Investigating Instruments with Meta-Regressions

N Aaron Pancost and Garrett Schaller

♦ Instrumental variable (IV) estimates are typically much larger than their ordinary least squares (OLS) counterparts, often suggesting implausible values of the omitted variable bias. We derive a meta-regression of OLS on IV estimates that can resolve this puzzle by separately identifying omitted variable bias from measurement error in the endogenous regressor, provided the instrument is valid. We then show that meta-regression estimates can also reveal when the underlying instruments are invalid. We conduct simulation exercises and apply our estimator to three empirical settings in finance. We include a Stata package, metaps, which implements the meta-regression.

Read it here.