A Model of Errors in BMI Based on Self-Reported and Measured Anthropometrics with Evidence from Brazilian Data

The economics of obesity literature implicitly assumes that measured anthropometrics are error-free and they are often treated as a gold standard when compared to self-reported data. We use factor mixture models to analyse and characterize measurement error in both self-reported and measured anthropometrics with national representative data from the 2013 National Health Survey in Brazil. Indeed, a small but statistically significant fraction of measured anthropometrics are attributed to data-recording errors. The estimated mean body weight (height) for those cases that are subject to error is 10% higher (2.9% lower) than the estimated mean of latent true body weight (height). As they are imprecisely measured and due to individual's reporting behaviour, only between 10% and 24% of our self-reported anthropometrics are free from any measurement error. Post-estimation analysis allows us to calculate hybrid anthropometric predictions that best approximate the true body weight and height distribution. BMI distributions based on the hybrid measures are close to those based on measured data, while BMI based on self-reported data under-estimates the true BMI distribution. Analysis of regression models for health care utilization shows little differences between the relationship with BMI when it is based on measured data or on our hybrid BMI measure, however some differences are observed when both are compared to BMI based on self-reported data.