JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica. This paper formulates a simple regenerative optimal stopping model of bus engine replacement to describe the behavior of Harold Zurcher, superintendent of maintenance at the Madison (Wisconsin) Metropolitan Bus Company. The null hypothesis is that Zurcher's decisions on bus engine replacement coincide with an optimal stopping rule: a strategy which specifies whether or not to replace the current bus engine each period as a function of observed and unobserved state variables. The optimal stopping rule is the solution to a stochastic dynamic programming problem that formalizes the trade-off between the conflicting objectives of minimizing maintenance costs versus minimizing unexpected engine failures. The model depends on unknown "primitive parameters" which specify Zurcher's expectations of the future values of the state variables, the expected costs of regular bus maintenance, and his perceptions of the customer goodwill costs of unexpected failures. Using ten years of monthly data on bus mileage and engine replacements for a subsample of 104 buses in the company fleet, I estimate these primitive parameters and test whether Zurcher's behavior is consistent with the model. Admittedly, few people are likely to take particular interest in Harold Zurcher and bus engine replacement per se. I focus on a specific individual and capital good because it provides a simple, concrete framework to illustrate two ideas: (i) a '"bottom-up" approach for modelling replacement investment, and (ii) a "nested fixed point" algorithm for estimating dynamic programming models of discrete choice. KEYWORDS: Optimal replacement, regenerative optimal stopping models, dynamic programming, controlled stochastic processes, nested fixed point algorithm. ' This research was made possible by financial support from the Graduate School of the University of Wisconsin and National Science Foundation Grant SES-8419570. I thank Alice Wilcox for an excellent job typing the manuscript and Tom Rust for his careful work in coding the data. I am especially grateful to Harold Zurcher for providing the data used in this study, and for his assistance in interpreting the estimation results. 999 1000 JOHN RUSTAdmittedly, few people are likely to take particular interest in Harold Zurcher and bus engine replacement, per se. I focus on a particular individual and a specific capital good because it provides a simple, concrete framework to illustrate two ideas: (i) a "bottom-up" approach for modelling replacement investment and (ii) a "nested fixed point" algorithm for estimating dynamic programming models of discrete choice...

This paper provides an empirical analysis of how the U.S. Social Security and Medicare insurance system affects the labor supply of older males in the presence of incomplete markets for loans, annuities, and health insurance. We estimate a dynamic programming (DP) model of the joint labor supply and Social Security acceptance decision, focusing on a sample of males in the low to middle income brackets whose only pension is Social Security. The DP model delivers a rich set of predictions about the dynamics of retirement behavior, and comparisons of actual vs. predicted behavior show that the DP model is able to account for a wide variety of phenomena observed in the data, including the pronounced peaks in the distribution of retirement ages at 62 and 65 (the ages of early and normal eligibility for Social Security benefits, respectively). We identify a significant fraction of "health insurance constrained" individuals who have no form of retiree health insurance other than Medicare, and who can only obtain fairly priced private health insurance via their employer's group health plan. The combination of significant individual risk aversion and a long tailed (Pareto) distribution of health care expenditures implies that there is a significant "security value" for these individuals to remain employed until they are eligible for Medicare coverage at age 65. Overall, our model suggests that a number of heretofore puzzling aspects of retirement behavior can be viewed as artifacts of particular details of the Social Security rules, whose incentive effects are especially strong for lower income individuals and those who do not have access to fairly priced loans, annuities, and health insurance.

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USING RANDOMIZATION TO BREAK THE CURSE OF DIMENSIONALITY BY JOHN RUST' This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the "curse of dimensionality" for a subclass of MDPs known as discrete decision processes (DDPs).

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