Testing exogeneity under distributional misspecification

We propose a general test for exogeneity that is robust against distributional misspecification. The test can also be used to identify other types of misspecifications, such as the presence of a random coefficient. The idea is to sort the data with respect to a variable (a sorting score) and then split the sample into two parts. Using a Chow test, it can then be tested whether estimated parameters in the two sub-samples are different. We give conditions under which it is possible to test for exogeneity by using the (supposedly) endogenous variable as a sorting score. The resulting test does not need instrumental variables. Evidence from a Monte Carlo study and an empirical application suggets that the test can be useful for practitioners.