This estimate stems from a statistical model that relates annual growth rates of real GDP per capita to the measure of educational quality, years of schooling, the initial level of income, and several other control variables (including in different specifications the population growth rates, political measures, openness of the economies, and the like). Hanushek and Kimko (2000) find that adding educational quality to a base specification including only initial income and educational quantity boosts the variance in GDP per capita among the 31 countries in their sample that can be explained by the model from 33 to 73 percent. The effect of years of schooling is greatly reduced by including quality, leaving it mostly insignificant. At the same time, adding the other factors leaves the effects of quality basically unchanged.

Several studies have since found very similar results. Another early contribution, by Lee and Lee (1995), found an effect size similar to Hanushek and Kimko (2000) using data from the 1970-71 First International Science Study on the participating 17 countries, also leaving quantitative measures of education with no significant effect on growth. Using a more encompassing set of international tests, Barro (2001) also finds that, while both the quantity and the quality of education matter for economic growth, quality is much more important. Employing the quality measure developed by Hanushek and Kimko (2000) in a development accounting framework, Wößmann (2002, 2003b) finds that the share of cross-country variation in levels of economic development attributable to international differences in human capital rises dramatically when quality of education is taken into account.<sup>40</sup> Extensions of the measure of Hanushek and Kimko (2000) and its imputation in Wößmann (2003b) are also used in the cross-country growth regressions by Bosworth and Collins (2003) and in the cross-country industry-level analysis by Ciccone and Papaioannou (2005). Both also find that educational quality strongly dominates any effect of educational quantity on growth.<sup>41</sup> Coulombe, Tremblay, and Marchand (2004) and Coulombe and Tremblay (2006) use test-score data from the International Adult Literacy Survey (see Section 2.4 above) in a panel of 14 OECD countries, confirming the result that the quality measure outperforms quantitative measures of education. Finally, Jamison, Jamison, and Hanushek (forthcoming) extend the Hanushek and Kimko (2000) analysis by

> 40 This work builds on Gundlach, Rudman, and Wößmann (2002) and analyzes output per worker in 132 countries in 1990. The variation that can be attributed to international differences in human capital rises from 21 percent to 45 percent once the quality of education is taken into account, and to over 60 percent in samples with reasonable data quality.

41 Bosworth and Collins (2003) cannot distinguish the effect of quality of education from the effect of quality of government institutions. The analysis in Section 4.5 below shows, however, that they can be separated when we use our new quality measure that also extends the country sample by several additional data points on international tests scores.

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