Bias and Bias Correction in Multisite Instrumental Variables Analysis of Heterogeneous Mediator Effects

MDRC Publication

74 Pages Posted: 30 Oct 2012

See all articles by Sean Reardon

Sean Reardon

Stanford University

Fatih Unlu

affiliation not provided to SSRN

Pei Zhu

MDRC

Howard S. Bloom

MDRC

Abstract

We explore the use of instrumental variables (IV) analysis with a multisite randomized trial to estimate the effect of a mediating variable on an outcome. We use a random-coefficient IV model that allows both the impact of program assignment on the mediator (compliance with assignment) and the impact of the mediator on the outcome (the treatment effect) to vary across sites and to covary with one another. This extension of conventional fixed-coefficient IV analysis illuminates a potential bias in IV analysis, which Reardon and Raudenbush (forthcoming) refer to as "compliance-effect covariance bias." We first derive an expression for this bias and then use simulations to investigate the sampling variance of the conventional fixed-coefficient two-stage least squares (2SLS) estimator in the presence of varying (and covarying) compliance and treatment effects. We next develop an alternate IV estimator that is less susceptible to compliance-effect covariance bias. We compare the bias, sampling variance, and root mean squared error of this "bias-corrected IV estimator" with those of 2SLS and ordinary least squares (OLS). We find that when the first stage F-statistic exceeds 10 (a commonly used threshold for instrument strength), the bias-corrected estimator typically performs better than 2SLS or OLS. In the last part of the paper, we use both the new estimator and 2SLS to reanalyze data from two large multisite studies.

Suggested Citation

Reardon, Sean and Unlu, Fatih and Zhu, Pei and Bloom, Howard S., Bias and Bias Correction in Multisite Instrumental Variables Analysis of Heterogeneous Mediator Effects. MDRC Publication, Available at SSRN: https://ssrn.com/abstract=2168559 or http://dx.doi.org/10.2139/ssrn.2168559

Sean Reardon (Contact Author)

Stanford University ( email )

Stanford, CA 94305
United States

Fatih Unlu

affiliation not provided to SSRN ( email )

Pei Zhu

MDRC ( email )

200 Vesey Street
New York, NY 10281
United States

Howard S. Bloom

MDRC ( email )

200 Vesey Street
New York, NY 10281
United States

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