اثرات سیاست در مقابل مدل نمایی هایپربولی مصرف و بازنشستگی

This paper constructs a structural retirement model with hyperbolic preferences and uses it to estimate the effect of several potential Social Security policy changes. Estimated effects of policies are compared using two models, one with hyperbolic preferences and one with standard exponential preferences. Sophisticated hyperbolic discounters may accumulate substantial amounts of wealth for retirement. We find it is frequently difficult to distinguish empirically between models with the two types of preferences on the basis of asset accumulation paths or consumption paths around the period of retirement. Simulations suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. Simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used.

The impending advance of the baby boom generation into their retirement years, and perhaps even more importantly, the decline in the birth rate, have created strains on the Social Security system (Goss, 2010). As a result, increasing attention is being paid to measures that might encourage workers to stay on the job longer, contribute more to the system, and hence relieve some of the strain.1 Some of the proposals which have been mentioned have been increases in the early entitlement age, increases in the normal retirement age (which amounts to a reduction in benefits), and elimination of the earnings test, among others. An important goal of current research in this field, including the present paper, is to gauge the likely success of such measures in increasing the retirement age. This paper brings together two important strands of the recent literature on retirement and savings. One of these strands is the development of increasingly realistic structural models of retirement and saving. Empirical structural models of retirement began as relatively simple decisions as to the optimal time to retire.2 Over time, advances in computational capacity have allowed these early models to evolve into far richer models involving more nuanced decision sets and more elements of uncertainty.3 The decision to retire now includes the possibility of partial retirement as well as the possibility of returning to work after a period of retirement.4 The stochastic environment includes not only mortality but also uncertainty as to the returns to assets and the degree to which an individual will find retirement enjoyable after the fact.5 Other authors introduce uncertainty in wages and unpredictable health and health care expenditures. The result has been that the structural models of retirement and saving have increasingly been able to encompass the major elements affecting the retirement decision. A second strand of literature is the analysis of so-called “hyperbolic” preferences. These preferences have been introduced in recent years to reflect the fact that many individuals place a heavy weight on current consumption, but do not distinguish incremental years in the future quite so much. Proponents of hyperbolic preferences (Laibson, 1997) point to a wide range of phenomena which hyperbolic preferences help to explain, such as simultaneously having high-interest credit card debt and low-interest individual retirement accounts. The hyperbolic preferences used in this paper are actually what are called “quasi-hyperbolic” preferences, with a high discount rate between the current period and the next period and lower discount rates between successive future periods. The literature on hyperbolic preferences focuses mainly on consumption and saving behavior. While saving for retirement may be an important element of this behavior, the actual retirement date is largely taken as fixed. On the other hand, the structural retirement models almost uniformly assume exponential preferences, where a uniform time preference rate, perhaps differing among individuals, is applied to all future periods. The purpose of this paper is to construct a structural retirement model that can encompass either exponential or hyperbolic preferences. We estimate the model twice, once using exponential preferences and once using hyperbolic preferences. Using these estimates, we can examine the differences in retirement and consumption outcomes between the two models, and estimate and compare the effects of several potential policy changes that would be implied by the two models. Such comparisons can indicate the sensitivity of the estimated structural models to assumptions regarding the type of preferences. The next section looks at several properties of hyperbolic models and examines the degree to which it is possible to differentiate hyperbolic preferences from exponential preferences in the data. Section 3 specifies in more detail a structural model which can encompass either exponential or hyperbolic preferences, and Section 4 discusses the stochastic specification and estimation of the model. Section 5 analyzes several simulations with the estimated model to examine what difference the choice of preferences makes to the estimated effects of potential policy changes. Concluding observations are contained in the last section.

Individuals with hyperbolic time preferences have inconsistent time preferences, in the sense that their relative valuation of consumption in two periods depends on when they are doing the valuation. In particular, they may value current consumption highly relative to future consumption, but have much less strong preferences between consumption at two future dates. Contrary to what one might expect, such individuals may nevertheless be able to accumulate substantial amounts of wealth for retirement, at least as long as they realize that in the future, they will behave the same way as today, and that today's preferences will not match future preferences. Simulations with two models, one using exponential preferences and one using hyperbolic preferences, suggest that it is frequently difficult to distinguish empirically between hyperbolic and exponential discounters, at least on the basis of asset accumulation paths or consumption paths around the period of retirement. The simulations also suggest that, despite the much higher initial time preference rate, individuals with hyperbolic preferences may actually value a real annuity more than individuals with exponential preferences who have accumulated roughly equal amounts of assets. This appears to be especially true for individuals with relatively high time preference rates or who have low assets for whatever reason. This affects the tradeoff between current benefits and future benefits on which many of the retirement incentives of the Social Security system rest. The policy simulations have presented a mixed bag. The simulations involving increasing the early entitlement age and increasing the delayed retirement credit do not show a great deal of difference whether exponential or hyperbolic preferences are used, but the simulations for eliminating the earnings test show a non-trivially greater effect when exponential preferences are used. This latter result probably reflects the differential tradeoffs between current and future benefits for the two kinds of preferences. Whether to use exponential preferences or hyperbolic preferences is an unsettled point in the literature. Proponents of hyperbolic preferences point to modes of behavior, such as simultaneously holding credit card debt and IRA's, which are difficult to explain otherwise. On the other hand, while there continues to be disagreement, some empirical studies conclude that in the absence of some kind of shock, older individuals do not spend down their wealth, which can be even more of a problem for hyperbolic behavior than it is for exponential behavior (Poterba et al., 2010). We have certainly not resolved the issue of whether to use exponential preferences or hyperbolic preferences in this paper. Since the predictions are the same for most outcomes and policies, the current literature, which is based on the exponential model, would seem to be adequate for most purposes. However, the paper does suggest that in the absence of a consensus, it would probably be wise to investigate the effects of potential policy changes in both scenarios and be aware of instances in which the effects are sensitive to which set of preferences is assumed.