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

Victor Aguirregabiria () and Arvind Magesan

No 2016-32, Working Papers from Department of Economics, University of Calgary

Abstract: 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 computation of a solution and to the evaluation of counterfactual experiments. We use a choice probabilities representation of the discrete decision problem to derive marginal conditions of optimality with the same features as the standard EEs in continuous decision problems. These EEs imply a Â…fixed point mapping in the space of conditional choice values, that we denote the Euler equation-value (EE-value) operator. We show that, in contrast to Euler equation operators in continuous decision models, this operator is a contraction. We present numerical examples that illustrate how solving the model by iterating in the EE-value mapping implies substantial computational savings relative to iterating in the Bellman equation (that requires a much larger number of iterations) or in the policy function (that involves a costly valuation step). We deÂ…fine 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 an unbiased (in fiÂ…nite samples) and consistent estimator 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 several Monte Carlo experiments.

Date: 2016-05-24
New Economics Papers: this item is included in nep-cmp, nep-dcm, nep-dge and nep-ecm
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Solution and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations (2016)
Working Paper: Solution and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations (2016)
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