Empirical Strategies for Estimating Discrete Games with Multiple Equilibria

I provide two practical estimators that can be used by empirical researchers to conduct inference on parameters in static discrete response models with many decision makers and/or when the strategy space is large. The inferential approach is to estimate directly the set of parameter values that satisfy the constraints imposed by the model. Every parameter in the identified set of interest is consistent with a model of the process that generated the observed data. In this paper, the first estimator is based on measuring the distance between the vector of observed choice probabilities and the set of predicted choice probabilities. This provides a sharp estimate of the set of identified parameter values. The second estimator exploits bounds on the true and unobserved likelihood function to obtain estimates of the set of identified parameters. This is a simple estimator to implement but is not sharp. A Monte Carlo experiment compares the small sample behavior of the two estimators. I also illustrate the estimator using data on entry in airline markets.