Interaction Terms in Nonlinear Models

Abstract

Although applied economists often estimate interaction terms to infer how the effect of one independent variable on the dependent variable depends on the magnitude of another independent variable, most researchers misinterpret the coefficient in nonlinear models. The magnitude of the interaction effect does not equal the marginal effect of the interaction term, can be of opposite sign, and its statistical significance is not calculated by standard software. We present the correct way to estimate the magnitude and standard errors of the interaction effect in nonlinear models, including the widely used log transformation model with unknown error distribution. The ratio of the estimated interaction effect divided by its estimated standard error has a standard normal distribution and must be used for statistical inference. An application to model the probability that an elderly person joins a Medicare HMO finds that not calculating the correct interaction effect would lead to wrong inference in a substantial percentage of the sample.