2.1 Inequality as a global issue

The first target of the first millennium development goal (MDG1) is to halve, between 1990 and 2015, the proportion of people whose income is less than $1 a day (http://www.un.org/millenniumgoals/poverty.shtml accessed 01/10/12). Growing inequality makes it harder to reach this goal. As Kofi Annan observed in 2005: “we cannot advance the development agenda without addressing the challenges of inequality within and between countries” [52]. Over the past 20 years inequality has risen within more countries than it has fallen [57]. In 2007 the UN News Centre reported that the United Nations Assistant Secretary-General for Economic Development, Jomo Kwame Sundaram, was concerned about a significant and disturbing increase in inequality within and between countries around the world, which he attributed to a worldwide decline in the number of jobs (http://www.un.org/apps/news/story.asp?NewsID=21526&Cr=globalization&Cr1#.UF9-vRiTbbs accessed 24/09/12). Even in countries in Northern Europe that have the world's lowest income inequalities [26], such as Germany, Denmark and Sweden [43] inequality grew in the 2000s probably because of increased income disparity [13].

Atkinson, Piketty, and Saez [3] see increasing income disparity as at least partly attributable to an unprecedented surge in top wage incomes [44]. They attribute the evolution of the top one per cent share of wealth in various countries to political changes (e.g. Reagan in the US and Thatcher in the UK), wars, financial crises, global factors and taxation. Whatever the reason the wealthiest 20 per cent now account for 86 per cent of all private consumption and the poorest account for around one per cent [55]. Even in China and Russia increases in income are invariably going to the top one per cent of the population [3], [12]. This matters because inequality within countries affects people's well-being [28], [56]; it breeds social resentment and generates political instability as people feel that they are losing out while others are becoming rich [43], [10]. Such inequality would seem to be a recipe for disaster.

2.2 Within country inequality

In the past it was assumed that globalisation would raise the income of almost all nations and help redress inequality [31]. However many studies have found no obvious relationship between a country's participation in globalisation and positive changes in inequality within countries [13], [26]. Although a study conducted by the IMF (2009:35) shows inequality in Mexico fell after the mid-1990s [19] other studies disagree. A 2008 study of wage inequality in Mexico found increased access to export markets led to growing wage inequality [58] with the need to produce better products for export than for domestic markets within industries and hence the need for upgrading of skills for some workers. Thus wage disparity increased within manufacturing industries where smaller less productive plants with less skilled labour supplied local markets while larger more productive plants with highly skilled labour produced goods for export. Other studies quoted by Pavcnik [45] found a similar process in Argentina and Indonesia [12], [52].

A related skill-based driver of wage inequality has been a general increase in use of information and communication technologies (ICT) by some industries, which has increased their demand for high-skilled, college educated, workers [45], [26]. Where access to technology skills and education are available only to the elite the poor have no ability to move from unskilled to higher skilled occupations (e.g. from agriculture to industry) thus increasing inequality. This selective apportioning of education is not confined to developing countries. A 2005 UN study found some of the highest income inequalities – as well as in Mexico and Turkey – were in the USA [52] much of which in the US was attributed to access to education, in particular skill-biased technological change (SBTC) [17], [6]. Coincidentally the life expectancy of poorly educated women in the US has also slipped in the last decade from a gap of 5.8 years to a gap of 8.6 years compared with women with a Bachelor's degree or higher [42]. Equal access to education, job creation and skill development opportunities are consistently seen to be the most important factors in the building of a more equitable society [43], [45].

The issue around access to education and its effect on inequality is not confined to the production of finished goods. Goldberg [18] suggest that global trade in intermediate goods also has an effect on wage inequality with some large firms from developed countries locating unskilled parts of production in developing countries and reserving any skilled part of production for developed countries [45]. Apart from relieving firms of the need to develop skills in workers in developing countries, this can also have the effect of firms shifting responsibility for wages and working conditions away from the regimes of developed countries where conditions are generally governed by industrial law to countries where such laws do not exist or else are only just emerging. In this case (i.e. production of intermediate goods) and in the case of final products the producer has some control over skill development, working conditions and wages and can act to alleviate inequality if motivated to do so.

At the other end of the supply chain consumers have some control over the demand for imported goods. For example consumers in Scandinavia live in some of the most equal of all OECD countries [44] and amongst the most equal in the world [26] yet they import goods from some of the most unequal. One such is China where although foreign demand has increased employment considerably [26] it has induced jobs mainly in low-paid, low and medium-skilled areas without generating new job opportunities for the growing number of college-educated workers in the middle thus adding to inequality [38]. Another Scandinavian trading partner, the Russian Federation, also has high inequality [50]. The economic recessions in Asia, Latin America and the Russian Federation following the financial crises of the 1990s brought increased unemployment and inequality, both of which contributed to the erosion of social cohesion. This was especially true of Russia, where the Gini inequality index rose from 0.397 in 2001 to 0.422 in 2009 [12] and which recorded one of the lowest life satisfaction scores in the world just above Moldova, Ukraine and Belarus [28]. Other Scandinavian trading partners such as Brazil and the Philippines are experiencing worsening inequality, which has been linked to trade liberalisation. For example a 2005 UN study [50] found that trade liberalisation caused wages to decline in Brazil and Mexico especially in the case of unskilled workers. The study went on to also link trade liberalisation with widening inequality in the Philippines and Eastern Europe.

2.3 Responsibility

The debate around the causes of within-country inequality, and even within which countries it is rising or falling, is unresolved [4]. Also different methodologies for studying inequality can produce different results [39] making it difficult to generalise causes and specific effects. So who may be held responsible for improving the situation? Blaming bad government in such countries [11] is to oversimplify the issues. After all, global companies do business with these countries. As Goldberg [18] point out, increasingly global trade is about movement of goods between firms located in different countries rather than the flow of goods between countries, so perhaps such firms should take the blame for supporting – and possibly exploiting – inequality. Blaming the final consumer for demanding goods contaminated by the implication that they arose from countries of gross inequality is also a simplification. Consumers could also be seen as providing jobs for the desperately poor. People need to work and often a poorly paid job in a country of high wage disparity is better than no job. Firms, governments and consumers all play a part in the complex web of production, wages and work. With a better understanding of within-country inequality all can play a part in bringing about a more equal society.

The ‘inequality footprint’ can provide a tool to assist in tracking the inequality implicated in goods as they move around the world. The concept of ‘footprint’ is familiar from the literature. Studies have been conducted, for example, on the emissions footprint showing that consumption in one country can cause emissions in another [59]. Or the water footprint that can track embodied water in goods as they move around the world and can distinguish ‘scarce water’ inputs from non-scarce water inputs [22]. We also know that consumption in one country requires the input of labour from other countries [38], which may or may not be problematic depending on work conditions and the age of workers. Just as campaigns for fair and ethical work conditions that distinguish unethical (e.g. child labour) from other labour we distinguish problematic (unequal) labour from equal labour. We define an inequality footprint as the Gini index of the workforce that is directly and indirectly required to satisfy the consumption of a given population. In this way we cast income inequality into the same footprint accounting framework as scarce water, GHG emissions and unethical work practices. These accounts may then be used to study the correlative or causal relationship between consumption and inequality.

3.1 Data sources

This section describes the data foundation of this work. We use three databases covering 187 countries:

1. Employment: the International Labour Organization's LABORSTA database [24], and the United Nations System of National Account UNSNA-Official Country database [53];
2. Income and global inter-industry transactions data: the Eora Multi-Regional Input-Output (MRIO) database [14], [32], [33];
3. Gini index: the Standardized World Income Inequality Database (SWIID) version 3.1 [47], and the Organization for Economic Co-operation and Development (OCED) database (http://stats.oecd.org/) provide Gini indices referring to both before-tax and after-tax income. In this paper we have used the after-tax Gini index data. Also we including Gini index database from the World Bank (http://data.worldbank.org/).

In essence, we use data on employment, income and Gini indices to construct income distributions for the 187 countries in our study (see Appendix S1 in File S1). These income distributions are then cast into the shape of a so-called national satellite account (see Appendix S3 in File S1) that accompanies global inter-industry (MRIO) transactions data. In unison, the MRIO data and income distribution satellite enable tracing economic activity in one location to income distributions in other locations around the world. This is explained in detail in the remainder of this section.

3.2 Basic input-output theory

This work is concerned with enumerating employment and inequality footprints for the world's economies. As in previous studies on carbon footprints [20], [46], water footprints [15], and biodiversity footprints [34], we apply the method of economic input-output (IO) analysis [36].

The centrepiece of any IO analysis is an assembly of three matrices: one N×N intermediate transactions matrix T with elements T_ij that represent monetary amounts intermediate demand from supplying economic sectors such as agriculture, forestry, fishing, mining, manufacturing, utilities, trade, transport, or services i = 1,…,N into using sectors j = 1,…,N; one K×N value added matrix v with elements v_kj that represent monetary amounts of primary input from value-added categories i.e. wages and salaries, gross operating surplus, and net taxes on production k = 1,…,K into using sectors j = 1,…,N; and one N×M final demand matrix y with elements y_jm that represent monetary amounts of final demand from supplying economic sectors i = 1,…,N into final demand categories i.e. household consumption, government final consumption, gross fixed capital expenditure, and changes in inventories m = 1,…,M.

This assembly is a balanced financial account in a sense that total uses x = T1^N+y1^M equal total supply x′ = 1^Kv+1^NT, where 1^N =  {1,1,…,1} etc are suitable summation operators, and where the prime (‘) symbol denotes transposition. Setting T1^N = Ax, we find the fundamental input-output identity x = Ax+y1^M, where I is a N×N identity matrix, A is the input coefficients matrix, and is the famous Leontief inverse.

3.3 Extended input-output analysis

It was always Leontief's intention to put IO analysis to use for solving environmental and social problems [35], [36]. To this end, the input-output account assembly (T, v, y) is supplemented by a 1×N environmental or social satellite account Q with elements Q_1j describing amounts of some environmental or social variable (for example energy, emissions, employment) associated with (used by, emitted by) economic sectors i = 1,…,N. Setting Q1^N = qx, we find environmental or social accounting identities as Q = Q1^N = q, where Q represents the economy-wide total of the satellite account Q. The vector q holds so-called intensity coefficients (for example energy intensities, employment intensities) that describe the amount of the satellite variable associated with (used, emitted per) one unit of total use. In contrast, the multiplier m describes the amount of the satellite variable associated with one unit of final demand. The multiplier m includes all direct and indirect flow-on effects rippling throughout the complex supply-chain network of the entire economy, as described by the Leontief inverse L, where m = qL. The environmental and social accounting identities are the basis of the widely used Leontief demand-pull model, which interprets Q as the total environmental or social inputs required to satisfy a final demand bundle y. Therefore, Q is also referred to as an environmental or social footprint (depending on the nature of the satellite variable).

Whilst emissions satellite accounts are the basis of many carbon footprint studies [20], [46], the satellite accounts Q used in this work are employment accounts E in units of full-time equivalent person-years, and wage and salary income accounts W in units of US$. These accounts were constructed at a detail of 187 countries (see Appendix S1 in File S1) with a combined 15,909 sectors in order to complement a matching Multi-Region Input-Output (MRIO) framework (T, v, y) of the world economy [33], [37], [40], [41]. Whilst the income satellite account W is based on a multitude of data sources [33], the employment satellite account E is based predominantly on data published by the ILO [24]. Further details on the construction procedures followed are given in Appendix S3 in File S1.

3.4 Inequality satellite accounts

The employment and income accounts E and W can be used to determine employment and income footprints of nations [1], [38]. In order to construct satellite accounts on income inequality, data on employment and income have to be collected, and assembled into a separate satellite account, for a number of income classes. Such detailed data are hard to come by for most countries as a whole, for example the Household Expenditure Surveys of Brazil [23], and Australia [2], let alone for a complete suite of world nations and broken down into economic sectors as represented in the MRIO database that we use. We have therefore devised a strategy to estimate distributions of income across C income classes for individual industry sectors in individual countries from three data items: a) the country's Gini index γ, b) the sector's total income payments for employees I_tot, and c) the sector's total workforce P_tot.

Income inequality is typically depicted in Lorenz curves (Fig. 1). Cumulative income I(c) at income class c (normalised to 100%)(1)is plotted against cumulative workforce (equally normalised).

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Figure 1. Lorenz Curve for Brazil’s Income Distribution in 2009.

Notes: Circles: data from IBGE [23]; solid line and regression equation: power function approximation from Eq. 3; dashed diagonal line: Lorenz curve for complete income equality. Further examples about the quality of the power function fit can be found in Fig. S1.

https://doi.org/10.1371/journal.pone.0110881.g001

(2)

In the case of perfect income equality, cumulative income increases proportionally with cumulative workforce, and the Lorenz curve is a diagonal connecting the origin with the point {1,1} (dashed line). Any degree of income inequality will see cumulative workforce increase more rapidly than cumulative income, thus leading to a convex Lorenz curve (circle markers in Fig. 1) (3)

This Lorenz curve can be approximated by a power function (solid line in Fig. 1)(4)

Total income equality corresponds to , and leads to increasing inequality. A power function also ensures that all Lorenz curve representations pass through the origin {0,0} and the point {1,1}.

The Gini inequality index can be calculated as the ratio of the area between the diagonal and the Lorenz curve, and the area below the diagonal:(5)

Since P(0)  = 0 and P(C)  = 1 according to the definition in Eq. 2, we can evaluate the integral, and find the relationship between and as(6)

Fig. 1 shows an example for an approximation of a Brazilian Lorenz curve with  = 2.51 (solid line), based on data (circles) yielding  = 0.43. We have added evidence in support of the power function approximation in Fig. S1.

Inserting Eq. 6 into Eq. 3, we find the income distribution(7)

Eq. 7 can be evaluated by choosing income intervals i(c), and calculating corresponding workforce fractions. Choosing a large number C of intervals will increase the resolution of the approximation. Fig. 2 shows an example for an approximation of a Brazilian Lorenz income distribution curve, based on data (circles) yielding  = 0.43.

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Figure 2. Income Distribution for Brazil in 2009.

Notes: Circles: data from IBGE [23]; solid line: power function approximation from Eq. 7.

https://doi.org/10.1371/journal.pone.0110881.g002

The average wage w(c) for each income class c can be determined via(8)

Assuming that an income class satellite would identify L « C classes according to wage intervals w_l<w(c) ≤w_l+1, and assuming that one satellite class l ∈ {1,…,L} contains n_l such wage classes {c_1,…,nl}, the income class satellite account Q simply reads(9)

The workforce in each satellite class l is then taken from Eq. 7 as(10)

The average wage in each satellite class l is (11)with . Repeated for all sectors in the MRIO database, this procedure will yield two satellite accounts Q and R sized C×N, one for employment by class, and one for income by class.

3.5 Inequality footprints

Inequality footprints of nations can now be calculated subjecting the income and employment class accounts to the Leontief-type demand-pull terms of income inequality would then proceed as follows. Assume a N×1 vector describing a final demand bundle originating from country X, the inequality footprint of which is to be evaluated. The impact of in terms of income earned in economic sectors j in various classes c is  =  {θ_χφ}  = , where holds income by sector and by class per unit of total use, and where is a diagonal matrix holding total use. The impact of in terms of employment in various classes is , where holds employment by sector and by class per unit of total use. In other words, and are the income and the workforce, respectively, broken down by economic sector and by class, that are required directly and indirectly to satisfy the final demand bundle , or in other words the income and employment footprints of the final demand bundle . The average wage paid to this workforce in sector j is .

The Gini index γ characterising this global workforce is (12)

includes people working in country X ανδ in other countries ( refers to the inequality within the entire world, and therefore relates to the between-country perspective of inequality described by the ‘World Inequality’ concept in Milanovic [39]. In general the more unequal the combination of import origins, the higher the global inequality footprint. This perspective is equivalent to Milanovic [39] also offers a method for decomposing global inequality into within-country, between-country, and overlapping effects). It is possible to isolate the inequality effect of the domestic final demand bundle on particular countries by only considering the income and workforce needed from the sectors j belonging to those countries :(13)

The inequality footprint of a nation can be defined as a weighted sum over countries of production origin(14)

The inequality footprint of imports can be defined as a weighted sum over countries of imports origin(15)

The origin country weights could be set to the income footprints or employment footprints , or to the product of both (compare with Part A in Eq. 1 in [39]). In general the more unequal the selection of import origins, the higher the inequality footprint of imports.

3.6 Qualifications

To our knowledge this is the first time that an income inequality indicator (through the Gini index measure) has been combined with an input-output calculus. Nevertheless, the implementation of the method we have so far described has a number of shortcomings.

First, as we described above, income distributions are largely unavailable for most countries, and therefore we needed to construct income distributions from Gini indices by fitting power functions. These power function fits will necessarily deviate from “true” income distributions, but as we have shown in the example for Brazil, and in more examples listed in Fig. S1, such deviations are likely to be small.

Second, Gini indices are not available as continuous time series for all countries. In the absence of continuous information, we interpolated the Gini indices for missing years on the basis of those for neighbouring years. We treat missing values at the beginning and the end of our period of analysis by setting them equal to the data available for the closest year. Large gaps exist only for countries with a combined small fraction of GDP, and associated errors are probably small. For Gini index availability see Appendix S2 in File S1.

Third, data for Gini indices, income distributions, or Lorenz curves are almost impossible to locate for individual industry sectors, therefore we needed to assume that the national Gini index applies to all sectors of the economy. This procedure will lead to allocation errors in cases where inequality varies significantly between sectors, and where a country predominantly exports those products made by sectors with significantly above- or below-average inequality (for example, soybean in Brazil as opposed to other sectors such as petroleum oils).