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

TL;DR

This paper examines the finite-sample properties of just-identified IV estimators, showing that common inference methods are generally reliable and that sign-based pretesting can reduce bias without harming coverage.

Contribution

It demonstrates that sign-based pretesting on the first-stage estimator reduces bias in just-ID IV without affecting confidence interval coverage.

Findings

Pretesting on the first-stage sign reduces median bias.

Sign-screening does not distort confidence interval coverage.

Usual inference strategies are reliable in most microeconometric applications.

Abstract

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 $t_{1}>c$, where $t_{1}$ 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 \textit{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.