An Investigation of Hierarchical and Empirical Bayesian Small Area Predictors Under Measurement Error

In this paper we focus on small area models with measurement error in covariates. Based on data from the Measuring Morality study, a nationally representative survey of United States residents, that contains a validated behavioural measure of generosity (the dictator game) along with the household income of respondents, we define a measurement error model suitable to obtain area-level estimates of generosity at the district level. We investigate the effect of introducing the measurement error in this model, focusing on fully Bayesian as well as Empirical Bayesian (EB) estimation proposed in the recent literature. We discuss the characteristics of each of the two approaches and analyze the impact of the measurement error on the resulting estimates based on real data and a simulation study.