FernándezMorales, Antonio (2016): Measuring poverty with the Foster, Greer and Thorbecke indexes based on the Gamma distribution.

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Abstract
The purpose of this paper is the estimation of the Foster, Greer and Thorbecke family of poverty indexes using the Gamma distribution as a continuous representation of the distribution of incomes. The expressions of this family of poverty indexes associated with the Gamma probability model and their asymptotic distributions are derived in the text, both for an exogenous and a relative (to the mean) poverty line. Finally, a Monte Carlo experiment is performed to compare three different methods of estimation for grouped data.
Item Type:  MPRA Paper 

Original Title:  Measuring poverty with the Foster, Greer and Thorbecke indexes based on the Gamma distribution 
Language:  English 
Keywords:  Poverty indexes; Income distribution; Gamma distribution 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics I  Health, Education, and Welfare > I3  Welfare, WellBeing, and Poverty > I32  Measurement and Analysis of Poverty 
Item ID:  69648 
Depositing User:  Antonio FernándezMorales 
Date Deposited:  22 Feb 2016 07:33 
Last Modified:  22 Feb 2016 09:47 
References:  Clementi, F. and Gallegati, M. (2016). The Parametric Approach to Income and Wealth Distributional Analysis. In F. Clementi and M. Gallegati (eds.) The Distribution of Income and Wealth (pp. 1115), Springer International Publishing. Hajargasht, G., and Griffiths, W. E. (2013). Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data. Economic Modelling, 33, 593604. García Péerez, C. and Prieto Aláiz, M. (2011) Using the Dagum model to explain changes in personal income distribution. Applied Economics 43, pp. 4377–4386. Giorgi, G.M. and Nadarajah, S. (2010). Bonferroni and Gini indices for various parametric families of distributions. Metron  International Journal of Statistics, vol. LXVIII, n. 1, pp. 2346. Chotikapanich, D. and Griffiths, W. E. (2008). Estimating income distri butions using a mixture of gamma densities, in D. Chotikapanich (ed.) Modelling income distributions and Lorenz curves (pp. 285302). Springer New York. Hajargasht, G., Griffiths, W.E., Brice, J., Rao, D.S.P. and Chotikapanich, D. (2012). Inference for Income Distributions Using Grouped Data. Journal of Business & Economic Statistics 30(4), pp. 563575. Foster, J., Greer, J. and Thorbecke, E. (1984). A class of decomposable poverty measures.Econometrica, vol. 52, pp. 761766. Foster, J.E. (1984). On economic poverty: A survey of aggregate measures. In R.L. Bassman and G.F. Rhodes (eds.) Advances in Econometrics, Vol. 3, Economic inequality: Measurement and policy, J.A.I. Press, Greenwich, pp. 215251. Salem, A.B. and Mount, T.D. (1974). A convenient Descriptive Model of Income Distribution: The Gamma Density. Econometrica, 42, pp. 1115 1127. Kloek, T. and Van Dijk, H.K. (1978). Efficient estimation of income distri bution tparameters. Journal of Econometrics, 8, pp. 6174. McDonald, J.B. (1984). Some generalized functions for the size distribution of income. Econometrica, vol. 52, 3, pp. 647663. Pinkovskiy, M. and SalaiMartin; X. (2009). Parametric Estimations of the World Distribution of Income, NBER Working Paper 15433. McDonald, J.B. and Jensen, B.C. (1979). An analysis of some properties of alternative measures of income inequality based on the gamma distribution. Journal of the American Statistical Association, vol. 74, pp. 856860. Rainville, E.D. (1960). Special Functions McMillan, New York. Satya R. Chakravarty, S.R., Chattopadhyay, N. and Silber, J. (2015). Reference groups and the poverty line. An axiomatic approach with an empirical illustration. WIDER Working Paper 2015/002. United Nations University World Institute for Development and Economics Research. Zhen, B. (2001). Statistical inference for poverty measures with relative poverty lines. Journal of Econometrics 101, pp. 337356. FernándezMorales, A. (2015). Using Nonparametric Conditional Distribu tions To Visualise LowIncome Mobility. Journal of Economics and Development Studies 3(3), pp. 3741. Johnson, N.L. and Kotz, S. (1970) Continuous Univariate Distributions 1 John Wiley & Sons, New York. Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics. Chapman and Hall, London. McDonald, J.B. and Ramson, R. (1979). Functional forms, estimating techniques and the distribution of income. Econometrica, vol. 47(6), pp. 1513 1525. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/69648 