Estimation of the distribution of income from survey data, adjusting for compatibility with other sources

Article type: Research Article

Authors: Bustos, Alfredo

Affiliations: Instituto Nacional de Estadística y Geografía (INEGI), H. de Nacozari 2301, Aguascalientes 20276, México . Tel.: +52 449 910 5431; E-mail: alfredo.bustos@inegi.org.mx

Abstract: In this paper, we present an approach for the estimation of income distributions, which deals with survey data shortcomings through simultaneous consideration of other statistical sources and through adjustment for compatibility with all of them. We show how our proposal deals both with survey income under-reporting, and with under representation of households with very large incomes, which are known to affect the results of the survey. Our proposal has the purpose of selecting the distributional model that best fits the data from the survey, using a Constrained Pseudo Log-likelihood criterion, and is based on well-established statistical criteria and methods and thus reduces the need for subjective or arbitrary choices. The proposed procedure is applied to Mexican data from the National Survey on Household Income and Expenditure for the year 2012 and from Mexico's System of National Accounts, two sources that produce widely differing results regarding total national household current income. We show that, among all fitted models, a satisfactory explanation is given by a 4-parameter Generalized Beta Type 2 distribution. The chosen distribution has little impact on the official poverty measurement. The Gini coefficient, however, reaches a value as high as 0.803.

Keywords: Income distribution, Log-normal, Gamma, Generalized Gamma, Generalized Beta, pseudo-likelihood, numerical optimization, nonlinear constraints

DOI: 10.3233/SJI-150923

Journal: Statistical Journal of the IAOS, vol. 31, no. 4, pp. 565-577, 2015