On the Economic Meaning of Interaction Term Coefficients in Non-Linear Binary Response Regression Models

Abstract

We show that it is perfectly correct to use just the interaction term, along with its standard error, to draw inferences about interactive effects in binary response regression models. This point is currently in dispute among applied econometricians, some of whom insist that simply relying on the interaction term is incorrect, since the cross partial derivative of the probability of occurrence with respect to interacted covariates can, for some observations, have the sign opposite to that of the interaction term coefficient. We show that this sign flip results from a mechanical saturation effect that is of no importance to researchers who recognize that small changes in probability are more important near the boundaries than near the center. For such researchers, the interaction term coefficient (which is the cross partial derivative of the logit or probit function of the probability) provides a more meaningful measure of interactive effects than does the cross partial derivative of the probability itself. We introduce an alternative cross partial derivative of the probability for which these sign changes cannot occur. Finally, we demonstrate some simple and intuitive ways of interpreting the economic meaning of interaction term coefficients.