A new index for measuring aging inequality: An application to Asian countries

Affiliation(s)

Department of Statistics, Shahjalal University of Science and Technology, Sylhet, Bangladesh.

Department of Statistics, Gauhati University, Guwahati, India.

Department of Statistics, Shahjalal University of Science and Technology, Sylhet, Bangladesh.

Department of Statistics, Gauhati University, Guwahati, India.

ABSTRACT

Although the Gini coefficient is an ideal measure of income inequality, it may be applied to measure the aging inequality in a society. In this paper, an attempt has been made to develop alternative measures of aging inequality based on the Gini index. The study uses the secondary population data of Asian countries collected from the international data base, US census Bureau. From the analysis it is observed that the Gini coefficient shows equally sensitivity at all levels. The coefficient is more concern for the country which are closed to the line of absolute equality. For example, the sensitivity level in the Gini coefficient is observed much higher in Israel than in Qatar. The logarithmic transformation of Gini coefficient does not work well because it violates the transfer principle. The Geometric measure of Gini coefficient fails to measure inequality because of violating the transfer principle. On the other hand, the logarithmic transformation of geometric equivalent of the Gini coefficient works better because it shows more sensitivity than the Gini coefficient and satisfies the transfer principle. From the analysis it is also found that the trigonometric measure of Gini coefficient works better than the logarithmic transformation of geometric equivalent of the Gini coefficient because it satisfies transfer principle as well as shows higher sensitivity. Therefore, the trigonometric measure of the Gini coefficient is the best measure of aging inequality among the measures considered in the study.

Although the Gini coefficient is an ideal measure of income inequality, it may be applied to measure the aging inequality in a society. In this paper, an attempt has been made to develop alternative measures of aging inequality based on the Gini index. The study uses the secondary population data of Asian countries collected from the international data base, US census Bureau. From the analysis it is observed that the Gini coefficient shows equally sensitivity at all levels. The coefficient is more concern for the country which are closed to the line of absolute equality. For example, the sensitivity level in the Gini coefficient is observed much higher in Israel than in Qatar. The logarithmic transformation of Gini coefficient does not work well because it violates the transfer principle. The Geometric measure of Gini coefficient fails to measure inequality because of violating the transfer principle. On the other hand, the logarithmic transformation of geometric equivalent of the Gini coefficient works better because it shows more sensitivity than the Gini coefficient and satisfies the transfer principle. From the analysis it is also found that the trigonometric measure of Gini coefficient works better than the logarithmic transformation of geometric equivalent of the Gini coefficient because it satisfies transfer principle as well as shows higher sensitivity. Therefore, the trigonometric measure of the Gini coefficient is the best measure of aging inequality among the measures considered in the study.

Cite this paper

Taj Uddin, M. , Islam, M. , Kabir, A. and Nath, D. (2012) A new index for measuring aging inequality: An application to Asian countries.*Health*, **4**, 685-694. doi: 10.4236/health.2012.429108.

Taj Uddin, M. , Islam, M. , Kabir, A. and Nath, D. (2012) A new index for measuring aging inequality: An application to Asian countries.

References

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[2] Allison, P.D. (1978) Measures of inequality. American Sociological Review, 43, 865-880. doi:10.2307/2094626

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[5] Kelley, J. and Klein, H.S. (1977) Revolution and rebirth of inequality. A theory of stratification in post revolutionary society.

[6] Kii, T. (1982) A new index for measuring demographic aging. The Gerontologist, 22, 438-442. doi:10.1093/geront/22.4.438

[7] Nath, D.C. and Islam, M.N. (2009) New indices. An application of measuring the aging process of some Asian countries with special reference to Bangladesh. Population Ageing, 2, 23-39. doi:10.1007/s12062-009-9016-2

[8] Islam, M.N. and Nath, D.C. (2010) Application of demographic components for measuring the ageing velocity: An explanation with Bangladesh context. Demography India, 39, 297-313.

[9] Atkinson, A.B. (1970) On the measurement of inequality. Journal of Economic Theory, 2, 244-263. doi:10.1016/0022-0531(70)90039-6

[10] Shalit, H. And Yitzhaki, S. (1984) Mean Gini, portfolio theory and pricing of risky assets. Journal of Finance, 39, 1449-1468. doi:10.1111/j.1540-6261.1984.tb04917.x

[11] Yitzhaki, S. (1982) Stochastic dominance, mean, variance and Gini’s mean difference. American Economic Review, 72, 178-185.

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[13] Hauser, R.M., Dickinson, P.J., Travis, H.P. and Kaffel, J.M. (1975) Structural changes in occupational mobility among men in the United States. American Sociological Review, 40, 585-598. doi:10.2307/2094197

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[18] D’Albis, H. and Collard, F. (2011) Age grouping and the measurement of population aging’ paper presented in the seminar at IZA. Universities of Montpellier and Paris-Dauphine for Insightful Discussions.

[19] Majumder, A. (2007) Alternative measures of economic inequality. Artha Beekshan, 16, 3-20

[20] Dalton, H. (1920) The measurement of the inequality of income. Economic Journal, 30, 348-361. doi:10.2307/2223525

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[24] Anand, S. (1983) Inequality and poverty in Malaysia: Measurement and decomposition. Oxford University Press, New York.

[25] Leclerc, A., Lert, F. and Fabien, C. (1990) Differential mortality: Some comparisons between England and Wales, Finland and France, based on in-equality measures. International Journal of Epidemiology, 19, 1001-1010. doi:10.1093/ije/19.4.1001

[26] Illsey, R. and Le Grand, J. (1987) The measurement of inequality in health. In: Williams, A., Ed., Health and economics, Macmillan, London, 13-36.

[27] Sen, A. (1999) On economic inequality (expended edition with a substantial annexure by James, E. and Amartya Sen). Oxford University Press, New Delhi.

[28] Ray, J.L. and Singer, J.D. (1973) Measuring the concentration of power in the international system. Sociological Methods and Research, 1, 403-437. doi:10.1177/004912417300100401

[29] Kendall, M. and Stuart, A. (1977) The advance theory of statistics. Vol. 1. 4th Edition, Macmillan, New York.

[30] Partha, D., Sen, A. and Starrett, D. (1973) Notes on the measurement of inequality. Journal of Economic Theory, 6, 180-187. doi:10.1016/0022-0531(73)90033-1

[31] Yitzhaki, S. (1994) Economic distance and overlapping of distributions. Journal of Econometrics, 61, 147-159. doi:10.1016/0304-4076(94)90081-7

[32] Milanovic, B. (1997) A simple way to calculate the Gini coefficient and some implications. Economic Letters, 56, 45-49. doi:10.1016/S0165-1765(97)00101-8

[33] Lerman, R. and Yitzhaki, S. (1985) Income inequality effects by income source: A new approach and applications to the US. The Review of Economics and Statistics, 63, 151-156.

[34] Pyatt, D., Chen, C.N. and Fei, J. (1980) The distribution of income by factor components. Quarterly Journal of Economics, 451-473. doi:10.2307/1885088

[35] Anand, S. (1997) The measurement of income inequality’ in measurement of inequality and poverty. Oxford University Press, New Delhi.

[1] Blau, P.M. (1977) A macrosociological theory of social structure. American Journal of Sociology, 83, 26-54. doi:10.1086/226505

[2] Allison, P.D. (1978) Measures of inequality. American Sociological Review, 43, 865-880. doi:10.2307/2094626

[3] Jackman, R. (1974) Political democracy and social inequality: A comparative analysis. American Journal of Sociology, 83, 78-99.

[4] Hewitt, C. (1977) The effect of political democracy and social democracy on inequality in industrial societies. American Sociological Review, 42, 450-465. doi:10.2307/2094750

[5] Kelley, J. and Klein, H.S. (1977) Revolution and rebirth of inequality. A theory of stratification in post revolutionary society.

[6] Kii, T. (1982) A new index for measuring demographic aging. The Gerontologist, 22, 438-442. doi:10.1093/geront/22.4.438

[7] Nath, D.C. and Islam, M.N. (2009) New indices. An application of measuring the aging process of some Asian countries with special reference to Bangladesh. Population Ageing, 2, 23-39. doi:10.1007/s12062-009-9016-2

[8] Islam, M.N. and Nath, D.C. (2010) Application of demographic components for measuring the ageing velocity: An explanation with Bangladesh context. Demography India, 39, 297-313.

[9] Atkinson, A.B. (1970) On the measurement of inequality. Journal of Economic Theory, 2, 244-263. doi:10.1016/0022-0531(70)90039-6

[10] Shalit, H. And Yitzhaki, S. (1984) Mean Gini, portfolio theory and pricing of risky assets. Journal of Finance, 39, 1449-1468. doi:10.1111/j.1540-6261.1984.tb04917.x

[11] Yitzhaki, S. (1982) Stochastic dominance, mean, variance and Gini’s mean difference. American Economic Review, 72, 178-185.

[12] Shalit, H. (1985) Calculating the Gini index of inequality for individual data. Oxford Bulletion of Economics and Statistics, 47, 185-189.

[13] Hauser, R.M., Dickinson, P.J., Travis, H.P. and Kaffel, J.M. (1975) Structural changes in occupational mobility among men in the United States. American Sociological Review, 40, 585-598. doi:10.2307/2094197

[14] Blau, P.M. (1977) Inequality and heterogeneity. Free Press, New York.

[15] Mueller, J.H., Schuessler, K.F. and Costner, H.L. (1977) Statistical reasonining in socilogy. 3rd Edition, Houghton-Mifflin, Boston.

[16] Aghevli, B.B. and Mehran, F. (1981) Optimal grouping of income distribution data. Journal of the American Statistical Association, 76, 22-26. doi:10.1080/01621459.1981.10477596

[17] Davies, J.B. and Shorrocks, A.F. (1989) Optimal grouping of income and wealth data. Journal of Econometrics, 42, 97-108. doi:10.1016/0304-4076(89)90078-X

[18] D’Albis, H. and Collard, F. (2011) Age grouping and the measurement of population aging’ paper presented in the seminar at IZA. Universities of Montpellier and Paris-Dauphine for Insightful Discussions.

[19] Majumder, A. (2007) Alternative measures of economic inequality. Artha Beekshan, 16, 3-20

[20] Dalton, H. (1920) The measurement of the inequality of income. Economic Journal, 30, 348-361. doi:10.2307/2223525

[21] Pigou, A.C. (1912) Wealth and Welfare.

[22] Sen, A. (1973) On Economic Inequality. Norton, New York. doi:10.1093/0198281935.001.0001

[23] Kendall, M.G. and Stuart, A. (1969) The advanced theory of statistics. Charles Griffin, London.

[24] Anand, S. (1983) Inequality and poverty in Malaysia: Measurement and decomposition. Oxford University Press, New York.

[25] Leclerc, A., Lert, F. and Fabien, C. (1990) Differential mortality: Some comparisons between England and Wales, Finland and France, based on in-equality measures. International Journal of Epidemiology, 19, 1001-1010. doi:10.1093/ije/19.4.1001

[26] Illsey, R. and Le Grand, J. (1987) The measurement of inequality in health. In: Williams, A., Ed., Health and economics, Macmillan, London, 13-36.

[27] Sen, A. (1999) On economic inequality (expended edition with a substantial annexure by James, E. and Amartya Sen). Oxford University Press, New Delhi.

[28] Ray, J.L. and Singer, J.D. (1973) Measuring the concentration of power in the international system. Sociological Methods and Research, 1, 403-437. doi:10.1177/004912417300100401

[29] Kendall, M. and Stuart, A. (1977) The advance theory of statistics. Vol. 1. 4th Edition, Macmillan, New York.

[30] Partha, D., Sen, A. and Starrett, D. (1973) Notes on the measurement of inequality. Journal of Economic Theory, 6, 180-187. doi:10.1016/0022-0531(73)90033-1

[31] Yitzhaki, S. (1994) Economic distance and overlapping of distributions. Journal of Econometrics, 61, 147-159. doi:10.1016/0304-4076(94)90081-7

[32] Milanovic, B. (1997) A simple way to calculate the Gini coefficient and some implications. Economic Letters, 56, 45-49. doi:10.1016/S0165-1765(97)00101-8

[33] Lerman, R. and Yitzhaki, S. (1985) Income inequality effects by income source: A new approach and applications to the US. The Review of Economics and Statistics, 63, 151-156.

[34] Pyatt, D., Chen, C.N. and Fei, J. (1980) The distribution of income by factor components. Quarterly Journal of Economics, 451-473. doi:10.2307/1885088

[35] Anand, S. (1997) The measurement of income inequality’ in measurement of inequality and poverty. Oxford University Press, New Delhi.