On the Economic Meaning of Interaction Term Coefficients in Non-Linear Binary Response Regression Models
Adam C. Kolasinski
Texas A&M, Mays School of Business
Andrew F. Siegel
University of Washington - Department of Finance and Business Economics; National Bureau of Economic Research (NBER)
August 30, 2010
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.
Number of Pages in PDF File: 26
Keywords: Logit regresion, probit regression, interactive effects
JEL Classification: C25, C12
Date posted: August 31, 2010 ; Last revised: October 27, 2010
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