Balancing weights for region-level analysis: The effect of Medicaid expansion on the uninsurance rate among states that did not expand Medicaid

Abstract

We predict the average effect of Medicaid expansion on the nonelderly adult uninsurance rate among states that did not expand Medicaid in 2014, as if they had expanded their Medicaid eligibility requirements. Using American Community Survey data aggregated to the region level, we estimate this effect by reweighting the expansion regions to approximately match the covariate distribution of the nonexpansion regions. Existing methods to estimate balancing weights often assume that the covariates are measured without error and do not account for dependencies in the outcome model. Our covariates have random noise that is uncorrelated with the outcome errors, and our assumed outcome model contains state-level random effects. To correct for measurement error induced bias, we propose generating weights on a linear approximation to the true covariates, extending an idea from the measurement error literature known as “regression calibration.” This requires auxiliary data to estimate the measurement error variability. We also propose an objective function to reduce the variance of our estimator when the outcome model errors are homoskedastic and equicorrelated within states. We then estimate that Medicaid expansion would have caused a −2.33 (−3.54, −1.11) percentage point change in the adult uninsurance rate among states that did not expand Medicaid.