Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models

Abstract

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.

A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators

“…4 Imbens and Wooldridge (2005) conjectured an equivalence in propensity score estimation. 5 Our numerical equivalence results are established for the two-step semiparametric estimators only when sieve (or series) methods are used in the first step. We doubt such a numerical equivalence result might still hold for other nonparametric first steps such as kernel, local linear regression, or nearest-neighbor methods.…”

“…These equivalence results are useful for applied researchers, since they imply that one can obtain estimates of standard errors for the finite-dimensional structural parameters using well-known and simple formulas from the parametric literature. 5 We hope that this simplicity will promote the use of asymptotic semiparametric variance estimates and lessen the need for computationally burdensome bootstrapping. 6 We start with a brief review of the standard two-step parametric approach in section II.…”

“…See their equation(5) or their plug-in estimation equations(6) and(7). In fact,Ai and Chen (2007) consider a much broader class of models, including misspecified semi/nonparametric models.…”

Nonstationary dynamic models with finite dependence

“… See Hotz and Miller (), Altug and Miller (), Arcidiacono and Miller (), Aguirregabiria and Magesan (, ), and Gayle (). …”

Identification and semiparametric estimation of a finite horizon dynamic discrete choice model with a terminating action

“…We build on that intuition by proposing a nonparametric estimator of the agents' expectations about their continuation values, and use the estimates to recover agents'preferences within a regression framework. 2 The resulting estimator involves only linear (or nonlinear) projections and does not require simulation. Our method is thus computationally light, easily scalable to data-rich settings, and can be implemented using prede…ned procedures from standard statistical software such as R, STATA or MATLAB.…”