Incomplete Draft Do Not Cite Interaction Terms in Nonlinear Models

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 coefficient on the interaction term, can be of opposite sign, and is conditional on all the independent variables. The statistical significance of the interaction effect may change substantially with changes in the independent variable. Implications are discussed for difference in difference models. We illustrate with an empirical example.