Multiple imputation of right-censored wages in the German IAB Employment Sample considering heteroscedasticity

Abstract

In many large data sets of economic interest, some variables, as wages, are top-coded or right-censored. In order to analyze wages with the German IAB employment sample we first have to solve the problem of censored wages at the upper limit of the social security system. We treat this problem as a missing data problem and derive new multiple imputation approaches to impute the censored wages by draws of a random variable from a truncated distribution based on Markov chain Monte Carlo techniques. In general, the variation of income is smaller in lower wage categories than in higher categories and the assumption of homoscedasticity in an imputation model is highly questionable. Therefore, we suggest a new multiple imputation method which does not presume homoscedasticity of the residuals. Finally, in a simulation study, different imputation approaches are compared under different situations and the necessity as well as the validity of the new approach is confirmed.