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Published September 2018 | Submitted
Journal Article Open

Nonparametric identification of the distribution of random coefficients in binary response static games of complete information


This paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification. The main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects. Under additional independence assumptions, we identify the joint density of the interaction coefficients. Moreover, we prove that in the presence of covariates that are common to both players, the player-specific coefficient densities are identified, while the joint density of all random coefficients is not point-identified. However, we do provide bounds on counterfactual probabilities that involve this joint density.

Additional Information

© 2018 Published by Elsevier B.V. Received 1 September 2015, Revised 10 June 2017, Accepted 22 January 2018, Available online 26 May 2018. We thank Andres Aradillas-Lopez, Arie Beresteanu, Iván Fernández-Val, Jeremy Fox, Eric Gautier, Yuichi Kitamura, Elie Tamer, Whitney Newey, seminar participants at Boston College, Boston University, Harvard, UCL, University of Pittsburgh, Yale, and conference participants at the Second CIREQ-CEMMAP Workshop on Incomplete Models and the 2013 North American Winter Meeting of the Econometric Society in San Diego. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft in the SFB 823 (projects C1 and C4) and by the Ministry of Education and Cultural Affairs of Lower Saxony in the project "Reducing Poverty Risk" (Dunker) and National Science Foundation SES-1357643 (Kaido). This paper contains parts of the identification section of Dunker, Hoderlein, and Kaido (2014) "Random Coefficients in Static Games of Complete Information," (DHK, henceforth). The estimation part of DHK will be part of a companion paper.

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