Interaction Terms In Poisson And Log Linear Regression Models

This paper develops a difference†in†semielasticities (DIS) interpretation for the coefficients of dichotomous variable interaction terms in nonlinear models with exponential conditional mean functions, including but not limited to Poisson, Negative Binomial, and log linear models. We show why these interaction term coefficients cannot be interpreted as a DIS or semielasticity in the same manner as continuous coefficients, which has been overlooked by some empirical researchers. Then we show how interaction terms can be easily transformed into a DIS and derive the asymptotic distribution of this estimator. We illustrate the discrepancy between the interaction term coefficient and the DIS using an empirical example evaluating the relationship between employment, private health insurance and physician office visits. Our results can be applied in treatment effect models when the outcome variable is logged and the dichotomous variables indicating treatment participation and the post†treatment time period.