Post-Instrument Bias in Linear Models

Adam N. Glynn, Miguel R. Rueda and Julian Schuessler

Sociological Methods & Research, 2024, vol. 53, issue 4, 1829-1845

Abstract: Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and without measurement error): IV with post-instrument covariates, IV without post-instrument covariates, and ordinary least squares. In large samples and when the model provides a reasonable approximation, these formulas sometimes allow the analyst to bracket the parameter of interest with two estimators and allow the analyst to choose the estimator with the least asymptotic bias. We illustrate these points with a discussion of the settler mortality IV used by Acemoglu, Johnson, and Robinson.

Keywords: causal inference; instrumental variables; measurement error; covariate adjustment; linear models (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:sae:somere:v:53:y:2024:i:4:p:1829-1845

DOI: 10.1177/00491241231156965

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