Testing the Exogeneity of Instrumental Variables and Regressors in Linear Regression Models Using Copulas

Abstract: We provide a Copula-based approach to test the exogeneity of instrumental variables in linear regression models. We show that the exogeneity of instrumental variables is equivalent to the exogeneity of their standard normal transformations with the same CDF value. Then, we establish a Wald test for the exogeneity of the instrumental variables. We demonstrate the performance of our test using simulation studies. Our simulations show that if the instruments are actually endogenous, our test rejects the exogeneity hypothesis approximately 93% of the time at the 5% significance level. Conversely, when instruments are truly exogenous, it dismisses the exogeneity assumption less than 30% of the time on average for data with 200 observations and less than 2% of the time for data with 1,000 observations. Our results demonstrate our test's effectiveness, offering significant value to applied econometricians.