19 pupil-teacher ratios, and school dropout rates<sup>29</sup> . The second focuses on measures of cognitive skills of individuals. Using measures of cognitive skills has the clear advantage of allowing for differences in quality that result from sources other than the formal education system. On the other hand, using measures of school inputs becomes preferable if there are economically relevant aspects of human capital that are not captured by cognitive tests.

One extensive data set using the latter method is that of Hanushek and Kimko (2000), who developed indices of educational quality for 38 countries based 6 voluntary international tests of academic performance in mathematics and science for the years 1965 to 1991. The International Association for the Evaluation of Educational Achievement (IEA) administered four of the tests, while the remaining two were administered by the International Assessment of Educational Progress (IAEP). The focus on mathematics and science is in line with the theoretical emphasis on the importance of research and development as the source of growth<sup>30</sup> . They argue that students with a good understanding of mathematics and science form the future pool of engineers and scientists. Bishop (1992) finds that, at least for the United States, the grasp of mathematics is important in determining one’s productivity and income.

To develop a single measure of educational quality, Hanushek and Kimko combined test scores from 26 available performance series, each reflecting different ages, subtest scores, years, and sets of countries, all with different mean percent correct<sup>31</sup> . Two approaches were taken to combining the separate tests available for each country. The first summary method uses a multiplicative transformation to convert each performance series to a mean of 50. The second method uses scores from the National Assessment of Education Progress (NAEP) tests for U.S. students to adjust the scores of the international tests so that they are comparable across countries and time<sup>32</sup> .

In order to extend their educational quality measures to a larger set of countries Hanushek and Kimko associated their educational quality indices with other correlates of 29 For example, see Barro (2001).

30 For example, see Romer (1990a).

31 The international math and science tests are given at different points in time, suggesting that it could be possible to look at changes in quality over the 30 year period considered. Hanushek and Kimko, note however that this approach is impractical because their emphasis was on the quality of the labor force and not the quality of the students. A change in observed test performance of current students might indicate future growth effects but not contemporaneous effects, because the achievement change would not have propagated through the labor force.

32 At varying times from 1969 to the present, U.S. students aged 9, 13 and 17 have taken NAEP tests in both mathematics and science. These NAEP tests are constructed on a consistent basis to provide comparisons over time and thus the NAEP scores provide a benchmark of performance to which U.S. scores on international tests can be keyed. The mean for each international test series is allowed to drift in accordance to U.S. NAEP score drift and the mean U.S. performance on each international comparison.