on levels of public spending provide a simple measure of the difference between a country’s actual and expected level of education outcomes at its current level of spending. Second, data envelopment analysis (DEA) estimates a non-parametric frontier that maps out the best possible education outcomes for a given level of spending.<sup>20</sup> A country’s efficiency level is then measured by the vertical distance between its current position and the frontier. Third, in a similar way to data envelopment analysis, stochastic frontier analysis (SFA) estimates a frontier using a regression model but uses a specified functional form and assumptions about the distribution of the error term (see for example, Jayasuriya and Wodon 2003). The fourth and final approach, based on (Wagstaff and Wang 2011), aims to address a number of limitations inherent in the DEA and SFA efficiency measures while at the same time incorporating the best elements of each approach. It uses a grid search to identify the most efficient countries within specific ranges of spending. It measures a country’s efficiency by the distance between its own outcomes and the closest “efficient” country in terms of spending.

These different measures of spending efficiency are all highly correlated and tend to rank countries in similar ways. In the main text of the paper, we used the efficiency measures derived from the stochastic frontier analysis approach as this is most highly correlated with other efficiency measures.<sup>21</sup> To check that these estimates are effectively measuring efficiency, we looked at their correlations with some common proxies for efficiency (see Annex Table A9). These generally confirm that the estimates are on the whole measuring efficiency appropriately.

# **_Patterns and Trends of Spending Changes and Outcomes_**

We used each country’s level of spending and efficiency scores to create four categories for countries based on where they were in the distribution of spending and efficiency.<sup>22</sup> The categories were: (i) high-spending, high efficiency, (ii) high spending, low efficiency, (iii) low spending, high efficiency, and (iv) low spending, low efficiency.<sup>23</sup> We then calculated elasticities for each category. The elasticities are presented in Table 7.

The elasticities varied significantly by country category. The elasticity of learning-adjusted years of schooling is highest for low-spending countries that are far from the efficiency frontier. Empirically, those are the countries that have experienced the fastest increases in learning-adjusted years of schooling in the past. As countries get closer to the efficiency frontier, their elasticity decreases, indicating that they tend to follow the frontier (that is, the maximum level of outcomes countries at the same level of expending have been able to achieve). For high-spending countries, the trends are similar. For those that started at a high efficiency point, increases in spending have been accompanied by small increases in learning-adjusted years of schooling, whereas high-spending countries that are far from the efficiency frontier have experienced higher elasticities of learning-adjusted years of schooling.

> 20 In this paper, we used output-based measures of efficiency since the primary policy focus of most countries was on improving outcomes from existing levels of resources rather than looking at ways to reduce funding while maintaining existing levels of education outcomes.

> 21 Results using the other efficiency measures are available from the authors on request.

> 22 Median values are used to categorize countries.

> 23 We define low (high) spending and low (high) efficiency as below (above) average spending and efficiency respectively.

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