Iterative Kernel Density Estimation Applied to Grouped Data: Estimating Poverty and Inequality Indicators from the German Microcensus

The estimation of poverty and inequality indicators based on survey data is trivial as long as the variable of interest (e.g., income or consumption) is measured on a metric scale. However, estimation is not directly possible, using standard formulas, when the income variable is grouped due to confidentiality constraints or in order to decrease item nonresponse. We propose an iterative kernel density algorithm that generates metric pseudo samples from the grouped variable for the estimation of indicators. The corresponding standard errors are estimated by a non-parametric bootstrap that accounts for the additional uncertainty due to the grouping. The algorithm enables the use of survey weights and household equivalence scales. The proposed method is applied to the German Microcensus for estimating the regional distribution of poverty and inequality in Germany.