One instrument to rule them all: The bias and coverage of just-ID IV

We revisit the finite-sample behavior of single-variable just-identified instrumental variables (just-ID IV) estimators, arguing that in most microeconometric applications, the usual inference strategies are 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.