Measures of downside risk

The paper characterizes a family of downside risk measures. They depend on a target value and a parameter reflecting the attitude towards downside risk. The indicators are probability weighted -order means of possible shortfalls. They form a subclass of the measures intro¬duced by Stone (1973) and are related to the measures proposed by Fishburn (1977). The axiomatization is based on some properties which are desirable and appropriate for the measurement of risk.

Linear Inequality Concepts and Social Welfare

The paper presents an abstract definition of linear inequality concepts leading to linearly invariant inequality measures and characterizes the class of linear concepts completely. Two general methods of deriving ethical measures are proposed. They imply an Atkinson-Kolm-Sen index and a new dual index reflecting the inequality of living standard. Then all separable social welfare orderings which generate linearly invariant measures are characterized. The measures are presented and their general properties discussed. Dual measures prove to be additively decomposable. Linear welfare orderings defined on rank-ordered income vectors are examined. They are consistent with all linear inequality and yield an inequality ordering for every concept.inequality concept, ethical inequality measures, decomposability, social welfare

Extending the cost function: A simple method of modeling environmental regulation

The paper shows that a variety of different scenarios in environmental economics can be modeled by one abstract concept, an extended cost function, which takes into account a firm's technological and regulatory constraints. It satisfies the usual properties of a cost function and reasonable properties with respect to the regulatory parameter. An extended cost function represents a simple unified approach which does not depend on the specific form of regulation and the way emissions are modeled.

On the definition of nonessentiality

Nonessentiality of a good is often used in welfare economics, cost-benefit analysis and applied work. Various definitions of this property are presented in the literature on public and environmental economics. This note clarifies their relationship.Preferences, nonessentiality

The Difficulty of Income Redistribution with Labour Supply

Two common principles in distributional analysis are that (i) a progressive transfer moves the Lorenz curve upwards, and (ii) progressive [neutral] taxation reduces [leaves unchanged] inequality. In order to establish these results it is currently assumed that the distribution of income is exogenously given. The relevance of these results is therefore limited in practice where incomes are determined by the working decisions of the agents in the economy. Considering a simple economy with two goods and two agents we indicate sufficient conditions for inequality in net income to decrease as a result of rich to poor transfers or progressive taxation. By means of simple examples we show that, when one incorporates labour supply responses, the fulfillment of these conditions is highly hypothetical and that everything can happen.Endogenous labour supply

Horizontal Equity and Progession when Equivalence Scales are not Constant.

Household needs must be taken into account when designing an equitable income tax. If the equivalence scale is income dependent it is not transparent how to achieve equity. In this paper we explore the question of horizontal equity and the implications for progression (vertical equity), when the equivalence scale depends on income level. In particular an 'equal progression among equals' criterion is articulated and shown to be achievable along with horizontal equity under specified conditions.

Inequality and Envy

Using a simple axiomatic structure we characterise two classes ofinequality indices - absolute and relative - that take into account "envy"in the income distribution. The concept of envy incorporated hereconcerns the distance of each person's income from his or herimmediately richer neighbour. This is shown to be similar to justiceconcepts based on income relativities.Inequality, envy, transfer principle.

Complaints and Inequality

Temkin (1986,1993) sets out a philosophical basis for the analysis of income inequality that provides an important alternative to the mainstream welfarist approach. We show that the Temkin principles can be characterised by a parsimonious axiomatic structure and we use this structure to derive a new class of inequality indices and an inequality ordering. This class of indices has a family relationship to well-known measures of inequality, deprivation and poverty. The ordering is shown to have properties analogous to second-order dominance results.Inquality, complaints, transfer principle.

Adjusting Incomes for Needs: Can One Avoid Equivalence Scales?

The aim of the paper is to provide guidelines in order to make meaningful comparisons of heterogeneous distributions when incomes are adjusted in order to accommodate differences in needs. We emphasize that the choice of the equivalent income function and the system of weights associated to the equivalent incomes affects significantly the conclusions to be drawn. Introducing simple but intuitively appealing normative conditions, we show that adjusting incomes by a scale factor and weighting the resulting equivalent incomes by the same factor -- as was proposed by Pyatt, ``Social evaluation criteria'', in C. Dagum and M. Zenga (Eds.), Income and Wealth Distribution, Inequality and Poverty, Springer-Verlag, 1990 -- does constitute the only consistent method of making comparisons of relative inequality and/or welfare across populations of heterogeneous households. When the focus is on comparisons in terms of absolute inequality, then lump-sum equivalent income functions and equal weights constitute the only admissible adjustment procedure.