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Towards an index of education outputs

In addition to the Data Bank, an important goal of the Learning Curve project has been to create a comparative index of educational performance – the Global Index of Cognitive Skills and Educational Attainment. The results are meant not only to be interesting in themselves, but to help identify likely sources of good practice.
First, a caveat
The exercise has not been simple. One hurdle was determining how to measure performance. While it would have been desirable to include broader labour market and social outcomes on which education arguably has an impact, this proved impossible. Even were it demonstrably clear that education played a definite role in these areas, it is impossible to determine a way – consistent across time and geography – to isolate and measure the impact of that effect.
While more direct measures of educational results abound, robust, internationally comparative ones are rare. PISA, TIMSS and PIRLS testing has had such an impact in part because of the void it helped to fill. The Index therefore, through necessity, takes a view of educational performance based on where reasonably good data exist. The first such area, drawing on the results of the aforementioned tests, is the inculcation of cognitive skills. The second is a broader measure of educational attainment, which relies on literacy levels and graduation rates.
This focus does not eliminate data issues. Education systems are local: international comparability will never be perfect. Canada’s tertiary graduation rate, for example, is modest in the calculations for this Index because they draw on university results. If one includes graduates from Canada’s community colleges, though – tertiary type-B institutions to use the international classification – the graduation rate becomes one of the highest in the OECD. A lack of data on the results for type-B colleges, though, makes it impossible to do so generally. Moreover, metrics selected for the Index suffer from data lacunae. Singapore’s low educational attainment score in the Index – 33rd out of 40 – arises largely from a complete lack of available data on graduation rates.[28] Finally, combining results from different tests in a meaningful way required rebalancing of the existing data.
Ultimately, these data are inevitably proxies for broader results, and far from perfect ones. As Dr Finn points out of graduation rates, "they are complicated. You can raise your graduation rate by lowering academic expectations.” On the other hand, such rates, like literacy levels, do indicate in a rough way the breadth of education in a country. Similarly, Professor Hanushek notes that “countries that do well on PISA do well on tests of deeper knowledge.”
The methodology appendix describes in more detail the Index’s construction and relevant data issues. The broader message of this lengthy disclaimer is that the Index is very much a first step. We hope that, as understanding of the outcomes of education grows, the Index will become more complex and nuanced as well as be populated with more robust and varied data. For now, however, it is better to light a candle than curse the statistical darkness.
What the leaders have – and don't have – in common
Given the attention paid to the results of international education tests, the leading countries in the cognitive skills category of the Index come as no surprise. The top five – Finland, Singapore, Hong Kong, South Korea and Japan – all score more than one standard deviation above the norm in this part of the Index. The educational attainment category, based on literacy and graduation rates, tells a slightly different story. Here South Korea leads, followed by the UK, Finland, Poland and Ireland, with Japan, Hong Kong and Singapore further down the table. Because of their strength in both measures, then, Finland and South Korea are the clear overall leaders of the Index.
Chart 9: Global Index of Cognitive Skills and Educational Attainment – overall results
Chart 9: Global Index of Cognitive Skills and Educational Attainment – overall results
Note: The Index scores are represented as z-scores. The process of normalising all values in the Index into z-scores enables a direct comparison of country performance across all the indicators. A z-score indicates how many standard deviations an observation is above or below the mean of the countries in the Index.
Source: Economist Intelligence Unit.
These results mirror the conventional wisdom: already in 2007, the BBC referred to the two countries as “among the superpowers of education.”[29] But what do these have in common that might help to identify the keys to educational success? On the face of it, there is remarkably little.
In many ways, it is hard to find two education systems more different. South Korea’s schools are frequently described as test-driven, with a rigid curriculum and an emphasis on rote learning. Most striking is the amount of time spent in study. Once the formal school day is over, the majority of students go to private crammer schools, or hagwons. According to OECD data, of 15-year-old students for whom data was available in 2009, 68% engaged in private study of the Korean language, 77% in mathematics, 57% in science and 67% in other subjects. In later years, students typically do far more privately. The government has become so worried about the extent of these studies that it has banned hagwons from being open after 10pm, but still needs to send out patrols to shut down those which mask illegal, after-hour teaching by posing as self-study libraries.
On the other hand Finland, in the words of Professor Schwartz, “is a wonderful case study. Kids start school later; school hours are shorter than most others; they don’t assign homework; their teachers are in front of kids less. By one estimate, Italians go to school three years longer.” The PISA data shows that very few Finns take out-of-school lessons either, and those who do typically do worse on standardised tests, suggesting that this is largely remedial help. Finally, the system has a reputation for being focussed on helping children understand and apply knowledge, not merely repeat it.
The existing data also paint a picture of two distinct approaches. In some cases, the systems are widely different: average teacher salaries in South Korea are over twice the national average, while those in Finland are almost exactly average; pupil-teacher ratios, on the other hand, are much higher in South Korea. Where the two systems are similar, they are usually near the average for all countries in the Index. The only difference is school choice, where both are highly restrictive. That said, the vast amount of after-school private education in South Korea brings into question the relevance of that metric.
The two systems, though, do share some important aspects when examined closely. “When you look at both, you find nothing in common at first,” says Professor Schleicher, “but then find they are very similar in outlook.” One element of this is the importance assigned to teaching and the efforts put into teacher recruitment and training. As discussed above, the practices of the two countries differ markedly, but the status which teaching achieves and the resultant high quality of instruction are similar. Professor Schleicher adds that both systems also have a high level of ambition for students and a strong sense of accountability, but again these are “articulated differently. In South Korea, accountability is exam driven; in Finland, it is peer accountability, but the impact is very similar.”
Finally, there are cultural parallels. The two societies are highly supportive of both the school system itself and of education in general. Of course, other countries are also highly supportive of education, but what may set Finland and South Korea apart is that in both, ideas about education have also been shaped by a significant underlying moral purpose.
Although discussions of Korean attitudes to education frequently reference Confucian ideals, under a quarter of South Koreans were even literate by the end of the Korean War. In the decades that followed, education was not just about self-improvement: it was a way to build the country, especially as the Japanese colonial power had restricted the access of ethnic Koreans to schooling. The immediate cause of this drive has disappeared, but it has helped inculcate a lasting ethic of education which only strengthened the more widespread attitude in Asia that learning is a moral duty to the family and society as well as a necessary means of individual advancement.
In Finland, the ethos is different but no less powerful. As Mr Mackay explains, that country has made “a commitment as a nation to invest in learning as a way of lifting its commitment to equity. They wish to lift the learning of all people: it is about a moral purpose that comes from both a deeper cultural level and a commitment at a political-social level.” In other words, education is seen as an act of social justice.
Both of these moral purposes can cause difficulties in different ways. The high expectations and pressure mean that studies regularly find South Korean teenagers to be the least happy in the OECD. In Finland, the egalitarian system seems less effective at helping highly talented students to perform to the best of their ability than at making sure average results are high. Nevertheless, the power of these attitudes in shaping cultural norms and political decisions in ways that help education attainment overall are undeniable. Mr Angula, after many years as a teacher, Minister of Education, and Prime Minister, believes that “the key ingredient [in creating a successful education system] is for everybody to be committed and to understand that they are doing a public good.”

[28]Singapore is one of 14 countries in the Index for which internationally comparable graduation data are lacking. (The countries were nonetheless included in the Index because they met all the other data inclusion criteria.) They were thus assigned the mean z-score of the entire country sample for the given graduation rate indicators. This represents an opportunity for further and improved data collection that will be reflected in later versions of the Learning Curve.
[29] “Finland stays top of global class”, 4 December 2007,

Conclusion and recommendations for further study

The lessons of the Index broadly reflect much which comes out of this study. The understanding of what inputs lead to the best educational outcomes is still basic, which is not surprising given that robust international benchmarking figures are few and often of recent date. Moreover, education remains an art, and much of what engenders quality is difficult to quantify.
General lessons to be drawn, then, are often still basic as well. Dr Finn says of studies looking at high-performing school systems, “I don’t detect many similarities other than high standards, solid curriculum, competent teachers and a supportive culture that is education-minded.” Other research might point to the importance of school choice and school autonomy.
These insights are valuable, but only up to a point. Education systems are local; so too are their problems and solutions. What Professor Hanushek says of improving autonomy and choice applies generally: “Local countries and institutions are extraordinarily important. Each country has its own system. It is difficult to take any of the specifics and apply them elsewhere.” In seeking those solutions, officials also need a dose of humility, remembering that formal education can do only so much. As Professor Woessmann notes, “a lot of these things [determinants of academic success] are not amenable to government action. They are really within families and how society operates.” Moreover, as the differing approaches of Finland and South Korea show, there are diverse paths to success.
While the local matters greatly, the universal still has an important contribution to make. This study, like others, ends with an appeal for more research. Both relatively straightforward work and more complex tasks lie ahead. The former includes the generation of basic information on inputs and outcomes in a number of countries; the assessment of a wider range of skills using standardised tests; and finding appropriate ways to compare dissimilar educational systems in various countries. The more complex challenges involve assessing the impact of culture on education and the value of different means of changing cultures; determining the attributes of those teachers that add the most value; and understanding in more detail how accountability and choice can interact in positive ways. Such studies might involve innovative new metrics, new approaches or both.
The other important plea is that what is known not be ignored. Too often, the world’s innumerable education reforms draw on assumptions and ideology rather than solid information. International comparisons of educational inputs and outputs have already awakened countries to their own strengths and deficiencies, as well as pointing toward possibly fruitful sources of solutions. The LCDB and Index are offered as tools toward furthering this understanding. It is hoped that they will be useful as researchers and analysts seek deeper and more nuanced insight in the years to come.

Appendix 1: methodology for the quantitative component of The Learning Curve

As part of the Learning Curve programme, the Economist Intelligence Unit (EIU) undertook a substantial quantitative exercise to analyse nations' educational systems’ performance in a global context. The EIU set two main objectives for this work: to collate and compare international data on national school systems’ outputs in a comprehensive and accessible way, and for the results to help set the editorial agenda for the Learning Curve programme.
The EIU was aided by an Advisory Panel of education experts from around the world. The Panel provided advice on the aims, approach, methodology and outputs of the Learning Curve’s quantitative component. Feedback from the Panel was fed into the research in order to ensure the highest level of quality.
The EIU developed three outputs as part of the quantitative component of the Learning Curve. These are an exhaustive data bank of high quality national education statistics, an index measuring national cognitive skills and educational attainment, and research on correlations between educational inputs, outputs and wider society. Each is described in more detail below.
Learning Curve Data Bank
The Learning Curve Data Bank (LCDB) provides a large, transparent and easily accessible database of annual education inputs and outputs and socio-economic indicators on 50 countries (and one region – Hong Kong) going back to 1990 when possible. It is unique in that its aim is to include data that are internationally comparable. The user can sort and display the data in various ways via the website that accompanies this report.
Country selection
Country selection to the Data Bank was on the basis of available education input, output and socio-economic data at an internationally comparable level. A particularly important criterion was participation in the international PISA and/or TIMSS tests. Forty countries (and Hong Kong) were included as 'comprehensive-data' countries within the Data Bank, and ten countries as 'partial-data' countries, according to availability of data.
Indicator selection
The EIU's aim was to include only internationally comparable data. Wherever possible, OECD data or data from international organisations was used to ensure comparability. For the vast majority of indicators, the EIU refrained from using national data sources, and when possible, used inter- and extrapolations in order to fill missing data points. Different methods for estimations were used, including regression when found to be statistically significant, linear estimation, averages between regions, and deductions based on other research. The source for each and every data point is cited in the Data Bank. The data were last collected and/or calculated in September 2012.
Over 60 indicators are included, structured in three sections: inputs to education (such as education spending, school entrance age, pupil teacher ratio, school life expectancy, teacher salaries, among others), outputs of education (such as cognitive skills measured by international tests such as PISA, literacy rates, graduation rates, unemployment by educational attainment, labour market productivity, among others) and socio-economic environment indicators (social inequality, crime rates, GDP per capita, unemployment, among others). The Data Bank’s indicators were used to create the Index and conduct a correlations exercise.
Global Index of Cognitive Skills and Educational Attainment
The Global Index of Cognitive Skills and Educational Attainment compares the performance of 39 countries and one region (Hong Kong is used as a proxy for China due to the lack of test results at a national level) on two categories of education, cognitive skills and educational attainment. The index provides a snapshot of the relative performance of countries based on their education outputs.
Country and indicator selection
For data availability purposes, country selection to the Index was based on whether a country was a 'comprehensive-data' country within the Data Bank. Guided by the Advisory Panel, the EIU’s goal in selecting indicators for the Index was to establish criteria by which to measure countries’ output performance in education. Initial questions included: What level of cognitive skills are national education systems equipping students with, and how are students performing on internationally comparable tests at different ages? What are levels of reading, maths and science in these countries? How successful are national education systems at attaining a high level of literacy in the population? How successful are national education systems at educating students to secondary and tertiary degree level?
Based on this set of questions, the EIU chose objective quantitative indicators, grouping them into two groups: cognitive skills and educational attainment. For cognitive skills, the Index uses the latest reading, maths and science scores from PISA (Grade 8 level), TIMSS (Grade 4 and 8) and PIRLS (Grade 4). For educational attainment, the Index uses the latest literacy rate and graduation rates at the upper secondary and tertiary level. Data for some countries were more recent than others; when the latest available data point was five years older than the latest, the EIU chose not to include it, although this was very rarely found to be an issue.
The EIU made estimations when no internationally comparable data were available. For example, a number of countries’ Grade 8 TIMSS Science scores were estimated by regression with PISA Science scores, when the regression was found to be statistically significant. In addition, when OECD data were not available for graduation rates, national ministry or statistics bureau data were sanity-checked and then used if deemed internationally comparable.
Calculating scores and weightings
In order to make indicators directly comparable across all countries in the Index, all values were normalised into z-scores. This process enables the comparison and aggregation of different data sets (on different scales), and also the scoring of countries on the basis of their comparative performance. A z-score indicates how many standard deviations an observation is above or below the mean. To compute the z-score, the EIU first calculated each indicator’s mean and standard deviation using the data for the countries in the Index, and then the distance of the observation from the mean in terms of standard deviations.
The overall index score is the weighted sum of the underlying two category scores. Likewise, the category scores are the weighted sum of the underlying indicator scores. As recommended by the Advisory Panel, the default weight for the Index is two-thirds to cognitive skills and one-third to educational attainment. Within the cognitive skills category, the Grade 8 tests’ score accounts for 60% while the Grade 4 tests’ score accounts for 40% (Reading, Maths and Science all account for equal weights). Within the educational attainment category, the literacy rate and graduation rates account for equal weights. The user can, however, change the weightings and recalculate scores according to personal preference via the website that accompanies this report.
Areas for caution
Because indexes aggregate different data sets on different scales from different sources, building them invariably requires making a number of subjective decisions. This index is no different. Each 'area for caution' is described below.
Z-scores for PISA, TIMSS and PIRLS
It is important to note that, strictly speaking, the z-scores for PISA, TIMSS and PIRLS are not directly comparable. The methodology applied both by the OECD and the International Association for the Evaluation of Educational Achievement (IEA) to calculate the performance of the participating countries consists of comparing the performance of the participating countries to the respective mean performance. (The countries’ ‘raw’ test scores before normalisation are not published; just their scores in comparison to the other participants.) Thus, which countries participate in each test and how well they perform in comparison to the other participants has a direct impact on the resulting final scores. Given that the sample of countries that take the PISA, TIMSS and PIRLS tests are not exactly the same, there are limitations to the comparability of their scores.
The EIU has chosen not to change these scores to account for this lack of direct comparability; however, it did consider other options along the way. The main alternative suggestion from the Advisory Panel was to use a pivot country in order to transform the z-scores of other countries in comparison to that pivot country’s z-score. Although this method is used in some studies, after substantial consideration, the EIU decided not to employ this method for the purpose of an index. The resulting z-scores after transformation depend heavily on the choice of pivot country; choosing one country as a pivot over another affects countries’ z-scores quite substantially. The EIU did not feel it was in a position to make such a choice. Despite these limitations to test scores’ direct comparability, the EIU believes that the applied methodology is the least invasive and most appropriate to aggregate these scores.
Graduation rate data
Some members of the Advisory Panel questioned the use of graduation rates in the Index in that it is not clear whether they add value as a comparative indicator of education performance. Unlike test results and literacy rates, standards to gaining an upper secondary and tertiary degree do differ across countries. Notwithstanding, the EIU believes that graduation rates do add value in evaluating a national educational system's performance, as there is common acceptance that national education systems should aim for their citizens to gain educational qualifications, especially at the secondary level. Including graduation rate data in the Index therefore awards countries that have put this aim into practice, albeit at varying levels of quality.
Because of the variation in how countries measure graduation rates, the EIU followed the Panel's suggestion in using OECD graduation rate data, which use one main definition. When OECD data were not available, national ministry or statistics bureau data were sanity-checked and then used if deemed comparable. In some cases, no data on graduation rates were available. In this case, the EIU awarded the country the mean score for this indicator. One disadvantage of giving a country the mean score is that if in reality it performs worse than the average in this indicator, the Index boosts its score, and vice versa.
The EIU used the most recent data available. Because graduation rates are based on the pattern of graduation existing at the time, they are sensitive to changes in the educational system, such as the addition of new programmes or a change in programme duration. As an extreme example, Portugal’s upper secondary graduation rate increased from a range between 50% and 65% in the early 2000s to 2008, to 104% in 2010, as a result of the government’s “New Opportunities” programme, launched to provide a second chance for those individuals who left school early without a secondary diploma. In order to treat countries consistently, the Index takes the 2010 figure. Although this inflates Portugal’s score in this indicator, this inflation should eventually fall out of the Index should it be updated on an annual or bi-annual basis. Given the limitations of graduation rate data, the EIU followed the Panel's suggestion of giving a smaller weighting (one-third) to educational attainment.
It is also important to note that the tertiary graduation rate indicator covers only tertiary-type A programmes. Tertiary-type B programmes are not included. This methodology was chosen largely because not all countries collect data and organise their education systems along the lines of A and B. As per the OECD, tertiary-type A programmes are largely theory-based and are designed to provide qualifications for entry into advanced research programmes and professions with high requirements in knowledge and skills. These programmes are typically delivered by universities, and their duration ranges from three to five years, or more at times. Tertiary-type B programmes are classified at the same academic level as those of type A, but are often shorter in duration (usually two to three years). They are generally not intended to lead to further university-level degrees, but rather to lead directly to the labour market.
Although excluding tertiary-type B programmes makes for a more relevant comparison among countries, it also slightly disadvantages a number of countries that have particularly high type B graduation rates (as these rates are not included). These countries are Canada, Ireland, Japan and New Zealand. Nonetheless, this exclusion has a limited impact on these countries’ ranking in the Index.
Other indicators
The EIU had wanted to include other education performance indicators in the Index, such as how well national education systems prepare students for the labour market and the performance of vocational studies. However, data availability was a limiting factor. The EIU found that sufficient data were not available that isolates educational attainment within labour market outcomes; and internationally comparable data on vocational studies covering all countries in the Index were not readily available either.

With the ‘comprehensive-data’ countries data from the Data Bank, a correlations exercise was undertaken in order to test relationships across countries between education inputs, outputs and wider society. The EIU tested for correlations between the inputs to and outputs of education, the inputs to education and socio-economic environment indicators (as a proxy for wider society), and the outputs of education and socio-economic environment indicators.
Definition of a correlation and thresholds used
The correlation coefficient is a measure of the degree of linear relationship between two variables. While in regression the emphasis is on predicting one variable from the other, in correlation the emphasis is on the degree to which a linear model may describe the relationship between two variables. Importantly, the presence of a correlation does not imply causality.
In order to ensure that relationships being found were indeed strong, the EIU looked for at least a 0.65 level of correlation (the higher it is, the stronger the relationship). It is important to acknowledge that some social science research uses a lower level of correlation, but the EIU wished to maintain a high level to avoid finding relationships between indicators that might not be significant.
Calculating correlations
Correlation tests were conducted on an indicator-by-indicator basis, between two variables over time (on an annual basis) and at three-year growth rates (for example, the three-year growth rate of 1999 (1996-99) against the three-year growth rate of 2007 (2004-07)). For the latter tests, adjustments were made to include TIMSS and PIRLS tests even though these are not taken every 3 years (they are taken every four and five years respectively). The EIU used the same time lags across countries on the same indicator, as per the Panel’s suggestions.
When looking for evidence of a strong correlation, the EIU sought a strong relationship over time. For example, although there may have been evidence of a strong correlation between one input variable in 1990 and an output variable in 2005; a strong level of correlation would also need to be found for 1991 and 2006, 1992 and 2007, and so on, for at least a number of years. In addition, correlation tests were only run if there were at least 15 countries with relevant data for both of the indicators being assessed.
Factors affecting the correlations
The EIU did not find a great number of strong relationships. Given the complexity of education, this was not totally surprising. However, other factors may also account for the lack of correlations. For one, not all indicators were available going back 15-20 years in time. There was also a lack of data availability for some countries (some of this due to the Data Bank’s focus on ensuring that data being used were internationally comparable). Finally, other qualitative factors that are difficult to measure, such as culture and the quality of teaching, were not included in the Data Bank. These factors may have a significant impact on education outputs, but the EIU was not able to take these into account within the correlations exercise.


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