On a property of Lorenz curves with monotone elasticity and its application to the study of inequality by using tax data

Miguel Angel Sordo Díaz; Ángel Berihuete Macías; Carmen Dolores Ramos González; Héctor Manuel Ramos Romero

Ayuda

On a property of Lorenz curves with monotone elasticity and its application to the study of inequality by using tax data

Miguel A. Sordo ^[1] ; A. Berihuete ^[1] ; C.D. Ramos ^[1] ; H.M. Ramos ^[1]
1. [1] Universidad de Cádiz
  
  Universidad de Cádiz
  
  Cádiz, España
Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 41, Nº. 1, 2017, págs. 55-72
Idioma: inglés
Enlaces
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Resumen
- The Lorenz curve is the most widely used graphical tool for describing and comparing inequality of income distributions. In this paper, we show that the elasticity of this curve is an indicator of the effect, in terms of inequality, of a truncation of the income distribution. As an application, we consider tax returns as equivalent to the truncation from below of a hypothetical income distribution. Then, we replace this hypothetical distribution by the income distribution obtained from a general household survey and use the dual Lorenz curve to anticipate this effect.
Referencias bibliográficas
- Aggarwal, V. (1984). On optimum aggregation of income distribution data. Sankhya B, 46, 343–355.
- Arnold, B.C. (1986). A class of hyperbolic Lorenz curves. Sankhya A, 48, 427–436.
- Arnold, B.C. (1987). Majorization and the Lorenz order: A brief introduction. Lecture Notes in Statistics, 43, Springer-Verlag.
- Arnold, B.C., Brockett, P.L., Robertson, C.A. and Shu, B.Y. (1987). Generating ordered families of Lorenz curves by strongly unimodal distributions....
- Atkinson, A.B., Piketty, T. and Saez, E. (2011). Top incomes in the long run of history. Journal of Economic Literature, 49, 3–71.
- Basmann, R.L., Hayes, K.J., Slottje, D.J. and Johnson,J.D. (1990). A general functional form for approximating the Lorenz curve. Journal of...
- Belzunce, F., Candel, J. and Ruiz, J. M. (1995). Ordering of truncated distributions through concentration curves. Sankhya A, 57, 375–383.
- Belzunce, F., Candel, J. and Ruiz, J. M. (1998). Ordering and asymptotic properties of residuals income distributions. Sankhya B, 60, 331–348.
- Belzunce, F., Pinar, J.F., Ruiz, J.M. and Sordo, M.A. (2012). Comparisons of risks based on the expected proportional shortfall. Insurance:...
- Belzunce, F., Pinar, J.F., Ruiz, J.M. and Sordo, M.A. (2013). Comparison of concentration for several families of income distributions. Statistics...
- Belzunce, F., MartÄ±Ìnez-Riquelme, C., Ruiz, J.M. and Sordo, M.A. (2016). On the Comparison of Relative Spacings with Applications. Methodology...
- Bhattacharya, N. (1963). A property of the Pareto distribution. Sankhya B, 25, 195–196.
- Eurostat (2010). Description of target variables: cross-sectional and longitudinal. EU-SILC 065/2010, Eurostat, Luxembourg.
- Greselin, F. and Zitikis, R. (2015). Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences...
- Gupta, M.R. (1984). Functional form for estimating the Lorenz curve. Econometrica, 52, 1313–1314.
- Kakwani, N.C. and Podder, N. (1973). On estimation of Lorenz curves from grouped observations. International Economic Review, 14, 278–292.
- Moothathu, T.S.K. (1986). A characterization of power distribution through a property of the Lorenz curve. Sankhya B, 48, 262–265.
- Ortega, P., FernaÌndez, M.A., Ladoux, M. and GarcÄ±Ìa, A. (1991). A new functional form for estimating Lorenz curves. The Review of Income...
- Piketty, T. and Saez, E. (2003). Income Inequality in the United States: 1913-1998. Quarterly Journal of Economics, 118, 1–39.
- Ramos, H., Peinado, A. and Ollero, J. (2013). Analysis of inequality in fertility curves fitted by gamma distributions. SORT, 37, 233–240.
- Rasche, R.H., Gaffney, J., Koo, A. and Obst, N. (1980). Functional forms for estimating the Lorenz curve. Econometrica, 48, 1061–1062.
- Rohde, N. (2009). An alternative functional form for estimating the Lorenz curve. Economics Letters, 105, 61–63.
- Ryu, H. and Slottje, D. (1996). Two flexible functional forms for approximating the Lorenz curve. Journal of Econometrics, 72, 251–274.
- Saez, E. and Zucman, G. (2014). Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data. NBER Working...
- Sarabia, J.M. (1997). A hierarchy of Lorenz curves based on the generalized Tukey’s lambda distribution. Econometric Reviews, 16, 305–320.
- Sarabia, J.M., Castillo, E., and Slottje, D.J. (1999). An ordered family of Lorenz curves. Journal of Econometrics, 91, 43–60.
- Sarabia, J.M., Castillo, E. and Slottje, D.J. (2001). An exponential family of Lorenz curves. Southern Economic Journal, 67, 748–756.
- Sarabia, J.M. and Pascual, M. (2002). A class of Lorenz curves based on linear exponential loss functions. Communications in Statistics-Theory...
- Sarabia, J. M., GoÌmez-DeÌniz E., Sarabia M. and Prieto, F. (2010). Revisiting a functional form for the Lorenz curve. Economics Letters,...
- Sarabia, J. M., Prieto, F. and Trueba, C. (2012). Modeling the probabilistic distribution of the impact factor. Journal of Infometrics, 6,...
- Shaked, M. and Shanthikumar, J.G. (2007). Stochastic orders. Series: Springer Series in Statistics, Springer.
- Sordo, M.A., Navarro, J. and Sarabia, J.M. (2014). Distorted Lorenz curves: models and comparisons. Social Choice and Welfare, 42, 761–780.
- Stone, C., Trisi, D., Sherman, A. and DeBot, B. (2015). A Guide to Statistics on Historical Trends in Income Inequality, Washington, DC: Center...
- VillasenÌor, J.A. and Arnold, B.C. (1989). Elliptical Lorenz curves. Journal of Econometrics, 40, 327–338.
- Wang, Z., Smyth, R. and Ng, Y.K. (2009). A new ordered family of curves with an application to measuring income inequality and poverty in...