Treatment Effect Estimation Methods with Misreported or Missing Data
These papers provide practical guidance on estimating treatment effects using survey data where treatment is missing or mismeasured due to a non-random process. Paper #1 addresses IV estimation when the treatment is endogenous and misreported. The authors establish that error-correction using regression calibration of an endogenous variable in IV can introduce asymptotic bias, and demonstrate this in small sample simulations. The authors corroborate their findings by estimating the health expenditure models of Cawley and Meyerhoefer (2012) using the NHANES as a source of external validation. Paper #2 addresses treatment effect estimation when treatment is endogenously mismeasured. The authors show that endogenous misreporting can cause significant bias and even sign reversal in OLS and IV estimators. The authors propose an alternative estimator that incorporates information related to both participation and misreporting, and establish its properties and its small sample performance through simulations. Paper #3 addresses IV estimation paired with imputation when treatment is missing-not-at-random. The authors argue that the most accurate imputation method is not necessarily the method that minimizes the finite sample bias of IV. The authors suggest instead choosing an imputation method to maximize the first-stage strength of the instrument(s), and illustrate this recommendation via simulations and an application estimating the causal effect of birthweight on subsequent child outcomes using the Early Childhood Longitudinal Survey – Kindergarten Cohort (ECLS-K). Each of these papers highlights a distinct plausible deviation from ideal measurement in survey data, and presents practical steps towards mitigating the resulting biases in treatment effects estimation.