VoxEU Column Education

The virtuous equity-efficiency trade-off in educational outcomes

Many interpret countries' scores in international testing as grades of their national educational policies. Summarising evidence from international maths exams, this column finds that the highest-scoring countries are those with the least inequality in test scores, suggesting a “virtuous” equity-efficiency trade-off. It also finds that countries perform even better when test scores are highly correlated with the number of books in the family home.

How countries fare in international tests of student achievement is a magnet for media attention the world over. In December 2010, for instance, two of the world's leading newspapers, the New York Times, and The Financial Times reported on the remarkable scores of students from Shanghai in the latest Programme for International Student Assessment (Pisa) tests, which assess the reading, maths and scientific skills of the world’s 15-year-olds (Cook 2010, Dillon 2010).

The reason for this attention is that the scores on international scholastic assessment tests are a report card of sorts on national educational policies. Given the relation of education to economic achievement, many policymakers and analysts take student performance as a possible leading indicator of the future success of their country’s economy.

All international tests show that test scores vary greatly among students within countries and across countries. There are many reasons for this variation. The family background of students differs. The quality and educational practices of schools differs. Learning resources outside of schools differ. In addition, the distribution of scores within countries and schools also differs. In some countries/schools test scores are narrowly distributed around the average score. In others, test scores are widely distributed around the average score.

Economic analysis often stresses the existence of an equity-efficiency trade-off in outcomes, in which equity refers to the inequality of outcomes among people while efficiency refers to the overall level of outcomes (Okun 1975). The standard view in macroeconomics is that increases in equity (usually reflected in reducing the dispersion of wages) come at the expense of reductions in efficiency (lower GDP per capita).

Our analysis of eighth-grade mathematics test scores from the 1999 and 2007 waves of the Trends in International Mathematics and Science Study shows a very different pattern across countries in the relation between educational equity and efficiency. Instead of the usual trade-off we find a “virtuous equity-efficiency relation” in test score outcomes among countries (Freeman et al. 2010). Countries with the highest test scores have low inequality in scores whereas countries with low test scores have high inequality.

In addition, we found large cross-country differences in the relation between family background measured by books in the household and students’ performance. In some countries, students with more books at home did a lot better in mathematics tests than students with fewer books in their home. In other countries the number of books in the home had relatively weak effects on student test scores. One might have expected that the countries where books at home mattered a lot on test scores would have greater dispersion in those scores.

We found the opposite. Countries in which books in the home had a greater impact on test scores had higher median test scores and lower variation in student test scores than in countries where books in the home was more weakly related to test scores. This is another virtuous relation governing student test scores.


Our finding that educational outcomes show a virtuous equity-efficiency trade-off supports policy interventions that aim primarily at helping students in the lower part of the distribution, such as possibly early childhood education programmes focused on disadvantaged children. Since books in the household presumably reflect various aspects of non-school educational resources, it directs attention at policies that seek to increase family resources that complement formal schooling. An interesting possible experiment would be to provide free books to families, as the Chilean government did (The Economist 2007), particularly those with lower incomes, and to see how that intervention would affect the accumulation of human capital and the distribution of test scores.


Cook, Chris (2010), “Shanghai tops global state school rankings”, Financial Times, 7 December.
Dillon, Sam (2010), “Top Test Scores From Shanghai Stun Educators”, The New York Times, 7 December.
Freeman, R, BSJ Machin, and MG Viarengo (2010), “Variation in Policies and Educational Outcomes across Countries and of Schools within Countries”, NBER Working Paper 16293.
Okun, A (1975), “Equality and Efficiency: The Big Tradeoff”, Brookings Institution.
The Economist (2007), “Let them eat Kafka”, 25 October.

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