Alternative Methods of Estimating Interaction Effects in Non-Linear Models

Introduction

This paper reviews alternative methods for estimating interaction effects in non-linear models. Interaction effects refer to the way in which the relationship between two variables can differ between categories of a third variable. Many researchers attempt to measure interaction effects, understanding that the relationship between variables of interest often differs between sub-groups or across contexts. The relationship between parenthood and wage outcomes, for example, is understood to vary between men and women; and the relationship between changing interest rates and economic activity is understood to vary with the broader economic context. Whilst the measurement of interaction effects is straightforward when the dependent variable is linear (as is usually the case for wages), Ai and Norton (2003) found that most applied researchers misinterpreted the coefficient of the interaction term in non-linear models. To address this issue, Norton, Wang and Ai (2004) developed a method for correctly estimating interaction effects in probit and logit models with a single interaction term. Seymour (2011a) makes an important addition to this literature by describing a method for computing the interaction effects in probit models where there are two or more interaction terms with the same independent variable. This paper examines the importance and application of this innovation by reviewing the alternative approaches to studying interaction effects and by assessing the impact of using the alternative methods to estimate interaction effects. To facilitate this review, it examines a particular case study: of the employment impacts of ill-health and informal care roles, and how these impacts can vary with the work environment. The paper trials a number of alternative methods for measuring the interaction between ill-health/informal care roles and characteristics of the work environment in the determination of employment retention using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey.