Measuring income inequality : an application of the population dynamic Theil's Entropy

ABSTRACTIn this paper we use the index we call Population Dynamic Theil's Entropy to analyze as the income inequality varies on time. The index may consider both the inequality among the classes in which we assign the individuals and the inequality within each class. This inequality measure working in a dynamic way allows to forecast inequality in time. Besides it may capture not only changes in the wealth but also changes in the population composition. The earned results are relevant for adopting a social and economic policy of wealth distribution. We fulfilled the model with statistics from the Organization for Economic Cooperation and Development and we applied it to Mexico, Portugal and Spain. We picked up economic data about population, means and medians of the equivalised net income for the three countries. The data refer to years from 2004 to 2011.JEL: E64, E27KEYWORDS: Income Distribution, Population Dynamic Theil's Entropy, Markov Chains(ProQuest: ... denotes formulae omitted.)INTRODUCTIONA recent approach in economics proposes measuring the income inequality through dynamic indices instead of the classic static indices, like those by Gini, Herfindahl-Hirsclunan and Theil. Theil (1967) introduced the Theil's entropy, since then most used in scientific papers. It holds the sum of the products of the shares of the total income of each individual (stood for by yi) multiplied by the logarithm of A/ty , being N the number of the agents in the economic system. The range of values is between 0 and ln(N). The index takes the value 0 when the wealth is equidistributed among the agents and the value ln(N) when one agent holds all the wealth.This paper belongs to this recent line of research aiming at measuring the income inequality in a dynamic way in the whole population of some countries. We considered countries with comparable socio-cultural life styles and religion but with different rates of change of Gross Domestic Product (GDP), like for example Mexico, Portugal and Spain. For this investigation we adopted the Population Dynamic Theil's Entropy (PDTE) because it may capture not only the changes in wealth but also changes in population composition. Therefore it is possible to justify' changes in the index when the population structure varies over time. The results show such analysis to be useful to decision makers to carry out policies of economic integration.Many papers make use of Markov chain modeling to describe how income changes (Quah, 1993, 1994, 1995, Dardanoni, 1995), also some papers consider Bayesian estimations of persistent income inequality (Nishino, Kakamu and Oga, 2012, Kakamu and Fukushige, 2009). Some applications related to the income inequality indices underline the importance of this research field. They include 1.) Influences of political regimes and financial reforms (Kemp-Benedict, 2011, Baland, Dagnelie and Rey, 2007), 2.) Relevance of geographical reasons (Banerjee, Mookherjee, Munshi and Rey, 2001, Chaudhuri, Ghatak, Guha, Mookherjee and Rey, 2007), 3.) Impact of immigration on the concentration of wealth distribution (D'Amico, Di Biase and Manca, 2011) and 4.) Impact of the fiscal system on wealth redistribution in the population (D'Amico, Di Biase and Manca, 2013). This paper is a follow-up study to the adjustment of the Dynamic Theil's Entropy to forecast the income inequality on a given time horizon in the whole population of some countries. Thanks to decomposing Theil's Entropy into three addenda (D'Amico, Di Biase and Manca, 2014) the paper makes a careful examination of the wealth distribution in Mexico, Portugal and Spain. The rest of the paper is organized as follows. In the next session the paper provides a review of the relevant literature. The following section briefly describes the stochastic model. Next we explain data and method to calculate the PDTE. Next section presents the results of the application to the three countries. …