Dynamic Models : single agent problems ∗ Spring 2009 1 Rust ( 1987 ) : “ Optimal Replacement of GMC Bus Engines : An Empirical Model of Harold Zurcher ”

Single-agent dynamic optimization models. In these lecture notes we consider specification and estimation of dynamic optimization models. Focus on single-agent models. • Rust (1987) is one of the first papers in this literature. Model is quite simple, but empirical framework introduced in this paper for dynamic discrete-choice (DDC) models is still widely applied. • Agent is Harold Zurcher, manager of bus depot in Madison, Wisconsin. Each week, HZ must decide whether to replace the bus engine, or keep it running for another week. • This engine replacement problem is an example of an optimal stopping problem, which features the usual tradeoff: 1. there are large fixed costs associated with " stopping " (replacing the engine), but new engine has lower associated future maintenance costs; 2. by not replacing the engine, you avoid the fixed replacement costs, but suffer higher future maintenance costs. * These notes rely on Matthew Shum's lecture notes.