2. See, for example, Dabla-Norris et al. (2015); Gurría (2011), ILO (2015); ISSC, IDS, and UNESCO (2016); Love (2016), OECD (2011, 2015); Ostry, Berg, and Tsangarides (2014); Oxfam (2016); Save the Children (2012); UNDESA (2011); UNDP (2014); UNICEF (2011); and World Bank (2016).
3. See, for example, https://www.nytimes.com/2016/10/16/upshot/whats-behind-a-rise-in-ethnic-nationalism-maybe-the-economy.html.
4. One of the key developments in economic theory has been the demonstration that, once the Arrow-Debreu conditions (no increasing returns, no monopolies, a complete set of markets for present and future goods, complete insurance markets, fully available and symmetric information, and available lump sum transfer instruments) are relaxed, there is no separation of efficiency and equity. With imperfect information, lump sum redistribution of endowments can improve efficiency (in the sense of making at least one person better off without making anyone else worse off) under certain conditions, or worsen it under others. In the absence of lump sum instruments, market interventions may reduce efficiency, but improve equity. Efficiency and equity have to be taken together, i.e., they are not separable.
5. See, for example, the Pew Research Global Attitudes Project. See also the discussion on the subject in World Bank (2017).
6. Measuring inequality of opportunity, horizontal inequality—that is, inequality among socio-economic and demographic groups—and intra-household inequality are discussed in other chapters of this volume.
7. For trends, see citations in endnote 2. For the properties and advantages and disadvantages of indicators, see, for example, Atkinson and Bourguignon (2000 and 2015a), Cowell (2009), Duclos and Araar (2006), and Jenkins and Van Kerm (2009). For discussions on inequality beyond the income dimensions, see Sen’s pioneering article “Equality of what?” (Sen, 1980) and the pertinent chapters in Atkinson and Bourguignon’s Handbook of Income Distribution (2015a) such as those by Aaberge and Brandolini (2015) on multi-dimensional inequality; Koen, Fleurbaey, and Schokkaert (2015) on inequality and well-being; and Roemer and Trannoy (2015) on inequality of opportunity. Also, on the latter, see Aaberge, Mogstad, and Peragine (2011). Also, see Akerlof and Kranton (2000) on identity-driven inequality. On measures of polarization, see Chakravarty (2009). For an overview of gender inequality, horizontal inequality, and inequality within the household, see the chapter by Deere, Kanbur, and Stewart in the present volume.
8. Atkinson et al. (2010) discuss a hierarchy of methodologies employed in the standardization of income inequality data sets. “In short,” they write, “we have a ‘hierarchy’ of degrees of standardization: (1) Common survey instrument (European Community Household Panel, ECHP); (2) Ex ante harmonized framework (EU-SILC); (3) Ex post standardized microdata (LIS); (4) Ex post customized results (OECD); 5) Meta-analyses of results (Kuznets)” (p. 103).
9. By “directly” here it is meant that indicators were calculated directly by the organization or by the National Statistical Office but following specific guidelines that ensure comparability. For details on each data set, see Table 2 in Ferreira, Lustig, and Teles (2015).
10. It should be noted that the inequality measures are not always produced directly from the micro-data, because in a number of countries, only grouped data is available.
11. For a discussion of the limitations of SWIID, see Jenkins (2015).
12. The first series from the DINA project are available on WID.world for the United States and France.
13. For a summary of how international data sets differ, see Table 2 in Ferreira, Lustig, and Teles 2015.
14. Such discrepancies suggest that caution is needed when interpreting the results of cross-country regression analysis based on the SWIID imputation-based data, such as those of Acemoglu et al. (2013) and Ostry, Berg, and Tsangarides (2014).
15. See the section on the limitations and shortcomings of international data sets below. Also see Ferreira, Lustig, and Teles (2015).
16. To put this number in perspective, in January 2016, the United Nations had 193 members and 2 permanent observers (the Vatican and Palestine).
17. “The geographical coverage across regions was not uniform. Of the 83 countries, 24 belonged to a single region, eastern Europe and central Asia, while East Asia and Pacific, Latin America and the Caribbean, and sub-Saharan Africa contributed 8, 16, and 9 countries, respectively. In South Asia, 4 countries were covered, and, in the Middle East and North Africa, 2.” (World Bank, 2016, p. 53).
18. The World Bank’s PovcalNet indicates the policy regarding public access in each country contained in their database, http://iresearch.worldbank.org/PovcalNet/data.aspx.
19. The GCIP database described above standardizes across the welfare concepts measured in surveys to supply income-based estimates of global inequality (Jayadev, Lahoti, and Reddy, 2015).
20. The OECD produced guidelines on how to measure wealth distribution in 2013 (OECD, 2013a), in response to the recommendations of the Stiglitz-Sen-Fitoussi Commission. The European Central Bank has also produced guidelines for members of the euro area in the context of the implementation of the Euro System Household Finance and Consumption Survey.
21. A framework for the joint analysis of micro-statistics on household income, consumption, and wealth was released by the OECD in 2013 (OECD, 2013b). An example of analysis of the joint distribution of income, consumption, and wealth for the United States is provided by Fisher et al. (2016). An OECD-Eurostat Expert Group is currently working to develop experimental measures of inequality in the joint distribution on household income, consumption, and wealth for around 25 countries.
22. Beyond OECD countries, most income surveys do not report data on direct taxes paid by households. Around one-third of all OECD countries lack micro-data on wealth distribution, a proportion that is much higher for developing countries. Micro-data on consumption expenditures in OECD countries are rarely used for distributive analysis.
23. See the proposed checklist to assess quality and comparability of data in Atkinson and Bourguignon (2015b).
24. Data on the distribution of household wealth, for 28 countries, are available through the OECD Wealth Distribution Database released in 2015. These data are sourced from national surveys, which may differ in significant aspects, and from register data from some Nordic countries.
25. For example, according to Fesseau and Mattonetti (2013), in the case of Mexico, the adjusted national accounts total was more than seven times higher than the micro total from the income and expenditures household survey.
26. For a formal discussion, see Deaton (2005) p. 11. Also see Alvaredo, Atkinson, and Morelli (2017), in the case of wealth. Deaton uses the term “selective under-sampling” while Jenkins (2015) calls it “underrepresentation.”
27. Regardless of its cause, I will call the issue at hand the “missing rich” problem. Other terminology has been used. Jenkins (2015), for example, refers to the problem as “under-coverage” of the rich.
28. See Alvaredo and Londoño-Velez (2013) for Colombia; Jenkins (2015) for the United Kingdom; Székely and Hilgert (1999) for Latin American countries.
29. See the pioneering work on this by Altimir (1987).
30. See, for example, the chapter by Alvaredo et al. in this volume.
31. The Report of the Commission on Global Poverty (Atkinson, 2016) includes a thorough discussion of these problems at the bottom of the distribution and recommendations on how to deal with them. Here we shall concentrate on the various approaches that have been proposed to address similar problems but at the other end of the distribution, i.e., the high incomes group or the so-called rich.
32. Put differently, the probability that Warren Buffett or Bill Gates are selected in a sample in US household surveys, or Carlos Slim in a Mexican household survey, is negligible.
33. As Deaton (2005) puts it “With greater nonresponse by the rich, there can be no general supposition that estimated inequality will be biased either up or down by the selective undersampling of richer households.
(The intuition that selective removal of the rich should reduce measured inequality, which is sometimes stated as obvious in the literature, is false, perhaps because it takes no account of reduction in the mean from the selection)” (p. 11). A simple example can illustrate this point. Let’s assume that we observe a population of 4 people, with the first three having $0 income and the fourth $1 (0, 0, 0, 1). The coefficient of variation for this distribution is 2 and the share of income of the richest person is 100%. Let’s now assume that one “rich” person is missing, so that the true distribution is (0, 0, 0, 1, 1): in this case, the coefficient of variation is 1.37 and the income share of the richest person is 50%, i.e., inequality is lower when the sample is corrected to fully capture the top end of the distribution.
34. Cowell and Flachaire (2015), classify the (right-) tail errors into two main types of “data problems”: (1) measurement error and data contamination; and (2) incomplete data. Their paper discusses a variety of methods to address them.
35. These concepts and how they affect households’ incomes are discussed in detail in Lustig (2018a).
36. The options are summarized by Bastagli (2015), p.12.
37. Atkinson and Bourguignon (1990); OECD (2015); Sahn and Younger (2000). By using averages, this approach ignores differences across income groups and regions. For example, governments may spend less (or more) per pupil on poorer students. We recommend averaging at as disaggregated a level as possible (not only by education level but also by state and rural/urban area within states, for example). The level at which it is possible to disaggregate will depend on data from national accounts. Data obtained from the education ministry is likely to be more disaggregated than that obtained from national accounts.
38. Barofsky and Younger (2018) describe the pros and cons of three methods that can be used to value the distributional impact of health care spending: average cost, behavioral-outcome approach, and willingness to pay. Their conclusion is that all the methods have their pros and cons: they provide different types of information and, as such, should be used as complements rather than substitutes.
39. See Lustig (2016). “Consumable income” in the CEQ project is defined as disposable income net of indirect taxes and subsidies. In other contexts, “consumable” has been referred to the income subject to consumption taxes (Ebel and Petersen, 2012). For more on the CEQ project, visit www.commitmentoequity.org.
40. These results are based on the CEQ Institute studies and are summarized in Lustig (2018b). Also, see Higgins and Lustig (2016) for estimates of the extent of fiscal impoverishment that taxes (net of transfers and subsidies) can generate and how to measure this phenomenon formally. Consumption subsidies work in the opposite direction.
41. The 2011 Canberra Group Handbook states that “ideally all indirect taxes that can be attributed in some way to individual households should be included in any comprehensive analysis of the effects of government benefits and taxes on the distribution of household income. This includes not only consumption taxes on final expenditure of households, but also taxes on inputs into the production process of goods and services” (UNECE [2011], pp. 47–48). See also Table 2.1 (p. 18) of the same report as well as Zwijnenburg, Bournot, and Giovannelli (2017).
42. See the fairly long list of finished and ongoing studies featured in the WID.world website and the studies they cite in turn.
43. The Uruguayan government has taken such a step and shared this type of information with academics. See Higgins, Lustig, and Vigorito (2017).
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