Welfare, state, and values: the winding road of the normative approach to inequality measurement (1912–1970)

Abstract

Embedded in the general history of income inequality measures, this paper seeks to understand the evolution of the normative approach to inequality measurement. To this end, it undertakes a joint consideration of selected works by Pigou, Dalton, Kolm, and Atkinson that have not previously been discussed in connection with each other. Noting that the normative approach to inequality measurement was neglected for almost five decades, the paper inquires into the reasons for this, proposing two explanations: first, that the normative approach was eclipsed by the pretensions to axiological neutrality supposedly proper to economic science; second, that there was a drift towards statistics in the study of personal income distribution, where the measurement of inequality became established as a central axis. Finally, the paper discusses the different factors that contributed to the rebirth of the normative approach and highlights the ways in which the new contributions manifest an awareness of previous discussions of values in economics.

Keywords:

• Personal income distribution
• inequality measurement
• normative criteria
• redistribution
• social welfare

JEL CLASSIFICATION CODES:

• B10
• B20
• B40
• D31
• D63

Acknowledgments

Versions of this paper were presented at the 25th ESHET Conference in Padua, Italy, at the EJHET Workshop “From Public Finance to Public Economics” in Graz, Austria, and at the 24th ESHET Summer School “Inequality and Social Justice in Economics and Beyond” in Strasbourg, France. I thank the editors of the Special Issue, Maxime Desmarais-Tremblay, Marianne Johnson, and Richard Sturn for their valuable comments and suggestions on each presentation, which greatly improved this paper. I also thank the two anonymous referees whose remarks and recommendations were of great help. I am particularly indebted to Steven G. Medema, Herrade Igersheim, and André Lapidus for their careful reading and constructive criticism. Finally, I thank Antoinette Baujard for her attention and advice throughout the process of development of this paper. All errors are my own.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Although a distinction between the “positive” and the “normative” theory of income distribution can be found in Tinbergen (1970), this distinction is not strictly linked to the measurement of inequality. We can probably attribute the nomenclature of “normative” measurement, along with contrast with the “objective” or “positive,” to Sen (1973, 2–3). Later, he even proposed the term “ethical measurement” as an alternative for normative measurement (Sen 1978).

2 Pigou borrows from Marshall the concept of the “national dividend,” a preliminary version of what would later become known as Gross Domestic Product (GDP).

3 These tests of the transfer principle against existing measures, and its being proposed as a desirable axiom for a measure of inequality, led Sen (1973, 27) to rename it the “Pigou–Dalton condition,” which then evolved into the “Pigou–Dalton transfer principle.”

4 It is important to clarify that Dalton only “tested” the Mean Difference proposed by Gini (1912), and not his concentration ratio R or “Gini coefficient” (1914).

5 Dalton then tested the measures under three additional principles. After the tests, he discarded the absolute measures in favor of relative ones and assigned them the same order of merit as they had according to the principle of transfers. See Dalton (1920b, 355–357).

6 Dalton was probably the first to propose a set of desirable properties for an inequality measure, with the principle of transfers at the forefront. This procedure has been widely endorsed throughout history and up to the present day. Over time other properties have been added. See Fleurbaey (1996).

7 Recently, King (2018) stated that Dalton’s work in the field of Public Finance was strongly driven by his belief in the need to reduce inequality, which, according to the author, was also his main motivation in advocating a tax on capital (King 2018, 305).

8 Aigner and Heins (1967) generalized Dalton’s approach, proposing an inequality index that allowed greater generalizations with respect to the social welfare function; but this measure continued to depend on the unknown relationship linking income and welfare, the same difficulty as the one exposed by Dalton. Bentzel (1970) somewhat pessimistically took up the relationships between income, consumption, and welfare, arguing for the impossibility of inferring meaningful conclusions from income distribution data, and put forward some views on the measurement of the degree of inequality in welfare distributions. Tinbergen (1970), for his part, inquired into the reasons underlying income distribution, contrasting what he called a “positive” theory, based on assumptions concerning the supply of and demand for each type of productive service, and two “normative” theories, based on the maximization of a utility or welfare function. However, we find no citations to Dalton (1920b) in Bentzel (1970) and Tinbergen (1970).

9 For Robbins, technicality should be embraced if necessary, and it should be made known that this economics would not be accessible to all: “The days are gone when Political Economy was a fit subject for a gentleman to study in his moments of relaxation” (Robbins 1930, 23).

10 For a detailed description of each approach and its nuances, see Baujard (2016).

11 In his book Robbins made a reference only to Dalton’s Some Aspects of the Inequality of Incomes in Modern Communities (1920a), citing it as Inequality of Incomes (Robbins 1932, 64).

12 In the acknowledgements to his paper, Atkinson notes that he had not discovered Kolm’s work until after his paper was accepted for publication (Atkinson 1970, 262), and admitted in a footnote the priority of Kolm’s publication as a turning point in the subsequent revival (note by Atkinson, in Atkinson and Brandolini 2015, 212).

13 As an illustration, a quick search in Google Scholar (3 May 2023) shows 1074 citations for Kolm’s article (adding both English and French versions), versus 9712 citations for Atkinson’s. In addition, bibliometric studies place Atkinson’s (1970) paper among the most cited articles published between 1970 and 2002 in major peer-reviewed economic journals (Kim, Morse, and Zingales 2006, 193, Table 2). Kolm’s article, which is over 40 pages long, only addresses inequality measurement in Sections 6 and 7. The rest of the work is mainly known for its contributions to Public Economics.

14 Harsanyi continued to develop this line of research in Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility (1955) or his Essays on Ethics, Social Behavior, and Scientific Explanation (1976).

15 The “certainty equivalent” is the sum of money or guaranteed return that a decision maker would accept now, rather than take the risk of obtaining a perhaps higher, but uncertain, return. An absolute measure of risk premium (among other potential measures) is the difference between the expected average outcome and the certainty equivalent. If it is equal to zero, the decision maker reveals his neutrality toward risk; if it is positive, he is a risk lover; if it is negative, he is risk averse. Certainty equivalents thus make it possible to determine decision-makers’ attitudes toward risk, which can be reflected in the form of their utility functions (Guyse 2001).

16 For his biography and more, see Lambert (2012).

17 For the full theoretical development and preconditions, such as the construction of the functional form behind the equal equivalent $\overline{\overline{x}},$ see Kolm ([1969] 2003, 279–280).

18 Atkinson had also read the earlier work linked to the normative approach by Wedgwood (1939) and Aigner and Heins (1967); he was not convinced by their results, however, and argued that “the particular numerical values calculated by these authors have no meaning” (Atkinson 1970, 250).