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A new ordered family of Lorenz curves with an application to measuring income inequality and poverty in rural China

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  • WANG, Zuxiang
  • SMYTH, Russell
  • NG, Yew-Kwang

Abstract

The most common data source on income distribution in China is grouped data. When income data is in grouped form, some acceptable Lorenz model is needed to approximate the underlying Lorenz curve. This paper presents a new family of Lorenz curves and applies the main model in our proposed family of Lorenz curves to income data for rural China over the period 1980 to 2006. We find that the income share of the rural population at the low end of the income scale has been shrinking, income inequality in rural China has increased over time and that income inequality has impeded attempts to reduce poverty. However, the welfare of the rural population is still improving in terms of the generalized Lorenz dominance criterion.

Suggested Citation

  • WANG, Zuxiang & SMYTH, Russell & NG, Yew-Kwang, 2009. "A new ordered family of Lorenz curves with an application to measuring income inequality and poverty in rural China," China Economic Review, Elsevier, vol. 20(2), pages 218-235, June.
  • Handle: RePEc:eee:chieco:v:20:y:2009:i:2:p:218-235
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    1. Guanghua Wan & Zhangyue Zhou, 2005. "Income Inequality in Rural China: Regression‐based Decomposition Using Household Data," Review of Development Economics, Wiley Blackwell, vol. 9(1), pages 107-120, February.
    2. Shaohua Chen & Yan Wang, 2001. "China's growth and poverty reduction - trends between 1990 and 1999," Policy Research Working Paper Series 2651, The World Bank.
    3. Ryu, Hang K. & Slottje, Daniel J., 1996. "Two flexible functional form approaches for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 251-274.
    4. Rothschild, Michael & Stiglitz, Joseph E., 1973. "Some further results on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 188-204, April.
    5. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    6. Galor, Oded & Tsiddon, Daniel, 1997. "Technological Progress, Mobility, and Economic Growth," American Economic Review, American Economic Association, vol. 87(3), pages 363-382, June.
    7. Sarabia, José María & Castillo, Enrique & Pascual, Marta & Sarabia, María, 2005. "Mixture Lorenz curves," Economics Letters, Elsevier, vol. 89(1), pages 89-94, October.
    8. Schader, Martin & Schmid, Friedrich, 1994. "Fitting Parametric Lorenz Curves to Grouped Income Distributions--A Critical Note," Empirical Economics, Springer, vol. 19(3), pages 361-370.
    9. Benabou, Roland, 1996. "Heterogeneity, Stratification, and Growth: Macroeconomic Implications of Community Structure and School Finance," American Economic Review, American Economic Association, vol. 86(3), pages 584-609, June.
    10. Zhang, Yin & Wan, Guanghua, 2006. "The impact of growth and inequality on rural poverty in China," Journal of Comparative Economics, Elsevier, vol. 34(4), pages 694-712, December.
    11. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    12. Gustafsson, Bjorn & Shi, Li, 2002. "Income inequality within and across counties in rural China 1988 and 1995," Journal of Development Economics, Elsevier, vol. 69(1), pages 179-204, October.
    13. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-986, September.
    14. Kakwani, N C & Podder, N, 1973. "On the Estimation of Lorenz Curves from Grouped Observations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 278-292, June.
    15. Alberto Alesina & Dani Rodrik, 1994. "Distributive Politics and Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 465-490.
    16. Galor, Oded & Tsiddon, Daniel, 1997. "The Distribution of Human Capital and Economic Growth," Journal of Economic Growth, Springer, vol. 2(1), pages 93-124, March.
    17. Gregory C. Chow, 2006. "Rural Poverty in China: Problem and Policy," Working Papers 68, Princeton University, Department of Economics, Center for Economic Policy Studies..
    18. Shujie Yao, 1999. "Economic growth, income inequality and poverty in china under economic reforms," Journal of Development Studies, Taylor & Francis Journals, vol. 35(6), pages 104-130.
    19. Rossi, Jose W., 1985. "Notes on a new functional form for the Lorenz curve," Economics Letters, Elsevier, vol. 17(1-2), pages 193-197.
    20. Fan, Shenggen & Zhang, Linxiu & Zhang, Xiaobo, 2002. "Growth, inequality, and poverty in rural China: the role of public investments," Research reports 125, International Food Policy Research Institute (IFPRI).
    21. repec:bla:revinw:v:37:y:1991:i:4:p:447-52 is not listed on IDEAS
    22. Benjamin, Dwayne & Brandt, Loren & Giles, John, 2005. "The Evolution of Income Inequality in Rural China," Economic Development and Cultural Change, University of Chicago Press, vol. 53(4), pages 769-824, July.
    23. Ogwang, Tomson & Gouranga Rao, U. L., 1996. "A new functional form for approximating the Lorenz curve," Economics Letters, Elsevier, vol. 52(1), pages 21-29, July.
    24. Gupta, Manash Ranjan, 1984. "Functional Form for Estimating the Lorenz Curve," Econometrica, Econometric Society, vol. 52(5), pages 1313-1314, September.
    25. Wan, Guanghua & Lu, Ming & Chen, Zhao, 2006. "The inequality-growth nexus in the short and long run: Empirical evidence from China," Journal of Comparative Economics, Elsevier, vol. 34(4), pages 654-667, December.
    26. Rasche, R H, et al, 1980. "Functional Forms for Estimating the Lorenz Curve: Comment," Econometrica, Econometric Society, vol. 48(4), pages 1061-1062, May.
    27. Kai-yuen, Tsui, 1998. "Trends and Inequalities of Rural Welfare in China: Evidence from Rural Households in Guangdong and Sichuan," Journal of Comparative Economics, Elsevier, vol. 26(4), pages 783-804, December.
    28. Chen, Shaohua & Ravallion, Martin, 1996. "Data in transition: Assessing rural living standards in Southern China," China Economic Review, Elsevier, vol. 7(1), pages 23-56.
    29. Park, Albert & Wang, Sangui & Wu, Guobao, 2002. "Regional poverty targeting in China," Journal of Public Economics, Elsevier, vol. 86(1), pages 123-153, October.
    30. Jyotsna Jalan & Martin Ravallion, 1999. "China's Lagging Poor Areas," American Economic Review, American Economic Association, vol. 89(2), pages 301-305, May.
    31. Kakwani, Nanak C & Podder, N, 1976. "Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations," Econometrica, Econometric Society, vol. 44(1), pages 137-148, January.
    32. Duangkamon Chotikapanich & D. S. Prasada Rao & Kam Ki Tang, 2007. "Estimating Income Inequality In China Using Grouped Data And The Generalized Beta Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(1), pages 127-147, March.
    33. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    34. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    35. Zhang, Xiaobo, 2006. "Fiscal decentralization and political centralization in China: Implications for growth and inequality," Journal of Comparative Economics, Elsevier, vol. 34(4), pages 713-726, December.
    36. Kakwani, Nanak, 1980. "On a Class of Poverty Measures," Econometrica, Econometric Society, vol. 48(2), pages 437-446, March.
    37. Foster, James E & Shorrocks, Anthony F, 1991. "Subgroup Consistent Poverty Indices," Econometrica, Econometric Society, vol. 59(3), pages 687-709, May.
    38. Gregory C. Chow, 2006. "Rural Poverty in China: Problem and Policy," Working Papers 68, Princeton University, Department of Economics, Center for Economic Policy Studies..
    39. Shaohua Chen & Martin Ravallion, 2004. "How Have the World's Poorest Fared since the Early 1980s?," The World Bank Research Observer, World Bank, vol. 19(2), pages 141-169.
    40. Rozelle Scott, 1994. "Rural Industrialization and Increasing Inequality: Emerging Patterns in China's Reforming Economy," Journal of Comparative Economics, Elsevier, vol. 19(3), pages 362-391, December.
    41. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    42. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    43. Kwang Soo Cheong, 2002. "An empirical comparison of alternative functional forms for the Lorenz curve," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 171-176.
    44. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-156, February.
    45. repec:cor:louvrp:-1676 is not listed on IDEAS
    46. Banerjee, Abhijit V & Duflo, Esther, 2003. "Inequality and Growth: What Can the Data Say?," Journal of Economic Growth, Springer, vol. 8(3), pages 267-299, September.
    47. Fishman, Arthur & Simhon, Avi, 2002. "The Division of Labor, Inequality and Growth," Journal of Economic Growth, Springer, vol. 7(2), pages 117-136, June.
    48. Zhu, Nong & Luo, Xubei, 2006. "Nonfarm activity and rural income inequality : a case study of two provinces in China," Policy Research Working Paper Series 3811, The World Bank.
    49. Kung, James K S & Lee, Yiu-fai, 2001. "So What If There Is Income Inequality? The Distributive Consequence of Nonfarm Employment in Rural China," Economic Development and Cultural Change, University of Chicago Press, vol. 50(1), pages 19-46, October.
    50. Ravallion, Martin & Chen, Shaohua, 2007. "China's (uneven) progress against poverty," Journal of Development Economics, Elsevier, vol. 82(1), pages 1-42, January.
    51. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    52. P. Ortega & G. Martín & A. Fernández & M. Ladoux & A. García, 1991. "A New Functional Form For Estimating Lorenz Curves," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(4), pages 447-452, December.
    53. Jose-Mari Sarabia, 1997. "A hierarchy of lorenz curves based on the generalized tukey's lambda distribution," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 305-320.
    54. repec:pri:cepsud:134chow is not listed on IDEAS
    55. José-María Sarabia & Enrique Castillo & Daniel J. Slottje, 2001. "An Exponential Family of Lorenz Curves," Southern Economic Journal, John Wiley & Sons, vol. 67(3), pages 748-756, January.
    56. Holm, Juhani, 1993. "Maximum entropy Lorenz curves," Journal of Econometrics, Elsevier, vol. 59(3), pages 377-389, October.
    57. Basmann, R. L. & Hayes, K. J. & Slottje, D. J. & Johnson, J. D., 1990. "A general functional form for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 77-90.
    58. Ogwang, Tomson & Rao, U. L. Gouranga, 2000. "Hybrid models of the Lorenz curve," Economics Letters, Elsevier, vol. 69(1), pages 39-44, October.
    59. Hare, Denise, 1994. "Rural nonagricultural activities and their impact on the distribution of income: Evidence from farm households in Southern China," China Economic Review, Elsevier, vol. 5(1), pages 59-82.
    60. Kristin J. Forbes, 2000. "A Reassessment of the Relationship between Inequality and Growth," American Economic Review, American Economic Association, vol. 90(4), pages 869-887, September.
    61. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
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    2. Kanbur, Ravi & Wang, Yue & Zhang, Xiaobo, 2021. "The great Chinese inequality turnaround," Journal of Comparative Economics, Elsevier, vol. 49(2), pages 467-482.
    3. Liu, Ying & Huang, Jikun & Zikhali, Precious, 2016. "The bittersweet fruits of industrialization in rural China: The cost of environment and the benefit from off-farm employment," China Economic Review, Elsevier, vol. 38(C), pages 1-10.
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    5. Miguel Sordo & Jorge Navarro & José Sarabia, 2014. "Distorted Lorenz curves: models and comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 761-780, April.
    6. Kanbur, Ravi & Wang, Yue & Zhang, Xiaobo, 2021. "The great Chinese inequality turnaround," Journal of Comparative Economics, Elsevier, vol. 49(2), pages 467-482.
    7. Cheong, Tsun Se & Wu, Yanrui, 2013. "Regional disparity, transitional dynamics and convergence in China," Journal of Asian Economics, Elsevier, vol. 29(C), pages 1-14.

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