Causal Inference and the Heckman Model

Abstract

In the social sciences, evaluating the effectiveness of a program or intervention often leads researchers to draw causal inferences from observational research designs. Bias in estimated causal effects becomes an obvious problem in such settings. This article presents the Heckman Model as an approach sometimes applied to observational data for the purpose of estimating an unbiased causal effect and shows how the Heckman Model can be used to correct for the problem of selection bias. It discusses in detail the assumptions necessary before the approach can be used to make causal inferences. The Heckman Model makes assumptions about the relationship between two equations in an underlying behavioral model: a response schedule and a selection function. This article shows that the Heckman Model is particularly sensitive to the choice of variables included in the selection function. This is demonstrated empirically in the context of estimating the effect of commercial coaching programs on the SAT performance of high school students. Coaching effects for both sections of the SAT are estimated using data from the National Education Longitudinal Study of 1988. Small changes in the selection function are shown to have a big impact on estimated coaching effects under the Heckman Model.