Properties of Selected Inequality Measures Based on Quantiles and Their Application to the Analysis of Income Distribution in Poland by Macroregion

Alina Jędrzejczak, Dorota Pekasiewicz

Abstract


Quantiles of income distributions are often applied to the estimation of various inequality, poverty and wealth characteristics. They are traditionally estimated using the classical quantile estimator based on a relevant order statistic. The main objective of the paper is to compare the classical, Huang-Brill and Bernstein estimators for these measures from the point of view of their statistical properties. Several Monte Carlo experiments were conducted to assess biases and mean squared errors of income distribution characteristics for different sample sizes under the lognormal or Dagum type-I models. The results of these experiments are used to estimate inequality, poverty and wealth measures in Poland by macroregion on the basis of micro data originating from the Household Budget Survey 2014.


Keywords


income distribution, inequality, poverty, wealth, quantile estimator

Full Text:

PDF

References


Arcagni, A. (2016) “On the Decomposition by Sources of the Zenga 1984 Point and Synthetic Inequality Indexes”. Statistical Methods & Applications 26 (1): 113–33, https://doi.org/10.1007/s10260-016-0360.0.

Brzeziński, M. (2014) “Statistical Inference for Richness Measures”. Applied Economics 46 (14): 1599–1608, https://doi.org/10.1080/00036846.2014.880106.

Greselin, F., Pasquazzi, L. and Zitikis, R. (2013) “Contrasting the Gini and Zenga Indices of Economic Inequality”. Journal of Applied Statistics 40 (2): 282–97, https://doi.org/10.1080/02664763.2012.740627.

Harrell, F. E. and Davis, C. E. (1982) “A New Distribution-Free Quantile Estimator”. Biometrika 69: 635–40, https://doi.org/10.1093/biomet/69.3.635.

Huang, M. L. and Brill, P. H. (1999) “A Level Crossing Quantile Estimation Method”. Statistics & Probability Letters 45: 111–19, https://doi.org/10.1016/s0167-7152(99)00049-8.

Jędrzejczak, A. (2012) “Estimation of Standard Errors of Selected Income Concentration Measures on the Basis of Polish HBS”. International Advances in Economic Research 18 (3): 287–97.

Jędrzejczak, A. (2015) “Asymptotic Properties of Some Estimators for Gini and Zenga Inequality Measures: a Simulation Study”. Statistica & Applicazioni 13: 143–62.

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences. Hoboken, New Jersey: John Wiley and Sons.

Panek, T. (2011) Ubóstwo, wykluczenie społeczne i nierówności. Teoria i praktyka pomiaru [Poverty, social exclusion, and inequality. The theory and practice of measurement]. Warsaw: SGH.

Peichl, A., Schaefer, T. and Scheicher, Ch. (2008) “Measuring Richness and Poverty: A Micro Data Application to Europe and Germany”. IZA Discussion Paper 3790, http://ftp.iza.org/dp3790.pdf (accessed: 11 June 2018).

Pekasiewicz, D. (2015) Statystyki pozycyjne w procedurach estymacji i ich zastosowania w badaniach społeczno-ekonomicznych [Order statistics in estimation procedures and their application in socio-economic research]. Łódź: Wydawnictwo Uniwersytetu Łódzkiego.

Zieliński, R. (2006) “Small-Sample Quantile Estimators in a Large Nonparametric Model”. Communications in Statistics Theory and Methods 35: 1223–41, https://doi.org/10.1080/03610920600692656.

Zenga, M. (1990) Concentration Curves and Concentration Indices Derived from Them, Income and Wealth Distribution, Inequality and Poverty. Berlin: Springer-Verlag, pp. 94–110.




DOI: https://doi.org/10.15678/AOC.2018.1803