Statistical inference with generalized gini indices of inequality, poverty, and welfare

Journal of Business and Economic Statistics

Volumn 27, Issue 1, 2009, Pages 1-17

  Barrett, Garry F ^a   Donald, Stephen G ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Functional delta method; Generalized gini index; Influence function.

Indexed keywords

EID: 64549136191     PISSN: 07350015     EISSN: None     Source Type: Journal    
DOI: 10.1198/jbes.2009.0001     Document Type: Article

References (43)

1. Atkinson, A. B. (1970), "On the Measurement of Inequality," Journal of Economic Theory, 2, 244-263.
2. Attanasio, O., Battistin, E., and Ichimura, H. (2004), "What Really Happened to Consumption Inequality in the US?" Working Paper 10338, National Bureau of Economic Research.
3. Barrett, G. F., and Donald, S. G. (2000), "Statistical Inference with Generalized Gini Indices of Inequality and Poverty," Working Paper, University of New South Wales, School of Economics.
4. Barrett, G. F., and Pendakur, K. (1995), "The Asymptotic Distribution of the Generalized Gini Indices of Inequality," The Canadian Journal of Economics. Revue Canadienne d'Economique, 28, 1042-1055.
5. Bhattacharya, D. (2005), "Asymptotic Inference from Multi-stage Samples," Journal of Econometrics, 126, 145-171.
6. Beach, C. M., and Davidson, R. (1983), "Distribution-free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, 50, 723-735.
7. Biewen, M. (2002), "Bootstrap Inference for Inequality, Mobility and Poverty Measurement," Journal of Econometrics, 108, 317-342.
8. Bishop, J. A., Chakraborti, S., and Thistle, P. D. (1990), "An Asymptotically Distribution-free Test for Sen's Welfare Index," Oxford Bulletin of Economics and Statistics, 52, 105-113.
9. Bishop, J. A., Formby, J. P., and Zheng, B. (1997), "Statistical Inference and the Sen Index of Poverty," International Economic Review, 38, 381-387.
10. Blackorby, C., and Donaldson, D. (1978), "Measures of Relative Equality and Their Meaning in Terms of Social Welfare," Journal of Economic Theory, 14, 665-685.
11. -(1980), "Ethical Indices for the Measurement of Poverty," Econometrica, 48, 1053-1060.
12. Booth, J. G., and Hall, P. (1994), "Monte Carlo Approximation and the Iterated Bootstrap," Biometrika, 81, 331-340.
13. Cameron, A.C., and Trivedi, PK. (2005), Microeconometrics: Methods and Applications, New York: Cambridge University Press, pp. 813-859.
14. Chakravarty, S. R. (1988), "Extended Gini Indices of Inequality," International Economic Review, 29, 147-156.
15. Cowell, p. A. (1989), "Sampling Variance and Decomposable Inequality Measures," Journal of Econometrics, 42, 27-41.
16. Cowell, F. A., and Victoria-Feser, M. (1996), "Robustness Properties of Inequality Measures," Econometrica, 64, 77-101.
17. Davidson, R., and Duclos, J.-Y. (1997), "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, 65, 1453-1466.
18. Deaton, A. (1997), The Analysis of Household Surveys: A Microeconomic Approach to Development Policy, Baltimore: Johns Hopkins University Press.
19. Donaldson, D., and Weymark, J. A. (1980), "A Single Parameter Generalization of the Gini Indices of Inequality," Journal of Economic Theory, 22, 67-86.
20. -(1983), "Ethically Flexible Gini Indices for Income Distributions in the Continuum," Journal of Economic Theory, 29, 353-358.
21. Fernholz, L. T. (1983), von Mises Calculus for Statistical Functionals, New York: Springer-Verlag.
22. Hall, P. (1992), The Bootstrap and Edgeworth Expansion, New York: Springer-Verlag.
23. Hampel, F. R. (1974), "The Influence Curve and Its Role in Robust Estimation," Journal of the American Statistical Association, 69, 383-393.
24. Kakwani, N. (1980), "On a Class of Poverty Measures," Econometrica, 48, 437-446.
25. Kolm, S. C. (1969), "The Optimal Production of Social Justice," in Public Economics, eds. J. Margolis and H. Guitton, New York: Macmillan, pp. 145-200.
26. Lambert, P. J. (1993), The Distribution and Redistribution of Income: A Mathematical Analysis (2nd ed.), Manchester: Manchester University Press.
27. Manski, C. F. (1988), Analog Estimation Methods in Econometrics, London: Chapman and Hall.
28. National Research Council (1995), Measuring Poverty: A New Approach, eds. C. F. Citro and R. T. Michael, Washington D. C.: National Academy Press, pp. 159-210.
29. Orshansky, M. (1965), "Counting the Poor," Social Security Bulletin, 28, 3-29.
30. Reid, N. (2005), "Influence Functions" in Encyclopedia of Statistical Sciences (2nd ed.), eds. S. Kotz, N. Balakrishnan, C. B. Read, and B. Vidakovic, Hoboken: Wiley, pp. 3495-3498.
31. Rongve, I., and Beach, C. M. (1997), "Estimation and Inference for Normative Inequality Indices of Distributions in the Continuum," International Economic Review, 38, 83-96.
32. Sen, A. (1973), On Economic Inequality, Oxford: Claredon Press.
33. -(1976), "Poverty: An Ordinal Approach to Measurement," Econometrica, 44, 219-231.
34. Shorrocks, A. F. (1983), "Ranking Income Distributions," Economica, 50, 3-17.
35. Thistle, P. D. (1990), "Large Sample Properties of Two Inequality Indices," Econometrica, 58, 725-728.
36. Van der Vaart, A. W., and Wellner, J. A. (1996), Weak Convergence and Empirical Processes: With Applications to Statistics, New York: Springer-Verlag.
37. Xu, K. (2000), "Inference for Generalized Gini Indices Using the Iterated-Bootstrap Method," Journal of Business & Economic Statistics, 18, 223-227.
38. Xu, K. (2006), "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," forthcoming in Econometric Reviews.
39. Xu, K., and Osberg, L. (1998), "A Distribution-Free Test for Deprivation Dominance," Econometric Reviews, 17, 415-429.
40. Yitzhaki, S. (1979), "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, 93, 321-324.
41. -(1983), "On an Extension of the Gini Inequality Index," International Economic Review, 24, 617-628.
42. Zitikis, R. (2003), "Asymptotic Estimation of the E-Gini Index," Econometric Theory, 19, 587-601.
43. Zitikis, R., and Gastwirth, J. L. (2002), "The Asymptotic Distribution of the S-Gini Index," Australian and New Zealand Journal of Statistics, 44, 439 -446.