Structural Estimation

Lecture 7 · 2026-04-28

Using Rust’s (1987) Harold Zurcher bus engine replacement problem as the organizing thread, this lecture develops the structural estimation of dynamic discrete choice models. It covers the stochastic dynamic programming formulation of the optimal stopping problem and its Bellman equation, the contraction-mapping property that justifies value function iteration, and the key distributional assumptions (additive separability, conditional independence, and Type-I extreme value shocks) that make the model estimable, yielding logit-form conditional choice probabilities. Building on this, it introduces maximum likelihood estimation and the inner and outer loops of the nested fixed point algorithm (NFXP), and contrasts it with alternative DDC estimators such as Hotz–Miller, Bajari–Benkard–Levin, and Su–Judd. A complete Python implementation and data are included.

Materials

Readings

This lecture’s slides follow Rust’s method as the main thread:

  • Rust (1987), “Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher,” Econometrica 55(5), 999–1033.
  • Bajari, Benkard & Levin (2007), “Estimating Dynamic Models of Imperfect Competition,” Econometrica 75(5), 1331–1370.

Extended background reading on structural estimation methods (at the course level, not directly covered by this lecture’s slides):

  • Hansen (1982), “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica 50(4), 1029–1054.
  • McFadden (1989); Pakes & Pollard (1989): simulated method of moments, Econometrica 57(5).
  • Gourieroux, Monfort & Renault (1993), “Indirect Inference,” J. Applied Econometrics 8, S85–S118.