# **1. Introduction**

Educational inequalities have long been a matter of significant policy concern, in both developed and developing countries. Some view educational achievement as a dimension of well-being in its own right, or at least as a fundamental input into a person’s functionings and capacity to flourish (Sen, 1985). Education is also a powerful predictor of earnings, as we have known since the early days of work on human capital. More recent research has also found that inequality in educational achievement and earnings inequality are correlated, both over time within the United States and across countries (see, e.g., Blau and Kahn, 2005; and Bedard and Ferrall, 2003). Education is also correlated with health status, and in some cases with political participation in the democratic process, so that inequalities in the former may translate into undesirable gaps and gradients in other dimensions as well.

For all of these reasons, people care about the distribution of education. Those concerned about fairness and social justice care also about the distribution of opportunities for acquiring a good education and, in particular, about the degree to which family background and other predetermined personal characteristics determine a person’s educational outcomes. Nevertheless, there is much less agreement on how those concepts – inequality in educational outcomes, and inequality of opportunity to a good education – should be measured. Constrained by data availability, early work comparing inequality in education across countries focused on educational attainment: the number of years of schooling a person had completed or, in some cases, broader ‘levels’ of education, such as primary, secondary, or higher. Thomas, Wang and Fan (2001) compiled a set of Gini coefficients for years of schooling for 85 countries, over the period from 1960 to 1990. Castelló and Doménech (2002) and Morrisson and Murtin (2007) also examine inequality in years of schooling across a large number of countries.

Interesting though those comparisons were, there is widespread agreement that a year of schooling is a problematic unit with which to measure “education”. Does a student learn the same amount in 6<sup>th</sup> grade in Zambia as in Finland? Is the value of one year of schooling the same even across different schools in a single country or city? The growing availability of data on student performance in comparable tests has confirmed what one already suspected: that the answer to these questions is generally ‘no’. The quality – and hence the ultimate value – of education varies considerably, both within and across countries.

Over the last decade, different projects have compiled school-based surveys that administer identical cognitive achievement tests to samples of students across a number of countries, as well as collecting (reasonably) comparable information about the students’ families and the schools they attend. The OECD’s _Program of International Student Assessment_ (PISA) and the International Association for the Evaluation of Educational Achievement’s _Trends in International Mathematics and Science Study_ (TIMSS) are perhaps the best known, but the 2