Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/334689 
Authors: 
Year of Publication: 
2025
Series/Report no.: 
IZA Discussion Papers No. 18274
Publisher: 
Institute of Labor Economics (IZA), Bonn
Abstract: 
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.
Subjects: 
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
Document Type: 
Working Paper

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