  We predict the average effect of Medicaid expansion on the non-elderly 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 finding
weights that approximately reweights the expansion regions to match the
covariate distribution of the non-expansion 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 outcome model has state-level random effects inducing dependence between
regions. To correct for the bias induced by the measurement error, we propose
generating our weights on a linear approximation to the true covariates, using
an idea from measurement error literature known as "regression-calibration"
(see, e.g., Carroll (2006)). This requires auxiliary data to estimate the
variability of the measurement error. We also modify the Stable Balancing
Weights objective proposed by Zubizaretta (2015)) to reduce the variance of our
estimator when the model errors follow our assumed correlation structure. We
show that these approaches outperform existing methods when attempting to
predict observed outcomes during the pre-treatment period. Using this method we
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.
