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Confidence intervals for causal effects with invalid instruments by using two‐stage hard thresholding with voting
Author(s) -
Guo Zijian,
Kang Hyunseung,
Tony Cai T.,
Small Dylan S.
Publication year - 2018
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12275
Subject(s) - thresholding , oracle , causal inference , voting , inference , computer science , set (abstract data type) , outcome (game theory) , instrumental variable , econometrics , statistics , artificial intelligence , mathematics , machine learning , mathematical economics , politics , political science , law , image (mathematics) , software engineering , programming language
Summary A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable. Typically one is unsure whether all of the putative IVs are in fact valid. We propose a general inference procedure in the presence of invalid IVs, called two‐stage hard thresholding with voting. The procedure uses two hard thresholding steps to select strong instruments and to generate candidate sets of valid IVs. Voting takes the candidate sets and uses majority and plurality rules to determine the true set of valid IVs. In low dimensions with invalid instruments, our proposal correctly selects valid IVs, consistently estimates the causal effect, produces valid confidence intervals for the causal effect and has oracle optimal width, even if the so‐called 50% rule or the majority rule is violated. In high dimensions, we establish nearly identical results without oracle optimality. In simulations, our proposal outperforms traditional and recent methods in the invalid IV literature. We also apply our method to reanalyse the causal effect of education on earnings.