One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV

Abstract

We revisit the finite-sample behavior of just-identified instrumental variables (IV) estimators, arguing that in most microeconometric applications, just-identified IV bias is negligible and the usual inference strategies likely reliable. Three widely-cited applications are used to explain why this is so. We then consider pretesting strategies of the form t1 > c, where t1 is the first-stage t-statistic, and the first-stage sign is given. Although pervasive in empirical practice, pretesting on the first-stage F-statistic exacerbates bias and distorts inference. We show, however, that median bias is both minimized and roughly halved by setting c = 0, that is by screening on the sign of the estimated first stage. This bias reduction is a free lunch: conventional confidence interval coverage is unchanged by screening on the estimated first-stage sign. To the extent that IV analysts sign-screen already, these results strengthen the case for a sanguine view of the finite-sample behavior of just-ID IV.