## Abstract

This paper is the first to decompose absolute global income inequality into its within-country and between-country component. The results show a continuous increase of absolute global inequality during 1850–2010, which can be separated into three distinct phases: (1) between 1850 and 1929, within-country inequality explained up to 76 % of absolute global inequality, yet the growth rates of within- and between-country inequality were very similar; (2) a sharp increase in the importance of between-country inequality occurred during the 1929–1950 period, which was followed by a period during which the within- and between-country components were approximately equally relevant; and (3) after 1985, the growth in absolute global inequality was driven primarily by the accelerated growth of within-country income differences. Currently, within-country inequality explains 70 % of absolute global market inequality, a figure close to that of the year 1850. Additional findings include that absolute income convergence between countries took place after 2005, that it is possible to reduce absolute inequality and to grow simultaneously, and that recently within-country net inequality has grown faster than market inequality. The main findings are preserved when different absolute decomposable inequality measures, sample sizes, and purchasing power parity exchange rates are used.

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## Notes

Suppose that a country has two citizens who have incomes of $1000 (A) and $100,000 (B). If the income of both grows by 10 %, the new income of citizen A is $1100, and that of citizen B is $110,000. The proportional income difference between the two remains constant (B has still 100 times more income than A), but the absolute gap between the two incomes increased by $9900.

Note that also from a technical perspective, absolute indices are as good inequality measures as relative indices (see Kolm 1976).

Market income is pre-tax and pre-transfer income, whereas net income considers tax payments and transfer receipts.

SYM means that the index is invariant with respect to the reordering of incomes. POP means that the value of the index does not depend on the population size. NOM means that the index is non-negative and that it has the value of zero only under the condition that all incomes are equal.

CON refers to continuity: for all \(n \in N, I^{n}\) is a continuous function. Bosmans and Cowell (2010) show that \(I_{\theta }^{n}\) and \(I_{V}^{n}\) are the

*only*class of absolute decomposable inequality measures, even when the CON property is absent.The variance has the additional advantages that it fulfills the Shorrocks and Theil criterion, that it is easy to compute, and that it can be interpreted as a measure of deprivation (Chakravarty 2001).

Ventile shares are frequently used in the literature; they allow for relatively exact inequality estimates when income differences within income share groups are not taken into account (see e.g., Davies and Shorrocks 1989; Milanovic 2012b). Each population ventile represent 5 % of the population. The ordering and grouping of the population takes place according to their income. (The lowest ventile represents the poorest 5 % of the population, etc.). Please note that our results are robust when decile or quintile shares are used instead of ventile shares.

It is a common procedure in global inequality studies to use GDP per capita in PPP and not in market exchange rates [see Anand and Segal (2008) for a discussion of the reasons].

“The literature suggests that when the whole distribution is covered, the log-normal is to be preferred [and] on average the difference between an assumed log-normal and a Pareto distribution [is] limited” [van Zanden et al. 2014, pp. 4–5 of their data appendix; see also Soltow (1998) and Lopez and Servén (2006)].

To verify that this method produces estimates that fit the existing income share data well, we compared our estimates with readily available income share data from the WDI database (see the “Appendix”).

When Solt’s database reports a Gini coefficient for a country in a benchmark year, this coefficient is taken for that year. Otherwise, we use either the Gini coefficient that was reported one year before or after the respective benchmark year, or when data for both years are available, the mean of the these two Gini coefficients is used.

Australia, Belgium, Brazil, Canada, Chile, China, Colombia, Czechoslovakia, Denmark, France, Germany, India, Indonesia, Ireland, Italy, Japan, Mexico, the Netherlands, Norway, Peru, the Philippines, Poland, Portugal, Russia, Spain, Sweden, Switzerland, Thailand, the United Kingdom, and the United States.

The 1980 estimates from the recent and historical series are nearly identical because (1) the same GDP per capita data are used for both series, (2) the population data from Maddison and WDI are very similar, and (3) the market Gini data from van Zanden et al. (2014) and SWIID are similar for many countries.

Anand and Segal (2014) also use ‘absolute versions’ of the Theil L and Theil T indexes to measure changes in absolute global inequality, that is, the mean income of a given year multiplied by the respective relative Theil L and Theil T index. Both Theil measures report the same trend changes as the absolute Gini index. Please note that these indices are not in line with the formal definition presented on p. 5.

GDP per capita in the core group of countries grew, on average, approximately 22 % between 1929 and 1950.

In approximately 60 % of the core group of countries, the Gini coefficient declined by more than 5 Gini points, and in approximately 30 % of the core group countries, the decrease was more than 10 Gini points.

Several studies report a slight increase in global inequality during recent decades (e.g., Milanovic 2005, 2013; van Zanden et al. 2014), whereas others report a significant decline (e.g., Sala-i-Martin 2006; Pinkovskiy and Sala-i-Martin 2009). See Anand and Segal (2008) and Goda (2013) for in-depth discussions of these inconclusive results.

Van Zanden et al. (2014) estimate that in 2000, approximately 70 % of relative global inequality could be explained by between-country inequality, and Milanovic (2012a, p. 125) finds that currently, “more than 80 % of global income differences is due to large gaps in mean incomes between countries”.

Net income inequality can be calculated only with for the recent data series due to data availability.

During the entire period, market income inequality grew approximately 3.3-fold, whereas net inequality grew approximately 3.5-fold.

These findings indicate that the exponential index \(I_{\theta }^{n} \left( x \right)\) is sensitive to relatively small changes of the subgroup weight \(\theta\) (an observation that was also made by Chakravarty (2001)).

For this calculation, only GDP per capita and population data are needed, which are available for many more countries each year than are the Gini coefficients.

This finding is consistent with Bosmans et al.’s (2014) results. Bosmans et al. show that absolute between-country inequality increased during the period 1980–2009. However, they find evidence only for an increase between 1980 and 2005, and their estimates suggest that absolute inequality subsequently decreased.

Argentina, Bangladesh, Brazil, China, Costa Rica, Dominican Republic, Honduras, Indonesia, the Philippines, Poland, Tunisia.

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## Acknowledgments

We thank Ange´lica Sanchez, Juliana Arias, and Natalia Gaviria for their outstanding research assistance. Furthermore, we are grateful to Bas van Leeuwen (and his co-authors) for providing us with an updated version of their historical Gini coefficient data based on their paper *The Changing Shape of Global Inequality 1850*–*2000*. We would also like to thank an anonymous referee, Maria Fernanda Quintero, Gustavo Canavire, Thedore Breton, and the participants of the 18th annual conference of the Research Network Macroeconomics and Macroeconomic Policies (FMM) for their helpful comments, which helped us to improve this paper substantially. We gratefully acknowledge financial support from Colombia’s Administrative Department of Science, Technology and Innovation (Colciencias), which partly financed the research assistance of Angélica Sanchez (*Jovenes Investigadores* program).

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## Appendix

### Appendix

### 1.1 The Goodness of Fit of the Income Share Estimation Methodology

To examine the robustness of our method to derive income shares [(6)–(7) in Sect. 2], we calculate income shares with Gini coefficients drawn from the WDI database and compare these estimates with readily available income share data from the same database. The WDI provides Gini coefficients and quintile income shares for 155 countries. The available data are very unbalanced (881 of 5115 possible observations between 1980 and 2012); we therefore use a benchmark year methodology (see Footnote 12) to calculate income shares for 1985, 1990, 1995, 2000, 2005 and 2010 (352 of 930 possible observations).

Table 4 shows that the correlation between the income shares readily available from the WDI database and our estimated shares is close to one (with the exception of Quintile 4), and Table 5 demonstrates that the average difference between the values of our estimated shares and the readily available shares is relatively small. However, our methodology consistently underestimates the two bottom quintile shares, overestimates the shares from Quintile 3 and 4, and underestimates the top quintile share. To examine whether this difference has an effect on the level and/or trend of absolute inequality estimates, we calculate the level of absolute within-country inequality for a core group of 11 countries^{Footnote 26} (66 observations) for which the WDI quintile share and Gini data are available in each benchmark year.

Figure 8 shows that the correlation between these two inequality series is close to one. This result suggests that our method produces income share estimates that fit the ‘real’ data very well and that they do not influence trend changes. It is important to note that the calculated shares lead to a slightly higher level of absolute inequality (by approximately 1 %) than the readily available WDI shares. This means that our income share estimation methodology might slightly overestimate absolute inequality levels.

### 1.2 The Goodness of Fit of the Income Share Estimation Methodology

To prevent imputations from affecting our main findings, we have not imputed more than 2 years of data per variable and country. For the imputation of GDP per capita, we have used regional averages because this approach is widely used in the existing literature (see e.g., Sala-i-Martin 2006). Please see Table 6 for an overview of the imputations.

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Goda, T., Torres García, A. The Rising Tide of Absolute Global Income Inequality During 1850–2010: Is It Driven by Inequality Within or Between Countries?.
*Soc Indic Res* **130**, 1051–1072 (2017). https://doi.org/10.1007/s11205-015-1222-0

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DOI: https://doi.org/10.1007/s11205-015-1222-0

### Keywords

- Absolute inequality
- Personal income distribution
- Global inequality
- Within-country inequality
- Between-country inequality