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, and are of great interest in both theoretical and empirical work. In this paper, by considering econometric models involving simultaneous discrete systems of equations, we study how the information available to economic agents regarding other economic agents can influence whether or not these strategic information parameters can be inferred 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's payoffs are privately observable. We find that in models with complete information, the strategic interaction parameters are more difficult to recover than they are in incomplete information models. We show this by exploring the Fisher information (from standard statistics literature) for the strategic interaction parameters in each of these models. Our findings are that in complete information models, the statistical (Fisher) information for the interaction parameters is zero, implying the difficulty in recovering them from data. In contrast, for incomplete information models, the Fisher information for the interaction parameters is positive, indicating that not only can these parameters be relatively easy to recover from data, but standard inference can be conducted on them. This finding is illustrated in two cases: treatment effect models (expressed as a triangular system of equations) and static game models.