier, 1994 instead make the alternative extreme assumption of perfect capital markets, in which individuals can freely borrow against future earnings and pension income, an assumption that is likely to lead to an underestimation of the importance of social security and employer linked health insurance. Other empirical studies have found the effect of assets other than social security and pension annuities on the timing of retirement to be weak (Blau, 1994, Diamond and Hausman, 1984 and Sickles and Taubman, 1986). However, these studies do not capture completely the complex interactions that exist between savings, health status, social security benefits, health insurance coverage and work decisions. Moreover, many of these studies take accumulated savings or assets to be exogenous in their analysis. Several studies, such as those by Feldstein (1974) and Bernheim and Levin (1989) have found social security to depress savings, which suggests that the exogeneity assumption may be incorrect. An accurate assessment of the magnitude and manner in which social security benefits influence behavior is crucial for credibly forecasting the impact of changing the social security program, a major goal of this paper. We, therefore, develop and estimate a model of retirement and savings incorporating limited borrowing, stochastic wage offers, health status and survival, social security benefits, Medicare and employer-provided health insurance coverage, and intentional bequests. The model is estimated on a sample of relatively poor households from the first three waves of the Health and Retirement Study (HRS), for whom we would expect social security income to be of particular importance. The estimated model is used to simulate the responses to several counterfactual experiments corresponding to changes in social security rules. These include changes in benefit levels, in the payroll tax, in the social security earnings tax and in early and normal retirement ages.1 Our model shares features with many recent papers that have estimated models of retirement behavior, but is more comprehensive and introduces a number of new elements. It incorporates savings behavior with limited borrowing as in Gustman and Steinmeier (2005), French (2005) and French and Jones (2007), and also models the joint labor supply decision of married couples as in Gustman and Steinmeier (2000) and Blau and Gilleskie (2008). The flexibility to augment household income through spousal work is potentially an important instrument to insure against wage and health shocks, as well as a tool for smoothing consumption. We explicitly incorporate the social security benefit rules which apply to couples, allow for health insurance coverage through the spouse and incorporate the possibility of direct preferences for shared leisure and of assortative mating on preferences and on health and market skill endowments. Wages in our model are stochastic as in French (2005), but also depend on accumulated work experience and tenure and we allow individuals to change jobs which may or may not offer health insurance. Like Berkovec and Stern (1991), in characterizing employment choices we distinguish between part-time and full-time work, model job-to-job transitions and instead of treating retirement as an absorbing state, allow returns from non-employment into the labor force. However, we do not explicitly consider the purchase of private health insurance and medical expenditure decisions (Blau and Gilleskie, 2006), private pensions on current jobs (Lumsdaine et al., 1992, Lumsdaine et al., 1994, Lumsdaine et al., 1996, French, 2005 and Blau and Gilleskie, 2006) nor do we model disability insurance applications and benefit receipt (Rust et al., 2003). Our model accommodates observed and unobserved heterogeneity in preferences, wages, health transitions and mortality risks. In addition, individuals in our model have expectations over changes in social security policy. Myopic beliefs about the social security system may be unrealistic given the long history of changes in the social security rules and benefit levels which have been enacted over the 1969–90 period, with major changes in 1972, 1977 and 1983. As Moffitt (1987) has argued, the magnitude of behavioral responses to policy changes will depend strongly on the extent to which these policy changes were anticipated. In an analysis of data from the Survey of Economic Expectations on subjective expectations of future social benefit receipt, Dominitz et al. (2003) in fact conclude that a sizeable proportion of their sample, and especially among the young, consider it fairly likely that the social security program will no longer exist at the time they retire. A final contribution of this paper is that we make explicit use of subjective expectations in the estimation of our model. The Health and Retirement Study contains a set of probabilistic questions on, among others, retirement and longevity expectations. For example, all those employed in 1992 were asked for their subjective probability that they would be working full-time after reaching ages 62 and 65, and all respondents were asked about their probabilities of surviving to age 75 and 85. Reported expectations about future choices have precise interpretations within the context of dynamic behavioral models. Just as current choices are taken to portray optimal behavior given current information, expectations about future choices portray optimal future behavior conditional on current information. As a result, subjective data provide useful information about the decision process in the same way as do objective data (Van der Klaauw, 2000 and Wolpin, 1999). We highlight a few of the results of the counterfactual policy changes.2 For example, for married couples, we find that a 50% reduction in social security benefits would lead to a small decline in the labor supply of both spouses at ages between 51 and 61, and a substantial increase at ages between 62 and 69, an increase that is particularly large for husbands whose full-time employment rate in this latter age range is predicted by the model to increase from 37.8% to 52.3%. Although average annual earnings thus increase in the latter age range and average net assets optimally falls, average annual household consumption falls over the 62–69 age range by 8.0% because of the reduction in benefits. Eliminating the earnings tax is predicted to have a substantial impact on labor supply, with average annual hours worked of married and single individuals between ages 62 and 69 predicted to increase by respectively 17% and 35%. Concomitantly, average net assets over that age range would increase by 8% and 21% for singles and married individuals. Finally, eliminating the option of early retirement is predicted to produce a comparable increase in average labor supply at ages 62–69, but leads to a small fall (increase) in net assets for marrieds (singles). An evaluation of these policies’ impact on welfare and government revenue indicates that while a 50% benefit reduction and an increase in the normal retirement age to 70 both lead to comparable losses in welfare, the net revenue gain associated with the former is only 40% as large as that from the latter. An increase in the payroll tax rate to 15% also generates a lower revenue increase (75% of that of the benefit cut), but produces much smaller welfare losses, exemplifying the trade-offs involved in policy makers’ choice decisions. The remainder of the paper is organized as follows. We present the model in the next section. The solution method used to solve the model and the HRS data are described in Section 3. The econometric specification and estimation method are discussed in Section 4. The auxiliary statistical model used for the indirect inference estimation procedure is presented in Section 5 and details about the simulation methodology used to implement the procedure are provided in Section 6. Estimation results and model fit are discussed in the following section and counterfactual experiments in Section 8. A brief conclusion is presented in Section 9.

In this paper, we have specified and estimated a dynamic model of retirement and savings decisions for a low-income subsample of households from the Health and Retirement Study. The model incorporated a discrete employment decision (non-employment, part-or full-time employment) and a continuous consumption decision for both unmarried men and women and for married couples. Additional features of the model included a detailed specification of social security rules, limited borrowing, probabilistic job offers from new firms specifying the wage and health insurance availability, a bequest motive, uncertain health and survival, wages that evolve with labor market experience and job tenure, and unobserved heterogeneity in preferences, wages and health status. The model was estimated using the method of indirect inference. The estimated model was shown to reasonably fit many different aspect of the data. The model was used to understand the impact of changes in social security rules on household labor supply, income and consumption. The estimated model forecasts large and heterogeneous behavioral responses, with those of singles generally exceeding those of married individuals, and those of husbands being considerably larger than those of wives. In the case of a reduction in social security benefits of 25%, we find moderately large reductions in labor supply at ages below 62 (2%–3% for married, 5%–7% for singles), and large increases in annual hours worked at ages 62–69 (12% for married, 8% for singles). Increasing the social security payroll tax to 15%, a large change in itself, is predicted to lead to considerable reductions in annual hours worked at all ages, with average annual hours of working at ages 62–69 falling by 5% for wives, 14% for single women, 16% for husbands, and 29% for single males, with similar but somewhat smaller reductions at ages 51–61. These reductions take the form of increases in both non-employment and in part-time work, except for single males for whom the part-time rate drops. We find qualitatively similar responses in labor supply to the removal of the earnings test, the elimination of early retirement, and a postponement of the earliest retirement age to 70. In all cases, we predict sharp increases in average annual hours of work (with estimates varying between 16% and 52%) and in full-time employment at ages 62–69. For couples most of this is due to a reduction in non-employment, while for singles it is primarily due to a shift from part-time into full-time employment. Again, we find smaller changes in the labor supply of wives compared to that of husbands, and somewhat smaller (although still substantial) increases for single women compared to single men. The policy changes have very little effect on the labor supply of married individuals at ages below 62, but this is not the case for singles for whom we predict varying positive and negative responses in labor supply that depend on the exact nature of the policy change. For example, removal of the work disincentives embedded in the earnings test leads to a 6.6 (2.6)% increase in annual hours of work for single males (females) at ages 51–61, but has a negligible impact on the labor supply of married couples in that age group. Overall, the counterfactual experiments indicate that the changes in the social security rules we consider would lead to large behavioral responses in the work behavior of low-income households, which in turn would have a substantial financial impact on the social security system. At the same time, we found the employment responses to these policy changes to be accompanied by modest, but not inconsequential, changes in net assets holding, indicating that both labor supply and savings decisions play important roles in mitigating the consequences for consumption and welfare of benefit reductions and of the elimination or postponement of the early and normal retirement age. The policy experiments also illustrate the existence of potentially important trade-offs faced by policy makers in balancing consumer welfare losses against revenue increases. We find that if the government had reduced social security benefits by 50% in 1992, the welfare (present discounted utility flow) loss to the population represented by the no-pension sample would have ranged from 4% for single females to 8% for married couples. The welfare loss would have been of a similar magnitude if the retirement age had been increased to 70 in 1992. However, the net revenue gain associated with the benefit reduction would have been only about 40% as large as that from the increased retirement age. In contrast, the welfare loss from increasing the payroll tax to 15% would have resulted in less than a 2% fall in welfare and an increase in net revenues that was about 75% as large as that from the increased retirement age. Thus, while a policymaker would necessarily have preferred either of the latter two policies, the choice between them would depend on how the larger net revenue obtained from one policy is weighed against its greater welfare loss.