THE INCOME UNIT AND THE ANATOMY OF INCOME DISTRIBUTION*

This paper focuses on a neglected aspect of the treatment of the income unit in the construction of size distributions of income. If the size distribution is to be an indicator of the distribution of economic welfare, and if the economic welfare of each individual in society is to count equally, then conventional distributions are inconsistent with individualistic welfare functions. We estimate size distributions with each person's welfare weighted equally, and contrast these results with those weighting each household unit's welfare equally. The choice of weights is shown to affect both the level and the trend in income inequality.     

Measurement error in models of welfare participation

We consider the problem of modeling welfare participation when measurement error may affect simulated welfare entitlement. We identify a flaw in past implementations of the ML approach and develop a more appropriate ML approach. A model of welfare participation is estimated for British pensioners, linking the probability of participation to the value of benefit entitlement, incorporating the nonlinear rule relating entitlement to the household's income and financial assets. The model is used to evaluate the claim costs incurred by participants. When we allow for measurement errors in income and assets, estimated claim costs are substantially reduced.     

A COMPARISON OF DISTRIBUTIONS OF ANNUAL AND LIFETIME INCOME: SWEDEN AROUND 1970.

The concern with income distribution has always mainly existed because of a concern with individuals' economic welfare. In recent years, the question has arisen whether the distribution of annual income—the distribution most often studied—is the best proxy for the distribution of economic welfare. Other measures, such as lifetime income, have been proposed instead.
The paper starts with a discussion of how to define and measure the distribution of lifetime income. By using a simulation model, which partly consists of estimated functions and partly of tax functions taken directly from tax laws, distributions of lifetime income, variously defined, are then constructed. These distributions are compared with each other, and with distributions of annual income. The simulations indicate that the distribution of lifetime income is considerably less unequal than the distribution of annual income. Whether inheritances are included or not seems to be of no importance for the inequality of lifetime income. If, on the other hand, we include the value of leisure time in lifetime income, inequality increases by about 10–15 percent. Distributions of income after tax have Gini coefficients which are approximately 25 percent less than the Ginis for the before-tax distributions. We thus find that the picture of inequality we get is very much dependent on which income concept we use.     

A POSITIVE AND A NORMATIVE THEORY OF INCOME DISTRIBUTION

A positive theory of income distribution based on assumptions concerning the supply of and demand for each type of productive service is presented. The demand function of the organizers of production may be derived from the maximization of profits with the income scale and the production function as restrictions. A normative theory based on the maximization of a social utility or welfare function is also considered. In the normative theory, production functions and balance equations (some representing compartmentalization of factor markets) are introduced as restrictions and again an income scale results, this time maximizing social welfare. Empirical testing is also considered. The positive theory was developed in part to take into consideration the fact that personal income distributions can reasonably well be described by log normal distributions, and that skill parameters are often normally distributed. Limited testing of the influence of wealth, intelligence, education, and sex suggest that these account for only a small part of the variance in the income distribution. This suggests the need for further research.     

Productivity Dispersion and Measurement Error

Several reasons have been put forward to explain the high dispersion of productivity across establishments: quality of management, different input usage and market distortions, to name but a few. Although it is acknowledged that a sizable portion of productivity dispersion may also be due to measurement error, little research has been devoted to identifying how much they contribute. We outline a novel procedure for identifying the role of measurement error in explaining the empirical dispersion of productivity across establishments. The starting point of our framework is the errors-in-variable model consisting of a measurement equation and a structural equation for latent productivity. We estimate the variance of the measurement error and subsequently estimate the variance of the latent productivity variable, which is not contaminated by measurement error. Using Norwegian data on the manufacture of food products, we find that about one percent of the measured dispersion stems from measurement error.     

Averaging Income Distributions

Various inequality and social welfare measures often depend heavily on the choice of a distribution of income. Picking a distribution that best fits the data involves throwing away information and does not allow for the fact that a wrong choice can be made. Instead, Bayesian model averaging utilizes a weighted average of the results from a number of income distributions, with each weight given by the probability that a distribution is ‘correct’. In this study, prior densities are placed on mean income, the mode of income and the Gini coefficient for Australian income units with one parent (1997–8). Then, using grouped sample data on incomes, posterior densities for the mean and mode of income and the Gini coefficient are derived for a variety of income distributions. The model‐averaged results from these income distributions are obtained.     

Bivariate income distributions for assessing inequality and poverty under dependent samples

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.     

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.     

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.     

Bayesian estimation of social welfare and tax progressivity measures

This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available. First version received: August 2000/Final version received: July 2001 RID="*" ID="*"  This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We should like to thank Bill Griffiths and two referees for comments on an earlier draft.     

Fuzzy Chronic Poverty: A Proposed Response to Measurement Error for Intertemporal Poverty Measurement

A number of chronic poverty measures are now empirically applied to quantify the prevalence and intensity of chronic poverty, vis‐à‐vis transient experiences, using panel data. Welfare trajectories over time are assessed in order to identify the chronically poor and distinguish them from the non‐poor, or the transiently poor, and assess the extent and intensity of intertemporal poverty. We examine the implications of measurement error in the welfare outcome for some popular discontinuous chronic poverty measures, and propose corrections to these measures that seeks to minimize the consequences of measurement error. The approach is based on a novel criterion for the identification of chronic poverty that draws on fuzzy set theory. We illustrate the empirical relevance of the approach with a panel dataset from rural Ethiopia and some simulations.     

HOW DO EUROPEANS EVALUATE INCOME DISTRIBUTIONS? AN ASSESSMENT BASED ON HAPPINESS SURVEYS

The purpose of this paper is to measure the evaluation of income inequality by European citizens. Starting from the concept of a social welfare function defined on income distributions the paper estimates the degree and nature of inequality aversion of Europeans. It uses subjective well-being (SWB) as an empirical measure of welfare and estimates how SWB is related to average income and measures of income inequality (from an appropriate class). The estimated relationship is used to determine those inequality measures which qualify as proper representations of people's inequality aversion.     

Welfare analysis of tax reforms using household data

This paper discusses a methodology for calculating the distribution of gains and losses from a policy change using data for a large sample of households. Estimates are based on the equivalent income function, which is money metric utility defined over observable variables. This enables calculations to be standardised and a computer program to compute the statistics presented in the paper is available for a general demand system. Equivalent income is related to measures of deadweight loss, and standard errors are computed for each of the welfare measures. An application to U.K. data for 5,895 households is given which simulates a reform that involves eliminating housing subsidies.     

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.     

Measuring the Welfare Effects of Price Changes: A Convenient Parametric Approach

This paper shows how compensating and equivalent variations, and the equivalent income, resulting from a set of price changes can be calculated. A linear expenditure system is estimated for each of a range of total expenditure groups using cross-sectional budget data. The measures of welfare change can be used to determine the effect on the welfare of individuals in different income groups. Alternative social welfare functions can be used to evaluate the resulting distribution of equivalent income. The parametric approach is particularly useful where few data are available     

Multidimensional Inequality Across Three Developed Countries

This paper produces comparable estimates of multidimensional inequality for the U.S., Germany, and Australia. Two alternative approaches with differing interpretations are employed. The first method projects all facets of welfare onto a single variable which is then analyzed using standard univariate techniques. The second approach establishes equivalent‐income distributions that would lead to an equalization of welfare, such that the difference between this counterfactual and the true income distribution can be measured. This difference is then interpreted as the degree of income redistribution required to offset welfare inequality. Using data on permanent incomes, health scores, years of education, and leisure times, we observe much higher levels of inequality in the U.S. than in Germany or Australia. Our results are highly statistically significant and hold over a large variety of weighting specifications.     

Multidimensional welfare distributions: empirical application to household panel data from Vietnam

This article explores the empirical application of theoretical multidimensional welfare distribution analysis techniques to real household welfare distributions. The article operationalizes recent conceptual developments in multidimensional distribution theory and assesses their usefulness for the measurement of multidimensional household inequality. The results strongly highlight the importance of bringing nonmonetary aspects of household welfare into the forefront of inequality analysis. Agreement over the various approaches to the measurement of multidimensional inequality entails, however, nontrivial decisions that may limit the practical usefulness of these measures. We suggest that the use of multidimensional inequality ranges and the application of restrictive dominance criteria to multidimensional welfare distributions may open significant scope for further developments in the empirical analysis of multidimensional inequality.     

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.     

HOW MISLEADING ARE INCOME DISTRIBUTIONS?

Starting from the proposition that economic welfare is better measured by the capitalized value of expected future income at age 18 than by income at a point of time, the present paper explores the bias introduced in comparison of earnings and income distributions.
The earning distribution chosen for study is that for males in 1959 in the United States. It is shown that earnings distributions are biased and therfore can be considered highly misleading in most comparisons unless the comparison involves two groups with identical age distributions and identical distributions of earnings over the working life of earners.
Further, a most striking effect can be discerned in comparing the earnings to the present value distributions by educational level. As one moves up the educational ladder, the within-group distribution of lifetime income becomes more and more equal, in sharp contrast to the findings for the distribution of earnings at a point in time.
The result are sufficiently interesting and striking to warrant further studies of distributions of present value of lifetime expected earnings (and income).     

DEMOGRAPHIC CHANGE AND INEQUALITY IN THE SIZE DISTRIBUTIONS OF LABOR AND NONLABOR INCOME

This paper utilizes a joint distribution model of labor and nonlabor income that allows us to analyze the impact of demographic change in the U.S. on the marginal distributions of these two income components over time. The beta distribution of the second kind is the hypothetical statistical distribution used in this study to approximate the observed income graduation. This distribution is sum stable which allows us to compare and contrast the marginal distributions in a consistent manner, a property most hypothesized functional forms of income distribution do not possess. We are in effect using a hyperparameter model to do our estimation. We examined the impact of changes over time in labor force participation and population on the marginal distributions of labor and nonlabor income. We disaggregated the variables by sex and age cohorts and found that changes in the age distribution and in the labor supply behavior of women in particular has had a significant effect on the marginal income distributions over time. We also found that the results vary when we examined overall changes in the labor force participation rate vis a vis changes in women's labor force participation separately. The findings are consistent for both income components.