Multivariate robust estimation of inequality indices

Purpose – The data employed to measure income inequality usually come from household surveys, which commonly suffer from atypical observations such as outliers and contamination points. This is of importance since a single atypical observation can make classical inequality indices totally uninformative. To deal with this problem, robust univariate parametric or ad hoc procedures are commonly used; however, neither is fully satisfactory. The purpose of this paper is to propose a methodology to deal with this problem. Design/methodology/approach – The author propose two robust procedures to estimate inequality indices that can use all the information from a data set, and neither of them rely on a parametric distributional assumption. The methodology performs well irrespectively of the size and quality of the data set. Findings – Applying these methods to household data for UK (1979) and Mexico (2006 and 2011), the author find that for UK data the Gini, Coefficient of Variation and Theil Inequality Indices are over estimated by between 0.02 and 0.04, while in the case of Mexico the same indices are over estimated more deeply, between 0.1 and almost 0.4. The relevance of including atypical observations that follow the linear pattern of the data are shown using the data from Mexico (2011). Research limitations/implications – The methodology has two main limitations: the procedures are not able to identify a bad leverage outlier from a contamination point; and in the case that the data has no atypical observations, the procedures will tag as atypical a very small fraction of observations. Social implications – A reduction in the estimate of inequality has important consequences from a policy maker perspective. First, ceteris paribus, the optimal amount of resources destinated to directly address inequality/poverty. Those “extra” resources can be destinated to promote growth. Notice that this is a direct consequence of having a more egalitarian economy than previously thought, this is due to the fact that poor people will actually enjoy a bigger share of any national income increment. This also implies that, in order to reduce poverty, public policies should focus more on economic growth. Originality/value – To the knowledge, in the inequality literature this is the first methodology that is able to identify outliers and contamination points in more than one direction. That is, not only at the tails of the distribution, but on the whole marginal distribution of income. This is possible via the use of other variables related to income.