Post-Instrument Bias in Linear Models

Adam Glynn; Miguel  Rueda; Julian Schüssler

doi:10.1177/00491241231156965

Post-Instrument Bias in Linear Models

Adam Glynn, Miguel Rueda, Julian Schüssler

Department of Political Science - CEPDISC

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

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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.

Original language	English
Journal	Sociological Methods & Research
Volume	53
Issue	4
Pages (from-to)	1829-1845
Number of pages	17
ISSN	0049-1241
DOIs	https://doi.org/10.1177/00491241231156965
Publication status	Published - Nov 2024

Keywords

causal inference
covariate adjustment
instrumental variables
linear models
measurement error

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https://osf.io/preprints/socarxiv/axn4t/

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title = "Post-Instrument Bias in Linear Models",

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.",

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T1 - Post-Instrument Bias in Linear Models

AU - Glynn, Adam

AU - Rueda, Miguel

AU - Schüssler, Julian

PY - 2024/11

Y1 - 2024/11

N2 - 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.

AB - 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.

KW - causal inference

KW - covariate adjustment

KW - instrumental variables

KW - linear models

KW - measurement error

U2 - 10.1177/00491241231156965

DO - 10.1177/00491241231156965

M3 - Journal article

SN - 0049-1241

VL - 53

SP - 1829

EP - 1845

JO - Sociological Methods & Research

JF - Sociological Methods & Research

IS - 4

ER -

Post-Instrument Bias in Linear Models

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Keywords

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