Practical Considerations when Error-Correcting BMI in Cost of Obesity Studies

Estimates of the impact of BMI and obesity on health and labor market outcomes often rely on survey data that only include self- or proxy-reported height and weight. Correcting for measurement error in these studies is necessary to reduce misclassification of individuals, and may mitigate bias in estimation of the impact of BMI on health and labor market outcomes. One common method to correct for reporting error is regression calibration (RC) using external validation data. Although RC is well defined for single-stage models, it is often paired with instrumental variables (IV) estimation to account for the endogeneity of BMI. However, correcting for measurement error may not always reduce bias in IV estimation. We derive the asymptotic bias of the regression calibrated IV estimator (RCIV), and determine under which conditions RCIV is consistent in large samples. We then use Monte Carlo simulations to compare the finite-sample performance of RCIV compared to IV under classical measurement error, as well as different non-classical measurement error regimes. We corroborate the findings in the simulations by estimating the health expenditure models of Cawley and Meyerhoefer (2012) and Cawley et al. (2015) using the National Health and Nutrition Examination Survey (NHANES) as a source of external validation for reported heights and weights in the Medical Expenditure Panel Survey (MEPS). We find that regression calibrating the endogenous variable in an IV regression can introduce additional bias. However, we argue that regression calibration is still useful to reduce misclassification of individuals by weight class, as correctly identifying which individuals are obese can be central to computing average marginal effects and aggregate costs associated with obesity.