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Instrumented difference‐in‐differences
Author(s) -
Ye Ting,
Ertefaie Ashkan,
Flory James,
Hennessy Sean,
Small Dylan S.
Publication year - 2023
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13783
Subject(s) - estimator , causal inference , instrumental variable , consistency (knowledge bases) , inference , identification (biology) , confounding , randomness , randomized experiment , observational study , econometrics , average treatment effect , statistics , mathematics , computer science , artificial intelligence , botany , biology
Unmeasured confounding is a key threat to reliable causal inference based on observational studies. Motivated from two powerful natural experiment devices, the instrumental variables and difference‐in‐differences, we propose a new method called instrumented difference‐in‐differences that explicitly leverages exogenous randomness in an exposure trend to estimate the average and conditional average treatment effect in the presence of unmeasured confounding. We develop the identification assumptions using the potential outcomes framework. We propose a Wald estimator and a class of multiply robust and efficient semiparametric estimators, with provable consistency and asymptotic normality. In addition, we extend the instrumented difference‐in‐differences to a two‐sample design to facilitate investigations of delayed treatment effect and provide a measure of weak identification. We demonstrate our results in simulated and real datasets.