Predictors and control variables

The most important predictor in this research is inequality of education achievement, which is measured as the proportion of reading scores variance explained by socioeconomic background, namely the OECD Economic, Social and Cultural Status index (ESCS). The variable has been transformed so that it follows a normal distribution with a mean of zero and a standard deviation of 1. In the rest of the chapter, I refer to it as inequality of school achievement. The reason why I use this variable instead of more traditional measures is as follows.

In order to deal with a measure of inequality, Gini coefficient is the most traditional measure. Income Gini coefficients are widely available for most countries but databases are not continuous and many countries report Gini every five to ten years. Instead, I use an uncommon indicator such as the proportion of scores variance explained by ESCS. This variable shows how determinant the student’s socioeconomic background is for achievement, i.e. how ‘predictable’ school achievement is, given ESCS in a country.

The measure shows an important variability between countries and this may reflect a broader conception of educational systems. Indeed, the extreme values for the model just containing ESCS as a predictor of PISA reading scores fluctuate between 1.8 and

59 27 per cent of the explained variance in PISA 2009 (1.8 to 22 percent are the values for PISA 2006). In fact, the variable accounts for the persistence of ESCS on scores but not necessarily just as a school education characteristic, but also as for how the country deals with providing equity of opportunities for school students. The more ‘predictable’ the country, the stronger the social reproduction that takes place. Therefore, I can also use this indicator as a proxy of how strong social reproduction mechanisms through education are for countries.

Alternatively, I may have considered other measures of inequality also coming from PISA. For instance, I could have calculated the ratio between the scores of the top quartile (or any other percentile) of ESCS and the bottom one, this way obtaining a relative measure of inequality of achievement. Other alternative measure might be to build a GINI-like index based on the distribution of achievement.

Nevertheless, such a measure would not necessarily reflect the persistence of SES on achievement and would only be sensitive to variations in country specific socioeconomic distributions of school achievement rather than the persistence of socioeconomic status. Despite the issues that may emerge when considering a rather untraditional indicator, and the fact that coefficients might be difficult to interpret, I maintain that having a measure of inequality and social reproduction through education in a cross-country setting would not be possible by other means.

I also include PISA reading scores as a predictor. The reasons why I selected PISA reading proficiency scores are as follows. PISA measures three proficiency domains: reading, maths and sciences. Every three years, the main subject is properly tested, whereas the remaining subjects are estimates coming from a small set of items as well as other estimation methods. In this case, I took data on reading performance because the reading subject has been the main one twice (2000 and 2009), the others being main subjects just once. For the remaining years (2003 and 2006) PISA scores are estimates of reading performance as the main subjects were, respectively, maths and sciences. There was no other option in order to count on as many test scores as

60 possible. This way I add a longitudinal component with the advantages it represents as it allows me to control for unobservables.

I include inequality of school achievement and the ESCS for the years 2000, 2003, 2006, and 2009 for all the models in this chapter. ESCS is an indicator including parental education and occupation, cultural assets, and educational resources in the household and it is used as an indicator of socioeconomic status. The base model, thus, considers inequality of school achievement and ESCS. The reason supporting this desicion I also introduce control variables related to PISA (OECD 2005, 2010). From there, I use the following variables: (i) and (ii) the percentage of score variance explained by within-school factors, which is sometimes called school inclusiveness index. Both variables consider crucial characteristics of school systems.

ESCS index is a unidimensional measure of SES that OECD has estimated by using the first factor from principal components factor analysis on the basis of the following indicators: (i) the International Socio-Economic Index of Occupational Status (ISEI); (ii) the highest parental education level in years of schooling; (iii) the PISA index of family wealth; (iv) the PISA index of home educational resources; and (v) the PISA index of possessions related to ‘classical’ culture in the family home (OECD 2012b). The index has a mean of zero -which is the OECD mean, and a standard deviation of 1. A negative value means that the country’s ESCS is lower than OECD average and positive values show the opposite. The index is not calculated as a country specific one but as a general index; this being the reason why some countries show means below or above zero (see OECD 2010, 2012b for more details).

In relation to variance composition, within-school variance as a proportion of the total variance has also been included. High within-variance proportion might mean that different schools achieve similar test scores in general, and may be more inclusive in the sense that schools are more likely to serve students with different performance levels. Low within-variance proportion, on the other hand, means that schools differ but are internally more homogeneous, this meaning that school education is segmented as there are low-performance schools that differ too much from high-performance

61 schools. Finding bad-school, poor-student, low-performance (or the opposite) at the same time would indicate a segregated school system. This indicator intends to measure the first and the third elements of the triad. Following this example, socioeconomic inequality of school achievement as understood in this thesis would account for the second and third elements of the triad.

As a robustness check, I shall also use maths scores and the variance composition indicators related to PISA maths. Maths scores in standardised tests have long been recognised as a better measure of school performance and as having a higher predictive value of future educational outcomes (e.g., university entry, college performance, labour market outcomes, etc.). Nevertheless, including PISA maths scores imposes important shortcomings I shall describe in detail in the results section.

An issue to address is why PISA and why these indicators have been used. Countries (regions and states in the US, for instance) measure school achievement by using a variety of tests and exams. Some tests check the fulfilment of curricular goals at different levels while some are properly exit tests leading to school leaving certifications or diplomas (A-levels in the UK, Baccalaureat in France, for instance). Most are used by HEIs to select students, so they are of critical importance for the student’s chances of being offered a place and continuing education. Countries like the US use standardised tests for HE admissions and school results. Since tests are used for different purposes, different aspects are measured. On the other hand, curricula differ amongst countries, thus a measure unaffected by curricula becomes necessary. Although I am aware of the fact that some research takes issue with this, threats to validity and technical critiques to PISA are well beyond this research.

More controls are also included in the models: GDP per capita (PPP), educational attainment of the labour force – as measured by the percentage of the labour force with HE –, the participation in unemployment of people having HE, and GER for secondary education, defined as the ratio enrolment to people in the target population (13 to 17 year-olds in most countries). I have also used variables to measure the investment in secondary and HE as a fraction of GDP per capita. Those indicators

62 give an account of the wider socio-economic context. Educational attainment of the labour force is important both in terms of productivity and returns to education. Secondary attainment sets the bottom line, as it is the main formal prerequisite to HE. A country with no universal enrolment rate at the secondary level could hardly increase HE GER within a 10-year period. Finally, investment, measured as expenditure in education as a percentage of the GDP per capita is one of the main indicators when focusing on policy. It may reflect countries’ priorities as well as the relative cost of specific educational levels when compared to a higher or lower one. In relation to that, it would have been useful to gather data on public-private expenditure as it shows the main features of educational policy: the role of the private sector and cost transfer. Regrettably, that information is only available for a few countries and there is not a systematic pattern in terms of periodicity.