Tools for intuition about sample selection bias and its correction

Abstract

We provide mathematical tools to assist intuition about selection bias in concrete empirical analyses. These new tools do not offer a general solution to the selection bias problem; no method now does that. Rather, the techniques we present offer a new decomposition of selection bias. This decomposition permits an analyst to develop intuition and make reasoned judgments about the sources, severity, and direction of sample selection bias in a particular analysis. When combined with simulation results, also presented in this paper, our decomposition of bias also permits a reasoned, empirically-informed judgment of when the well-known two-step estimator of Heckman (1976, 1979) is likely to increase or decrease the accuracy of regression coefficient estimates. We also use simulations to confirm mathematical derivations.