Set Inference for Semiparametric Discrete Games

• Main Author: KIM, Kyoo-il
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2006
• Subjects: Semiparametric Estimation; Set Inference; InÖnite Dimensional Parameters; InequalityMoment Conditions; Signaling Game with Discrete Types; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/900; https://ink.library.smu.edu.sg/context/soe_research/article/1899/viewcontent/ProfiledSetInference_res.pdf
• Institution: Singapore Management University

We consider estimation and inference of parameters in discrete games allowing for multiple equilibria, without using an equilibrium selection rule. We do a set inference while a game model can contain infinite dimensional parameters. Examples can include signaling games with discrete types where the type distribution is nonparametrically specified and entry-exit games with partially linear payoffs functions. A consistent set estimator and a confidence interval of a function of parameters are provided in this paper. We note that achieving a consistent point estimation often requires an information reduction. Due to this less use of information, we may end up a point estimator with a larger variance and have a wider confidence interval than those of the set estimator using the full information in the model. This finding justifies the use of the set inference even though we can achieve a consistent point estimation. It is an interesting future research to compare these two alternatives: CI from the point estimation with the usage of less information vs. CI from the set estimation with the usage of the full information.