Using this data and a combination of value-added estimates, instrumental variables, and regression discontinuity methods, Singh (2020) finds that the causal effect of an additional year of primary school in Vietnam is 0.76 _σ_ , the largest value among the four countries. This is likely a lower bound for “high performance” on a global scale, since Vietnam—while an excellent performer for its income class—ranks in the second decile of average Harmonized Learning Outcomes (which, as noted above, covers 164 countries from 2000-2017). We can compare these results to an alternative high-benchmark year-on-year comparison: changes analyzed in the United States by Bloom, Hill, Black, and Lipsey (2008), building on methods used by Kane (2004). The largest year-on-year learning gains are between grade 1 and 2, and range from 0.97 _σ_ in reading to 1.03 _σ_ in math. Finally, we can derive approximate year-on-year changes for global high performers. We assume that the appropriate high-performance rescaled HLO benchmark is a score of 325 at the primary level. This score is assumed to be obtained over four years, since most primary international assessments occur in grade 4; average high-performance learning per year is thus 81.25 points. We then assume a within-country standard deviation of 85 points, based on the values for the five highest-performing countries using 2006 PISA microdata. Taking the ratio of these two values yields a year-on-year gain of 0.96 _σ_ .

The second approach examines large, system-level gains. Here, we explore what would constitute a large learning gain in systemic terms, as a way to benchmark what high-performing learning progress would look like. One example is to consider cross-country learning gaps in terms of HLO scores used for the World Bank Human Capital Index. A gain of 0.8 _σ_ would enable the United Kingdom or Vietnam to catch up to Singaporean learning levels: because the cross-country standard deviation is equivalent to 70 HLO points, a 0.8 _σ_ gain for the United Kingdom (517) or Vietnam (519) translates into nearly closing the gap with Singapore (581). In another example, consider that the black-white achievement gap in the United States in math ranges from 0.99 _σ_ to 1.04 _σ_ in grades 4 and 8 (Bloom et al., 2008). A gain large enough to nearly close either of these gaps would be highly meaningful in policy terms.

The final approach uses rules of thumb. Cohen (1988) proposed the following standardized effect-size benchmarks: at least 0.20 for “small” effects, 0.50 as “medium” effects, and 0.80 for “large” effects. This framework has been broadly applied across interventions and contexts for decades. However, there is debate about the relevance of these indicators to education interventions, given that almost all interventions in high-, middle-, and low-income countries have much smaller impacts. For high-income countries, the 90th-percentile effect size is 0.47 (Kraft, 2020); for low- and middle-income countries, it is 0.38 (Evans & Yuan, 2022). Both of those fall below the traditional Cohen benchmark for even medium effects.

In summary, these various approaches—particularly those focused on high-performance learning trajectories and meaningful systemic improvements—yield high-performance benchmark learning rates ranging from around 0.8 _σ_ to 1.0 _σ_ . In this paper, we use an artificial benchmark of 0.8 _σ_ for learning gains, which is a conservative high-performance benchmark consistent with this range.

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