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11.4.1 Household Surveys and National Accounts
Household surveys are the most widely available source of data for estimating income distributions within countries, and it is the great expansion in their global coverage that has permitted estimates of global inequality.
One could in principle use census data or other sources—but in practice these are available for far fewer country-years than household surveys. Survey coverage has expanded dramatically in the last 30 years; the surveys used by the World Bank to estimate global poverty in 1981 covered only 51.3% of the population of the developing world, whereas in 2005 they covered 90.6% (Chen and Ravallion, 2008).Although there is no credible alternative to using household surveys for estimates of global inequality, they do suffer limitations. Beyond the obvious sampling and measurement errors, surveys may suffer from biases due to underreporting of incomes by the rich and undersampling of both very rich and very poor households. Most important for our purposes, differences in definitions and coverage mean that different surveys are typically not strictly comparable with one another (see Anand and Kanbur, 1993, pp. 33-36). Atkinson and Brandolini (2001) described such problems in the Deininger and Squire database, which collates estimates of inequality within countries; Anand and Segal (2008) discussed these issues in the context of measuring global inequality, observing that in some surveys incomes are gross-of-tax and in others net-of-tax; some refer to cash incomes, whereas others include certain items of income-in-kind; some impute the rental value of owner-occupied housing, whereas others do not. Moreover, all global data sets of household surveys combine surveys of income and of consumption expenditure. There is no reliable way to infer an income distribution from an expenditure distribution, or vice versa, so one simply has to live with the noncomparability.
For brevity we will refer to “income or consumption expenditure distributions” as “income distributions.”The World Bank’s Living Standards Measurement Surveys, initiated in 1980, have been instrumental in increasing both the quantity of survey data available and its quality. The Luxembourg Income Study (LIS) specifically attempts to harmonize survey data to ensure their comparability, and the LIS data set currently covers 47 countries. Still, noncomparability cannot be avoided in a global data set of household surveys, which cover most of the world’s population.
Although all recent studies of global inequality use survey data for estimates of within-country inequality, most then “scale” the within-country distributions to national accounts estimates of mean income or consumption expenditure. For instance, Chotikapanich et al. (1997), Dowrick and Akmal (2005), Sala-i-Mart#953;n (2006), and Schultz (1998) use the Deininger and Squire (1996) inequality database for estimates of relative inequality within countries and peg the relative distributions around an absolute mean from the national accounts.[661] Milanovic (2002, 2005, 2012) and Lakner and Milanovic (2013) are the only studies we know of that estimate global income inequality using levels of income or expenditure directly from surveys, rather than scaling relative distributions to NA means (though Lakner and Milanovic do use NA means in imputing top incomes, as we discuss later). The World Bank also uses absolute incomes from household surveys for its estimates of global poverty (Chen and Ravallion, 2001, 2008, 2012).[662] The distinction between using survey data directly and scaling them to national accounts categories matters because both the levels and rates of change of global inequality and poverty can vary substantially (Deaton, 2005).
For studies that use household surveys only for their relative distributions and scale them to national accounts means, there are two widely available estimates of NA “mean income”: per capita GDP and per capita household final consumption expenditure (HFCE).
In principle, one would want to use the category of personal income, but countries do not usually report this category. Most studies of global inequality simply use per capita GDP as a proxy for individual mean (per capita household) income.[663]As argued in Anand and Segal (2008, pp. 66-68), if it is national household consumption expenditure that one wishes to measure, then there is no reason to use GDP when HFCE is available. Moreover, GDP is also a poor measure of household income: GDP includes depreciation, retained earnings of corporations, and the part of government revenue (taxes) that is not distributed back to households as cash transfers. Deaton (2005, p. 4) noted that “much of saving may not be done by households, but by corporations, government, or foreigners, so that household income may be closer to household consumption than to national income.” In the case of the United States, which is one of the few countries that does report measures of aggregate household income (referred to as “personal income”), it amounts to only about 70% of GDP. Deaton estimates that, across 272 surveys of household income from around the world, survey household income amounts on average to only 57% of GDP, but equals 90% (101% population-weighted) of HFCE from National Accounts.
The question remains, however, whether one would want to use any National Accounts figures when mean household income (or consumption) is available in the surveys themselves, which are the source of the income (or consumption) distribution for countries. We saw earlier that surveys have their own problems. But they are at least a direct measure of the variable of interest. HFCE, on the other hand, includes the category of “non-profit institutions serving households” (e.g., religious organizations and political parties), and suffers from being calculated as a residual of aggregate consumption minus estimates of firms’ consumption and government consumption. Errors in any of the latter magnitudes will translate into errors in estimates of HFCE.[664]
New evidence on national accounts data in low-income countries casts more general doubts on their reliability.
Jerven (2013) noted that Ghana revised its GDP upward by 60.3% in November 2010 owing to a change in base year,[665] and argues that similarly large revisions are to be expected in other sub-Saharan African countries.[666] Young (2012) also found that national accounts provide a poor measure of growth in sub-Saharan Africa and produces independent estimates of consumption growth based on data from Demographic and Health Surveys.[667]Most of our analysis that follows will refer to the global distribution based on mean incomes from household surveys, but we also calculate global inequality where mean per capita household income is taken to be equal to per capita HFCE as reported in the National Accounts and compare the differences in the results.
11.4.2 Top Income Data
Perhaps the most important recent innovation in estimating national income inequality has been the collation of data on top income shares from income tax records. These estimates present the incomes of the top 0.1%, top 1%, and top 10% as a share of “control” income, where control income is an estimate of total personal income in the economy (not just taxable income). They are important primarily because they make a substantial difference to estimated inequality. Household surveys typically undersample (exclude) the richest individuals or underreport their incomes, or both. In the United States in 2006, for instance, tax data excluding capital gains imply a top percentile share of 18.0%, whereas survey data imply a share of 13.7%. Using data for 2006, the U.S. Gini based on household survey data (the Current Population Survey) is 0.470, whereas correcting the top percentile’s income using the tax data raises it by nearly 0.05 to 0.519. Moreover, the increase in the U.S. Gini from 1976 to 2006 using survey data alone (corrected for a change in definition) was 0.053, which more than doubles to an increase of 0.108 using the top income data (including capital gains; Atkinson et al., 2011, p.
31; see Burkhauser et al., 2009 for further discussion of U.S. data).Atkinson et al. (2011, pp. 4-5) describe the top income data in detail, and discuss their limitations. These include the fact that the income shares refer to gross income before tax; the data vary with respect to the unit of observation, some referring to individuals and others to households; in some cases they are not consistent over time, as tax regimes change; and they may be biased owing to tax avoidance and tax evasion. Although they are typically much better than surveys at capturing capital income, this varies depending on the extent to which capital income is taxed and hence reported in the tax records (Atkinson et al., 2011, p. 35). Alvaredo and Londoilo Velez’s (2013) study of top incomes in Colombia notes that different definitions of the control income, of which top incomes are expressed as a share, lead to somewhat different estimates. For these reasons international comparisons of these top income shares may suffer from inconsistencies. Nonetheless, we will set aside such concerns and use these data on the presumption that excluding them would cause a large negative bias in estimates of global inequality. Clearly, however, these noncomparabilities do add uncertainty to the estimates.
11.4.3 PPP Exchange Rates
International comparisons of living standards require the use of PPP exchange rates to convert national currencies into a common numeraire.[668] Two standard sets of PPPs are publicly available: those produced by the International Comparison Program (ICP) of the World Bank (World Bank, 2008) and those produced by the Penn World Tables (PWT), which also uses the underlying price survey data collected by the 2005 ICP.[669] PPPs for years before and after the “benchmark” year 2005 are derived from each country’s domestic price indices.
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The price surveys undertaken for the 2005 ICP were both more detailed and more representative globally than in previous rounds of the ICP.
China had never taken part in an ICP before the 2005 round, and India had not taken part since 1985, but both countries were surveyed in the 2005 ICP. Previous estimates of PPPs were therefore based on imputations. Partly for this reason, the results from the 2005 ICP have in some cases led to dramatic changes in estimated GDP. Both China and India were found to have real GDPs nearly 40% lower than previous estimates[670] [671] because prices were found to be higher than previously estimated. In the case of China, at least some of this downward revision appears to have been due to sampling problems: its price surveys took place in cities and their environs and did not cover rural areas. For this reason Chinese prices are likely to have been overestimated, and its real income underestimated. Following Chen and Ravallion (2010), and like Milanovic (2012), we make an adjustment to account for this (described later). Milanovic (2012) found that the revisions in the 2005 ICP make a substantial difference to estimated global inequality, raising the Gini by 4.4-6.1 percentage points over the period 1988-2002 and Theil T by 12.5-16.4 percentage points. Other studies that use the 2005 PPPs are Lakner and Milanovic (2013) and Bourguignon (2011), and we discuss their findings later.Starting from the vector of prices in each country provided by the ICP, the World Bank and PWT use different methods to calculate PPPs. World Bank PPPs are based on the Elteto-Koves-Szulc (EKS) method, whereas PWT uses the Geary-Khamis (GK) method (both with a variety of adjustments made in the process of estimation). 0 EKS arose from a statistical approach to index numbers (Deaton and Heston, 2010) and is a multilateral generalization of the Fisher index for two countries (for further discussion, see Anand and Segal, 2008, p. 71). However, under certain assumptions EKS applied to incomes yields an index of real living standards, or utility, and for this reason Neary (2004) included it as an example of the “economic” approach to index numbers. Under the economic approach it is assumed that observed quantities arise from the optimizing behavior of some representative agent with a well-defined utility function. Real relative incomes measured using EKS PPPs represent relative utility levels when utility is quadratic (i.e., in these circumstances it is a “true” index).
GK, on the other hand, is an example of the “test” or “axiomatic” approach. The GK index has no interpretation in terms of optimizing behavior, but its putative advantage with respect to EKS is that it passes the test, or obeys the axiom, of matrix consistency. That is to say, GK provides a vector of “international prices” for individual goods that enable disaggregation of the economy into subsectors whose values at those prices sum to the total value of the economy. This is not true ofEKS, which computes the relative size of aggregate incomes but does not provide a set of international prices with which economies can be consistently disaggregated. If one is interested in analyzing the structure of economies, then matrix consistency would seem to be a useful property. For instance, it is hard to interpret the relative size of manufacturing in two different countries when manufacturing plus nonmanufacturing within each country does not add upto 100% of its economy.
Matrix consistency would seem less relevant, however, when our concern is international comparisons of living standards. In this case, it is the overall value of consumption, not its composition, that concerns us. More important for our purposes is the drawback of the GK method, which is that it suffers from Gershenkron (or substitution) bias. Because consumers tend to substitute away from goods that are relatively expensive and toward goods that are relatively cheap, valuing the output of both country A and country B at country B’s prices will lead to an overestimation of the income of country A relative to that of country B. The relative prices arising from the standard GK method more closely resemble those in rich countries than in poor countries, leading to an overvaluation of the incomes of poor countries relative to rich countries and therefore to an underestimation of inequality between countries. Ackland et al. (2004) found that the GK method overvalues the incomes of poorer countries compared to EKS. They regress log per capita GDP from GK on log per capita GDP from EKS and find the slope to be 0.94 and to be significantly less than 1.0. Deaton and Heston (2010) found that the Gini for concept 2 (between-country) global inequality, with per capita GDP as the income concept, is slightly higher using EKS than GK, at 0.533 as opposed to 0.527.
Almas (2012) also found that PWT PPPs underestimate global inequality when accounting for both substitution bias and differences in the quality of goods across countries. However, her estimates are based on the strong assumption that “there is a stable relationship between the budget share for food and household income; i.e., there is a unique Engel relationship for food in the world” (Almas, 2012, p. 1094). Deaton and Heston (2010, p. 5) pointed out that “there are many places in the world, such as North and South India, where there are large differences in consumption patterns of food in spite of only modest differences in relative prices.”
Neary (2004) presents a method that he denotes “Geary-Allen International Accounts” (GAIA) for constructing PPPs that is “economic” in the sense of being based on the assumption of optimizing behavior and therefore does not suffer from substitution bias, but that also satisfies a form of matrix consistency. However, the form of matrix consistency satisfied is not the form that GK satisfies; the sectoral quantities that sum to the value of the whole economy are not the actual observed sectoral quantities, but virtual quantities that a reference consumer, whose preferences are estimated from the data, would have chosen. So it is also the case in the GAIA method that observed manufacturing plus observed nonmanufacturing within an economy will not, in general, add upto 100% of the economy.
The theoretical advantage of GAIA over EKS is that it is a “true” index (i.e., produces estimates of relative real incomes that are consistent with optimizing behavior) for a wider range of utility functions. But because all such indices make the false assumption of identical tastes in all countries worldwide, this seems a rather limited benefit. EKS, on the other hand, has the advantage of being relatively transparent. Although GAIA requires the estimation of a demand system, the EKS exchange rate for a country is simply the geometric mean of that country’s Fisher price indices relative to every other country and, as already mentioned, has a natural statistical interpretation that is attractive to national income accountants if not to consumer theorists (Deaton and Heston, 2010).
In our calculations that follow, we use the EKS-based World Bank consumption PPPs from the 2005 ICP. Following Chen and Ravallion (2008, 2010) we make the following adjustments. For both India and China, where the survey data are provided separately for rural and urban strata, we deflate urban incomes relative to rural incomes from price indices used for the construction of domestic urban and rural poverty lines. For India we assume that the World Bank estimated PPP is a weighted average of the urban and rural PPPs. For China we assume that the reported PPP is for urban areas and adjust rural prices downward. This is because the price surveys in China in 2005 were restricted to 11 metropolitan areas, which did not include any rural areas (Chen and Ravallion, 2010). The result is a lower overall price level for China, and thus higher average living standards, than those implied by the use of the 2005 ICP.
A limitation to all standard PPP estimates is that they assume all households within a country face the same price level for their expenditure basket. This may be problematic for at least two reasons. First, urban and rural areas typically have different price levels, and although we have taken this into account for China and India, where the urban and rural price surveys are distinct, it is not possible to do so for most countries. Second, different quantiles of a national income distribution will typically consume different baskets of goods and services,[672] and hence face different costs of living. For instance, the poor may face higher unit costs for a good because they have to buy it in smaller quantities. Moreover, they purchase goods in different proportions from the nonpoor so the prices of goods will have different expenditure weights for them. At the other end of the
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distribution, the very rich (such as those captured by the top income data) may tend to buy more goods from outside their country of residence, to which market exchange rates would apply. But to the extent that the very rich spend their income on nontradable goods and services—for example, country estates, urban mansions, and domestic labor within their country of residence—PPPs with different expenditure weights may be more appropriate than market exchange rates.
11.4.4 Estimation Errors
The preceding discussion of the available data indicates that there are several sources of error in estimates of global inequality, including our own. These include sampling errors, which arise from the sample not being representative of the world population. Our global income distribution is constructed as the union of national income distributions, each of which is based on a national household income (or expenditure) survey with a distinct sampling frame and sampling errors (including undersampling of both the rich and the poor in a country). This global distribution is not estimated from a stratified random sample of the world population, so standard methods are not applicable to calculate sampling errors or confidence intervals for estimates of global inequality.
It is important to distinguish sampling errors from other types of estimation error, which arise from imprecise data and invalid or inaccurate assumptions and methods used to calculate global inequality. For example, there are measurement errors in the income or expenditure data in household surveys (e.g., underreporting of incomes of the rich) and in any national accounts data that may be used; there are also estimation errors in the PPP exchange rates used to construct a global income distribution from national distributions. Major revisions in the estimation of PPPs in the 2005 ICP round, discussed earlier, suggest great sensitivity to the assumptions and methods employed. Given such instability, we may expect further revisions in the next set of PPPs from the 2011 round of the ICP.[673] Moreover, as mentioned earlier, a single PPP exchange rate for a country may fail to capture differences in price levels faced by households in different quantiles of the income distribution or in different geographical locations in the country.
Bourguignon and Morrisson (2002) estimated global inequality from 1820 to 1992 through the use of inevitably limited data and manifold assumptions. Given the limitations of their data, they simulated “uncertainty” in their mean income (i.e., GDP) numbers and in their country-group distributions (11 data-points for each of 33 countries or groups of countries) and calculated standard errors for global inequality on this basis. Under their simulation assumptions, the resulting standard errors on the global Gini turn out to be small: in 1820 the standard error is 0.9 Gini points, in 1950 it is 0.2 Gini points, and in 1992 it is 0.1 Gini points (where 1 Gini point is 0.01 in the Gini scale of
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0.00—1.00). In our view the other sources of error discussed earlier would imply much larger confidence intervals than these standard errors suggest.
11.5.