Abstract. The way poverty is measured is important for an understanding of what has happened to poverty as well as for anti-poverty policy evaluation. Sen’s (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should satisfy certain properties or axioms and the desirability of a poverty measure should be evaluated by these axioms. During the last two decades, many researchers have adopted the axiomatic approach pioneered by Sen to propose additional axioms and develop alternative poverty measures. The objective of this survey is to provide a clarification on the extensive literature of aggregate poverty measures. In this survey, we first examine the desirability of each axiom, the properties of each poverty measure, and the interrelationships among axioms. The desirability of an axiom cannot be evaluated in isolation, and some combination of axioms may make it impossible to devise a satisfactory poverty measure; some axioms can be implied by other axioms combined and so are not independent; some others are ad hoc and are disqualified as axioms for poverty measurement. Based on the interactions among axioms, we identify the ‘core ’ axioms which together have a strong implication on the functional form of a poverty measure. We then review poverty measures that have appeared in the literature, evaluating the interrelationships among different measures, and examining the properties of each measure. The axioms each measure satisfies�violates are also summarized in a tabular form. Several ‘good ’ poverty measures, which have not been documented by previous surveys, are also included.

We consider hypothesis testing in a context where several populations satisfy a discretized version of the Lorenz curve ordering. Using Beach and Davidson's (1983) results on the asymptotic distribution of Lorenz curve ordinates, we reparametrize the model as a multivariate inequality testing problem. We introduce distance test statistics and derive their asymptotic distribution. We also discuss and extend other testing procedures currently available in the literature, and compare their relative performance in a Monte Carlo study. Two brief examples on inequality comparisons across regions and across time conclude the paper. 1 0 1 2 0 1 2 m m H m H m H m H H H without any specific assumption Lorenz ordering null alternative nested hypotheses The Lorenz curve is one of the most frequently used descriptive devices for depicting the inequality in the distribution of income or wealth in a society. Since Kolm's (1969), Atkinson's (1970) and Dasgupta, Sen and Starrett's (1973) papers, t...

Abstract: Rural households have been suspected to rely heavily on goods and services freely provided by environmental resources. However, there has been no adequate quantitative analysis of this issue due to a lack of appropriate household data sets encompassing economic and environmental data. We use a purpose-collected 213 household data set from rural Zimbabwe to investigate the impact of incorporating this missing source of household welfare on quantitative analysis of the measurement and causes of rural poverty and inequality. Incorporating environmental income in the household accounts results in dramatic and significant reductions in measured poverty, 50 percent or more over income as conventionally measured. Environmental income is also strongly and significantly equalising, bringing about roughly a 30 percent reduction in measured inequality. So access to commons resources has a substantial impact on poverty and inequality. However, including the value of environmental utilisations leaves analysis of the causes of rural differentiation unchanged: these resources do not alleviate the poverty trap.

Interest in economic mobility stems largely from its perceived role as an equalizer of opportunities, though not necessarily of outcomes. In this paper we show that this view leads very naturally to a methodology for the measurement of social mobility which has strong parallels with the theory of progressive taxation. We characterize opportunity–equalizing mobility processes, and provide simple criteria to determine when one process is more equalizing than another. We then explain how this mobility ordering relates to social welfare analysis, and how it di¤ers from existing ones. We also extend standard indices of tax progressivity to mobility processes, and illustrate our general methodology on intra- and intergenerational mobility data from the United States and Italy.

Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schur-concavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schur-concave functions, which are the class of functions consistent with the so-called Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schur-concave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.

recherche of Université de Sherbrooke. Abstract: This paper extends the previous literature on the ethical links between the measurement of poverty, social welfare and inequality. We show inter alia, how, when the range of possible poverty lines is unbounded above, a robust ranking of absolute poverty may be interpreted as a robust ranking of social welfare, and a robust ranking of relative poverty may be interpreted as a robust ranking of inequality, and this, for any order of stochastic dominance.

The constrained egalitarian solution of Dutta and Ray (1989) for TU-games is extended to asymmetric cases, using the notion of weight systems as in Kalai and Samet (1987, 1988). This weighted constrained egalitarian solution is based on the weighted Lorenz-criterion as an inequality measure. It is shown that in general there is at most one such weighted egalitarian solution for TU-games. Existence is proved for the class of convex games. Furthermore, the core of a postive valued convex game is covered by weighted constrained egalitarian solutions.

What is the best way to reward innovation? While prizes avoid deadweight loss, intellectual property screens out projects generating low consumer surplus per unit sold. We build a model that formalizes this trade-off and develop tools for solving the resulting multidimensional screening problem. Optimal policy generally calls for some market power but never full monopoly pricing. The appropriate degree of market power is determined by a value-weighted average of the innovation supply elasticity multiplied by the log-variance of innovation quality. This quantifies the value of the materialistic genius long associated with entrepreneurship, opening it to empirical calibration. Our results also apply to the pricing of platforms and public infrastructure.

We propose graphical methods to determine whether commodity-tax changes are “socially efficient”, in the sense of improving social welfare or decreasing poverty for large classes of social welfare and poverty indices. We also derive estimators of critical poverty lines and economic efficiency ratios which can be used to characterize socially-efficient tax reforms. The statistical properties of the various estimators are derived in order to make the method implementable using survey data. The methodology is illustrated using a recently-proposed reform of

The Kuznets curve postulates a dynamic relationship between growth and income inequality for a given economy. These two aggregate phenomena are linked through compositional changes in individual characteristics when self-selection is constrained by personal wealth. This paper attempts to identify the crucial characteristics associated with this dynamic relationship, by studying the evolution of the income distribution in Thailand between 1976 and 1996, during which the economy experienced strong growth with diminution of poverty, but with a rapid increase in income inequality. Applying comprehensive decomposition analyses to the data from the Thai Socio-Economic Survey, this paper shows that growth and income distribution dynamics were closely related to an expansion of education and credit, and to an occupational transformation. These three factors account for 39 percent of the average income growth, 39 to 54 percent of poverty reduction depending on the poverty index, and 53 percent of increase in inequality. Each of these factors contributed to growth by a similar magnitude. However, the expansion of education and credit was concentrated among wealthy households and increased inequality while the transformation of occupation occurred mainly among middle class and reduced poverty.