Information Structure and Statistical Information in Discrete Response Models

Strategic interaction parameters characterize the impact of actions of one economic agent on the payoff of another economic agent. In this paper we study how the information available to economic agents regarding other economic agents can influence the ability of an econometrician to recover strategic information parameters from the observed actions. We consider two extreme cases: the complete information case where the information sets of participating economic agents coincide, and the incomplete information case where each agent has a privately observable type. We find that in models with incomplete information the statistical (Fisher) information for the interaction parameters is zero, implying that estimation and inference become nonstandard. In contrast, in the incomplete information models with any non-zero variance of player types, the statistical information is positive, implying the existence of regular estimators for these parameters converging at the parametric rate. This finding is illustrated in two cases: treatment effect models (expressed as a triangular system of equations), and the static game models. In both types of models the observed discrete outcomes are driven by continuously distributed errors with an unknown distribution (unobserved heterogeneity). We find that the key factor driving the result in these models is the relative tail behavior of the distribution of unobserved heterogeneity of economic agents’ payoffs and the distribution of covariates. Our result has important implications for experimental design in economic systems where unobserved heterogeneity plays a major role: a failure to provide sufficient independent randomization of the payoffs of participating agents may lead to non-robustness of estimated parameters to the distribution of unobserved heterogeneity. JEL Classification: C35, C14, C25, C13.