Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models

57 Pages Posted: 23 May 2018

See all articles by Victor Aguirregabiria

Victor Aguirregabiria

University of Toronto - Department of Economics

Jiaying Gu

University of Toronto

Yao Luo

University of Toronto - Department of Economics

Date Written: May 10, 2018

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.

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

JEL Classification: C23; C25; C41; C51; C61

Suggested Citation

Aguirregabiria, Victor and Gu, Jiaying and Luo, Yao, Sufficient Statistics for Unobserved Heterogeneity in Structural Dynamic Logit Models (May 10, 2018). Available at SSRN: https://ssrn.com/abstract=3176616 or http://dx.doi.org/10.2139/ssrn.3176616

Victor Aguirregabiria (Contact Author)

University of Toronto - Department of Economics ( email )

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

HOME PAGE: http://individual.utoronto.ca/vaguirre/

Jiaying Gu

University of Toronto

Yao Luo

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S3G7
Canada

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