Measuring inequality using censored data: a multiple-imputation approach to estimation and inference

• Published in: Journal of the Royal Statistical Society. Series A, Statistics in society Vol. 174; no. 1; pp. 63 - 81
• Main Authors: Jenkins, Stephen P., Burkhauser, Richard V., Feng, Shuaizhang, Larrimore, Jeff
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.01.2011; Blackwell Publishing; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series A
• Subjects: Applications; Censored data; Censorship; Current Population Survey; Data analysis; Distribution theory; Estimating techniques; Estimation; Estimation methods; Exact sciences and technology; General topics; Generalized beta of the second kind distribution; Household income; Income distribution; Income estimates; Income inequality; Inequality; Inference; Mathematics; Measurement; Methodology; Multiple imputation; Nonparametric inference; Parameter estimation; Probability and statistics; Probability theory and stochastic processes; Public use; Sciences and techniques of general use; Statistical analysis; Statistical inference; Statistical significance; Statistical variance; Statistics; Top coding; United States > US; Censored data; Data analysis; Variance estimation; Generalized beta of the second kind distribution; Statistical estimation; Parametric model; Mean estimation; Parametric method; Statistical method; Income inequality; Current Population Survey; Model matching; Coding; Point estimation; Distribution function; Sample survey; Multiple imputation; Top coding
• ISSN: 0964-1998; 1467-985X
• DOI: 10.1111/j.1467-985X.2010.00655.x

To measure income inequality with right-censored (top-coded) data, we propose multiple-imputation methods for estimation and inference. Censored observations are multiply imputed using draws from a flexible parametric model fitted to the censored distribution, yielding a partially synthetic data set from which point and variance estimates can be derived using complete-data methods and appropriate combination formulae. The methods are illustrated using US Current Population Survey data and the generalized beta of the second kind distribution as the imputation model. With Current Population Survey internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using Current Population Survey public use data with cell mean imputations may lead to incorrect inferences. Multiply-imputed public use data provide an intermediate solution.