Understanding IV Versus OLS Estimates of Treatment Effects and the Coefficient Difference Check - David J. Bjerk (Institute of Labor Economics (IZA), 2025)
This article derives an equation characterizing the difference between OLS and IV coefficients under potentially heterogenous treatment effects. This leads to what I call the Coefficient Difference Check, which consists of checking that the difference between the estimated OLS and IV coefficients has the same sign as the expected selection effect. I show failures of this check can arise because: IV is invalid, the expected selection story is incorrect, or there are particular heterogenous treatment effects that imply the IV estimate is both "fragile" and that it provides a more biased estimate of the ATT than OLS. Failures of this check are relatively common in the literature. I describe best practices given such failures.
Keywords: 330; instrumental variables; selection; heterogenous treatment effects; average treatment-on-the-treated; judge fixed-effects; adjudicator propensity to treat IV; examiner tendency IV; returns to schooling