Analysis of the Gini Coefficient: evidence for the state of Puebla with a non-linear approach

Emmanuel Olivera Pérez


The objective of this article is to measure the Gini Coefficient by Nonlinear Ordinary Least Squares (NLOLS), following a different methodology for the design of the Lorenz Curve so that it fits better for the purposes of estimation. The estimation is based on the fact that the Lorenz curve can be simulated through a function of root n with coefficients a and b of the form , where  and the Gini Coefficient can be calculated in the form Gini = 1-b. The main findings using data from the EnBienComún survey of the State of Puebla 2015, are that the estimate of the inequality is greater than that reported by CONEVAL in 2015 for the State of Puebla, this estimate is statistically significant. AIC and BIC criteria are favorable for the specification of the estimate in terms of sample size.


Gini Coefficient, Inverted Lorenz Curve, Nonlinear Ordinary Least Squares, Empirical Intervals, Equity Intervals

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Aaron, S., y McGuireciety, M. (1970). Public Goods and Income Distribution. Econometrica, 38(6), 907–920.

Allison, P. D. (2018). Inequality Measures for Nominal Data. American Sociological Review, 46(3), 371–373.

Allison, P. D. (1978). Measures of Inequality. American Sociological Review, 43(6), 865–880.

Armour, B. P., Burkhauser, R. V, y Larrimore, J. (2013). Deconstructing Income and Income Inequality Measures : A Crosswalk from Market Income to Comprehensive Income. The American Economic Review, 103(3), 173–177.

Barrett, G., y Pendakur, K. (1995). The Asymptotic Distribution of the Generalized Gini Indices of Inequality. The Canadian Journal of Economics, 28(4b), 1042–1055.

Braun, D. (1988). Multiple Measurements of U. S. Income Inequality. The Review of Economics and Statistics, 70(3), 398–405.

Buchanan, A. (1986). Inequality. Philosophy and Public Affairs, 15(2), 99–121.

Chakravarty, S. R. (1988). Extended Gini Indices of Inequality. International Economic Review, 29(1), 147–156.

Champernowne, D. G. (1974). A Comparison of Measures of Inequality of Income Distribution. The Economic Journal, 84(336), 3787–3816.

CONEVAL. (2009). Metodología para la medición multidimensional de la pobreza en México. (CONEVAL, Ed.), CONEVAL, México DF. (Primera Ed). México: CONEVAL.

Corrado, G. (1921). Measurement of Inequality of Incomes. The Economic Journal, 31(121), 124–126.

Cowell, F. A., y Jenkins, S. P. (1995). How Much Inequality Can we Explain ? A Methodology and an Application to the United States. The Economic Journal, 105(429), 421–430.

Cowell, F. A., y Victoria-Feser, M.P. (1996). Robustness Properties of Inequality Measures. Econometrica, 64(1), 77–101.

Dalton, H. (1920). The Measurement of the Inequality of Incomes. The Economic Journal, 30(119), 348–361.

Ebert, U. (1999). Dual Decomposable Inequality Measures. The Canadian Journal of Economics, 32(1), 234–246.

Éltetö, S. Ö., y Frigyesociety, E. (1968). New Income Inequality Measures as Efficient Tools for Causal Analysis and Planning. Econometrica, 36(2), 383–396.

Farnsworth, D., y Orr, R. (1986). Gini Means. The American Mathematical Monthly, 93(8), 603–607.

Farris, F. A. (2010). The GINI index and measures of inequality. American Mathematical Monthly, 117(10), 851–864.

Fields, G. S., y Efe, A. (1999). Measuring Movement of Incomes. Economica, 66(264), 455–471.

Frees, E., Meyers, G., y Cummings, D. (2011). Summarizing Insurance Scores Using a Gini Index. Journal of the American Statistical Association, 106(495), 1085–1098.

Futing, T. (2006). Measuring and Analyzing Class Inequality with the Gini Index Informed by Model-Based Clustering. Sociological Methodology, 36(2006), 201–224.

Garner, T. I. (1993). Consumer Expenditures and Inequality : An Analysis Based on Decomposition of the Gini Coefficient. The Review of Economics and Statistics, 75(1), 134–138.

Gary S. Fields. (1979). Decomposing LDC Inequality. Oxford Economic Papers, 31(3), 437–459.

Gastwirth, J. L. (1974). Large Sample Theory of Some Measures of Income Inequality. Econometrica, 42(1), 191–196.

Gini, C. (1912). Variabilità e Mutabilità (Variability and Mutability). Memorie Di Metodologica Statistica (Ed. Pizetti E, Salvemini, T), 156.

Golden, J. (2008). A Simple Geometric Approach to Approximating the Gini Coefficient. The Journal of Economic Education, 39(1), 68–77.

Gruen, C., y Klasen, S. (2008). Growth, inequality, and welfare: Comparisons across space and time. Oxford Economic Papers, 60(2), 212–236.

Guillermina, J. (1980). A New Theory of Distributive Justice. American Sociological Review, 45(1), 3–32.

Haughton, J., y Khandker, S. (2009). Handbook on Poverty and Inequality. (T. W. B. Group, Ed.) (First Edition). Washington, DC: The World Bank.

Hodler, R. (2009). Redistribution and Inequality in a Heterogeneous Society. Economica, 76(304), 704–718.

Jacobs, D. (1980). Dimensions of Inequality and Public Policy in the States. The Journal of Politics, 42(1), 291–306.

Jantzen, R. T., y Volpert, K. (2012). On the mathematics of income inequality: Splitting the gini index in two. American Mathematical Monthly, 119(10), 824–837.

Jenkins, S. P., Burkhauser, R. V., Feng, S., y Larrimore, J. (2011). Measuring inequality using censored data : a multiple-imputation approach to estimation and inference. Journal of the Statistical Society, 174(1), 63–81.

Johannesson, M., y Gerdtham, U. (2004). Absolute Income, Relative Income, Income Inequality, and Mortality. The Journal of Human Resources, 39(1), 228–247.

Johnson, E., Rymon, T., y Sen, S. (2003). The Small-Sample Bias of the Gini Coefficient : Results and Implications for Empirical. The Review of Economics and Statistics, 85(1), 226–234.

Kakwani, N. C. (1974). A Note on the Efficient Estimation of the New Measures of Income Inequality. Econometrica, 42(3), 597–600.

Kakwani, N. C., y Podder, N. (2008). Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations. Econometrica, 44(1), 137–148.

Kokko, H., Mackenzie, A., Reynolds, J. D., Lindström, J., y Sutherland, W. J. (1999). Measures of Inequality Are Not Equal. The American Naturalist, 154(3), 358–382.

Krieckhaus, J., Son, B., Bellinger, N. M., y Wells, J. M. (2013). Economic inequality and democratic support. Journal of Politics, 76(1), 139–151.

Krishnan, P. (1981). Measures of Inequality for Qualitative Variables and Concentration Curves. American Sociological Review, 46(3), 368–371.

Lang, V. F., y Lingnau, H. (2015). Defining and Measuring Poverty and Inequality Post-2015. Journal of International Development, 27(2), 399–414.

Leigh, A. (2007). How Closely Do Top Income Shares Track Other Measures of Inequality? The Economic Journal, 117(524), F619–F633.

Lerman, R. I., y Yitzhaki, S. (1985). Income Inequality Effects by Income Source : A New Approach and Applications to the United States. The Review of Economics and Statistics, 67(1), 151–156.

Li, H., Xie, D., y Zou, H.-F. (2000). Dynamics of Income Distribution. The Canadian Journal of Economics, 33(4), 937–961.

McDonald, J. B., y Jensen, B. C. (1979). An analysis of some properties of alternative measures of income inequality based on the gamma distribution function. Journal of the American Statistical Association, 74(368), 856–860.

McGranahan, D. (1981). The Meaning and Measurement of Income Inequality. American Sociological Review, 46(2), 240–241.

Mehran, F. (1976). Linear Measures of Income Inequality. Econometrica, 44(4), 805–809.

Menard, S. (1986). A Research Note on International Comparisons of Inequality of Income. Social Forces, 64(3), 778–793.

Mills, J. A., y Zandvakili, S. (1997). Statistical Inference Via Bootstrapping for Measures of Inequality. Journal of Applied Econometrics, 12(2), 133–150.

Minarik, J. J. (1977). The Measurement and Trend of Inequality : Comment. The American Economic Review, 67(3), 513–516.

Formby, J., y G. Seaks, T. (1980). Paglin’s Gini Measure of Inequality : A Modification. The American Economic Review, 70(3), 479–482.

Paglin, M. (1975). American Economic Association The Measurement and Trend of Inequality : A Basic Revision. The American Economic Review, 65(4), 598–609.

Paglin, M. (1989). On the Measurement and Trend of Inequality : Reply. The American Economic Review, 79(1), 265–266.

Perotti, R. (1992). Income Distribution, Politics, and Growth. The American Economic Review, 82(2), 311–316.

Praag, B., Hagenaars, A., y Eck, W. (1983). The Influence of Classification and Observation Errors on the Measurement of Income Inequality. Econometrica, 51(4), 1093–1108.

Pyatt, G. (1987). Measuring Welfare, Poverty and Inequality. The Economic Journal, 97(386), 459–467.

Reardon, S. F., y Bischoff, K. (2011). Income Inequality and Income Segregation. American Journal of Sociology, 116(4), 1092–1153.

Sastry, D., y Kelkar, U. R. (1994). Note on the Decomposition of Gini Inequality. The Review of Economics and Statistics, 76(3), 584–586.

Schwartz, J., y Winship, C. (1980). The Welfare Approach to Measuring Inequality. Sociological Methodology, 11(1), 1–36.

Smeeding, T. M. (2009). New Comparative Measures of Income, Material Deprivation, and Well-Being. Journal of Policy Analysis and Management, 28(4), 745–752.

Thomas Demuynck, y Gaer, D. Van de. (2012). Inequality Adjusted Income Growth. Economica, 79(316), 747–765.

Thurow, L. C. (1971). The Income Distribution as a Pure Public Good. The Quarterly Journal of Economics, 85(2), 327–336.

Tillé, Y., y Langel, M. (2012). Histogram-based interpolation of the Lorenz curve and Gini index for grouped data. American Statistician, 66(4), 225–231.

Tinbergen, J. (2018). American Economic Association Welfare Economics and Income Distribution. The American Economic Review, 47(2), 490–503.

World Bank Group. (2016). Poverty and Shared Prosperity 2016. World Bank GRoup.

World Bank Group. (2016). Poverty and Shared Prosperity: Taking on Inequality. (World Bank Group, Ed.) (First Edition). Washington, DC: The World Bank.

Yntema, B. Y. D. B. (1933). Measures of the Inequality in the Personal Distribution of Wealth or Income. Journal of the American Statistical Association, 28(184), 423–433.


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