TOOLS FOR INTUITION ABOUT SAMPLE SELECTION BIAS AND ITS CORRECTION

We provide mathematical tools to assist intuition about selection bias in concrete empirical analyses. These new tools do not offer a genera l solution to the selection bins problem; no method now does that. Rat her, the techniques we present offer a new decomposition of selection bias. This decomposition permits an analyst to develop intuition and m ake reasoned judgments about the sources, severity, and direction of s ample selection bins in a particular analysis. When combined with simu lation results, also presented in this paper our decomposition of bias also permits a reasoned empirically-informed judgment of when the wel l-known two-step estimator of Heckman (1976, 1979) is likely to increa se or decrease the accuracy of regression coefficient estimates. We al so use simulations to confirm mathematical derivations.