Exogeneity and Robustness

A common practice for detecting misspecication is to perform a \robustness test", where the researcher examines how a regression coecient of interest behaves when variables are added to the regression. Robustness of the regression coecient is taken as evidence of structural validity. However, there are numerous pitfalls that can befall a researcher when performing such tests. For example, we demonstrate that certain regressors, when added to the regression, will induce a shift in the coecient of interest even when structurally valid. Such robustness tests would produce false alarm, suggesting that the model is misspecied when it is not. For a robustness test to be informative, the variables added to the regression must be carefully chosen based on the model structure. We provide a simple criterion that allows researchers to quickly determine which variables, when added to the regression, constitute informative robustness tests. We also explore the extent to which robustness tests are able to detect bias, demonstrating that robustness tests enable detection of bias due not only to omitted observable variables but omitted unobservable variables as well. Finally, we give two extended examples using simulated data to demonstrate how the material in this paper can be used to conduct informative robustness tests.