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

49 Pages Posted: 29 Oct 2016

See all articles by Victor Aguirregabiria

Victor Aguirregabiria

University of Toronto - Department of Economics

Arvind Magesan

University of Calgary

Multiple version iconThere are 2 versions of this paper

Date Written: October 28, 2016


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.

Keywords: Dynamic programming discrete choice models, Euler equations, Relative Value Function iteration, Estimation; Approximation bias

JEL Classification: C13, C35, C51, C61

Suggested Citation

Aguirregabiria, Victor and Magesan, Arvind Nathan, Solution and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations (October 28, 2016). Available at SSRN: or

Victor Aguirregabiria (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
4169784358 (Phone)


Arvind Nathan Magesan

University of Calgary ( email )

University Drive
Calgary, Alberta T2N 1N4

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