%0 Report
        %A Bjerk, David J.
        %T Understanding IV Versus OLS Estimates of Treatment Effects and the Coefficient Difference Check
        %D 2025
        %8 2025 Nov
        %I Institute of Labor Economics (IZA)
        %C Bonn
        %7 IZA Discussion Paper
        %N 18274
        %U https://www.iza.org/index.php/publications/dp18274
        %X 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.
        %K adjudicator propensity to treat IV
%K judge fixed-effects
%K average treatment-on-the-treated
%K heterogenous treatment effects
%K selection
%K instrumental variables
%K examiner tendency IV
%K returns to schooling