Rising poverty and inequality increases the risk of social instability in countries all around the world. For measuring poverty and inequality there exists a variety of statistical indicators. Estimating these indicators is trivial as long as the income variable is measured on a metric scale. However, estimation is not possible, using standard formulas, when the income variable is interval censored (or grouped), as in the German Microcensus. This is the case for numerous censuses due to confidentiality constraints or in order to decrease item non-response. To enable the estimation of statistical indicators in these scenarios, we propose an iterative kernel density algorithm that generates metric pseudo samples from the interval censored income variable. Based on these pseudo samples, poverty and inequality indicators are estimated. The standard errors of the indicators are estimated by a non-parametric bootstrap. Simulation results demonstrate that poverty and inequality indicators from interval censored data can be unbiasedly estimated by the proposed kernel density algorithm. Also the standard errors are correctly estimated by the non-parametric bootstrap. The kernel density algorithm is applied in this work to estimate regional poverty and inequality indicators from German Microcensus data. The results show the regional distribution of poverty and inequality in Germany.
direct estimation interval censored data grouped data poverty inequality kernel density estimation German Microcensus