Using this approach, which builds on Altinok _et al._ (2014), Angrist, Patrinos & Schlotter (2013), and Altinok and Mureseli (2007), regional test scores for countries participating in an RSAT but not in an ISAT can be transformed into an internationally comparable score over time. These test scores allow the inclusion of developing countries which participate only in regional assessments to be included in our international achievement data set. We conduct this analysis for all countries, including those that participated in an ISAT to apply this transformation equally and limit bias. As a result of this relatively simple methodological innovation, we can build a globally comparable database of _Harmonized Learning Outcomes (HLOs)_ for 163 countries/areas from 1965-2010.<sup>14</sup>

# _3.2.2. Grade, Subject and Year Grouping_

While it would be ideal to have a test score for every year and grade, test frequency is too low and sporadic. To this end, we group test scores into five-year and grade range intervals. Specifically, we construct a score for each subject (Math, Reading and Science) and grade range (Primary or Secondary) for every 5-year interval. This increases data and country coverage substantially and is aligned to the approach taken by Barro and Lee (2001) for educational attainment. We conduct this exercise by grouping test scores that are comparable by subject and grade if they are administered a few grade levels or years apart. If countries participated in several comparable tests in or around a specific year, we build the average over the tests.

This approach has obvious limitations. Namely, an extra grade or year of learning would mechanically improve learning. For example, grouping grade 4 and grade 6 into ‘primary’ schooling or 2000 and 2001 tests in to a 2000-year interval ignores the fact that students perform better as the moves across grades and over time. However, these differences within group (primary vs secondary, or a few years over or above a five-year step) are often small, limiting bias. Moreover, since this methodology is applied across all countries and intervals it unlikely that one country is transformed differently from another, further limiting the scope for bias. The main instance in which bias might arise is if data availability is correlated with a countries’ education quality our progress. For example, if countries that perform worse only have available

> 14We standardize our final dataset with a standard deviation of 30 and mean of 500. This is analogous to many of the ISAT and RSATs means and standard deviation at the country-level is approximately the same as the observed value in our dataset. We do this for a group of stable countries, the OECD, in line with the methodology proposed by Hanushek and Woessmann (2016). This enables us to know where Finland, for example, lies relative to the average OECD country. We conduct this ex post standardization for all countries. However, for countries off the OECD scale, this standardization is biased and less relevant. For these countries, their relative position and rank is robust, although their absolute score difference should be caveated appropriately.

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