Total Bias in Income Surveys when Nonresponse and Measurement Errors are Correlated

Abstract Household surveys on income might suffer from quality limitations mainly due to the difficulty of enrolling households (unit nonresponse) and retrieving correct information during the interview (measurement error [ME]). These errors are likely to be correlated because of latent factors, such as the threat of disclosing personal information, the perceived sensitivity of the topic, or social desirability. For survey organizations, assessing the interplay of these errors and their impact on the accuracy and precision of inferences derived from their data is crucial. In this article, we propose to use a standard sample selection model within a total survey error framework to deal with the case of correlated nonresponse error (NR) and ME in estimating average household income. We use it to study the correlation between the two errors, quantify the ME component due to this correlation, and evaluate ME among nonrespondents. Using the Italian Survey on Income and Wealth linked with administrative income data from tax returns, we find a positive correlation between the two errors and that households at the extremes of the income distribution mainly cause this association. Our results show that ME contributes more to the total error than unit nonresponse and that it would be larger in absence of the correlation between the two errors. Finally, efforts to reduce nonresponse rates are worthwhile only for nonrespondents in the lowest estimated response propensity group. If these households participate, the bias decreases because of the reduction in NR that offsets the increase in ME.