Calculating marginal effects in dichotomous - continuous models

Abstract

In many economic settings, individual decisions can be viewed as a sequential process where a dichotomous choice is followed by a continuous choice. These processes are frequently encountered in consumption demand studies, where the decision of whether or not to consume a particular commodity is followed by the choice of how much to consume. The Heckman two-step approach has been extensively used in estimating these models. Expressions are derived for calculating marginal effects of regressors in dichotomous-continuous models. It is proposed that the marginal effect expressions are incomplete in almost all consumption demand studies that use the Heckman approach. In dichotomous-continuous models, a change in an explanatory variable that is common to both stages of the decision process has two effects: (1) it affects the likelihood of whether the commodity will be consumed; and (2) if the commodity is consumed, it affects the expenditure on that commodity. The first effect has so far been omitted from applied demand studies. The correct marginal effect expressions are derived for single-commodity and multiple-commodity demand models. An application to consumption survey data on 12 food commodities shows that erroneous marginal effect expressions can introduce substantial bias in demand elasticity estimates.