Adjusting Body Mass for Measurement Error with Invalid Validation Data

We propose a new method for using validation data to correct self-reported weight and height in surveys that do not weigh and measure respondents. The standard correction from prior research regresses actual measures on reported values using an external validation dataset, and then uses the estimated coefficients to predict actual measures in the primary dataset. This approach requires the strong assumption that the expectations of actual weight and height conditional on the reported values are the same in both datasets. In contrast, we use percentile ranks rather than levels of reported weight and height. Our approach requires the much weaker assumption that the conditional expectations of actual measures are increasing in reported values in both samples, making our correction more robust to differences in measurement error across surveys. We then examine three nationally representative datasets and confirm that misreporting is sensitive to differences in survey context such as data collection mode. When we compare predicted BMI distributions using the two approaches, we find that the standard correction is biased by differences in misreporting while our correction is not. Finally, we present several examples that demonstrate the potential importance of our correction for future econometric analyses and estimates of obesity rates