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

26 Pages Posted: 31 Aug 2010 Last revised: 27 Oct 2010

See all articles by Adam C. Kolasinski

Adam C. Kolasinski

Texas A&M University - Department of Finance

Andrew F. Siegel

University of Washington - Department of Finance and Business Economics; National Bureau of Economic Research (NBER)

Date Written: August 30, 2010

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.

Keywords: Logit regresion, probit regression, interactive effects

JEL Classification: C25, C12

Suggested Citation

Kolasinski, Adam C. and Siegel, Andrew F., On the Economic Meaning of Interaction Term Coefficients in Non-Linear Binary Response Regression Models (August 30, 2010). Available at SSRN: https://ssrn.com/abstract=1668750 or http://dx.doi.org/10.2139/ssrn.1668750

Adam C. Kolasinski (Contact Author)

Texas A&M University - Department of Finance ( email )

360 Wehner
College Station, TX 77843-4218
United States

Andrew F. Siegel

University of Washington - Department of Finance and Business Economics ( email )

Box 353200
Seattle, WA 98195
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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