Income Imputation in Longitudinal Surveys: A Within-Individual Panel-Regression Approach

Abstract

Unlike for cross-sectional data, there is only little research on income imputation for longitudinal data. The current best practise is the Little and Su (L&S) method, which is based on individual-specific mean income over time. While the L&S method performs well for cross-sectional analysis, longitudinal estimates such as income mobility or fixed effects models tend to be biased. We argue that this bias arises from the L&S method treating within-individual variance - which is the basis of longitudinal analysis – as random. In this paper, we present an imputation approach, which uses information available in the missing wave which correlated with a changed income. The expected value is the sum of the individual mean across the observed waves and the within-individual deviance for the wave with missing information. We evaluate this new approach using employment income from the Swiss Household Panel and allow data to be missing at random and not at random. We compare different variants of this approach to the listwise deletion and the L&S method. The missingness mechanisms are estimated on the basis of an external data source containing both registry information and survey questions on income. We use performance criteria proposed in previous evaluations of longitudinal imputation methods. As an additional criterion, we consider the performance in application examples, by testing the bias of regression coefficients in typical longitudinal multivariate regression models. Our results indicate no systematic difference between imputation methods for cross-sectional criteria and for multivariate regression models, but a better performance of the new approach for longitudinal criteria. In applied fixed effects models, no imputation generally reduce bias compared to listwise deletion.