Measurement of Poverty: Takayama Index Reconsidered

1996

The aim of this paper is twofold. The first is to illustrate that a poverty index can be derived from a decomposition of an appropriate inequality index. The advantage of decomposing an inequality index is that the decomposition supplies additional information that is useful for poverty measurement. The second purpose is to illustrate the kind of policy analysis that can be performed with a decomposed inequality index by decomposing the Gini coefficient into Sen's poverty index and other components. The methodology suggests an answer to the following question: Assume that a tax has been imposed on an expenditure item or an income source, what will be the impact on the components of the inequality index? The analysis is performed with data from Romania. D 2002 Published by Elsevier Science B.V. 0176-2680/02/$ -see front matter D 2002 Published by Elsevier Science B.V. PII: S 0 1 7 6 -2 6 8 0 ( 0 1 ) 0 0 0 6 9 -6 www.elsevier.com/locate/econbase *

1991

We propose a poverty measure that satisfies *a number of properties that make it sensitive to the level of absolute deprivation of the poor. These properties are often violated by several poverty measures discussed in the literature. The measure corresponds to a Cobb-Douglas social welfare function which has a number of egalitarian features.

The Economic Journal, 1981

When discussing the state of research on poverty and social security in Britain Atkinson (I977) pointed out that, in measuring the prevalence of poverty, attention has been focused upon the proportion of the population with an income below the poverty line. It is well known that as an index of poverty this has serious shortcomings-in particular, it is insensitive to how far below the poverty line the incomes of the poor fall. Alternative indices have been proposed: the United States Social Security Administration introduced the notion of poverty gaps (see Batchelder (I97I)), that is, the aggregate value of the difference between the incomes of the poor and the poverty line, while Sen (I976) has suggested that income inequality among the poor is also an important dimension of poverty. Atkinson (I977) therefore proposed that researchers experiment with a range of indices which incorporate such aspects of poverty, given the possibility that the measurement of poverty may be sensitive to the precise index employed. Beckerman (I979) has shown that the information content of poverty gaps very usefully supplements that provided by the aggregate incidence approach. However, to our knowledge, there has been no attempt in Britain to compute indices which take account of inequality among the poor. In this paper we hope to correct this omission, and in doing so comments will be offered on some proposed methods of incorporating such a consideration. A close examination of these has prompted us to propose two further indices which, although relying on the setting up of an alternative structure for analysing this problem, are firmly based on the approaches favoured in the existing literature. THE ECONOMIC JOURNAL [JUNE

Econometrica, 1984

2009

A particular scale-invariant index of poverty is subjected to careful analysis. This leads to a new perspective, not seen before, on the family of subgroup-consistent and scaleinvariant poverty indices. Parametric families of new poverty indices are presented which offer the analyst a degree of flexibility in the choice of transfer sensitivity and distribution sensitivity which has not been available before now.

1984

Review of Income and Wealth

Recent popular and professional writing on economic inequality often fails to distinguish between change in a summary index of inequality, such as the Gini Index, and change in the inequalities which that index tries to summarize. This note constructs a simple two class example in which the Gini Index is held constant while the size of the rich and poor populations change, in order to illustrate how very different societies can have the same Gini index and produce very similar estimates of standard inequality averse Social Welfare Functions. The rich/poor income ratio can vary by a factor of over 12, and the income share of the top one per cent can vary by a factor of over 16, with exactly the same Gini Index. Focussing solely on the Gini Index can thus obscure perception of important market income trends or changes in the redistributive impact of the tax and transfer system. Hence, analysts should supplement the use of an aggregate summary index of inequality with direct examination of the segments of the income distribution which they think are of greatest importance.

In this paper we discuss the axiomatic approach to poverty measures and propose a unified framework for the Sen indices of poverty intensity which shows an explicit connection between the indices and their common underlying social evaluation function. We also identify the common multiplicative decomposition of the indices that allows simple and similar geometric interpretations and easy numerical computation. These results are easy to understand and useful to policy makers in both developed and developing countries.

2003

This paper discusses various measures of poverty and inequality found in the literature. Inequality measures discussed include the range, the variance, the coefficient of variation, the standard deviation of logarithms, the Gini coefficient, Theil's Entropy measure and Atkinson's inequality measure. Of these the mean log deviation, the Theil index and the coefficient of variation have come to be known as the Generalised Entropy class of inequality measures. As far as poverty indicators are concerned the Foster-Greer-Thorbecke measures, a class of generalised decomposable poverty measures, have become very popular in the literature. The paper also discusses some Stata do-files that were written in order to calculate poverty and inequality measures, with application to the Income and Expenditure Survey data of 1995.

Review of Income and Wealth, 2000

Our aim in this paper is to show how recent developments in the theory and methods of poverty measurement can be applied to provide more accurate descriptions of poverty trends to the typical consumers of these statistics-policy analysts, policy-makers and their critics. Since Amartya Sen's (1976) classic critique of the "headcount" approach to poverty measurement, considerable progress has been made in constructing axiomatically-driven measures of "poverty intensity." These measures have had little influence outside the small world of experts who devised them largely because their mathematical representation has made their meaning obscure to potential users. We focus on the Sen-Shorrocks-Thon (SST) index and its elaboration by Osberg and Xu which provides the information contained in the index in a format that is easily accessible within traditional categories of poverty analysis. The SST index and its decomposition provide an analytical framework for discussing the underlying components of aggregate trends that allows for unambiguous answers to the usual policyrelated questions concerning the components of change as well as their magnitude and direction.