Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher

Abstract

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...

Consumer Stockpiling and Sales Promotions

“…Without any assumptions, we have to numerically integrate over the errors for every future value term. To avoid this, we make a simplifying assumption that was ini-tially proposed by Rust (1987) and since then has become a standard in the literature:…”

“…We use the nested fixed-point algorithm proposed and made popular by Rust (1987). This is an iterative gradient search method to obtain the maximumlikelihood estimates of the structural parameters.…”

A link based network route choice model with unrestricted choice set

“…The traveler chooses the next link given the current state in a stochastic process having the Markov property (Rust;1987;2010). In our setting the next state is just the chosen link and it is given with certainty by the action.…”

“…This paper is the first to provide links between the sequential link based route choice model and the finite multinomial logit model in the context of route choice. Second, we are also the first to provide an interpretation of the model as a dynamic discrete choice model (Rust;1987;2010), connecting the path choice problem to that literature. Third, we are the first to discuss estimation of the model, including by sampling of alternatives 1978).…”

“…The recursive logit model corresponds to a dynamic discrete choice model (Rust;1987) where the path choice problem is formulated as a sequence of link choices. At each node the decision maker chooses the utility-maximizing outgoing link with link utilities given by the instantaneous cost, the expected maximum utility to the destination (value function) and i.i.d.…”