Comparison of Parametric and Non-Parametric methods to correct for reporting heterogeneity

This paper compares the use of parametric and non-parametric approaches to adjust for heterogeneity in self-reported data. Despite the growing popularity of the HOPIT model to account for reporting heterogeneity when dealing with self-reported categorical data, recent evidence has questioned the validity of this heavily parametric approach. We compare the performance of the HOPIT model with the non-parametric estimators put forward by King et al. (2004) and King and Wand (2007). Using data relating to the health domains of mobility and memory from the Survey of Health, Ageing and Retirement in Europe (SHARE) we perform pairwise country comparisons of self-reported health, objective measures of health, and measures of health adjusted for the presence of reporting heterogeneity. Our study design focuses on comparisons of countries where there exist a discrepancy between the distribution of self-reported data and objective measures of health and assesses whether vignettes are able to reconcile this difference. Comparisons of distributions are based on first order stochastic dominance. In general, HOPIT and non-parametric estimation produce similar results in terms of first order stochastic dominance for the domains of both mobility and memory. Neither method consistently explains discrepancies across countries between self-reported and objective measures of health mobility and memory.