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 in…nite dimensional parameters. Examples can include signaling games with discrete types where the type distribution is nonparametrically speci…ed and entry-exit games with partially linear payo¤s functions. A consistent set estimator and a con…dence 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 con…dence interval than those of the set estimator using the full information in the model. This …nding justi…es 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.
Semiparametric Estimation, Set Inference, InÖnite Dimensional Parameters, Inequality Moment Conditions, Signaling Game with Discrete Types
Set Inference for Semiparametric Discrete Games. (2006). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/900
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