Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models
Advances in Econometrics, Volume 31, Structural Microeconometrics, E. Choo and M. Shum, eds. (December 2013), 3-44.
34 Pages Posted: 3 Jun 2013 Last revised: 30 Oct 2016
Date Written: December 1, 2013
We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for or approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.
Keywords: Dynamic discrete choice structural models; Euler equations; Choice probabilities
JEL Classification: C13, C35, C51, C61
Suggested Citation: Suggested Citation