Robust Tests of Model Incompleteness in the Presence of Nuisance Parameters

Economic models exhibit incompleteness for various reasons. They are, for example, consequences of strategic interaction, state dependence, or self-selection. Whether a model makes such incomplete predictions or not often has policy-relevant implications. We provide a novel test of model incompleteness using a score-based statistic and derive its asymptotic properties. The test is computationally tractable because it suffices to estimate nuisance parameters only under the null hypothesis of model completeness. We illustrate the test by applying it to a model of market entry and a triangular model with a set-valued control function.