Frank A. Cowell

Robustness Properties of Inequality Measures

Inequality measures are often used to summarize information about empirical income distributions. However the resulting picture of the distribution and of changes in the distribution can be severely distorted if the data are contaminated. The nature of this distortion will in general depend upon the underlying properties of the inequality measure. This issue is investigated theoretically using a technique based on the influence function, and the magnitude of the effect is illustrated using a simulation. Both direct nonparametric estimation from the sample, and indirect estimation using a parametric model are considered; in the latter case the application of a robust estimation procedure is demonstrated. The results are applied to two micro-data examples. Copyright 1996 by The Econometric Society.

Inequality measurement: An axiomatic approach

The theory of inequality measurement is examined using some basic axioms which extend the Pigou/Dalton principle of transfers. From these basic axioms various inequality indices may be derived as an alternative to ad hoc methods, or to methods involving prior specification of a social welfare function. The key idea is the concept of ‘distance’ between two income shares. Conventional inequality indices are analysed in terms of their implied distance functions.

Parametric Equivalence Scales and Scale Relativities

The authors respond to J. Banks and P. Johnsons (1994) comment on Coulter et al. (1992) drawing on a more general discussion of parametric equivalence scale and scale relativity issues and new empirical results. The authors show that criticisms of their earlier work are unfounded. When the McClements scale is properly characterized, the scale does indeed provide lower estimates of poverty and inequality levels than most other scales. The authors reiterate their conclusion that relationships between scale relativities and inequality and poverty indices may be index-specific. Moreover, the picture about distributional trends may differ from that about levels. Copyright 1994 by Royal Economic Society.

Sampling variance and decomposable inequality measures

Abstract The purpose of this paper is twofold: (1) to draw together and interpret results on sampling variance of this important class of inequality measures and (2) to illustrate the way in which the bivariate nature of the underlying problem affects the estimates of inequality measures and their sample variances.

Tax evasion with labour income

Allingham and Sandmo’s (1972) classic paper on tax evasion set out a simple framework for looking at the effects of regular tax parameters and of the structure of penalties on the amount of tax-dodging carried out by a tax evader. Subsequent papers have enriched the basic model of individual behaviour’ and have attempted to adduce some empirical evidence,2 but with few exceptions the essential nature of the assumed underlying problem has remained the same: ‘How much income shall I reveal to the authorities in the face of the known penalties and the known possibility of getting caught? Whilst this approach is useful for some types of tax evasion by individuals, it is clearly inappropriate for others, such as the phenomenon of ‘working off the books’: rather than concealing a portion of a uniform lump of income that is undistinguished as to its source, the person cheats the government by taking one or more different jobs ~ either in addition to or as a replacement for his regular employment the income from which is administratively difficult to tax. This paper examines the implications of the possible diversity of form of the tax evasion problem for the analysis of the fundamental questions which Allingham and Sandmo addressed the effect of government instruments on the incentives to participate in legal and illegal work activities. To do this we must concentrate on one major development of the original model, namely that where income is endogenous. In effect we construct a particular version of the analysis of labour supply under uncertainty within which to

Generalized entropy and the measurement of distributional change

Abstract The analogy between information theory and income distribution analysis is exploited to derive a number of measures of distributional change. These include not only counterparts of the regular entropy measures, but also of the entire, rich ‘generalised entropy’ family. The paper analyses the properties of these measures, and in particular their performance in response to ‘independent’ transfers and to cases where an income transfer in the old distribution automatically produces a corresponding transfer in the new distribution. The relationship of such ‘functionally dependent’ transfers to a measure of tax progression is examined.

Tax evasion and inequity

Abstract A number of concepts of inequity are examined in a model that incorporates tax-enforcement parameters, personal resources, personal attributes, and perceived inequity. The role of risk aversion and its interaction with attitudes toward inequity, interaction with other tax evaders, and the means that each person has of influencing inequity are considered as determinants of individual tax-compliance decisions.

Poverty measurement with contaminated data: A robust approach

We examine the sensitivity of poverty indices to data contamination using the concept of the influence function, and demonstrate that an important commonly used subclass of poverty measures will be robust under data contamination. This is illustrated using simulations. In this respect poverty and inequality indices have fundamentally different robustness properties. We investigate both the case where the poverty line is exogenously fixed and where it must be estimated from the data.

Equivalence scales and inequality

At the heart of any distributional analysis there is the problem of allowing for differences in peoples non-income characteristics. We examine the role of standard equivalence scales in distributional comparisons and the welfare implications of the basis for constructing equivalence scales. We consider the use of alternative approaches that do not require the specification of a single scale and implement one of these in practical comparison of Spain and the UK.

Risk perceptions and distributional judgments

Abstract We examine the role of laboratory questionnaire-experiments and recent applied empirical research on attitudes in understanding the relationships between peoples perceptions of inequality and their perceptions of risk. We consider risk in three interpretations: ‘in vacuo’, in day-to-day life and in the original position.