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Income distribution dependence of poverty measure: A theoretical analysis

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  • Chattopadhyay, Amit K.
  • Mallick, Sushanta K.

Abstract

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the ‘global’ mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy.

Suggested Citation

  • Chattopadhyay, Amit K. & Mallick, Sushanta K., 2007. "Income distribution dependence of poverty measure: A theoretical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 241-252.
  • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:241-252
    DOI: 10.1016/j.physa.2006.10.103
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    1. Angus Deaton, 2005. "Measuring Poverty in a Growing World (or Measuring Growth in a Poor World)," The Review of Economics and Statistics, MIT Press, vol. 87(1), pages 1-19, February.
    2. Angus Deaton, 2005. "ERRATUM: Measuring Poverty in a Growing World (or Measuring Growth in a Poor World)," The Review of Economics and Statistics, MIT Press, vol. 87(2), pages 395-395, May.
    3. Sen, Amartya, 1979. " Issues in the Measurement of Poverty," Scandinavian Journal of Economics, Wiley Blackwell, vol. 81(2), pages 285-307.
    4. Menno Pradhan & Martin Ravallion, 2000. "Measuring Poverty Using Qualitative Perceptions Of Consumption Adequacy," The Review of Economics and Statistics, MIT Press, vol. 82(3), pages 462-471, August.
    5. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    6. Indranil Dutta & Prasanta K. Pattanaik & Yongsheng Xu, 2003. "On Measuring Deprivation and the Standard of Living in a Multidimensional Framework on the Basis of Aggregate Data," Economica, London School of Economics and Political Science, vol. 70(278), pages 197-221, May.
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    Cited by:

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    2. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    3. Li, Jiaxin & Wang, Zihan & Cheng, Xin & Shuai, Jing & Shuai, Chuanmin & Liu, Jing, 2020. "Has solar PV achieved the national poverty alleviation goals? Empirical evidence from the performances of 52 villages in rural China," Energy, Elsevier, vol. 201(C).
    4. Bertotti, M.L. & Chattopadhyay, A.K. & Modanese, G., 2017. "Stochastic effects in a discretized kinetic model of economic exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 724-732.
    5. Sebastian Guala, 2009. "Taxes in a Wealth Distribution Model by Inelastically Scattering of Particles," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 7(1), pages 1-7.
    6. Fredj Jawadi & Ricardo M. Sousa, 2012. "Consumption and Wealth in the US, the UK and the Euro Area:A Nonlinear Investigation," NIPE Working Papers 24/2012, NIPE - Universidade do Minho.

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