Post-Instrument Bias in Linear Models

SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: [email protected]; Web site: https://sagepub.com

Y

17

Causal Models; Statistical Inference; Error of Measurement; Least Squares Statistics; Statistical Bias; Mathematical Models; Comparative Analysis; Mathematical Formulas

10.1177/00491241231156965

0049-1241
1552-8294

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.

As Provided

2024

EJ1444065