Robust Likelihood-ratio Tests for Incomplete Economic Models
This paper develops a framework for testing hypotheses on structural parameters in incomplete economic models. Examples of hypotheses include those on the presence of strategic interaction in discrete games of complete information. Incomplete economic models make set-valued predictions and hence do not generally yield a unique likelihood. The model structure, however, allows to construct tests based on least favorable pairs of likelihoods using the theory of Huber and Strassen (1973). Building on this, we develop likelihood-ratio tests that are robust to model incompleteness. The tests can be implemented in a computationally tractable manner by solving convex programs. We show that sharp identifying restrictions play a key role in constructing tests that achieve robustness and statistical optimality. We further consider hypothesis tests in the presence of nuisance parameters and develop a likelihood-ratio test that minimizes a certain risk function. We then establish a minimax theorem for this setting.