Measurement Error and the Distribution of Income

Abstract

Measurement error can impact estimator precision, obscure estimated relationships between variables, and distort the estimated inter-temporal behaviour of important economic characteristics. A model for measurement error is presented, based on the common assumption that measured income is the product of true income and multiplicative measurement error which is distributed independently of the level of true income. Flexible parametric forms are utilized to model the distributions of true income (generalized gamma) and measurement error (inversed generalized gamma). The corresponding probability density of measures income is shown to be a generalized beta of the second kind (GB2) which can be estimated using MLE. An identification problem is solved with additional information as to the average function of true income reported. The procedure is applied to income data from several Latin American economies. It is found, in some cases, that true and measured income inequality move in opposite directions over time. This finding has important implications for the evaluation of policies designed to affect relative equality in the distribution of income and underscores the importance of obtaining accurate data.