Interaction Terms in Poisson and Log Linear Regression Models

8 Pages Posted: 11 Jan 2018

See all articles by Shengwu Shang

Shengwu Shang

Ball State University - Department of Economics

Erik Nesson

Ball State University - Department of Economics

Maoyong Fan

Ball State University - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: January 2018

Abstract

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.

Keywords: differences‐in‐differences, difference‐in‐semielasticities, exponential conditional mean function, interaction effect, log‐linear model

JEL Classification: C10, C18

Suggested Citation

Shang, Shengwu and Nesson, Erik and Fan, Maoyong, Interaction Terms in Poisson and Log Linear Regression Models (January 2018). Bulletin of Economic Research, Vol. 70, Issue 1, pp. E89-E96, 2018. Available at SSRN: https://ssrn.com/abstract=3099825 or http://dx.doi.org/10.1111/boer.12120

Shengwu Shang (Contact Author)

Ball State University - Department of Economics ( email )

Muncie, IN 47306-0340
United States

Erik Nesson

Ball State University - Department of Economics ( email )

Muncie, IN 47306-0340
United States

Maoyong Fan

Ball State University - Department of Economics ( email )

Whitinger Business Building, room 201
2000 W. University Ave.
Muncie, IN 47306-0340
United States
765-285-5741 (Phone)

HOME PAGE: http://https://sites.google.com/site/maoyongfan/home

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