Abstract Mendelian randomization (MR) has been a popular method in genetic epidemiology to estimate the effect of an exposure on an outcome using genetic variants as instrumental variables (IV), with two‐sample summary‐data MR being the most popular. Unfortunately, instruments in MR studies are often weakly associated with the exposure, which can bias effect estimates and inflate Type I errors. In this work, we propose test statistics that are robust under weak‐instrument asymptotics by extending the Anderson–Rubin, Kleibergen, and the conditional likelihood ratio test in econometrics to two‐sample summary‐data MR. We also use the proposed Anderson–Rubin test to develop a point estimator and to detect invalid instruments. We conclude with a simulation and an empirical study and show that the proposed tests control size and have better power than existing methods with weak instruments.
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Weak Instruments in Instrumental Variables Regression: Theory and Practice
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.
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- Award ID(s):
- 1654234
- PAR ID:
- 10142670
- Date Published:
- Journal Name:
- Annual Review of Economics
- Volume:
- 11
- Issue:
- 1
- ISSN:
- 1941-1383
- Page Range / eLocation ID:
- 727 to 753
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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