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Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models

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  • Victor Aguirregabiria
  • Arvind Magesan

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.

Suggested Citation

  • Victor Aguirregabiria & Arvind Magesan, 2013. "Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models," Working Papers tecipa-489, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-489
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    File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-489.pdf
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    Cited by:

    1. Jeremiah Harris & Ralph Siebert, 2015. "Driven by the Discount Factor: Impact of Mergers on Market Performance in the Semiconductor Industry," CESifo Working Paper Series 5199, CESifo Group Munich.
    2. David Canning & Declan French & Michael Moore, 2016. "The Economics of Fertility Timing: An Euler Equation Approach," CHaRMS Working Papers 16-03, Centre for HeAlth Research at the Management School (CHaRMS).
    3. repec:eee:indorg:v:53:y:2017:i:c:p:32-62 is not listed on IDEAS

    More about this item

    Keywords

    Dynamic discrete choice structural models; Euler equations; Choice probabilities.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • 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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