Solution and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations

This paper extends the Euler Equation (EE) representation of dynamic decision problems to a general class of discrete choice models and shows that the advantages of this approach apply not only to the estimation of structural parameters but also to the solution of the model and the evaluation of counterfactual experiments. We use a choice probabilities representation of the discrete decision problem to derive marginal conditions of optimality with similar features as standard EEs in continuous decision problems. These EEs imply a fixed point mapping in the space of conditional choice values, that we denote the Euler Equation-value (EE-value) operator. We show that this operator is a stronger contraction than both the standard and the relative value function operators. Solving the dynamic programming problem by iterating in the EE-value operator implies substantial computational savings compared to value function and relative value function iterations (that require a much larger number of iterations) and to policy function iterations (that involves a costly valuation step at every iteration). We define a sample version of the EE-value operator and use it to construct a sequence of consistent estimators of the structural parameters, and to evaluate counterfactual experiments. The computational cost of evaluating this sample-based EE-value operator increases linearly with sample size, and provides a consistent estimator of the counterfactual. As such there is no curse of dimensionality in the consistent estimation of the model and in the evaluation of counterfactual experiments. We illustrate the computational gains of our methods using Monte Carlo experiments