A Robust Test for Instrument Exogeneity in Ordinal Response Models with Endogenous Regressors: A CF-GMM-Bootstrap Approach

Testing whether instrumental variables (IV) are truly exogenous is crucial for reliable causal inference, especially when dealing with discrete ordered outcomes (e.g., survey ratings) and an endogenous explanatory variable. Existing tests often perform poorly in this complex setting. We develop a robust new test that combines Control Function (CF) and Two-Stage Residual Inclusion (2SRI) to correct for endogeneity, uses Generalized Method of Moments (GMM) to construct the test statistic, and employs Bootstrap to ensure accurate results in real-world sample sizes. Simulations show our method is reliable, and we provide easy-to-use software for researchers. JEL Classification: C12, C26, C35