Using Experiments to Correct for Selection in Observational Studies

TL;DR

This paper introduces a new method to correct for selection bias in observational studies by leveraging experimental data on secondary outcomes, enabling unbiased estimation of primary treatment effects.

Contribution

The paper develops a novel estimator that combines observational and experimental data under latent unconfoundedness to accurately estimate treatment effects on primary outcomes.

Findings

Corrects for selection bias using secondary outcomes and experimental data

Replicates experimental results in observational data

Estimates that reducing class size increases graduation rates by 0.7 percentage points

Abstract

Researchers increasingly have access to two types of data: (i) large observational datasets where treatment (e.g., class size) is not randomized but several primary outcomes (e.g., graduation rates) and secondary outcomes (e.g., test scores) are observed and (ii) experimental data in which treatment is randomized but only secondary outcomes are observed. We develop a new method to estimate treatment effects on primary outcomes in such settings. We use the difference between the secondary outcome and its predicted value based on the experimental treatment effect to measure selection bias in the observational data. Controlling for this estimate of selection bias yields an unbiased estimate of the treatment effect on the primary outcome under a new assumption that we term latent unconfoundedness, which requires that the same confounders affect the primary and secondary outcomes. Latent unconfoundedness weakens the assumptions underlying commonly used surrogate estimators. We apply our estimator to identify the effect of third grade class size on students outcomes. Estimated impacts on test scores using OLS regressions in observational school district data have the opposite sign of estimates from the Tennessee STAR experiment. In contrast, selection-corrected estimates in the observational data replicate the experimental estimates. Our estimator reveals that reducing class sizes by 25% increases high school graduation rates by 0.7 percentage points. Controlling for observables does not change the OLS estimates, demonstrating that experimental selection correction can remove biases that cannot be addressed with standard controls.