Pairwise-difference estimation of incomplete information games

This paper contributes to the literature on econometric estimation of incomplete information games with Nash equilibrium behavior by introducing a two-step estimation procedure that makes no parametric assumptions about the distribution of unobservable payoffs shocks. Instead, its asymptotic properties rely on assuming only that these distributions satisfy an invertibility condition, and that the underlying equilibrium selection mechanism is degenerate. Our methodology relies on a pairwise-differencing procedure which, unlike Aradillas-Lopez (2010), does not require computing the equilibria of the game. Furthermore, if normal-form payoffs are linear in the parameters of interest, our procedure results in an estimator with a closed-form expression. We contribute to the pairwise-differencing econometric literature by introducing the first model, where both the control variables being matched and the regressors in the index function parameterized by θ contain nonparametric functions. In particular, the asymptotic theory developed in Aradillas-Lopez et al. (2007) does not cover this setting. We describe conditions under which nonparametrically estimated plug-ins yield a N-consistent and asymptotically normal estimator for the parameter of interest. A consistent specification test based on semiparametric residuals is also developed. It appears to be the first test of this type for a model involving nonparametric or "generated" regressors. Several extensions of our method are also discussed. A series of Monte Carlo experiments are used to investigate the properties of our estimator and our specification test.