Smile: A Simple Diagnostic for Selection on Observables

Abstract

This paper develops a simple diagnostic for the selection on observables assumption in the case of a binary treatment variable. I show that, under common assumptions, when selection on observables does not hold, designs based on selection on observables will estimate treatment effects approaching infinity or negative infinity among observations with propensity scores close to 0 or 1. Researchers can check for violations of selection on observables either informally by looking for a "smile" shape in a binned scatterplot, or with a simple formal test. When selection on observables fails, the researcher can detect the sign of the resulting bias