A Directional Test for Average Partial Effects in Linear Regression

For the OLS estimators in a classical linear model to have average partial effects interpretation, one usually imposes the so-called “strict exogeneity”condition. In practice, testing strict exogeneity condition can be done by omnibus nonparametric test. However, there are cases where strict exogeneity condition fails but the average partial effects interpretation of OLS estimator still survives. Therefore, an omnibus test is too “omnibus” in the sense that it wastes much power in situations where a researcher cares only about the validity of the interpretation of estimators rather than validity of the pure “strict exogeneity”condition. This paper proposes a directional test that distributes power exclusively against the alternatives that one has particular concerns. The paper also shows that the new test is more powerful than omnibus test in many simple simulation settings.