Advances in Econometrics, Income Distribution and Scientific Methodology

On several occasions throughout the years I had the pleasure of discussions with Camilo Dagum. They always concerned the state of our common discipline, economics, of which the two of us were not always criticizing the same theoretical developments. But we shared a common interest for quantitative methods and for their role in the advancement of economic knowledge. This book gives me an excellent opportunity for looking again into the methodology of that role. In order to avoid long repetitions with what I already wrote elsewhere on the same broad issue, I shall more precisely consider here the interplay between the systematic use of microeconomic data and the continual respecification of models of aggregate phenomena.

A continuing interest of Camilo Dagum has been with the methodology of economics and of econometric modeling as seen in Dagum (1968), (1985) and (1989). Since the appearance of that work two areas of possible importance that have been developed concern the re-emergence of deterministic processes and relationships and the new, growing emphasis on the evaluation of theories and models. In this essay I will discuss these topics and their inter-action. It builds on the work by Camilo but I will not attempt to discuss it, as mainly I would be taken too far from my theme, although into interesting and important topics concerning methodology.

The presence of fixed and stochastic parameters in a mixed linear regression model has been dealt with for the case where the stochastic parameters follow a stationary process. The solution is given either by Generalized Least Squares (e.g. Rao, 1965, p. 192) or by a recursive state space estimation procedure such as the Kalman filter and smoother (e.g. Sallas and Harville 1981). The estimation of non-stationary stochastic parameters has been mainly approached in the state space framework, either as an initial condition problem (see among others, Ansley and Kohn, 1985, 1989; Kohn and Ansley, 1986; Bell and Hillmer, 1991 and De Jong, 1989, 1991); or as a hierarchical model with “fixed” effects in the hierarchy given a flat prior distribution (see Sallas and Harville, 1981, 1988; Tsimikas and Ledolter, 1994).

The subject of this paper is some computational aspects of macroeconometric models, over a period of roughly sixty years that such models have been in existence. Ironically, my presentation will be mainly in literary terms, with no proofs and only passing references to algorithms.

Measuring informativeness of data or news is particularly important as it quantifies the amount of “learning”. This is central to scientific progress as well as to assessing the direction and value of “information” and technologies. As is the case with all “indices”, the desirability of any measure of information depends on at least two considerations: First is the inference/investigative technique that would utilize the information. The second is the distributional characteristics of the information which is to be summarized. As examples, least squares techniques are, by design, incapable of utilizing any information other than the “variation” in a distribution/data. And, the Gaussian distributions/data are entirely characterized by the first two moments; any index will thus be a function of the same moments. These two considerations need to be borne in mind when contrasting entropy and variance as indices of informativeness or uncertainty.

Whenever a neoclassical direct utility function is in close (even perfect) agreement with consumer behavior data, there is always an alternative direct utility function that agrees at least as closely with the same data. Existence of this equally well (if not better) fitting alternative to such a neoclassical direct utility function has considerable significance for the rational conduct of potential problem analysis in the policymaking arena. [We shall give an important example later in this note.] However the nonuniqueness of the neoclassical utility function on empirical data is rarely mentioned in the literature of economic theory, it appears to be little understood among economists generally, and most doctoral students are never told about it in advanced economic theory courses.

The aim of this paper is to examine the properties and then disaggregate a social welfare function (SWF) by subgroups of population. The functional form of the SWF was axiomatically derived by Sen and has recently been given a utilitarian foundation by Dagum. Since the function contains the Gini coefficient as the inequality parameter, it could not be disaggregated by subgroups of population in the conventional manner. In this paper, using an alternative method of subgroup decomposition of the Gini coefficient recently suggested by Podder (1993), the SWF has now been disaggregated. Among other things, with the application of this method it is now possible to identify the disadvantaged groups by their relative shares in total welfare. However, the main use of the method is probably the determination of the effect of economic growth in specific subgroups on total social welfare of the society as a whole. The method has been empirically illustrated with Australian Household Expenditures data of 1988–89 . The subgroups are based on the geographical region of residence. The effect of a percentage change in income of a specific group on total welfare is also computed. This information is crucially important in a variety of social decision making situations including optimum social security decisions and cost benefit analysis.

The aim of studies of the welfare change imposed by actual or hypothetical price changes is to provide a money measure of the change in welfare facing different types of individual. In public finance contexts the price changes are considered to arise from the imposition of, or changes in, commodity and income taxes. This gives rise to the concept of the excess burden resulting from taxation, reflecting the excess of the money measure of welfare change over the tax revenue, in well-specified situations. There is a corresponding concept of the marginal excess burden arising from a change in taxation. It may also be required to provide an overall evaluation of a change in taxation, using a specified social welfare, or evaluation function that reflects the value judgements of the judge.

Two ethical norms, vertical equity and horizontal equity, are generally applied to assess the fairness and distributive justice of a tax system. Due to tax induced rerankings controversy surrounds the exact meaning and joint empirical application of the two equity concepts. This paper adopts Aronson and Lambert’s (1994) recently proposed measure of horizontal equity and demonstrates that overall or “net vertical equity” can be additively decomposed into three separate, distinct and quantifiable terms — “vertical equity”, “tax rerankings”, and “post-tax income rerankings”. The latter two terms involve vertical inequities that are embedded into an otherwise progressive tax system. To separate the two inequities from net vertical equity we make use of the relative deprivation interpretation of the Gini coefficient and decompose the redistributive effect of taxes into four distinct terms, three of which measure and decompose vertical equity and inequity. To illustrate the decomposition method we use individual income tax return data and measure the effects of the Tax Reform Act of 1986 on horizontal inequity, vertical equity, tax-rerankings, and post tax income rerankings. Horizontal inequity is measured using the recently developed procedure of Aronson and Lambert (1994). The remainder of the redistributive effect is decomposed using the new procedures developed in this paper.

This paper is about the structure of income inequality comparisons. The analysis of income inequality is, of course, essentially about the sharing-out of a “cake” or “pie” and some of the elementary principles which apply to comparisons of alternative cake-divisions are usually assumed to be well known. However, except in the very simplest cases, more is required than these elementary principles. For inequality analysis to have economic meaning, or for it to be used as a basis for rational social decisions, it is important that judgments of alternative share-outs should conform to some sort of structure. We examine the issues that arise in connection with this structure and employ a new experimental test to investigate a specific hypothesis about the relationship between income levels and inequality orderings.

Much of the work that has been carried out since the early 1970s on the properties of alternative inequality measures has been concerned with the relationship between the inequality measures and basic value judgements. In the empirical measurement of inequality and in tax policy simulation analyses, such as the calculation of optimal tax rates, the usual approach is to explore the implications of using alternative value judgements. For example, in the context of the Atkinson (1970) inequality measure, this involves using a range of values of constant relative inequality aversion. The idea is to report results that are capable of representing a reasonably wide diversity of distributional views, so that different readers may formtheir own conclusions.

This paper has attempted to derive some implications from Dagum’s (1997) recent proposal for a new interpretation of the decomposition of the Gini inequality index by population subgroups. His approach draws on his earlier work which stressed the importance in income inequality analysis of measures such as what Dagum called Relative Economic Advantage (REA) and income intensity of transvariation between subpopulations, the idea of transvariation being itself a concept originally invented by Gini (1916).

There has never been a dearth of prophets who announce the beginning or the end of something big. In recent years we have heard, among many other prophecies, the birth of the cybersociety and of a new world order, as well as the death of philosophy and even the end of science.

It’s a great honor for me to dedicate these scattered annotations (extracts from wider writings or simple discussion issues) to Camilo Dagum, great scientist and fraternal friend. They draw inspiration from the topics, we both started to debate a long time ago with our common master Corrado Gini. Under his guidance we learned to be wary of the widespread schemes of a certain philosophy of science still dealing with “ravens all black”, “swans all white”, “emeralds all green” (if not “grue”).

Defining the conditions of the scientific training is a vast and fundamental subject. While a thorough and complete analysis of that subject is impossible, a very brief analysis may be very useful. In this paper, I shall limit myself to defining what is the scientific mind and to stating a few fundamental principles which should be applied for the scientific training.

Removal of poverty has been and continues to be one of the primary aims of economic policy in many countries. Two important questions that arise in this context are: What exactly do we mean by poverty? In what sense do we say that poverty of a nation has increased or decreased over a certain time period? The first question addresses the problem of ‘perception of poverty’. The second question deals with ‘measurement of poverty’. In this paper we are interested in the measurement aspect of poverty. Since the efficacy of an antipoverty policy is evaluated by observing changes in the level of poverty, the way poverty is measured is important both for an understanding of poverty and for policy applications.

It has been suggested that the size distribution of income follows a pure random walk. If true, this has serious implications for the effectiveness of U.S. Government income transfer policies. In this paper the random walk hypothesis is addressed by examining whether changes in the size distribution of income are independent. Conventional linear second-order time series analysis suggests that the first differenced series indeed are white noise processes. Results obtained with Mizrach’s SNT test, based on developments in the recent literature on nonlinear dynamics, strongly reject the independence null for changes in each of the income inequality measures examined. While this suggests that year-to-year shifts in the income distribution are not random, it does not show that U.S. Government income redistribution policies have been either efficient or effective.

Almost all functions used in economics are concave, but there are important examples of convex functions, e. g., cost functions and poverty or concentration indices. In these cases one can choose between working with convex or concave functions (e.g., poverty indices or welfare functions).