Dealing with negative observations while calculating inequalities

Examining asset declarations of Polish deputies

Abstract

Researchers and statisticians often face challenges when it comes to measuring inequalities of income, expenditures, and wealth. The aim of this paper is to bring attention to the problem of negative inputs, which are often ignored or treated as errors when measuring poverty and inequality. We present the current state of proposals for normalizing the Gini index in the presence of negative inputs, followed by a thorough data analysis of Polish deputies' asset declarations for the year 2021. After theoretical comparison of different Gini index normalization methods, empirical results show, that even with a relatively small amount of negative values, differences between normalization methods are significant and need to be addressed. Also, two methods of decomposition of the Gini index are shown to asses how inequality looks between parties and how different inputs impact the overall inequality. Later these decompositions show how influential on Gini index are debts and liabilities.