One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV
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| Format: | Preprint |
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2021
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| author | Angrist, Joshua Kolesár, Michal |
| author_facet | Angrist, Joshua Kolesár, Michal |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_10556 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV Angrist, Joshua Kolesár, Michal Econometrics Methodology 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. |
| title | One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV |
| topic | Econometrics Methodology |
| url | https://arxiv.org/abs/2110.10556 |