REDI for Binned Data: A Random Empirical Distribution Imputation Method for Estimating Continuous Incomes

Researchers often need to work with categorical income data. The typical nonparametric (including midpoint) and parametric estimation methods used to estimate summary statistics both have advantages, but they carry assumptions that cause them to deviate in important ways from real-world income distributions. The method introduced here, random empirical distribution imputation (REDI), imputes discrete observations using binned income data, while also calculating summary statistics. REDI achieves this through random cold-deck imputation from a real-world reference data set (demonstrated here using the Current Population Survey Annual Social and Economic Supplement). This method can be used to reconcile bins between data sets or across years and handle top incomes. REDI has other advantages for computing values of an income distribution that is nonparametric, bin consistent, area and variance preserving, continuous, and computationally fast. The author provides proof of concept using two years of the American Community Survey. The method is available as the redi command for Stata.