Introduction to Modern Economic Growth schooling; if this is the case, these omitted factors may be removed when we look at changes While we cannot reach a firm conclusion on these alternative explanations, the strong correlation between the level of average schooling and economic growth documented in Figure 1.17 is interesting in itself The narrowing of income per capita differences in the world economy when countries are weighted by population is explored in Sala-i-Martin (2005) Deaton (2005) contains a critique of Sala-i-Martin’s approach The point that incomes must have been relatively equal around 1800 or before, because there is a lower bound on real incomes necessary for the survival of an individual, was first made by Maddison (1992) and Pritchett (1996) Maddison’s estimates of GDP per capita and Acemoglu, Johnson and Robinson’s estimates based on urbanization confirm this conclusion The estimates of the density of income per capita reported above are similar to those used by Quah (1994, 1995) and Jones (1996) These estimates use a nonparametric Gaussian kernel The specific details of the kernel estimates not change the general shape of the densities Quah was also the first to emphasize the stratification in the world income distribution and the possible shift towards a “bi-modal” distribution, which is visible in Figure 1.3 He dubbed this the “Twin Peaks” phenomenon (see also Durlauf and Quah, 1994) Barro (1991) and Barro and Sala-i-Martin (1992) emphasize the presence and importance of conditional convergence, and argue against the relevance of the stratification pattern emphasized by Quah and others The first chapter of Barro and Sala-i-Martin’s (2004) textbook contains a detailed discussion from this viewpoint The first economist to emphasize the importance of conditional convergence and conduct a cross-country study of convergence was Baumol (1986), but he was using lower quality data than the Summers-Heston data This also made him conduct his empirical analysis on a selected sample of countries, potentially biasing his results (see De Long, 1991) Barro’s (1991) and Barro and Sala-i-Martin’s (1992) work using the Summers-Heston data has been instrumental in generating renewed interest in cross-country growth regressions The data on GDP growth and black real wages in South Africa are from Wilson (1972) Feinstein (2004) provides an excellent economic history of South Africa 35