The Measurement of Ordinal and Multidimensional Inequalities – ORDINEQ

Our research methodology is based on the following requirements:
- Provide a coherent and unified framework within which the different topics addressed in the project can be casted.
- Make clear the value judgements used when deriving individual well-being and computing social performance.
- Confront these value judgements with the public's perceptions.
- Provide empirically implementable criteria.
- Illustrate the value added of our approach by using available and appropriate databases.
- Provide statistical inference tests.

One of the main questions investigated in this project deals with the measurement of inequality and social welfare when the available information consists of categorical ordered data (example: self-reported health, ranging from «bad health« to «very good health«). The approach initiated by Allison et Foster (2004, Journal of Health Economics 23, 503-524) remains the reference in this domain, even though it is not free from criticism.

As the main result of the project, we proposed new measurement tools, easy to apply empirically, and based on transparent axiomatic foundations.We believe that this approach represents a significant advance, breaking with the existing literature and allowing the public institutions to assess inequalities and social well-being when variables are ordinal (e.g., health or education).
This research has given rise to three papers, two of which have already been published:
- Cowell and Flachaire, Inequality with ordinal data, with F. A. Cowell, Economica, 2017, 334(84), 290-321.
- Gravel, Magdalou and Moyes, Inequality measurement with a continuous and ordinal variable, Social Choice and Welfare, forthcoming.
- Gravel, Magdalou and Moyes, Ranking distributions of an ordinal variable, mimeo.

The tools provided in the project in order to assess social welfare with an ordinal variable are now ready to be used empirically.
Our first objective is to apply this approach to the different domains we proposed to investigate: as health and education.
Our second objective is to propose new multidimensional social welfare measures that take full account of the way ordinal variables interact in the determination of a person's well-being.

- Basili, Casaca, Chateauneuf and Franzini, Multidimensional Pigou-Dalton Transfers and Social Evaluation Functions, Theory & Decision, forthcoming.
- Dufour, Flachaire and Khalaf, Permutation tests for comparing inequality measures, Journal of Business & Economic Statistics, forthcoming.
- Cowell and Flachaire, Measuring Mobility, Quantitative Economics, 2018, 9(2), 865-901.
- Cowell and Flachaire, Inequality with ordinal data, Economica, 2017, 334(84), 290-321.
- Attema, Bleichrodt, l’Haridon, Ambiguity preferences for health, Health Economics, forthcoming.
- Gravel, Magdalou and Moyes, Inequality measurement with a continuous and ordinal variable, Social Choice and Welfare, forthcoming.
- Gravel, Marchant and Sen, Conditional Expected Utility Criteria for Decision Making under Ignorance or Objective Ambiguity, Journal of Mathematical Economics, 2018, p. 79-95.

While greater GDP per capita has often been assimilated with higher society welfare in the past, following the persuasive arguments of A.K. Sen (Commodities and Capabilities, North-Holland, Amsterdam, 1985), it is now widely accepted among the economic profession that a person's well-being comprises many other dimensions than income. The need for a more comprehensive approach to well-being has been reiterated by the Stiglitz-Sen-Fitoussi Commission that further recommended that the distribution among the citizens of well-being and of its different components is taken into account in the computation of social welfare. The recognition of the multidimensional nature of well-being has given rise to distinct approaches among which the construction of dashboard indices and composite measures has played a prominent role. Focusing on each dimension of well-being in isolation, the dashboard approach fails to provide an overall view of the society's performance. The Human Development Index (HDI) of the United Nations, that incorporates the three essential dimensions of a person's well-being (namely, income, health and education), is a follow-up of Sen's ideas. More recently, the Better Life Index (BLI) of the OECD has extended the scope of the HDI by introducing eight dimensions in addition to those used in the computation of the HDI.

While they represent notable advances in the measurement of the overall performance of the society and, beyond that, of the well-being of its members, both the HDI and the BLI are not exempt of deficiencies. The HDI and the BLI are aggregate indices and, as such, they do not care much of the distribution among the population of the different attributes that contribute to a person's well-being, not to speak of the distribution of well-being in the society. By combining aggregates - one for each attribute - without paying attention to the possible associations between the different dimensions of well-being, the HDI and the BLI leave aside important determinants of a society's welfare like the exposure and vulnerability of the individuals to various sorts of risks. Finally, by transforming heterogenous data into distributions of scores for each attribute and applying to them standard measures, the HDI and the BLI neglect the fact that the prime data are of different nature, ranging from cardinally-measurable attributes (like income) to variables involving ordered categories (like health status).

Building on the fiction of the paternalistic ethical observer, we propose to construct measures of socio-economic performance and well-being that (i) acknowledge the multidimensional nature of well-being, (ii) pay due attention to the distribution and interaction between the attributes, and (iii) take full account of the measurability nature of the attributes. These measures will make one able to provide answers to questions of interest for the policy-maker and the general public like the following:

Q1. Can we correctly claim that our health system guarantees equal access to medical care whatever the circumstances of the individuals? Is a move in direction to the British health care system likely to reduce the inequalities of health statuses among the population?

Q2. Does the poor performance on average of French students at the PISA tests go along with high inequalities in the distributions of the scores suggesting that the French educational system might be doubly inefficient? To which extent inequalities - provided that there is evidence of such inequalities - in reading, mathematics and problem solving are related to the socio-economic characteristics of the parents and more generally to their origins?

Q3. Is ex-post redistribution by means of progressive tax-benefit systems more effective in reducing the long run income inequalities than an ex-ante redistributive policy that would tax more heavily the intergenerational transmission of wealth?