Greselin, Francesca and Pasquazzi, Leo and Zitikis, Ricardas (2009): Zenga’s new index of economic inequality, its estimation, and an analysis of incomes in Italy.
Download (212Kb) | Preview
For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their diﬀerences with respect to geographic regions, and changes over time periods. It is a challenging area due to a number of reasons, one of them being the fact that diﬀerent measures, or indices, are needed to reveal diﬀerent features of income distributions. Keeping also in mind that the notions of ‘poor’ and ‘rich’ are relative to each other, M. Zenga has recently proposed a new index of economic inequality. The index is remarkably insightful and useful, but deriving statistical inferential results has been a challenge. For example, unlike many other indices, Zenga’s new index does not fall into the classes of L-, U-, and V -statistics. In this paper we derive desired statistical inferential results, explore their performance in a simulation study, and then employ the results to analyze data from the Bank of Italy’s Survey on Household Income and Wealth.
|Item Type:||MPRA Paper|
|Original Title:||Zenga’s new index of economic inequality, its estimation, and an analysis of incomes in Italy|
|Keywords:||Zenga index, lower conditional expectation, upper conditional expectation, conﬁdence interval, Bonferroni curve, Lorenz curve, Vervaat process.|
|Subjects:||C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General|
|Depositing User:||Leo Pasquazzi|
|Date Deposited:||08. Sep 2009 14:03|
|Last Modified:||19. Feb 2013 11:20|
Bank of Italy (2006). Household Income and Wealth in 2004. Supplements to the Statistical Bulletin–Sample Surveys, XVI–n.7. 26
Davison A.C., Hinkley D.V. (1997). Bootstrap Methods and their Application. Cambridge University Press, Cambridge.
Efron B. (1987). Better bootstrap conﬁdence intervals (with discussion). Journal of the American Statistical Association, 82, 171–200.
Gastwirth, J.L. (1971). A general deﬁnition of the Lorenz curve. Econometrica, 39, 1037–1039.
Gini C. (1914). Sulla misura della concentrazione e della variabilit´a dei caratteri. In: Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti. Anno Accademico 1913– 1914, Tomo LXXII parte seconda. Premiate Oﬃcine Graﬁche C. Ferrari, Venezia, 1201–1248.
Greselin, F. and Pasquazzi, L. (2009). Asymptotic conﬁdence intervals for a new inequality measure. Communications in Statistics: Computation and Simulation, 38(8), 17-42.
Greselin, F., Puri, M.L. and Zitikis, R. (2009). L-functions, processes, and statistics in measuring economic inequality and actuarial risks. Statistics and Its Interface, 2, 227–245.
Karian, Z.A. and Dudewicz, E.J. (2000). Fitting Statistical Distributions: The Generalized Lambda Distribution and Generalized Bootstrap Methods. CRC Press, Boca Raton, FL.
Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. Wiley, New York.
Lehmann, E.L. (1966). Some concepts of dependence. Annals of Mathematical Statistics, 37, 1137–1153.
Maasoumi E. (1994). Empirical analysis of welfare and inequality. In: Handbook of Applied Econometrics, Volume II: Microeconomics. (Eds.: M.H. Pesaran and P. Schmidt). Blackwell, Oxford.
Pietra G. (1915). Delle relazioni fra indici di variabilit´a, note I e II. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, 74, 775-804. Zenga, M. (2007). Inequality curve and inequality index based on the ratios between lower and upper arithmetic means. Statistica & Applicazioni 5, 3–27.
Zitikis, R. (1998). The Vervaat process. In: Asymptotic Methods in Probability and Statistics, pp. 667–694. North-Holland, Amsterdam.