On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth
- 1 LERSTAD, Université Gaston Berger de Saint-Louis, Saint-Louis, Sénégal
- 2 LERSTAD, Université Gaston Berger de Saint-Louis, Saint-Louis, Sénégal;LSTA, Université Pierre et Marie Curie, Paris, France
Abstract
We set in this paper a coherent theory based on functional empirical processes that allows to consider both the poverty and the inequality indices in one Gaussian field in which the study of the influence of the one over the other is done. We use the General Poverty Index ( GPI ), that is a class of poverty indices gathering the most common ones and a functional class of inequality measures including the Entropy Measure, the Mean Logarithmic Deviation, the different inequality measures of Atkinson, Champernowne, Kolm and Theil called Theil-Like Inequality Measures ( TLIM ). Our results are given in a unified approach with respect to the two classes instead of their particular elements. We provide the asymptotic laws of the variations of each class over two given periods and the ratio of the variation and derive confidence intervals for them. Although the variances may seem somehow complicated, we provide R codes for their computations and apply the results for the pseudo-panel data for Senegalwith a simple analysis.
- G. S. Lo, S. T. Sall and C. T. Seck, “Une Théorie Asymptotique des Indicateurs de Pauvreté,” Comptes Rendus Mathématiques de l’Académie des Sciences. Mathematical Reports of the Academy of Canada, Vol. 31, No. 2, 2009, pp. 45-52.
- G. S. Lo, “The Generalized Poverty Index,” Far East Journal of Theoretical Statistics, Vol. 42, No. 1, 2013, pp. 1-22.
- B. Zheng, “Aggregate Poverty Measures,” Journal of Economic Surveys, Vol. 11, No. 2, 1997, pp. 123-162. doi:10.1111/1467-6419.00028
- K. A. Sen, “Poverty: An Ordinal Approach to Measurement,” Econometrica, Vol. 44, No. 2, 1976, pp. 219-231. doi:10.2307/1912718
- N. Kakwani, “On a Class of Poverty Measures,” Econometrica, Vol. 48, No. 2, 1980, pp. 437-446. doi:10.2307/1911106
- A. Shorrocks, “Revisiting the Sen Poverty Index,” Econometrica, Vol. 63, No. 5, 1995, pp. 1225-1230. doi:10.2307/2171728
- S. Clark, R. Hemming and D. Ulph, “On Indices for the Measurement of Poverty,” Economic Journal, Vol. 91, 1981, pp. 525-526. doi:10.2307/2232600
- J. E. Foster, J. Greer and E. Thorbecke, “A Class of Decomposable Poverty Measures,” Econometrica, Vol. 52, No. 3, 1984, pp. 761-766. doi:10.2307/1913475
- S. T. Sall and G. S. Lo, “The Asymptotic Theory of the Poverty Intensity in View of Extreme Values Theory for Two Simple Cases,” Afrika Statistika, Vol. 2, No. 1, 2007, pp. 41-55.
- S. T. Sall and G. S. Lo, “Uniform Weak Convergence of the Time-Dependent Poverty Measure for Continuous Longitudinal Data,” Brazilian Journal of Probability and Statistics, Vol. 24, No. 3, 2010, pp. 457-467. doi:10.1214/08-BJPS101
- F. A. Cowell, “Theil, Inequality and the Structure of Income Distribution,” London School of Economics and Political Sciences, London, 2003. doi:10.1016/0014-2921(80)90051-3
- H. Theil, “Economics and Information Theory,” North Holland, Amsterdam, 1967.
- F. A. Cowell, “Generalized Entropy and the Measurement of Distributional Change,” European Economic Review, Vol. 13, No. 1, 1980, pp. 147-159.
- A. B. Atkinson, “On the Measurement of Inequality,” Journal of Economic Theory, Vol. 2, No. 3, 1970, pp. 244263. doi:10.1016/0022-0531(70)90039-6
- D. G. Champernowne and F. A. Cowell, “Economic Inequality and Income Distribution,” Cambridge University Press, Cambridge, 1998.