share of total public expenditure and the expenditure per student or per school‐age child. While public education spending as a share of GDP or as a share of total government expenditure reflects government efforts towards education financing given the available resources, it does not perfectly capture the actual flows of public financial resources into the education sector. These variables do not account for the demand for education in countries as reflected by the size of the school‐age population. Given the differences in the demographic structures, the demand for education as well as the resources needed may differ across countries. In the current paper, total public expenditure (government expenditure + education aid received) per school‐age individual (population of pre‐primary, primary, secondary and higher education age) is used as an input variable. To control for differences in purchasing power across countries as well as the inflation, public expenditure is expressed in constant PPP terms.

# _Output variable (y)_

The ideal output variable should capture both access to education and learning. The World Bank’s Human Capital Project introduced a Human Capital Index (HCI) that measures the productivity of the labor force in countries, taking into consideration three key dimensions of human capital: Survival, health and quality education (Kraay, 2018; 2019). The learning‐adjusted years of schooling (LAYS) is the indicator used for the education component. The LAYS captures the number of years of quality schooling a child can expect to obtain by age 18. It includes two components: Expected years of schooling and a harmonized test score. Learning is measured by a relative learning score calculated from global and regional learning assessments (Altinok, Angrist, & Patrinos, 2018; Patrinos & Angrist, 2018). The harmonized learning score is currently the only comparable measure of learning that covers a large number of countries.<sup>7</sup> Without ignoring the limitations surrounding the LAYS, this appears to be one of the most reliable indicators of quality education that is available and covers a large number of countries including developing countries.

# _Control variables (z)_

The education production function theory shows that inputs can be grouped into two main categories: financial and non‐financial resources. Financial resources come from three main sources: aid to the education sector ( _aid_ ), government expenditure ( _govspend_ ) and households’ spending ( _hhspend_ ).<sup>8</sup> Non‐ financial resources are related to supply‐side factors (availability of teachers for instance) and demand‐ side factors (population’s demand for education for instance). This implies that public expenditure may not be the only input for educational outcomes and the efficiency measurement may be adjusted accordingly. From the financial inputs side, _aid_ and _govspend_ are already captured by the input variable _x._ Countries’ income level dummies are included in _z_ to control for the population income, and to some extent, _hhspend_ . Regarding the non‐financial resources used by the education sector, the primary completion rate ( _pcr_ ) is included as a measure of the households’ demand for education and the capacity of the education system to deliver basic education, while the students‐to‐trained teachers ratio ( _sttr_ ) is a supply‐side indicator capturing the availability of trained teachers. Availability of qualified teachers has been recognized as one of the key ingredients for quality education (World Development Report, 2018). The unemployment rate ( _unemploy_ ) is introduced as an additional control variable capturing the economic environment and, to some extent, the demand for labor in the economy. The share of official development assistance ( _odashare_ ) is also included as a control variable for aid dependency.

> 7 See Patrinos & Angrist (2018) for a discussion on the harmonized test score as well as its imitations.

> 8 Education aid include sector allocable ODA to the education sector received by countries included in the sample.

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