Income distribution dependence of poverty measure: A theoretical analysis

Amit K. Chattopadhyay and Sushanta Mallick ()

Physica A: Statistical Mechanics and its Applications, 2007, vol. 377, issue 1, 241-252

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.

Keywords: Poverty; Inequality; Income distribution; Consumption deprivation; Inflexion point (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Related works:
Working Paper: Income Distribution Dependence of Poverty Measure: A Theoretical Analysis (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:377:y:2007:i:1:p:241-252

DOI: 10.1016/j.physa.2006.10.103

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