Aging and Labor Force Participation: A Review of Trends and Explanations

The American population is aging rapidly. Persons 65 and over who now constitute about one-fifth of the population will constitute about two-fifths of the population by 2040. In addition, individuals are living longer. Yet the labor force participation of older Americans has fallen dramatically in recent years. This paper discusses this trend and the principal arguments put forth to explain it. The paper is in two parts. The first part reviews trends in labor force participation and associated trends in Social Security (SS) coverage, firm pension plan coverage, and other factors that are likely to be associated with the labor force participation trends, including demographics. The second part of the paper discusses the incentive effects of SS and retirement plans, with emphasis on firm pension plans.

Why are Retirement Rates So High at Age 65?

In most data sets of labor force participation of the elderly, an empirical regularity that emerges is that retirement rates are particularly high at age 65. While there are numerous economic reasons why individuals may choose to retire at 65, empirical models that have attempted to explain the age-65 spike have met with limited success. Interpreted another way, while many models would predict a jump in the hazard rate at age 65, the magnitude of the spike indicates excessive response given the economic considerations that retirees typically face. This paper considers the puzzle of why retirement rates are so high at age 65 and explores a variety of explanations.

Three Models of Retirement: Computational Complexity Versus Predictive Validity

Empirical analysis often raises questions of approximation to underlying individual behavior. Closer approximation may require more complex statistical specifications, On the other hand, more complex specifications may presume computational facility that is beyond the grasp of most real people and therefore less consistent with the actual rules that govern their behavior, even though economic theory may push analysts to increasingly more complex specifications. Thus the issue is not only whether more complex models are worth the effort, but also whether they are better. We compare the in-sample and out-of-sample predictive performance of three models of retirement -- "option value," dynamic programming, and probit -- to determine which of the retirement rules most closely matches retirement behavior in a large firm. The primary measure of predictive validity is the correspondence between the model predictions and actual retirement under the firm's temporary early retirement window plan. The "option value" and dynamic programming models are considerably more successful than the less complex probit model in approximating the rules individuals use to make retirement decisions, but the more complex dynamic programming rule approximates behavior no better than the simpler option value rule.

The local universes model: an overlooked coherence construction for dependent type theories

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types. Precisely, we take as input a "weak model": a comprehension category, equipped with structure corresponding to the desired logical constructions. We assume throughout that the base category is close to locally Cartesian closed: specifically, that products and certain exponentials exist. Beyond this, we require only that the logical structure should be *weakly stable* --- a pure existence statement, not involving any specific choice of structure, weaker than standard categorical Beck--Chevalley conditions, and holding in the now standard homotopy-theoretic models of type theory. Given such a comprehension category, we construct an equivalent split one, whose logical structure is strictly stable under reindexing. This yields an interpretation of type theory with the chosen constructors. The model is adapted from Voevodsky's use of universes for coherence, and at the level of fibrations is a classical construction of Giraud. It may be viewed in terms of local universes or delayed substitutions.Comment: 36 pages. Definition of "pseudo-stable" corrected from earlier version. To appear in ACM Transactions on Computational Logi