Dual interpersonal comparisons of utility and the welfare economics of income distribution

Interpersonal comparisons can be of utility levels and/or of utility differences. Comparisons of levels can be used to define equity in distributing income. Comparisons of differences can be used to construct an additive Bergson social welfare function over income distributions. When both utility levels and utility differences are compared, one can require the constructed additive Bergson social welfare function to indicate a preference for more equitable income distributions. This restricts the form of both the individual utility functions and the optimal distribution of income. The form of these restrictions depends on whether the levels and differences of the same utility functions are being compared.     

Social welfare and the unrepresentative representative consumer

If, for all prices, income distribution is optimal for a planner with a social welfare function, then aggregate demand is the same as that of a single “representative consumer” whose preferences over aggregate consumption are the same as the planner's. This paper shows that the converse is false. Aggregate demand may be the demand function of a representative consumer although the income distribution is not optimal for any social welfare function. The representative consumer may be Pareto inconsistent, preferring situation A to B when all the actual consumers prefer B to A. We give conditions under which existence of a representative consumer implies that the income distribution satisfies first order conditions for optimality. Satisfying the first order optimality conditions for an additively separable social welfare function is essentially equivalent to aggregate demand for every pair of consumers having a symmetric Slutsky matrix.     

A SOCIAL WELFARE VIEW OF THE MEASUREMENT OF INCOME EQUALITY

Economists' use of the term "equality" in reference to a distribution of incomes has historically been in the sense of a consensus for some statistical characteristic(s) of the distribution rather than a firm concept of equality. Of course such a concept rests on appropriate welfare assumptions about income and its distribution, assumptions which, for the most part, have been left implicit (and unknown) in discussions of income equality in the literature.
Our purpose in this paper is dual: first, we wish to discover an unambiguous, welfare-related equality measure. This we accomplish through suitable assumptions on a social welfare function. What is produced is an "index" of equality which describes the performance of a given distribution relative to the maximum welfare derivable from the total income it represents. The measure thus depends functionally on the welfare attributes of income, something which in reality we know little about.
This impasse leads us to inquire into the sensitivity of the index over specifications of the welfare function, which is done by comparing equality ranks for the states of the United States for 1960 under various functional forms and among curves within a given form. As an interesting secondary issue, the performance of traditional equality measures is tested relative to the welfare-oriented index to discover implications about their welfare content.
It is found that the equality index is, in certain ranges for the welfare function, insensitive to its specification. The findings lead directly to conclusions concerning traditional equality measures, their usefulness in correctly accounting for equality differences among alternative income distributions and, concomitantly, their implicit welfare inputs.     

A Class of Social Welfare Functions That Depend on Mean Income and Income Polarization

A well‐established strategy for evaluating alternative income distributions is based on the use of an abbreviated social welfare function that depends only on mean income and an inequality index. In keeping with this literature, we study the existence of social welfare functions that can be written as a trade‐off between efficiency and income polarization. This paper proposes a class of social welfare functions consistent with the Esteban and Ray, and Duclos, Esteban and Ray income polarization indices. For this result, we expand the domain for personal preferences to incorporate not only own income but also the well‐being of others. In addition, we link our proposal to the literature on relative satisfaction. The approach is illustrated by an empirical application using the CPS database for the United States in the period 1991–2010.     

Comparisons of heterogeneous distributions and dominance criteria

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of A.B. Atkinson and F. Bourguignon (1987) [3] to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the planner?s judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the household?s utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.     

Pareto and contemporary economic theory

This paper provides explanations for Pareto’s apparently contradictory approach to demand theory in simultaneously insisting that measurability of utility is not needed to explain the equilibrium of consumers in competitive markets, and embracing concavifiability and thus measurability of utility when this implies restrictions on consumers’ behavior such as the law of demand. It also treats his method of calibrating an aggregate demand function by employing his law of income distribution, so as to reproduce “Gregory King’s law”. Finally, some disputed issues are dealt with concerning the nature of Pareto’s contributions to welfare economics. (JEL: B13, D11, D60).     

Income Mobility, Inequality and Social Welfare

It is often argued that an observation of rising annual income inequality need not have negative normative implications. The argument is that if there has been a sufficiently large simultaneous increase in mobility, the inequality of income measured over a longer time period can be lower despite the rise in annual inequality. In this paper, it is shown by example that if normative implications are drawn from a standard social welfare function, the set of circumstances put forward in the above argument are not sufficient to guarantee that social welfare will improve. The reason is that even though rising mobility does reduce longer term inequality, it also increases the variability of income profiles over time and the latter has a detrimental social welfare effect. Hence, there are two types of mobility: one which reduces inequality (regression to the mean), but another that increases inequality (relative movements uncorrelated with incomes). Further, if individuals' aversion to income variabiltiy is sufficiently larger than the social welfare judge's aversion to inequality, then an increase in mobility, no matter how large, cannot offset the negative normative effect of rising annual inequality.     

The Distributional Incidence of Growth: A Social Welfare Approach

This paper provides a normative framework for the assessment of the distributional incidence of growth. By removing the anonymity axiom, such framework is able to evaluate the individual income changes over time and the reshuffling of individuals along the income distribution that are determined by the pattern of income growth. We adopt a rank dependent social welfare function expressed in terms of initial rank and individual income change and we obtain partial and complete dominance conditions over different growth paths. These dominance conditions account for the different components determining the overall impact of growth, that is the size of growth and its vertical and horizontal incidence. We then provide an empirical application for Italy: this analysis shows the distributional impact of the recent economic crisis suffered by the Italian populaltion.     

Exact welfare measurement for double-log demand with partial adjustment

This paper demonstrates that a double-log demand with partial adjustment (DLPA) is consistent with the theory of consumer utility maximization. It offers an approach for calculating the compensating variation (CV), the exact welfare effect of a change in a price series when a DLPA is employed. Significant bias may result if the CV is based on a static double-log demand when a DLPA function is appropriate. We revisit a recent study of demand for gasoline in the U.S., finding that the CV based on the static double-log would overstate the welfare effect of a 6-month temporary gasoline tax by 7.5%.     

Economic inequality and paretian welfare economics: Some insinuating questions

This paper examines the academic soundness of the Pareto welfare criterion as a normative rule for evaluating alternative economic inequality scenarios and suggests that the criterion has several weaknesses, which weaken its usefulness. First, the Pareto principle is of limited use in the inequality debate because labor markets hardly satisfy the conditions of perfect competition, the pivotal assumption of the theory. Second, the proposition that competitive equilibrium leads to the “common good” of society is difficult to defend. Third, the Paretian welfare economics barely answers the questions society demands, because perfect competition does not guarantee fairness in the determination of relative prices in the initial situation of income distribution. Fourth, in the distribution theory, the marginal productivity principle determines the rewards to the factors of production. If we assume that rent, wage and interest incomes are determined by this theory, then questions arise about how profits, the potentially huge surpluses generated by the businesses, are distributed. Fifth, income distribution, being a public policy topic, is a political issue. However, Pareto's primary motivation in formulating the principle was to alienate the income distribution debate from political and policy discourses. Finally, by invoking the Pareto principle, economists are in fact avoiding the real issues of the public debate on personal distribution of income. Personal income distribution truly refers to division of income generated by a group of people working together and therefore, ought to be analysed with reference to the sector of employment. Thus, Tommy Franks' earning should be compared with that of a private, while an ordinary worker's salary should be compared with that of the CEO. History testifies that the public earning structure is much more equitable than that of the private sector. This poses a very serious question: Which earning structure reflects improvement in social welfare: public or private?     

Salience and social choice

The axioms of expected utility and discounted utility theory have been tested extensively. In contrast, the axioms of social welfare functions have only been tested in a few questionnaire studies involving choices between hypothetical income distributions. In a controlled experiment with 100 subjects placed in the role of social planners, we test five fundamental properties of social welfare functions to determine the efficacy of traditional social choice models in predicting social planner allocations when presented with choice sets designed to test the axioms of the theory. We find that three properties of the standard social welfare functions tested are systematically violated, producing an Allais paradox, a common ratio effect, and a framing effect in social choice. We find support for scale invariance and a preference for tail-increasing transfers. Our experiment also enables us to test a model of salience-based social choice which predicts the systematic deviations and highlights the close relationship between these anomalies and the classical paradoxes for risk and time.

     

Size and distribution of incomes as determinants of social welfare

The paper is concerned with the relationship between the inequality of income distributions and the social welfare they imply. Starting-point is an ordering of income distributions in terms of inequality. Based on explicit value judgments about the trade-off between size and distribution of incomes an ordering in terms of social welfare is derived. The welfare functions representing this ordering allow a size-distribution split up. It is shown that the procedure can be reversed. This ordinal approach is considerably more flexible and less arbitrary than most methods proposed in the literature.     

Consumer welfare from publicly supplemented private goods: age and income effects on demand for health care

In spite of major advances in the theoretical, positive and normative, literature analysing the welfare implications of public provision of private goods, empirical investigation is often limited to contingent valuation studies, for example, of health care programmes. In this article we argue that when a market for a (subsidised or free of charge) publicly provided good exists, a consumer demand approach can be used to construct a money metric of welfare corresponding to the consumption of public provision. We illustrate this approach in investigating age and income effects on household demand for health care in Cyprus, where free public provision is not universal and those entitled to it often resort to private supplementation. Our findings suggest that the money metric of welfare, which consumers attach to free access to publicly provided health care, varies with age and to a lesser extent with household income.     

Interdependent welfare functions and optimal income distribution

The relationship between income distribution and social welfare is empirically analyzed, while explicitly allowing for the interdependence of individual welfare functions. The social welfare function is taken to be an additive function of individual welfare functions of income (WFIs). On the basis of Dutch data it is found that under certain conditions (such as absence of effects of income redistribution on productivity) an equal distribution of incomes is suboptimal. The interdependence of WFIs appears to have a pronounced effect on policy conclusions concerning the desirability of income redistribution vis-à-vis economic growth.     

Hoglex Demand Systems and Welfare Policy in Major Asean Developing Countries: A Bayesian Analysis Using Expenditure Unit Records

The HOGLEX demand system (Tran Van Hoa (1983, 1985)) is integrable and flexible in the sense that it is based on utility maximization and encompasses most other well-known demand systems (e.g., LINEX, AIDS) in the literature on consumer behaviour (Laitinen et al. (1983)). HOGLEX studies to date have been based on conventional OLS or MLE methods and panel aggregate income and price data, and restricted to investigating consumption patterns. The paper elaborates on three important subsets of the HOGLEX demand system and, using household expenditure unit records from two major ASEAN developing countries (i.e., Thailand and the Philippines), estimates by the Bayesian method these subsets for 20 socio-demographic cohorts, and discusses their substantial implications in social security and welfare policy analysis. We also estimate the models in the more practical case of measurement errors in total expenditure and compare the results with those without measurement errors.

     

POSSIBLE SOCIAL POLICY DEVELOPMENTS AND CORRESPONDING STATISTICAL REQUIREMENTS

Production maximization, together with an appropriate distribution of income and wealth, can no longer be considered as the exclusive objective of socio-economic policies. Economic and social life is accompanied by numerous hardships, constraints and damages which demand to be minimized. Combining these dual aims is not easy as no single model has yet been set up taking into account all these inter-relations. However, one may try to reduce the uncertainty about the statistical material that could be required for decision-making in this new context.     

A metric for assessing the “goodness” of income distributions and the effect of price changes

Social welfare evaluation depends in part on value judgments as to income distribution. This paper proposes a metric for assessing the “goodness” of particular income distributions. That metric is then used to examine the effect of price changes on the “goodness” of a given distribution. Consider an increase in the price of a commodity that is disproportionately consumed by households with incomes that are high relative to the preferred income distribution. One naturally supposes that such a price increase will make the given income distribution appear less bad. Surprisingly, this is not invariably the case.     

Tax policy in the presence of emigration

This paper investigates the relationship between utilitarianism and horizontal equity in models of income taxation in particular and self-selection in general. An example involving well-behaved individual preferences is constructed in which a maximization of a utilitarian social welfare function leads via income taxation to horizontal inequities. Sufficient conditions for utilitarianism to bring horizontal equity are derived. The results are applied to the question of whether income tax credits are an appropriate way to treat differences in family size.