Inference in Limited Dependent Variable Models Robust to Weak Identification

We propose tests for structural parameters in limited dependent variable models with endogenous explanatory variables using the classical minimum distance framework. These tests have the correct size whether the structural parameters are identified or not. Relating to the current tests, the application of ours is appropriate especially to models whose moment conditions are nonlinear in parameters. Moreover, the computation of ours tests is simple, allowing their implementation in a large number of statistical software packages. We compare our tests with Wald tests by performing simulation experiments. We use our tests to analyze the female labor supply and the demand for cigarette.