_{1}

This paper analyses the incidence and intensity of low performance among 15-year old students in the OECD countries according to PISA 2012. Taking level 2 of proficiency as the baseline competence, we approach the measurement of low performance by applying a multidimensional poverty measure that permits interpreting educational poverty as a welfare loss. We use a conventional welfare evaluation function to derive an index that combines the incidence, intensity and inequality of educational poverty. The results show that OECD countries differ in educational poverty much more than in PISA average scores and also that they present different mixes of incidence and intensity.

The OECD’s Programme for International Student Assessment (PISA) provides the richest and most comprehensive database for the evaluation of the educational achievements of 15 year-old students in three different subjects: mathematics, reading, and science. The age of the students is very close to the end of compulsory education for most of the participating countries. Those results, therefore, are a good proxy of the basic knowledge ensured by the different countries to their citizens. Sixty-five countries and large economies participated in the 2012 wave of PISA. About half a million students participated in the study, representing 26 million 15 year-old students of those 65 countries and large economies [

Level 2 is considered as the baseline level of proficiency so that those students who do not achieve this level are considered as low performers. ^{1}“The proportion of students who perform below this baseline proficiency level thus indicates the degree of difficulty countries face in providing their populations with a minimum level of competencies” [

Low performance is a problem that affects one fourth of the students of the OECD (and a larger proportion of those outside the OECD) with a sizeable variability between country members. It is therefore a widespread phenomenon and also a source of inequality between and within countries. Low performance has long-term consequences and affects the future of the individual and the society as a whole. As stated in the recent OECD report on this matter, “Students who perform poorly at age 15 face a high risk of dropping out of school altogether. When a large share of the population lacks basic skills, a country’s long-term economic growth is severely compromised” [

The relevance of the problem makes it important measuring properly the extent of low performance, by considering not only its incidence (the share of low performers), but also its intensity (how far from the threshold students are), and the inequality among low performing students. The purpose of this paper is contributing to such a measurement by interpreting low performance as educational poverty and then applying the tools that are usual in the welfare analysis of inequality and poverty. From this perspective, measuring educational poverty regarding the competencies in mathematics, reading comprehension and science calls for a multidimensional measure that permits one identifying those students who can be deemed educationally poor, and also estimates how poor and unequal they are (the three poverty dimensions postulated by Sen [

The work is organised as follows. Section 2 presents a methodology that permits one measuring educational poverty in terms of a welfare loss by applying the type of reasoning used in the analysis of income inequality and poverty (see for instance Chakravarty [

Section 3 applies this methodology to the measurement of educational poverty in the OECD countries. The data show that the variability of educational poverty among the OECD countries is much larger than that of average scores, in spite of the high (negative) correlation between both variables. They also show that OECD countries exhibit different mixes of incidence and intensity of educational poverty.

A few final comments in Section 4 close the work.

The measurement of educational poverty will be conducted in terms of a poverty index derived from an explicit welfare evaluation function. In that way the interpretation of educational poverty is that of a welfare loss due to the insufficient achievements of the students. ^{2}The relevant data for our evaluation problem refer to the OECD students’ test scores in mathematics, reading comprehension and science, using the 2012 wave of PISA [

A welfare evaluation function, relative to a society with n members (15-year old students of a given country), is in this context a mapping

We shall define our poverty index as the relative welfare loss due to low performance, measured by the welfare evaluation function, W, with respect to a three-dimensional threshold z = (z_{m}, z_{r}, z_{s}), where sub-indices m, r and s refer to mathematics, reading and science, respectively. Those thresholds correspond to the minimum scores of level 2 in each competence (see below for details).

Given a n × 3 matrix Y of the students scores and a vector z = (z_{m}, z_{r}, z_{s}) of poverty thresholds, we define a student as educationally poor whenever

We now define our educational poverty index as the relative welfare loss of the poor, measured by the welfare evaluation function restricted to the set of the poor. Let p denote the number of poor students and let

unit vector of dimension m.

in the understanding that

The poverty index is defined, therefore, as the relative welfare loss due to the existence of students who do not reach the minimum admissible value of the reference variables. It is easy to check that this index moves into the interval (0, 1).

In order to give a precise expression to the generic Equation (1) we need to specify the welfare evaluation function W. We shall adopt here the one that has been used by United Nations in order to estimate the inequality adjusted human development index [

where

Note that

Which says that the welfare measure corresponds to the geometric mean of Atkinson’s equally distributed equivalent values for^{3}

Plugging this welfare evaluation function (2) into Equation (1) yields:

which in turn can be rewritten as follows:

where the first term, p/n, measures the incidence of poverty (the share of the poor in society) and the second term:

is the coefficient that measures the inequality-adjusted intensity of poverty.

Equation (3) is an intuitive and easy-to-handle formula, based on clear-cut assumptions, which corresponds to the poverty counterpart of the standard Atkinson’s welfare evaluation function for the unit value of the inequality aversion parameter. ^{4}Moreover, the two components of the index provide separate information on the extent and intensity of educational poverty (where the intensity measure is to be understood as adjusted by inequality). This is interesting because they permit uncover different patterns behind societies with similar values of educational poverty.

Note that

We now apply this methodology to the measurement of educational poverty using the results in the 2012 wave of the PISA report. Students’ performance is measured by a 0 - 1000 scale with mean around 500 and standard deviation 100. ^{5}The Programme establishes six levels of proficiency, parameterized in terms of the scores of the tests that students perform for each subject. It is understood that Level 2 is the baseline level of proficiency for an individual to be able to develop a reasonable integration in the labor market and, more generally, in society. Students who do not reach that level are considered to have insufficient knowledge (low performance). It is only natural to interpret insufficient knowledge as educational poverty and thus use the thresholds that define those minimum levels to set the corresponding poverty lines in mathematics, reading competence and science, respectively.

According to PISA 2012 the thresholds that define low performance in those competencies are: 420.1 test score points for mathematics (m), 407.5 points for reading competence (r), and 409.5 points for science (s). Therefore, our vector z of poverty lines is given by:

The micro-data of the PISA report provide information about the test scores of individuals that conform the representative sample for each country. We take those individual micro-data as our starting point, focusing on the test scores on mathematics, reading comprehension, and science. Out of these data we are able to compute, for each student i in the sample of every OECD country, the corresponding individual poverty index. That is, the number:

A student is considered educationally poor whenever this number is strictly positive and non-poor otherwise. So our first step is computing this expression for each individual student in every country. We then select those students for which this expression is positive within each country, which gives us the set of poor students in that country. Once this set has been determined, we calculate all the elements required to compute the poverty index. That is, for each OECD country we compute:

We present now the results that are obtained when analysing educational poverty in the OECD using the methodology described in Section 2.

The main results are reported in

A prominent feature of educational poverty, as clearly illustrated in

Educational poverty is highly correlated (negatively) with the average scores of the tests, with some 94% of common variance. There is a positive but relatively weak correlation between the Educational Poverty Index and the index of economic and socio-cultural status (ESCS). This is not surprising since it is already well established that the correlation between the ESCS index and average test scores is not very high (about one third of common variance).^{6}

Remark: It is worth noting that those data underestimate educational poverty in some countries, as all the information refers to the students who actually keep attending formal education. There are some countries in which the rate of 15-year olds who have abandoned the school is very high (in particular Mexico and Turkey), which implies that educational poverty would be substantially higher. For a discussion on how to combine data regarding access and achievement see Ferreira & Ginoux (2011), Ferreira, Ginoux & Aran (2011), Carvalho, Gamboa & Waltenberg (2012), Gamboa & Waltenberg (2012), and Tansel (2015) [

Note that Equation (3) describes the Educational Poverty Index as the product of two terms. The first one, p/n, captures the incidence of educational poverty. The second one, ρ(Y, z), is a measure of the intensity of educational poverty adjusted by inequality. The correlation between both components is positive but moderate (a coefficient of 0.4), which indicates that OECD countries exhibit different mixes of both ingredients. The variability of those two components is also quite diverse. The coefficient of variation of the incidence is three times that of the inequality adjusted intensity (0.476 versus 0.153).

Country | EPI | Relative EPI | Ranking test scores | Ranking EPI |
---|---|---|---|---|

Australia | 0.0177 | 75 | 11 | 13 |

Austria | 0.0195 | 83 | 15 | 15 |

Belgium | 0.0245 | 104 | 12 | 21 |

Canada | 0.0113 | 48 | 5 | 6 |

Chile | 0.0470 | 199 | 33 | 32 |

Czech Republic | 0.0180 | 76 | 16 | 14 |

Denmark | 0.0172 | 73 | 19 | 11 |

Estonia | 0.0051 | 22 | 4 | 1 |

Finland | 0.0104 | 44 | 3 | 4 |

France | 0.0284 | 120 | 17 | 25 |

Germany | 0.0162 | 69 | 10 | 10 |

Greece | 0.0363 | 154 | 31 | 30 |

Hungary | 0.0253 | 107 | 26 | 23 |

Iceland | 0.0301 | 127 | 27 | 27 |

Ireland | 0.0120 | 51 | 9 | 7 |

Israel | 0.0487 | 206 | 29 | 33 |

Italy | 0.0255 | 108 | 24 | 24 |

Japan | 0.0107 | 45 | 2 | 5 |

Korea | 0.0081 | 34 | 1 | 2 |

Luxembourg | 0.0302 | 128 | 22 | 28 |

Mexico | 0.0621 | 263 | 34 | 34 |

Netherlands | 0.0151 | 64 | 7 | 9 |

New Zealand | 0.0219 | 93 | 13 | 18 |

Norway | 0.0245 | 104 | 20 | 20 |

Poland | 0.0091 | 38 | 6 | 3 |

Portugal | 0.0250 | 106 | 25 | 22 |

Slovak Republic | 0.0439 | 186 | 30 | 31 |

Slovenia | 0.0176 | 75 | 18 | 12 |

Spain | 0.0217 | 92 | 23 | 17 |

Sweden | 0.0339 | 144 | 28 | 29 |

Switzerland | 0.0131 | 56 | 8 | 8 |

Turkey | 0.0291 | 123 | 32 | 26 |

United Kingdom | 0.0226 | 96 | 14 | 19 |

United States | 0.0210 | 89 | 21 | 16 |

OECD | 0.0236 | 100 |

Country | p/n | (Y, z) | Relative p/n | Relative ρ(Y, z) |
---|---|---|---|---|

Australia | 0.14 | 0.12 | 78 | 98 |

Austria | 0.17 | 0.11 | 93 | 91 |

Belgium | 0.17 | 0.15 | 92 | 115 |

Canada | 0.10 | 0.11 | 55 | 88 |

Chile | 0.40 | 0.12 | 218 | 94 |

Czech Republic | 0.15 | 0.12 | 84 | 93 |

Denmark | 0.15 | 0.12 | 80 | 93 |

Estonia | 0.06 | 0.08 | 35 | 63 |

Finland | 0.09 | 0.12 | 49 | 92 |

France | 0.19 | 0.15 | 103 | 119 |

Germany | 0.14 | 0.12 | 77 | 92 |

Greece | 0.26 | 0.14 | 140 | 113 |

Hungary | 0.21 | 0.12 | 113 | 97 |

Iceland | 0.20 | 0.15 | 111 | 117 |

Ireland | 0.11 | 0.11 | 59 | 88 |

Israel | 0.28 | 0.17 | 153 | 138 |

Italy | 0.20 | 0.13 | 107 | 104 |

Japan | 0.09 | 0.12 | 48 | 98 |

Korea | 0.07 | 0.12 | 37 | 94 |

Luxembourg | 0.22 | 0.14 | 120 | 109 |

Mexico | 0.48 | 0.13 | 261 | 103 |

Netherlands | 0.13 | 0.11 | 73 | 90 |

New Zealand | 0.17 | 0.13 | 92 | 103 |

Norway | 0.18 | 0.14 | 96 | 111 |

Poland | 0.09 | 0.10 | 52 | 76 |

Portugal | 0.20 | 0.13 | 107 | 101 |

Slovak Republic | 0.27 | 0.16 | 148 | 129 |

Slovenia | 0.16 | 0.11 | 89 | 86 |

Spain | 0.17 | 0.13 | 94 | 100 |

Sweden | 0.22 | 0.15 | 122 | 120 |

Switzerland | 0.12 | 0.11 | 63 | 91 |

Turkey | 0.28 | 0.10 | 155 | 81 |

United Kingdom | 0.16 | 0.14 | 88 | 111 |

United States | 0.19 | 0.11 | 104 | 88 |

OECD | 0.18 | 0.12 | 100 | 100 |

Educational poverty has been identified here the product of two different factors: the incidence of educational poverty, given by the share of students who do not reach level 2 of proficiency, and the inequality adjusted intensity, which measures how unequal they are and how far away are their scores from the threshold defining level 2.

The Educational Poverty Index is to be interpreted as a quantitative assessment of the welfare loss due to the failure of educational systems to provide a minimal knowledge to all citizens. This is so because the basic data (the PISA scores) are collected at the end of the period of compulsory education.

The data show that the OECD countries are much more diverse regarding educational poverty than with respect to the average scores. In all cases we find that most of the observed differences in the Educational Poverty Index are due to the differences in the incidence, whereas the impact of the equality adjusted intensity is smaller, with a positive but weak correlation between those variables (a common variance of about 0.17).

The high negative correlation between educational poverty and average scores tells us that reducing low performance appears as the most effective way of improving the overall educational outcomes. In other words, making the educational system more inclusive is the best strategy to get simultaneously higher equity and higher efficiency.

Finally, let us briefly comment on the possible causes of educational poverty, even if this question is outside the scope of this work. The analysis presented by the PISA team in OECD [

1) Family environment: Low performance increases in socio-economic disadvantaged families, in students with immigrant background, in those who speak at home a language different from that in the school, those students living in rural areas, and those from single-parent families.

2) Individual characteristics: Attitudes and behaviours also influence the probability of low performance. The two main variables that seem to increase low performance are not having attended pre-primary education and having repeated a grade.

3) School-related factors: There is some evidence showing that more socio-economic diversity among students and less grouping by ability between classes tends to provide a better learning environment.

Identifying these elements helps designing measures to reduce educational poverty and increase the efficiency and equity of educational systems. Yet, as there are substantial differences in the profile of low performers among countries, as already pointed out, those measures have to be very much tailor-made. There are already some particular experiences illustrating that there are effective ways of reducing educational poverty in countries with very different characteristics [

The judgements contained in this paper express the views of the author and not those of the OECD or any of its state members.

Antonio Villar, (2016) Educational Poverty as a Welfare Loss: Low Performance in the OECD According to PISA 2012. Modern Economy,07,441-449. doi: 10.4236/me.2016.74049