 Srečen sem zelo, da se przenem fokusonu vsečen in vsečen došli vsečen in počutnih. Vsečen sem izgleda, da se možete vsečen in odpočnega se vsečenja. To je vstupovana mjelj. Zato sem izgleda, da se počutim, da se je zelo, da se je vsečen, da se je vsečen in da se počutim. Zato se prezentem, da se je vsečen in vsečen. Tudi, da se je izgleda, da se je izgleda, da se je vsečen. in z njih. We measure educational achievements by looking at the results that students obtain in the PISA test score. And we do that to see first, if there is any change in the ranking of country, when we switch the focus of the analysis from the average test score to fairness, which is measured in terms of both the level and the degree of fairness. nam znošimo, da ne Here's the difference between the two. Then we wonder if there is any counter that outperform in both these two dimension of fairness And finally by using four ways of the PISA survey we track changes occurred over time in the strength of the association between socioeconomic characteristics and students' performances. But why we decided to focus on education? Well, this choice can be motivated by using both positive or normative arguments. So the relevance of education has been underlying in the first presentation today and yesterday the Brazilian minister told us that great part of the reduction in equality was caused by an increase in the skill endowment. And also the topic on education is not new. in ekonomi ste in past years have started, for example, the persistence across generation in educational achievements or inequality in the distribution of attainments or achievements. But more recently, some scholars have focused more explicitly on inequality in educational opportunities. And among these, some of these scholars also used the PISA test score. For example, De La Vega in Le Cuona used PISA 2009 to measure inequality in educational opportunity in reading. While Gambo and Valdemburg used PISA 2006 and 2009 to look at the changes over time in inequality in educational opportunities in six Latin American countries. And finally, Ferreira and Ginu measure inequality in educational opportunities by using the PISA 2006. And they also provide the rationale for using the variance as the proper index of inequality when the outcome of interest is the PISA test score. And this is mainly due to the standardization procedure, which is carried on by the EOECD to transform the rota score into standardized test score. So, what we add to these findings. First, we consider the last wave of the PISA, relased by the EOECD, referred to PISA 2012. Second, as I said, by considering PISA 2003, 2006, 2009 and 2012, we also look at changes over time in terms of fairness. And finally, we consider, as our measure of fairness, an ordinary pair that allows us to look at both, again, the level and the degree of fairness, which is the difference. Well, the difference is that the first component that is called WEOP focuses just on the worst of students, while the second one looks at the whole sample of students involved in the test. The starting point is the standard one in the equality of opportunity framework. So, basically, we assume a test score production function, where this outcome depends only on two groups of variables. The first one are called circumstances, and the second one are called effort. The main difference, the only difference between the two variables, is that students are considered to be not responsible for the first group of variables. Then this first group is used to divide the population into a number of subgroups, which are called types. And each type is formatted by individuals who share a common set of these characteristics. As regards the efforts on the other side, this is not directly observable. So, Romer firstly proposed in 1998 to measure it by looking at the CDF of the outcome distribution within each type, and then deduce the level of effort, which is exerted by each individual, by the rank that an individual occupy in his own type distribution. So, basically, what does it mean? If we have, let's say, two type, type J and type L, and two individuals are both in the second centile of the distribution of test scores of their type, but the test scores that they obtain are different, then this difference is due to inequality of opportunity, and so is considered unfair. Empirically, what does it mean? For each, once we have divided the population into types, for each type we compute the, and within each count we compute this type-specific CDF. Then, to obtain our first component, if this CDF does not cross, the first component corresponds simply to the average scores of the worst of students. And when they cross, the first component is computed by looking at the area, which is at the left of the left hand envelope of the CDF of each type. For the second component we simply assume a parametric, sorry, a linear approximation of the test score production function. And then our index of inequality is given simply by the ratio between the variance in the conditional distribution and the variance in the unconditional one. As I said, our measure of educational achievements are the PISA test scores. Now, all of us, I think, know that this test is carried on by the UACD every three years, and it involves all the member countries plus a number of partner countries. And this is why we observe a difference in the number of participating countries in the four waves. What does not change is the fact that every year students are tested in three domains, mathematics, science and reading. There is a change in the main domain, which is tested every three years, but the difference is mainly that there are more questions for one specific subject, but the three of them are evaluated every year. And the students who take part to the test are selected through a two-stage sampling procedure. And there are all the students who are enrolled in grade seven or higher and are aged around 15. So the main advantage of this survey is that it contains a lot of information which are comparable across countries on variables related to both the school characteristics and students' characteristics. There are information on school policies and practices, on students' background, their motivation, their learning style, and so on and so forth. But we couldn't exploit the fully potential of this survey, and this is mainly due to the way the two components of our measure are computed. Because when we have more characteristics in our group of circumstances and increase in the number of these types as an opposite effect on the two components, so when the number of circumstances increase, our first component goes down and the second one goes up. So in order to find a kind of compromise between the need of having a sufficient number of observations within each type to compute our first component and the need of having, let me say, a reliable measure of inequality of opportunity, the set of variables that we use as students' circumstances are the student gender, their parental level of education, and the job classification. And we consider three levels of education and distinguish between white color and blue color so that at the end within each country we have 12 types. Well, the first thing that we notice when we look at our results is that there is great variability depending on the subject we consider. So what does it mean that the circumstances we use affect differently the test scores depend on the subject that we are considering. But what doesn't change is the fact that the ranking of country does not really depend on the subject that we are considering. So also considering again that the effect of parental background tends to be higher on cognitive abilities, which are related to the use of language. I'll show you here just the results related to reading and all the other results are in the paper. We see in this graph that there is great variability in our first component. So, for example, the average test score of the less advantaged students ranges between 200, sorry, in the Slovak Republic to around 15 in Shanghai. But when we look at the second component, we have Shanghai, I'm sorry, I'm really sorry. Should be... More or less here in the middle. I can see here, but not there, between Brazil and the Czech Republic, I think. Well, we see that the percentage of variation in the distribution of the score, which is explained by our set of circumstances, ranges between the 5% to the more than 25% in Macau and Bulgaria. And just to confirm that the ranking of countries is not really affected by the domain we consider, we notice that OECD reports similar results for this country in month. Even if equity in that case is measured in a slightly different way. But coming back to our first question, we observe that there is indeed a positive relationship between the average score of the whole population and our degree of fairness. Meaning that an average country which are in the northeast panel of this graph, which are those who perform above the overall average in terms of test scores and below the average in terms of inequality and educational opportunity, the graphs show that there is in an average a positive relationship between the two dimension. Well, when we wonder if there is any country that outperforms in both dimension of fairness, then the answer is negative. In fact, here again we have on the vertical axis the average score of the worst of students. And on the horizontal axis, the strength of the association between parental background and students test score, which are ordered in a decreasing way. And we see that there is no country that dominates, let me say, the other one. So a couple of them, which are Hong Kong and Macau, do quite well compare it to the others. But while the worst of students reach quite high results in Hong Kong, still the degree of inequality of opportunity is higher than in Macau. Then if we look at the geographical pattern, then this is not really clear. I mean, the only thing that we can say that fairness tends to be higher in both components in some Asiatic country, the triangle and the neighborhood in Western European and North American country, which are the sandiam on the empty circle. And in these last two areas, there is also less variability between countries. That on the other side is quite large in the country within the Eastern European area. Finally, the changes over time. Again, in the paper we analyzed changes between 2003 and 2006, 2006 and 2009 and so on and so far. But here I thought I wouldn't have enough time, so I present just the results, the changes that we can observe between the first and the last wave. And what emerged is that on average in the number of countries where the average performance of the worst of students is increased over time is higher than those where there has been a reduction in the impact of circumstances on students' score. And in fact also, we see that there are really few countries where we can observe both an improvement or a worsening in both our dimension of fairness. Now before I conclude, let me just underline two of the main limit of the analysis. The first one is the fact that as I said, the emission of circumstances allow us just to provide an upper bound of the level of fairness and a lower bound of the degree of fairness. So we have to be cautious when we interpret these results. The second limit is due to the fact that the PISA involves only students who are enrolled in education and we have not repeated too many grades because they have to be enrolled at least in grade seven. Now the second one maybe could not be really a problem in the OECD member country where the coverage rate is quite high, while it could be in some of the partner country. So a possible solution would be to the second problem could be to use some ancillary survey or to focus only on the OECD country. Well, as for the first problem, a possibility and probably a future development of this study would be to consider just the second component of our measure that is just the variance explained by circumstances and add an eigen number of circumstances, potentially all those which are useful and available in the survey and maybe looking at the variation that has been occurred over time in the share of the variance explained by each circumstances. So, for example, if being a female could have a positive or negative impact in 2003 then in 2012. Now, by the way, right now this is what we have so we still do not have addressed these two problems, so we discovered in mind what we can conclude from this study is that there is agraterogeneity across countries in terms of both the level and the degree of fairness in education and that the strength of the association between parental background and students score is an average lower in math and science than in reading. And this association, let me say, both the level and the degree of fairness tend to be lower in countries that perform better in terms of average test score. But there are no countries that outperform in both dimension. The geographical patterns shows that the level of fairness tend to be higher and the degree of fairness also tends to be higher than inequality tends to be lower in some Asiatic countries and in North American and Western European countries where there is also less variability. While in Eastern European countries occupy an intermediate position in terms of inequality in educational opportunity. As regards the changes observed over time so that there has been an increase in the first component in the level of fairness between 2003 and 2003 but also an increase, on average, in the degree of unfairness. So this means that in few countries have moved toward a lower degree of inequality of educational opportunities all the while improving the performances of the less advantaged students and most of them with the exception of Indonesia and Mexico or Western European countries. Thank you. Thank you very much.