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Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models

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  • Victor Aguirregabiria
  • Jiaying Gu
  • Yao Luo

Abstract

We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is nonparametric, i.e., fixed-effects model. We consider models with two endogenous state variables: the lagged decision variable, and the time duration in the last choice. This class of models includes as particular cases important economic applications such as models of market entry-exit, occupational choice, machine replacement, inventory and investment decisions, or dynamic demand of differentiated products. The identification of structural parameters requires a sufficient statistic that controls for unobserved heterogeneity not only in current utility but also in the continuation value of the forward-looking decision problem. We obtain the minimal sufficient statistic and prove identification of some structural parameters using a conditional likelihood approach. We apply this estimator to a machine replacement model.

Suggested Citation

  • Victor Aguirregabiria & Jiaying Gu & Yao Luo, 2018. "Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models," Working Papers tecipa-603, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-603
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    More about this item

    Keywords

    Panel data discrete choice models; Dynamic structural models; Fixed effects; Unobserved heterogeneity; Structural state dependence; Identification; Sufficient statistic.;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • 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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