Accounting for measurement error in small area models: a study on generosity

In this paper we focus on a recently documented effect of economic in- equality, namely that higher income individuals tend to be less generous than poorer individuals, but only in contexts where macro-level economic inequality is high, or is perceived as high. We consider data from the Measuring Morality study, a na- tionally 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 fit a small area model to this data with the aim of inves- tigating the role of economic inequality on generosity in the US. We observe that model covariates (reported income and Gini index) are subject to measurement error and investigate the effect of introducing the measurement error in this model.