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Income Distribution Dependence of Poverty Measure: A Theoretical Analysis

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  • Amit K Chattopadhyay
  • Sushanta K Mallick

Abstract

With a new 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. Following these results, we make quantitative predictions to correlate a developing with a developed economy.

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  • Amit K Chattopadhyay & Sushanta K Mallick, 2005. "Income Distribution Dependence of Poverty Measure: A Theoretical Analysis," Papers physics/0507035, arXiv.org.
  • Handle: RePEc:arx:papers:physics/0507035
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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. 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.
    5. 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.
    6. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
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    1. 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.
    2. 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.
    3. Luca Agnello & Ricardo M. Sousa, 2014. "How Does Fiscal Consolidation Impact on Income Inequality?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(4), pages 702-726, December.
    4. 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).
    5. 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.
    6. 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.

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