Abstract
We investigate the evolution of global welfare in two dimensions: income per capita and life expectancy. First, we estimate the marginal distributions of income and life expectancy separately. More importantly, we consider income and life expectancy jointly and estimate their joint global distribution for 137 countries during 1970–2000. We reach several conclusions: the global joint distribution has evolved from a bimodal into a unimodal one, the evolution of the health distribution has preceded that of income, global inequality and poverty has decreased over time and the evolution of the global distribution has been welfare improving. Our decomposition of overall welfare indicates that global inequality would be underestimated if within-country inequality is not taken into account. Moreover, global inequality and poverty would be substantially underestimated if the dependence between income and health distributions is ignored.
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Notes
- 1.
The two most popular concepts are β-convergence according to which countries that begin at a lower level of income per capita grow at faster rates and σ-convergence according to which the dispersion of country growth rates decreases over time. For a discussion see, for example, Maasoumi et al. (2007) and references therein.
- 2.
Milanovic (2005) discusses the issues and controversies surrounding the definition of the term global inequality.
- 3.
The HDI is an equally weighted average measure of three indicators of achievement: per capita income, life expectancy, and educational attainment (itself a weighted average of the rates of literacy and school enrollment). The HPI is also an equally weighted average measure of three indicators of deprivation: probability of survival to age 40, adult illiteracy, and lack of a decent standard of living (itself an equally weighted average of the proportion of the population without access to improved water source and the proportion of under weight children).
- 4.
For example, suppose there exists a simple economy with two individuals A and B, each endowed with two attributes X and Y. Consider the following two scenarios: (1) \(\left (X_{A} = 2,Y _{A} = 2\right )\) and \(\left (X_{B} = 0,Y _{B} = 0\right )\) and (2) \(\left (X_{A} = 2,Y _{A} = 0\right )\) and \(\left (X_{B} = 0,Y _{B} = 2\right )\). Since the marginal distributions of X and Y are identical for these two scenarios, any “hybrid” index that fails to account for the dependence between the marginal distributions will conclude that the two share the same level of welfare.
- 5.
For a comprehensive discussion of the forces that have shaped changes in mortality and life expectancy during the post-WWII period, see Cutler et al. (2006).
- 6.
The results reported in the next section remain virtually the same when we exclude these countries.
- 7.
Bourguignon and Morrisson (2002) provide data on income distribution for almost two centuries, the last three years being 1970, 1980, and 1992. We used their 1992 income data to represent 1990 in our data set (see also the next footnote). They provided data for few individual countries but in most cases for geographic groups of countries (see their study for group definitions). Our study is based on country-level data. Therefore when individual-country interval data were unavailable we used the corresponding geographic-group data.
- 8.
Income interval data from the WDI are available only for selected years. When referring to data for 2000, we chose the year closest to 2000 with available data (in most cases the late 1990s). This practice is widely adopted in the literature as a practical matter because distribution data are sparse. Many researchers acknowledge that it would not affect results much because income share data do not show wide fluctuations from year to year.
- 9.
For some mainly small countries in our smaple (37 out of the 137), the WDI does not provide share data; we assumed that the distribution of income did not change between 1990 and 2000. These countries account for only 5% of global population in 2000. The results reported in the next section remain virtually the same when we exclude this group from our analysis.
- 10.
To see this, consider again the simple example given in footnote 5. If the data are in the format of \(\left (X_{A} = 2,Y _{A} = 2\right )\) and \(\left (X_{B} = 0,Y _{B} = 0\right )\), then both marginal distributions (of X and Y ) and their joint distribution are identified. In contrast, if the data are reported in the format X = (2, 0) and Y = (2, 0), then only the marginal distributions of X and Y are identified, but not their joint distribution. Our data on income and health for each country are of the second format.
- 11.
Wu and Perloff (2005) use the maximum entropy density approach to estimate China’s income distributions from interval summary statistics.
- 12.
Wu (2003) provides details and additional references. Most of the commonly used mathematical distributions can be characterized or closely approximated by a maxent density. For example, if the first two moments of a distribution are known, maximizing the entropy subject to these two moments yields a normal probability density function.
- 13.
See the monograph by Nelsen (1998) for a general treatment of copulas.
- 14.
In our discussion estimated densities, we use the term “mode” generally such that it refers to both global and local maxima of densities.
- 15.
Bourguignon and Morrisson (2002) plot the estimated density only for 1950 and 1992 and work with relative income (per capita income relative to that of the richest country for each year). Nonetheless, a bimodality is present for 1950 in their graphical analysis as well as a rightward shift of the distribution between 1950 and 1992. A similar “Twin Peaks” phenomenon is reported in Quah (1996).
- 16.
In this issue, see the debate through the pages of The Economist of July 18 2002, March 11 2004, and April 7 2004.
- 17.
Results using the Chen/Ravallion poverty line and other reasonable poverty lines are qualitatively similar in terms of their evolution over time. These additional results are available from the authors upon request.
- 18.
- 19.
The bivariate Gini index used in our calculation, which places equal weights to income and health, is defined in the Appendix. As was discussed in Section 12.1, most commonly used inequality and poverty indices for a single attribute are not uniquely defined in a multidimensional framework. This underlines the importance of joint distribution estimation, which facilitates any welfare inference of interest.
- 20.
Any reasonably defined poverty index resides within the range between the lower and upper bound. Atkinson (1987) discusses the relationship between the bounds of poverty measures and multidimensional stochastic dominance.
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Wu, X., Savvides, A., Stengos, T. (2014). The Global Joint Distribution of Income and Health. In: Ma, J., Wohar, M. (eds) Recent Advances in Estimating Nonlinear Models. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8060-0_12
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