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

Author

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  • Victor Aguirregabiria
  • Arvind Magesan

    (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.

Suggested Citation

  • Victor Aguirregabiria & Arvind Magesan, "undated". "Soultion and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations," Working Papers 2016-32, Department of Economics, University of Calgary, revised 24 May 2016.
  • Handle: RePEc:clg:wpaper:2016-32
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    File URL: https://econ.ucalgary.ca/sites/econ.ucalgary.ca.manageprofile/files/unitis/publications/1-7218080/Magesan_Aguirregabiria.pdf
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    References listed on IDEAS

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    1. Solution and Estimation of Dynamic Discrete Choice Structural Models Using Euler Equations
      by Christian Zimmermann in NEP-DGE blog on 2016-06-16 19:45:29

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    1. Robert L. Bray, 2019. "Markov Decision Processes with Exogenous Variables," Management Science, INFORMS, vol. 65(10), pages 4598-4606, October.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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