Imputation strategies for rightcensored wages in longitudinal datasets

Censoring from above is a common problem with wage information as the reported wages are typically top-coded for confidentiality reasons. In administrative databases the information is often collected only up to a pre-specified threshold, for example, the contribution limit for the social security system. While directly accounting for the censoring is possible for some analyses, the most flexible solution is to impute the values above the censoring point. This strategy offers the advantage that future users of the data no longer need to implement possibly complicated censoring estimators. However, standard cross-sectional imputation routines relying on the classical Tobit model to impute right-censored data have a high risk of introducing bias from uncongeniality (Meng 1994) as future analyses to be conducted on the imputed data are unknown to the imputer. Furthermore, as we show using a large-scale administrative database from the German Federal Employment agency, the classical Tobit model offers a poor fit to the data. In this paper, we present some strategies to address these problems. Specifically, we use leave-one-out means as suggested by Card et al. (2013) to avoid biases from uncongeniality and rely on quantile regression or left censoring to improve the model fit. We illustrate the benefits of these modeling adjustments using the German Structure of Earnings Survey, which is (almost) unaffected by censoring and can thus serve as a testbed to evaluate the imputation procedures.