Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models

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.