Interpreting the outcomes of two-part models

Abstract

Interaction effects capture the impact of one explanatory variable x ₁ on the marginal effect of another explanatory variable x ₂. To explore interaction effects, the so-called interaction terms x ₁ x ₂ are typically included in estimation specifications. While in linear models the effect of a marginal change in the interaction term is equal to the interaction effect, this equality generally does not hold in nonlinear specifications (Ai and Norton, 2003). This article provides for a general derivation of marginal and interaction effects in both linear and nonlinear models and calculates the formulae of the marginal and interaction effects resulting from the Two-Part Model (2PM), a commonly employed censored regression model. Drawing on a survey of automobile use from Germany, we illustrate several subtleties inherent to the substantive interpretation of interaction effects gleaned from nonlinear models, such as the 2PM.

Keywords:

• censored regression model
• interaction terms
• marginal and interaction effects

JEL Classification:

• C34

Acknowledgements

We are very grateful for invaluable comments and suggestions by Christoph M. Schmidt. This work has been supported by the Collaborative Research Center ‘Statistical Modelling of Nonlinear Dynamic Processes’ (SFB 823) of the German Research Foundation (DFG), within the framework of Project A3, ‘Dynamic Technology Modelling’.

Notes

¹ Note that the coefficient estimate of 0.009 of the interaction effect pertaining to age and the number of children, for example, which appears on the left-hand panel of Table 1, is calculated on the basis of Equation 10(10), rather than Equation 16(16), and, hence, is not simply the marginal effect of the interaction term age × # children.