On the Economic Meaning of Interaction Term Coefficients in Nonlinear Binary Response Regression Models

• Activity Number: 519
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Andrew F. Siegel*+ and Adam C. Kolasinski
• Companies: University of Washington and University of Washington
• Keywords: Logit regression ; Probit regression ; Categorical data analysis ; Interactive effects ; Estimation techniques

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 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.