Weak Instruments in Instrumental Variables Regression: Theory and Practice

Abstract

When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables (IV) estimation and inference become unreliable. A large literature in econometrics has developed procedures for detecting weak instruments and constructing robust confidence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for nonhomoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the American Economic Review from 2014 to 2018 that use IV. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps that researchers can take to better handle weak instruments in applications.

Effects of Rural Electrification on Employment: A Comment on Dinkelman

“…These AR confidence intervals account for the decreasing precision that weak instruments generally induce (Andrews et al 2019;Nelson and Startz 1990;Murray 2017). From this interval we can learn that the positive effect of electrification on female employment is between 3 and 26 percentage points, so a much wider range than the "9 to 9.5 percentage points" Dinkelman refers to in her introduction, the results section and the conclusion (Dinkelman 2011, p. 3080, 3096, 3105).…”

“…3 percentage points) or massive (26 percentage points). Moreover, even this interval interpretation is at stake if the exclusion restriction is violated (Andrews et al 2019), which will be assessed in the following section.…”

“…A statistically more substantiated weak instruments test has been developed after the publication of Dinkelman's study by Montiel Olea and Pflueger (2013). The authors propose that an IV is weak if there is a 5% chance that the bias in the IV estimator is 27 10% of a 'worst case' scenario in which the IV is assumed to be completely irrelevant (see also Ramey and Zubairy 2018, Kovandzic et al 2015, and Andrews et al 2019.…”

Two applications of wild bootstrap methods to improve inference in cluster‐IV models

“…However,Bun and de Haan (2010) show that, with a nonscalar error covariance structure, the use of the rule-of-thumb for the standard and the cluster-robust first-stage F-tests combined is a poor guide for detecting instrument strength. I Andrews, Stock, and Sun (2019). survey manuscripts published at the American Economic Review from 2014 to 2018, and find clear evidence that authors and journals favor specifications that satisfy this rule-of-thumb even when residuals are heteroskedastic.4 Stock and Yogo (2005) andSanderson and Windmeijer (2016) propose similar tests under the assumption that the residuals are homoskedastic.…”

Do Movie Production Incentives Generate Economic Development?

“…Andrews, Stock, and Sun (Forthcoming) recommend using the effective F ‐statistic developed by Montiel Olea and Pflueger () for heteroskedastic and clustered data when testing for weak instruments.…”