امنیت اجتماعی سن استحقاقی زودرس در یک مدل ساختاری از بازنشستگی و ثروت

A structural life cycle model of retirement and wealth attributes retirement peaks at both ages 62 and 65 to Social Security rules and wide heterogeneity in time preferences. Those with high discount rates often retire at 62. They have few assets and heavily value lost benefits from working after 62, largely ignoring potential increases in later benefits. Declining actuarial adjustments beginning at 65 induce those with low discount rates to retire at 65. Raising the Social Security early entitlement age to 64 induces 5% of the population to delay retiring, shifting the retirement spike from 62 to 64.

The most common age of retirement, by a considerable margin, is 62.1 Perhaps not coincidentally, this age is also the first age at which Social Security benefits can be collected under normal circumstances. It is certainly plausible that these two facts are related. And yet, constructing empirical models to reflect why Social Security early entitlement causes such a spike in retirement is not as easy as it might at first appear. The problem arises because of the way future benefits are adjusted if an individual works beyond the entitlement age. If the individual foregoes benefits because he or she continues to work, future benefits are increased in an amount that is actuarially fair, and in many cases slightly better than actuarially fair. Thus, there appears to be no penalty to delaying the receipt of benefits beyond the early entitlement age, and hence no big incentive to retire at that age. This difficulty in explaining age 62 retirement has serious and unfortunate implications for analyzing Social Security policy. It is well known that Social Security will face a funding crisis in the next several decades, and there is much debate as to how best to avoid the crisis. One step was taken in 1983 by gradually increasing the Social Security normal retirement age to 67 in the coming two decades, with concomitant reductions in benefits for those who take benefits at the early entitlement age of 62. Some additional proposals under consideration include increasing the normal retirement age further, and some include increasing the early entitlement age, both to encourage individuals to work longer and to avoid having benefits that are reduced too much (Congressional Budget Office, 1999). The only problem is that no one is quite sure what will happen to retirement if the early entitlement age is increased. Reduced form empirical work has had at best limited success in explaining the age 62 retirement spike. The early entitlement age has not changed since early retirement was introduced in 1961, so using the early entitlement age as a right-hand side variable is not likely to be useful or even feasible. Measures such as option values or peak values typically are slightly positive up to the early entitlement age, after which they slowly decline toward zero. Either in levels or in first differences, they do not exhibit the sharp spike at age 62 which could explain the spike in retirement. Introducing a binary variable at age 62 can capture the retirement spike, but it provides a tenuous link to economic variables and complicates any policy analysis. For instance, if the early entitlement age were to move to age 64 or 65, it is difficult to say how much retirement remains at 62, how much shifts to intermediate age such as 63, and how much moves to the new early entitlement age. Current structural models have had only moderately better success. The fact that Social Security is roughly actuarially neutral remains as a problem. Structural or reduced form models can explain the age 62 spike by assuming a high discount rate, but this approach generally means that the model has trouble explaining the smaller retirement spike at age 65. Older models were able to explain the age 62 spike as a reaction to pensions, but recent changes in pensions and pension laws have reduced the impact of pensions at that age. Liquidity constraints are a possibility, but then the question arises as to why individuals on the cusp of retirement would have no assets. Our approach to this vexing problem is to abandon one assumption made in almost all previous empirical work on retirement. Namely, we will abandon the assumption of a uniform time preference rate across the population. We propose a model of retirement and saving in which individuals have differing rates of time preference. Individuals with high time preference perceive the actuarial adjustments in Social Security to be highly unfair, rather than the actuarial fairness that arises if these adjustments are calculated at the usual interest rates. The fact that additional work requires them to give up substantial benefits with little perceived gain in the future provides them with a powerful incentive to retire when benefits first become available. Heterogeneous time preference rates are certainly consistent with a wide dispersion in wealth, even among households with similar lifetime incomes. There are other plausible and consistent explanations of the wealth distribution.2 But none of the alternatives simultaneously provides an explanation of the retirement spike at age 62. In addition, heterogeneous time preferences explain common complaints against the earnings test, in which many individuals seem to view the lost benefits simply as a tax, without considering the offsetting future benefit increases. They also help to explain why so may individuals collect benefits at the earliest opportunity, even when there might be some actuarial advantage to delaying for a year or two. The model we estimate is a life-cycle model of retirement and saving. At each point in time, the individual must decide how much to save and whether or not to retire. The estimation essentially uses the accumulated wealth of each individual to infer the time preference rate of that individual. This is not necessarily a monotonic transformation, in that an individual may be inferred to have a low time preference even with low wealth if Social Security and pension benefits will be relatively high. Nevertheless, in most cases low wealth relative to lifetime earnings translates to high time preference, and vice versa. Given the time preference, the other parameters of the model help to determine when the individual retires. The resulting model approximates the retirement peak at 62 and the smaller peak at 65 relatively well. In an out-of-sample prediction, it calculates roughly the correct amounts by which the changes in Social Security over the past 30 years have reduced the peak at 65 and increased the peak at age 62. It is also consistent with Kahn's (1988) observation that higher wealth individuals do not exhibit nearly the same propensity to retire at 62 that is true for lower wealth individuals, and with Samwick's (1998) estimates of the distribution of time preference rates. The next section looks at some of the previous work on this topic. Section 3 describes the model, and Section 4 describes data and the estimates. The following section examines some external consistency tests of the model, and Section 6 presents simulations to examine changes in the Social Security early entitlement age. The final section contains some final thoughts.

In many of the currently estimated retirement models, it is difficult to generate the observed retirement peaks at age 62 and age 65 without using binary variables for each age. The principal difficulty is that the Social Security early retirement penalty is approximately actuarially fair between ages 62 and the normal retirement age. And if a model does not predict a bunching of retirement at the early entitlement age of 62, it is unlikely to have much to say about what will happen if that age is changed. There are several clues in the data that point to heterogeneous time preference rates as a way around this problem. One clue is the wide variation in asset holding among the population. The variation occurs almost regardless of the level of lifetime income and is too wide to be explained by things like different educational levels or different rates of return on assets. A second clue is the widespread dissatisfaction expressed with the Social Security earnings test, which reduces benefits with additional earnings above an exempt amount. Many individuals seem to regard the foregone benefits as a tax and do not appear to value at all the fact that later benefits will be increased. A third clue is the high take-up rate of Social Security benefits when individuals first become eligible for them, even though the actuarial value of benefits is frequently increased by delaying benefits to a later age. In this paper, we estimated a retirement model that allows for heterogeneous time preferences. We showed that such a model can indeed generate a bunching of retirement both at ages 62 and at 65, each of which is nearly as large as the observed magnitude. Some of the bunching at age 62 is undoubtedly due to the fact that individuals with high time preferences will not have saved and hence will not have the assets to finance retirement before 62. Perhaps a more important reason is that individuals with high time preferences will heavily discount the future benefit increases that delaying retirement fosters, and hence will see the foregone benefits as a reduction in net compensation. Simulations indicated that if the early entitlement age is increased, perhaps three-fifths of the bunching of retirements at age 62 will shift to the new early entitlement age. Since the bunching amounts to about 8% of the population of married men, an increased retirement age from three-fifths of them will have a substantial effect on the Social Security system and its finances that should not be overlooked. In closing, we should mention two further analyses we conducted to determine the robustness of the findings. First, we considered a potential interaction with the disability program, which we found to be minor. In 2000, the number of men entering the disability rolls from ages 55 to age 62 ranges between 12,000 and 16,000 at each single year of age (Social Security Administration, 2001, Table 6A4). There is no evidence that the number of rewards is increasing precipitously as the Social Security early entitlement age approaches. After the attainment of the early entitlement age, there appears to be a slight tail-off of awards, on the order of perhaps 1500, at age 62, and a further tail-off of 7000 to 8000 at ages 63 and 64. Since the relevant population is about 925,000 per year of age, these figures amount to 0.16% at age 62 and 0.81% at age 63.15 A change of 0.16% is simply too small to have any significant bearing on these results. Although the total number of workers who begin disability insurance in any given year is sizeable (about 330,000 workers in 2000), most of the disability awards are made to individuals far away from retirement, and the number who enter the rolls near retirement are relatively small. Second, we tested the model for a correlation between time preference and leisure preference by including the time preference parameter in the βX term, which indicates the strength of leisure preferences. When the time preference term is included, however, its estimate is insignificant and very small numerically. To investigate this result further, we ran the simulations separately for groups with low, medium, and high time preferences. Even without any correlation between time preference and leisure preference, the group with high time preferences are simulated to retire earlier than the others, and by just about the same magnitude as we find in the observed retirements. Evidently, the possibility of future rewards to current work makes current work more attractive for those with low time preference rates, and this leads to later retirement.