weights, replication weights, and the assessment’s plausible values. These data are then used to estimate the Lorenz parameters.<sup>37</sup> The Lorenz curve captures the pattern of _relative learning inequalities_ in the student population. It is independent of any considerations of the absolute learning level. The share of students below a proficiency level captures an absolute standard of the student population. Two functional forms—the Beta Lorenz<sup>38</sup> curve and the General Quadratic (GQ)<sup>39</sup> Lorenz curve—were tested for calculating the Lorenz curve parameters. For this exercise, the General Quadratic (GQ) Lorenz curve was preferred, since it provided better results in terms of both internal and external validation.<sup>40</sup> This exercise computes learners’ share below the end-of-primary minimum proficiency level (MPL), the average learning gap with respect to the MPL, and the average learning gap severity for the same MPL.

Some of the main assumptions of this work are:

- A focus on first-order effects of COVID-19-related school closures in the crisis’s first 12 months. Given the definition of the indicator in terms of children at the end of primary, the work does not look at cumulative effects at other grades.

- Children in high-income countries are learning more than children in low-income countries. The expected learning gains, based on the literature and empirical work, are 0.5 of a standard deviation for high-income countries, 0.4 for upper-middle-income countries, 0.3 for lowermiddle-income countries, and 0.2 for low-income countries.

- Dropout estimates used are based on October 2020 growth projections and consider only children in primary (ages 4–11). The expected dropout rate of primary school age children is substantially smaller than that of secondary school age children (35% of the total Primary and Secondary drop out), given the greater income generating opportunities of secondary school age children and far greater supply constraints in the developing world. The dropout estimates are only affected by income shock, and ignore the potential effects of concerns about school safety concerns and of school disengagement, which are likely to be relevant but are extremely hard to measure at this stage. If anything, these further effects have a clear upward bias, so the out-of-school numbers presented here can be seen as lower-bound estimates. In any case, this crisis is not over, and our understanding of the ramifications to the economy and household welfare are being updated daily.  Since March 2020 global growth projections have been frequently revised, and the recently released Global Economic Prospects indicates that growth projections are likely to continue to go down. In each of these revisions, our expected number of student’s dropping out due to the household income shock is revised upwards. Our initial estimate, based on the March MPO suggested that approximately 1.4 million primary students would drop out of the education system; by October, this number had already been revised to 3.8 million, and is likely to be revised further upward based on revisions to the magnitude of the economic recession (Figure 1).

> 37 For details in the methodology, see Azevedo et al. (2020).

> 38 Kakwani 1980.

> 39 Villasenor and Arnold 1989.

> 40 Lorenz parameters were estimated using the user written Stata ADO function GROUPDATA, available at <u>https://github.com/jpazvd/groupdata.</u>

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