Inequality Indices as Tests of Fairness

Ravi Kanbur and Andy Snell

No 11930, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: Standard income inequality indices can be interpreted as a measure of welfare loss entailed in departures from equality of outcomes, for egalitar- ian social welfare functions defi…ned on the distribution of outcomes. But such a welfare interpretation has been criticized for a long time on the grounds that these indices are snap shot outcomes-based measures which do not take into account the process generating the observed distribution. Rather than focusing on outcomes, it is argued, we should be interested in whether the underlying process is “fair.”Following this line of argument, this paper develops statistical tests for fairness within well defi…ned income distribution generating processes and a well speci…fied notion of fairness. We fi…nd that the likelihood ratio (LR) test for fairness versus unfairness within two such processes are proportional to Theil’'s first… and second in- equality indices respectively. The LR values may either be used as a test statistic or to approximate a Bayes factor that measures the posterior probabilities of the fair version of the processes over that of the unfair. The answer to the process versus outcomes critique is thus not to stop cal- culating inequality measures, but to interpret their values differently—--to compare them to critical values for a test of the null hypothesis of fairness, or to use them directly as a measure of the chance that the process was fair relative to the chance it was unfair. We also apply this perspective to measurement of “"inequality of opportunity".”

Keywords: Snapshot inequality indices; Process versus outcomes; Fair versus unfair process; Likeliood ratio test of fairness; Bayes factor (search for similar items in EconPapers)
JEL-codes: A10 A13 C01 C12 D63 (search for similar items in EconPapers)
Date: 2017-03
New Economics Papers: this item is included in nep-hpe
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://cepr.org/publications/DP11930 (application/pdf)
CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org

Related works:
Journal Article: Inequality Indices as Tests of Fairness (2019)
Working Paper: Inequality indices as tests for fairness (2017)
Working Paper: Inequality Indices as Tests of Fairness (2017)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cpr:ceprdp:11930

Ordering information: This working paper can be ordered from
https://cepr.org/publications/DP11930

Access Statistics for this paper

More papers in CEPR Discussion Papers from C.E.P.R. Discussion Papers Centre for Economic Policy Research, 33 Great Sutton Street, London EC1V 0DX.
Bibliographic data for series maintained by ().