# Do School Resources Increase School Quality ?

Nadir Altinok

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Les Documents de Travail de l'IREDU

Working Papers

Institut de Recherche sur l'Education

Sociologie et Economie de l'Education

Institute for Research in the Sociology and Economics of Education

# Do School Resources Increase School Quality?

Nadir Altinok

Mai 2010

DT 2010/3
# Do School Resources Increase School Quality?

Nadir Altinok<sup>a1</sup>

<sup>a</sup> University of Metz (ID2)

CNRS (French National Center for Scientific Research)

BETA (Department of Economics, University of Strasbourg)

IREDU (Institute for Research in Education, University of Bourgogne)

**Abstract:**

The aim of this paper is to verify whether school resource factors have an impact on the quality of education. This latter is measured with the help of a unique database on student scores in international skills tests. The general difficulties inherent in this type of study are the possibility of endogeneity bias and measurement errors. After estimation bias correction, we show that improvement in the quality of educational systems does not necessarily require an increase in school resources. When an alternative indicator of the performance of educational systems is used, our results are confirmed. Consequently, one should remain cautious about recommending purely financial measures to improve quality of education.

**Key words:** Quality of education, School performance, School resources.

**J.E.L. Classification:** H5, I2, O4

<footnote n="1">¹ Corresponding author: Tel. +33.387.54.71.38. Fax +33.380.39.54.79. E-mail address: nadir.altinok@gmail.com. The author is very grateful to Saloua Bennaghmouch.</footnote>
# 1. Introduction

The majority of countries throughout the world devote between 1% and 11% of their GDP to education; equally often, this item of expenditure accounts for one fifth of government spending. Given the rapid growth and large magnitude of education spending, governments have been increasingly interested in ways of controlling education costs. One possible strategy is to modify the institutional structure of the educational system in order to improve the quality of education. There is a lack of clear consensus on whether the quality of an educational system can be improved simply by increasing educational expenditure. More generally, school resource factors as a whole do not appear to explain school performance in any satisfactory manner. In one of the very first studies in this field, Coleman et al. (1966) found very weak effects of school resources on student performance. Their report was very influential, giving rise to several hundred articles seeking to measure the impact of school resource variables on student performance. Effects such as class size, the level of educational expenditure and teachers' pay were tested.

Recent exchanges between Eric Hanushek and Alan Krueger underline the lack of consensus about the validity of a relation between educational inputs (such as spending) and the output of the system, often measured by students' scores in skills tests. For example, Hanushek (1998) and Krueger (1998, 2000) analyze the panel data on educational expenditure and the results of NAEP tests (National Assessment of Educational Progress) in the United States. The NAEP is a survey of American students' acquired skills in reading, writing, mathematics and science. From his analysis, Krueger concludes that the increase in spending has led to a slight increase in students' scores, whereas Hanushek finds no clear and robust relation between school resources and student performance.

The aim of this paper is to test the extent to which school resource factors influence educational performance. This latter is measured by the quality of education, itself estimated
on the basis of international surveys on student skills. The aim is to calculate an educational
production function (EPF) in which an output (the quality of education) is related to certain
inputs (school resource factors). Although many studies have estimated the relation between
educational inputs and student test scores, these studies are most often based on
microeconomic analyses. International comparisons are rare, due to the lack of comparable
and homogeneous data. Below, we describe the most influential studies in this field.

Two major studies (Hanushek and Kimko, 2000; Lee and Barro, 2001) have been
conducted into the relation between educational variables and test results, using aggregate
data. Hanushek and Kimko (2000) construct an international database of student test scores
for a sample of 39 countries (for the complete methodology, see Hanushek and Kim, 1995).
To test for the existence of an educational production function, the authors regress the
measurements of educational performance with input indicators. They emphasize that the
conventional measurements of education (such as class size at primary level, government
spending per student or the share of GDP allocated to educational expenditure) have no
significant effect on the results achieved in the international tests.

Lee and Barro (2001) look for the determinants of school quality in a panel database that
includes measurements of education inputs and outputs for a larger number of countries. The
authors take into account the results in mathematics, science and reading for students of
different ages, in the same surveys as those used by Hanushek and Kimko (2000), for several
years from 1964 and 1991. To the contrary of Hanushek and Kimko (2000), they show that
school resources, including teachers' pay, have a significant impact on the skills tests, while
class size have a significant negative effect on test scores.

Other works have performed the same type of estimation. Al Samarrai (2002) presents a
review of the literature together with further results. Without testing survey data, Gupta,
Verhoeven and Tiongson (1999) show the need to differentiate between countries according
to their economic level in the estimation of the educational production function. Finally, Hanushek and Luque (2003) carry the analyses of Hanushek and Kimko (2000) further. More complete reviews of the literature can be found in Leclercq (2005) and Al Samarrai (2002).

In itself, we do not take into account, in this paper, the dimension relating to the organization of educational systems or the internal workings of the “black box” that they constitute. Our viewpoint is from a macroeconomic level, centered rather on the concept of educational production function. The objective here is to assess the extent to which school resource factors do or do not affect levels of school performance.

Nevertheless, compared with previous works, this paper proposes several advances. Firstly, we take into account two different indicators for the measurement of educational performance, where most of the studies limit themselves to one. Using two complementary measurements gives us the possibility of verifying the validity of our results. Further, our comparative international study adopts a panel perspective, enabling us to control for unobservable fixed effects. In fact, most of the previous studies do not control for bias due to omitted variables and fixed effects. Because we have panel data, we can take into account all the invariant effects whose characteristics are specific to the countries’ educational systems. Another advantage of the panel database is that it enables us to take into account the possible endogeneity of school resource factors. To our knowledge, no other macroeconomic study uses regressors to purge endogeneity bias. Yet it seems fairly logical to imagine that a double relation of causality might exist between resource factors and the performance of educational systems. For example, an educational system may perform well because classes are small in size. In parallel, because of its high performance, the government may opt for a voluntary reduction in class size. Other examples can be found, and they all underline the need to take into account the bias generated by this possible endogeneity. That is we set out to do in this paper.
The rest of the paper is structured as follows. In section 2, we describe the methodology used to construct our data on the quality of education (which we call the "qualitative indicators of human capital" or QIHC) and the other input indicators. Section 3 presents the modelling and the main results obtained. Section 4 concludes.

## 2. Data and methodology

### 2.1. Database relative to the quality of education

The data used to measure the quality of education comes from the international surveys on educational achievement. Since 1964, international tests are administered to students from different countries in order to evaluate their level on mathematics, science and other skills. These qualitative indicators of human capital (QIHC) can be considered an alternative to the strictly quantitative variables of education, such as school enrollment. The studies by Hanushek and Kimko (2000) and Lee and Barro (2001) have already adopted such an approach.

Strictly speaking, the aim is to *quantify*, on a scale of 1 to 100, the *quality* of education, or more precisely the scores of representative samples of students from different countries in international achievement tests. We take into account 6 groups of international surveys into student achievement. Our data have been taken from Lee and Barro (2001) for the surveys prior to 1995 and from the official reports for the other surveys (see table 2 for a presentation of the surveys). Below, we present the general methodology. For a more detailed presentation, see Altinok and Murseli (2007) and Altinok (2009)<fnref n="2" />.

<footnote n="2">² The database used in this paper is the same of the one which can be found in Altinok and Murseli (2007). The updated database presented in Altinok (2009) is slightly different. Please see Altinok (2009) for the differences between the two databases.</footnote>
We have used the most recent results from 6 different groups of international surveys (IEA, PISA, SACMEQ, PASEC, LLECE and MLA<fnref n="3" />). For the meaning of all these initials, see the note to Table 2. Previous analyses have used surveys from the period 1961 to 1990, without considering the question of their quality. Lee and Barro (2001), for example, took the scores for all the tests available between these two dates, for all the skills tested, without any readjustment. Hanushek and Kimko (2000) took into account the quality of the data, to a certain extent, by weighting the gross results by standard errors. But they re-calibrated the data solely on the basis of the American NAEP survey (National Assessment of Educational Progress). The authors assumed that the results from this survey were sufficient for overall anchoring of the data. In addition, they did not take into account the results of surveys conducted after 1990. Yet most international surveys actually started after this date. Widening the analysis to cover all the available surveys can, in particular, help us to confirm or disprove the results of previous studies.

The database is in the form of a panel, covering the period 1964-2005. We compile the results from all the surveys measuring student achievements at primary and secondary level. We have two groups of surveys: those in which the United States took part (series A), where we can anchor the data to a specific survey (NAEP), and those in which the United States did not take part (series B), where we anchor the data on countries that have taken part in several different surveys. The anchoring we use in series A, on the American NAEP survey, is the same as that used by Hanushek and Kimko (2000). The NAEP has been the principal tool for measuring student achievements in the United States since 1969. The IAEP is the international equivalent of the NAEP. Thus, the procedure of evaluation is based on American curricula. At different periods since 1970, American students aged 9, 13 and 17 have been

<footnote n="3">³ For the meaning of all these initials, see the note to Table 2.</footnote>
tested on their achievements in science and mathematics. These tests provide an absolute
measurement of reference for the level of achievements in the United States. In order to
collect the data from both the IEA and the IAEP surveys at the same time, Hanushek and
Kimko (2000) used the American results as "references". Thus, they modified the means of
the IEA surveys to make them equal to the nearest means in the IEAP surveys (for age, school
year and skill tested). Unlike Hanushek and Kimko, in order to obtain indicators comparable
to those obtained in series B, we have not re-weighted the scores by the measurement errors.
For series B – the surveys in which the United States did not take part – we have adopted the
methodology of anchoring. This consists in evaluating the level of difficulty of the different
tests based on the results of countries that have taken part in several different surveys. For
example, if country x performs better in test A than in test B, with the two tests taking place at
about the same date, then we can assume that test A is easier than test B, and a readjustment
proportional to the difficulty is therefore necessary. In the end, we obtain 42 series of tests for
all age groups (9, 10, 13, 14, 15). As a next step, given that certain series concern the same
year and the same level of schooling (primary or secondary), grouping these together brings
the final number of test series down to 26.

In this study, we use the scores in mathematics, because this is a skill that is easier to
compare between countries than reading or science. Furthermore, we use the standardized
tests for secondary education, because this is probably the most appropriate educational level
for measuring the quality of education. This is also the level for which we have the most
observations. It should be noted that our sample is relatively small and unbalanced, because
not all the countries took part in all the surveys. Nevertheless, it does enable us to perform
econometric analyses that can confirm or disprove previous studies. In addition, to make up
for the lack of data and to be able to compare results, we use another educational output (the
net enrolment rate at secondary education, see below).
## 2.2. Database relative to school factors and alternative output measure

As well as the qualitative variables on education constructed and described above, we have also used a set of input variables, to estimate the school production function. For the data from the period 1960-1990, these are drawn mainly from the database of Barro and Lee (1996). The following variables are considered: teacher pay at primary school level as a percentage of GDP per capita (variable *SHSALP*), class size at primary and secondary school level (variables *TEAPRI* and *TEASEC* respectively), government spending on education per student as a percentage of GDP per capita (variables *SHPUPP* and *SHPUPS*, for primary and secondary levels respectively) and repetition rates (*REPPRI* and *REPSEC*). As these data are only available up until 1990, we have updated them by drawing mainly on data from UNESCO and the World Bank (see UNESCO, 2004, 2005, 2007 and World Bank, 2002, 2007). As regards the variable *SHSALP*, we have estimated it using data available from UNESCO and then completed the missing data from the World Bank (2002). We have calculated teachers' pay as a percentage of GDP per capita by dividing the total amount paid to teachers over one year by the number of teachers employed during the year in question. The variable *SHSALP* is then obtained by expressing this as a fraction of GDP per capita. The variables of government spending on education per student have been updated using data extracted from the UNESCO Institute for Statistics: these are expressed as percentages of GDP per capita, for primary and secondary school levels separately.

The variable concerning the average number of years in education for those aged 25 or over (variable *ADEDU*) has been drawn from Barro and Lee (2001). In their study, Lee and Barro (2001) preferred to use the average number of years spent by adults in primary school education, without giving any specific justification. They even pointed out that they had not included the average number of years spent in secondary education because the variable was
not significant. Consequently, we prefer to use the number of years spent in school by adults
without distinguishing between the levels of education, for there are no grounds for not
including the years spent in secondary education and above. As the sample of countries
available in the database of Barro and Lee (2001) is fairly small, we have predicted the
variable *ADEDU* from the school life expectancy (expressed in years), available in the
UNESCO databases (see UNESCO, 2004 and 2005). These two variables are closely linked
by a lag effect: as a general rule, the school life expectancy for youngsters is higher than that
for adults, for the first variable takes into account evolutions in the school enrollment of the
young.

Indicators of educational inequalities have been drawn from Altinok (2007). These
indicators cover several dimensions of inequality in education by grouping together Gini
index scores and other forms of inequality (notably gender inequalities and drop-out school
rate). See Altinok (2007) for a presentation of the methodology. The values of the index range
from 0 to 100; the higher the value, the higher the level of inequalities. The data are available
for the period 1960-2000, with intervals of 5 years between each observation.

To compare the results, we use a second indicator of educational expenditure: spending on
education as a percentage of GDP. Although it is impossible for us to distinguish between
each level of education, this indicator can serve as an alternative to the above measurements.
The data are drawn from UNESCO and are available for the period 1970-2005. The sources
of the data are indicated in Table 1. In addition, elements of descriptive statistics are presented
in Table 3.
## 2.3. Drawbacks relative to the qualitative indicators of human capital

Although the methodology used was designed to measure level of equivalence between the different surveys, it has its limits. Three such limits are discussed below, although there may be others.

The first concerns the anchoring of data to scores obtained in the United States of America. When gauging the difficulty of a particular survey, its data are adjusted to the score of the United States of America both in the survey and in the NAEP. This implies that the NAEP is a sound benchmark for measuring the performance in the United States of America. Yet the published NAEP findings may include a measure of distortion, which could in turn lead to distortion when adjusting the survey concerned. Nevertheless, the anchoring of data on a separate source is the only known procedure for the optimal calibration of surveys in relation to each other. Ideally, data on learning achievement since the mid-1960s should be available for another country, but only the United States of America is believed to have compiled such data at the time. Moreover, to avoid adjustments reliant on the NAEP only, an anchoring methodology is used which consists of an identical linear conversion for surveys administered by the same body (the “general NAEP anchoring methodology”).

Furthermore, the nature of the skills assessed may differ from survey to survey, in which case the surveys may not be readily comparable. While some surveys (such as the IEA surveys) tend to measure learning achievement in terms of knowledge, others (such as the OECD surveys) focus more on the level of pupils' skills. In this particular case, any equivalence established may be distorted, as the “products” of education measured in this way are not clearly equivalent. Despite this difference in the kind of “acquisition” measured, the surveys arguably yield a sound assessment of pupils' attainment in mathematics, science and reading.
Finally, as the adjustments are based on scores obtained by the United States of America, irrespective of the methodology used, the database cannot include surveys in which the United States of America has not taken part, such as regional SACMEQ, PASEC, LLECE and MLA surveys. Another methodology that would include regional surveys have been used, but it has its own drawbacks.

# 3. Model and results

In this section, we estimate the educational production function. We start by presenting the general model. The following subsection describes the econometric techniques used to correct estimation bias. Finally, we discuss the results of the estimations.

## 3.1. The model

We estimate the educational production function using qualitative indicators of human capital (QIHC) and the net enrollment ratio at secondary school level. The educational production function includes both input and output indicators.

Two different variables are used for educational output, including the scores in student skill tests (QIHC). In order to compare our results with the classic indicator of education quality, a second indicator is used. The net enrollment ratio at secondary level (NERSEC) can be considered as a measure of the performance of an educational system. Clearly, this cannot be treated as a formal indicator of student performance; nevertheless, if a large proportion of students succeed in leaving the secondary level without either dropping-out or repeating years, we can assume that the good performance of the educational system is at least partly responsible. Family factors are represented by a proxy variable of parents' education. This is measured by the number of years spent at school by adults aged 25 and over (ADEDU). It should be noted that this variable can also measure the education level of the teachers. There
are four variables relating to school resources. The first concerns government spending on education. This is measured on the basis of each country's effort, not in absolute terms: we therefore use a variable measuring educational expenditure per student for each educational level as a percentage of GDP per capita (SHPUPP and SHPUPS for primary and secondary schools respectively). However, as Lee and Barro (2001) observe, as private spending is not taken into account by these variables, there may be important errors of measurement. To verify the validity of our results, we also use the indicator of educational expenditure as a percentage of GNP (EXPGNP). Unfortunately, this indicator reflects the whole of educational expenditure, not the spending on particular levels. Teachers' pay is also measured in relation to GDP per capita (SHSALP). Class size represents another resource factor (TEAPRI and TEASEC for the primary and secondary levels respectively). Unlike Lee and Barro (2001), we include the repetition rates as an input indicator, because we believe it has more to do with a choice of educational policy than a question of educational efficiency (REPPRI and REPSEC for the primary and secondary levels respectively). Lastly, it is also possible to consider the level of educational inequalities as a lever of economic policy. A country may quite deliberately choose to favour selective access to a given level of education and so accentuate inequalities in schooling. For that reason, we include the indicators of educational inequalities (INEDU) in the estimation.

It is important to note that the panel is unbalanced and the number of observations varies considerably depending on the estimations. For example, less than 200 observations are available with the indicators of educational quality in mathematics at the secondary level. Using the net enrollment rate for secondary education provides about 370 observations. We now move on to discuss the regression methods used.
## 3.2. Regression methods used

We employ several econometric techniques to estimate the educational production function. We start by using the ordinary least squares (OLS) estimator, introducing dummies for the different years in order to capture intrinsic temporal variations. As we cannot, in this case, use the whole database of test scores, we restrict it to the indicators of the quality of schooling in mathematics. The model is written as follows:

$$q_{it} = \alpha_{it} + \beta_{1}f_{it-1} + \beta_{2}s_{it-1} + \mu_{t} + v_{it} \quad (1)$$

where $q$ denotes educational output, $f$ denotes family factors, $s$ covers all the school resource variables, $\mu$ represents indicator variables for the years and $v$ denotes the error term. The index $i$ represents the country level and the index $t$ the temporal level. The sample is unbalanced and the intervals are every 5 years, from 1965 through to 2000, so we have 7 different periods.

Random-effects estimation assumes that the relations between inputs and outputs are distributed randomly between countries and between years. Now, it is highly probable that unobserved effects of countries are present in the estimations and interfere with the $\beta$. If such is the case, then the relations found in a random-effects estimation are potentially biased. To correct this bias, we then perform a fixed-effects estimation. Here, the estimator is that of the panel OLS with dummy variables $\delta$ for each country $i$, and dummy variables $\mu$ pour for each year $t$:

$$q_{it} = \alpha_{it} + \beta_{1}f_{it-1} + \beta_{2}s_{it-1} + \mu_{t} + \delta_{i} + v_{it} \quad (2)$$

There are three main reasons why the relation described above might be biased when the fixed effects are taken into account. Firstly, there may be no direct relation between an
educational investment or a form of organization of education in a country and the school performance in that same country. In this case, the relations found with the fixed-effects estimator can be biased in many different ways and indicate significant relations where there are none. Another possible reason comes from measurement errors in the estimation of the quality of education. If, for example, the measurement errors are greater for a specific year, the fixed-effects estimator tends to bias the specification even further. Another likely reason arises out of the problem of endogeneity. For example, if a country can improve its education quality by reducing the size of classes, the opposite relation is equally possible: it can reduce class size because its population has access to high-quality education. The same relation of reciprocal causality may exist for the other variables. Because of this bias of causality, the fixed-effects estimator itself may be biased. To correct all these biases, we use the generalized method-of-moments estimator, where the endogenous variables are instrumented by the values of the lags of the same variables. In this case, we estimate the following equation:

$$ \Delta q_{it} = \beta_1 \Delta f_{it-1} + \beta_2 \Delta s_{it-1} + \Delta \mu_t + \Delta u_{it} \quad (3) $$

As can be seen, we regress the variation of output with the variation of each of the inputs, so as to purge the whole estimation of fixed effects. In this precise case, it is no longer the level of an input that determines the level of an output, but the variation of the former that determines the variation in the latter. The estimator we use consists in adding instruments in levels to the classic instruments, so as to form a system of the generalized method-of-moments. To correct these biases, we use another regressor, that of the generalized method of moments (the GMM system), with an application by Blundell and Bond (1998). This regression is performed on a dynamic panel model and uses the levels and lags of endogenous variables as instruments. While Arellano and Bond (1991) use the first-difference estimator to avoid the correlation between the lagged values of the dependent variable and the fixed
effects included in the term of error, Arellano and Bover (1995) again include the equations expressed in levels, in addition to the lagged values of the first differences, to avoid being confronted with the problem of the validity of the instruments, as highlighted by Staiger and Stock (1997). In addition, they show that the inclusion of equations in levels considerably increases the accuracy of the estimators, particularly when the auto-correlation of the dependent variable is strong.

However, the total number of instruments sometimes becomes too high in relation to the observations, sometimes even higher than the number of countries included in the panel. Because of the new level constraints introduced, this problem arises more often with the Blundell and Bond estimator (1998) that we use for our regressions. The improvement made by Roodman (2006) to this estimator in the Stata® software enables us to use an original method to limit the problem of the number of instruments. The "collapse" option in Stata can be used to restrict the number of instruments by only considering some of the lagged variables instead of all of them. In our analysis, this option is only used when the number of observations is lower than 200, in other words when the qualitative indicators of human capital are used to measure school performance and sub-samples are used. With Blundell and Bond's estimator (1998), we have a choice between one-step and two-step estimation. The simulations carried out by Arellano and Bond (1991) suggest that two-step estimation can improve the accuracy of estimated coefficients and considerably increase the quality of the estimation in the event of heteroskedasticity, but the standard errors tend to be systematically undervalued. For this reason, we have chosen not to use the two-step version.

It is important to note that we make use of proxy variables, notably in order to take family factors into account. As McCallum (1972) demonstrates, when there are no errors in the measurement of either the proxy variables or the other inputs, it is preferable to include such
variables in the specification. Nevertheless, we are still confronted with the problem of
whether the use of such proxies might not add even more bias to the model. For example, we
use the variable of educational expenditure per student as a proxy to offset the lack of other
educational inputs, assuming that it can explain all the educational inputs. But the inclusion of
such a proxy can induce an even greater estimation bias (Wolpin, 1995, 1997; Todd and
Wolpin, 2003). Todd and Wolpin (2003) show that the use of proxies in an educational
production function can complicate the interpretation of coefficients. They consider the
example of a model relating performance to an input such as class size. To avoid having to
leave out the missing variables for other inputs, a researcher might include a variable such as
the level of educational expenditure per student. However, it is perfectly possible that schools
with the same level of spending per student, but with smaller-sized classes, spend less on
other, unobservable variables (such as employing less experienced teachers). Consequently,
the effect of class size on school performance, with a given level of educational spending per
student, is measured with the hypothesis of constancy in the unobservable input factors. If
class size and unobservable inputs are not correlated, then the bias due to omitted variables is
null in the model without proxy. By including the proxy of educational expenditure in the
regression, we assume that the variations in class size are merged with the variations in
unobserved inputs. In this sense, the inclusion of proxies can exacerbate the biases.
Alternatively, proxies such as income per capita or educational expenditure can be used to
verify the importance of biases due to omitted variables. These biases exist if the inclusion of
these proxies affects school performance, with the other inputs remaining unchanged. If it
turns out that the effects of included inputs change considerably when the proxies are
included in the regression, Wolpin (1995) shows that the researcher cannot know which of the
estimations is the least biased. For these reasons, we estimate each regression again, using one
sole input each time, but including the variable of the educational level of adults to control for
family effects. As we use a fixed-effects estimator and the generalized methods-of-moment estimator of Blundell and Bond (1998), the fixed effects are purged, which theoretically limits the biases due to omitted variables. Consequently, with such estimators, the inclusion of only part of the variables in the regression should not lead to an overestimation of their impact on educational output.

### 3.3. Results of the estimations

In Table 3, we estimate the educational production function with random effects using the results of mathematics tests at secondary level and the net enrollment ratio at secondary level as output indicators (equation 1). To capture the variations due uniquely to the temporal dimension, we introduce indicator variables for each year considered. Fisher's test of global significance of the indicators for each year shows the importance of incorporating them into the estimation. Even when their significance is rejected at the 10% level, the value of the other coefficients is not changed. In addition, the standard deviations are corrected by the cluster method and are robust to heteroskedasticity.

Column (1) shows the analysis carried out on the basis of the first spending indicator, i.e. educational expenditure per student at secondary level as a percentage of GDP per capita. Only the variable of the educational level of adults is positive and significant. Whatever other inputs are included, their coefficients are never significant. The relations are different with the use of net enrolment ratio (NER) as output indicator (columns 7 to 12). Likewise, the educational level of adults has a positive and significant relation to the enrollment rate. Educational expenditure is either negatively correlated (column 7), or not significant (column 8). Teachers' pay is negatively correlated with both of the outputs used, but only significantly with the enrollment rate. In addition, the same negative relation exists for class size and for the repetition rates. Only the coefficients in the estimation with the enrollment rate are
significant. Lastly, despite a negative coefficient, educational inequalities do not appear to
have an impact on school performance, whichever output is used.

These results may be biased, because our estimations consider that the variations in the
different variables between and within countries are distributed randomly. Moreover it is
probable that omitted variables exist which influence both inputs and outputs, thus leading to
estimation biases. Table 5 presents the fixed-effects estimations, where we include the
indicator variables for each country. When the fixed effects are taken into account, the inputs
no longer appear to have any effect on educational performance, whatever the nature of this
latter. Even the variable of the educational level of adults is only significant for 3 estimations
out of a total of 12 (columns 7, 9 and 10), which raises doubts about its actual effect on school
performance. When the test scores are used, no variable is significant. The samples are
relatively small and in general we only have three observations for each country considered.
Still, if the sample size was the main problem, we should obtain more significant results when
we use net enrollment rates. But this is not the case. Only educational inequalities appear to
have a negative influence on the enrollment rate at secondary level. A reduction of one
standard deviation in the level of educational inequalities induces an increase of about 11
percent. This effect is very powerful, but the causal relation between enrollment rate and the
level of educational inequalities is not controlled for by the fixed-effects method of
regression. To correct these biases, we use the generalized method-of-moments estimator.

The results of the estimation using the GMM system are presented in Table 6. As in the
previous estimations, the estimations are performed with a limited number of independent
variables, to avoid bias in the estimated coefficients. There is no possible bias due to the
presence of omitted variables, because the estimation is made on the rates of variation, which
theoretically eliminates the unobservable characteristics. In columns 1 to 6, we use the student
test scores as output, while columns 7 to 12 show the results of estimations using the
enrollment rate. When we use the test scores, only the variable relating to parents' income is
significant: an increase of one standard deviation in the educational level of adults (i.e. about
2.7 years in 1995) induces an increase of about 6 percent in student scores, representing more
than double the impact when the regression is performed with random effects (2.72 × 2.22 =
6.04). When the variable of educational expenditure is introduced, it is still not positive and
significant. Even more importantly, its impact appears to be negative and significant for the
enrollment rate. The other indicator of educational expenditure also produces negative, but
not significant coefficients. This strengthens our idea of the lack of relation between the level
of spending on education and the quality of education. None of the other inputs has a direct
influence on the quality of education when the test scores are used as output. With the
enrollment rate as output, teachers' pay even has a negative and significant effect on it.
Educational inequalities also have a negative, significant impact on the enrollment rate.
Consequently, when the estimation biases are controlled for, the educational production
function loses its relevance. At most, the educational level of adults explains the level of
school performance.

It should be noted that both educational performance and the structure of educational
systems differ strongly between different countries and different economic levels. In this case,
it is possible that our estimations are biased because they include very diverse countries,
notably both developed and developing countries. Although Blundell and Bond's estimator
(1998) is usually operated with fixed effects, we require each country to follow one sole
production function. To verify this hypothesis, we estimate the above specifications once
again, distinguishing between the economic levels of the countries. As our sample is fairly
small, we have chosen to distinguish between OECD countries and non-OECD countries. The
results presented in Table 7 show that the difference in the educational production function
between countries of different economic levels is not proven. Only four variables are
significant. It is important to note that the samples are very small, and this may reduce the
significance of the coefficients. Notwithstanding, it is surprising to observe that the
educational level of adults seems no longer to have an effect on test scores when the
distinction is made between countries of different economic levels. Only two estimations for
the non-OECD countries produce a positive and significant impact of the educational level of
adults. Educational expenditure has no effect on test scores, whatever the economic level of
the countries considered. In an unremarkable way, teachers' pay has a negative and significant
impact on the quality of education for the developing countries (column 9). The increase of a
standard deviation of teachers' pay (i.e. a rise of 241% in 1995 for non-OECD countries)
induces a fall of 11 percent in the quality of education. This effect is about five times higher
than it is with the random-effects estimator and concerns all the countries in the sample
(column 3 in Table 7), but remains fairly weak considering that this increase in pay represents
a multiplication by more than 3. The size of classes has a positive effect for OECD countries
and negative for developing countries. However, the effect is only significant for the former
group. In any event, we observe no negative and significant effect, whatever the economic
level of the countries considered. In addition, the repetition rates have a negative and
significant impact for the developing countries. Here, the effect of repeated years is very
strong: a reduction of one standard deviation (i.e. 7.3 in 1995 for the non-OECD countries)
induces an increase of 6 percent in the test scores. We repeat the same procedure with the
enrollment rate as the educational output (Table 8). The educational level of adults retains its
positive and significant effect, whatever the economic level of the countries. On average, the
impact of the educational level of adults on the enrollment rate is stronger for developing
countries than for OECD countries. In this difference, we can read a process of educational
convergence between countries with different economic levels. The impact of educational
expenditure is unconvincing, to say the least. Admittedly, its effect on the enrollment rate is
positive and significant for OECD countries, but only at a level of significance of 10%. When educational expenditure as a percentage of GNP is used as an alternative variable, the relation disappears. The effects are equally contrasting for the developing countries, where only the use of the second indicator produces a negative and significant relation. One quite surprising result is the positive effect of repeated years on the enrollment rate in OECD countries. But this appears to be of lower amplitude. These results underline the need to distinguish the economic level of the countries clearly, which leads us to reject the existence of the educational production function.

## 4. Conclusion

The objective of this paper has been to determine the extent to which, within an educational system, school resource factors have an impact on school quality. For this purpose, we have estimated an educational production function. As it would for a firm, this function relates inputs to an output. In this case, we have chosen two outputs. The first concerns student scores in international achievement tests. It is reasonable to consider that the performance of an educational system can be measured through student scores in standardized tests of skills such as mathematics, science and reading. However, given the limited nature of data on international tests, we have also used net enrollment rate at the secondary level. By choosing such an indicator as an alternative to the international tests, we have favored the quantitative dimension.

Each country seeks to achieve the best performance for its educational system, at the lowest possible cost. As we have seen over the course of this paper, there is no established relation between resource factors and the performance of an educational system. With the growing globalization of economic activities, governments are more and more preoccupied with the performances of their educational systems. It appears important to search for specific
educational policies that can improve them. But increasing school resources have not established effects on school quality at the macroeconomic level: educational systems are so complex, and there are so many factors at work that it remains very difficult to search for the sources of the quality of education.

What are the main reasons conducting to a lack of relationship between school resources and the quality of education? We can think that there can be two main hypotheses. Firstly, as we suggested it in the section 2.3., our data can suffer for measurement bias. Obviously, we computed a new database, using many different surveys. Despite the meticulous work done for making these data comparable, it could be possible that our analysis of difference-in-difference may suffer for measurement error, as it is often the case in growth econometrics estimations. However, it will never possible to obtain a precise measure of education quality, since this is a multidimensional variable of the education system. The second reason of the lack of relationship is perhaps an established lack of effect from school resources to education quality. Why in a given country, due to an increase of school resources, will education quality systematically improve?

Still, it remains fundamentally important for a country to evaluate the quality of its educational system. International surveys surely have a promising future. If existing databases of standardised skills tests remain limited in the number of observations, it may be possible to verify the existence of an educational production function in the coming years, thanks to the new surveys that are being conducted now or will be conducted in the future.

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<table><caption>Table 1 - Sources of data used</caption><thead><tr><td>Indicator</td><td>Abbreviation</td><td>Period</td><td>Source</td></tr></thead><tbody><tr><td>Quality of education</td><td>QIHC</td><td>1965-2002</td><td>Altinok and Murseli (2007)</td></tr><tr><td>Net enrollment rate in secondary education</td><td>NERSEC</td><td>1970-2005</td><td>UNESCO-Institute for Statistics</td></tr><tr><td>Parents' education: average number of years schooling for adults aged over 25</td><td>ADEDU</td><td>1960-2005</td><td>Barro and Lee (2001), UNESCO-Institute for Statistics</td></tr><tr><td>Govt. spending per student at primary level as % of GDP per capita</td><td>SHPUPP</td><td>1960-2002</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Govt. spending per student at secondary level as % of GDP per capita</td><td>SHPUPS</td><td>1960-2002</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Govt. spending at primary level as % of GNP</td><td>EXPGNP</td><td>1970-2005</td><td>UNESCO-Institute for Statistics</td></tr><tr><td>Teachers' pay at primary level as % of GDP per capita</td><td>SHSALP</td><td>1960-2002</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Class size at primary level</td><td>TEAPRI</td><td>1960-2005</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Class size at secondary level</td><td>TEASEC</td><td>1960-2005</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Repetition rates at primary level</td><td>REPPRI</td><td>1970-2005</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Repetition rates at secondary level</td><td>REPSEC</td><td>1970-2005</td><td>Barro and Lee (1996), UNESCO-Institute for Statistics</td></tr><tr><td>Indicators of educational inequalities</td><td>INEDU</td><td>1960-2000</td><td>Altinok (2007)</td></tr><tr><td>Expected number of years in education</td><td>EXPEN</td><td>1970-2005</td><td>UNESCO-Institute for Statistics</td></tr></tbody></table>
<table><caption>Table 2 – Student achievement tests used</caption><thead><tr><th>Year</th><th>Abbreviation</th><th>Field</th><th>Countries</th><th>Age of students</th></tr></thead><tbody><tr><td>1964</td><td>IEA</td><td>Mathematics</td><td>13</td><td>13, Fin sec.</td></tr><tr><td rowspan="2">1970-72</td><td rowspan="2">IEA</td><td>Science</td><td>19</td><td>10,14, Fin sec.</td></tr><tr><td>Reading</td><td>15</td><td>10,14, Fin sec.</td></tr><tr><td>1982-83</td><td>IEA</td><td>Mathematics</td><td>20</td><td>13, Fin sec.</td></tr><tr><td>1984</td><td>IEA</td><td>Science</td><td>24</td><td>10,14, Fin sec.</td></tr><tr><td rowspan="2">1988</td><td rowspan="2">IAEP</td><td>Mathematics</td><td>6</td><td>13</td></tr><tr><td>Science</td><td>6</td><td>13</td></tr><tr><td>1991</td><td>IEA</td><td>Reading</td><td>31</td><td>9,14</td></tr><tr><td rowspan="2">1990-91</td><td rowspan="2">IAEP</td><td>Mathematics</td><td>20</td><td>9,13</td></tr><tr><td>Science</td><td>20</td><td>9,13</td></tr><tr><td rowspan="2">1993-98</td><td rowspan="2">IEA</td><td>Mathematics</td><td>41</td><td>9,13, Fin sec.</td></tr><tr><td>Science</td><td>41</td><td>9,13, Fin sec.</td></tr><tr><td rowspan="3">1992-97</td><td rowspan="3">UNESCO-MLA</td><td>Mathematics</td><td>13</td><td>10</td></tr><tr><td>Science</td><td>11</td><td>10</td></tr><tr><td>Reading</td><td>11</td><td>10</td></tr><tr><td rowspan="2">1997</td><td rowspan="2">UNESCO-LLECE</td><td>Mathematics</td><td>11</td><td>10</td></tr><tr><td>Reading</td><td>11</td><td>10</td></tr><tr><td>1999</td><td>UNESCO-SACMEQ</td><td>Reading</td><td>7</td><td>10</td></tr><tr><td rowspan="2">1999</td><td rowspan="2">IEA</td><td>Mathematics</td><td>38</td><td>14</td></tr><tr><td>Science</td><td>38</td><td>14</td></tr><tr><td rowspan="3">1995-2005</td><td rowspan="3">CONFEMEN-PASEC</td><td>Mathematics</td><td>11</td><td>9,10</td></tr><tr><td>Reading</td><td>11</td><td>9,10</td></tr><tr><td>Mathematics</td><td>43</td><td>15</td></tr><tr><td rowspan="3">2000</td><td rowspan="3">OECD-PISA</td><td>Science</td><td>43</td><td>15</td></tr><tr><td>Reading</td><td>43</td><td>15</td></tr><tr><td>Mathematics</td><td>35</td><td>9,10</td></tr><tr><td rowspan="2">2001</td><td rowspan="2">IEA</td><td>Reading</td><td>35</td><td>9,10</td></tr><tr><td>Mathematics</td><td>14</td><td>10</td></tr><tr><td rowspan="3">2002</td><td rowspan="3">UNESCO-SACMEQ</td><td>Reading</td><td>13</td><td>10</td></tr><tr><td>Mathematics</td><td>26,48</td><td>10,14</td></tr><tr><td>Science</td><td>26,48</td><td>10,14</td></tr><tr><td rowspan="2">2003</td><td rowspan="2">IEA</td><td>Mathematics</td><td>41</td><td>15</td></tr><tr><td>Science</td><td>41</td><td>15</td></tr><tr><td rowspan="2">2003</td><td rowspan="2">OECD-PISA</td><td>Reading</td><td>41</td><td>15</td></tr><tr><td>Mathematics</td><td>41</td><td>15</td></tr></tbody></table>

Note: Fin sec. denotes the final year of secondary school. Abbreviations: IAEP (International Assessment of Educational Progress), IEA (International Association of the Evaluation of Educational Achievement), TIMSS (Third International Mathematics and Science Study), PIRLS (Progress in International Reading Literacy Study), PISA (Programme for International Student Assessment), UNESCO (United Nations Educational, Scientific and Cultural Organization), LLECE (Latin American Laboratory for Assessment of the Quality of Education), CONFEMEN (Conference of Ministers of Education in countries sharing the French language), PASEC (Programme of Analysis of the CONFEMEN), SACMEQ (Southern and Eastern Africa Consortium for Monitoring Educational Quality), MLA (Monitoring Learning Achievement).
<table><caption>Table 3 - Descriptive statistics</caption><thead><tr><th>Variable</th><th></th><th>Mean</th><th>Standard deviation</th><th>Min</th><th>Max</th><th>Obs</th><th>Obs</th></tr></thead><tbody><tr><td rowspan="3">QIHC</td><td>Overall</td><td>51.58</td><td>10.06</td><td>18.75</td><td>78.31</td><td>N</td><td>244</td></tr><tr><td>Between</td><td></td><td>9.37</td><td>18.75</td><td>70.99</td><td>n</td><td>106</td></tr><tr><td>Within</td><td></td><td>5.52</td><td>24.53</td><td>64.83</td><td>T</td><td>2.30</td></tr><tr><td rowspan="3">NERSEC</td><td>Overall</td><td>54.20</td><td>29.04</td><td>0.90</td><td>100</td><td>N</td><td>577</td></tr><tr><td>Between</td><td></td><td>27.62</td><td>2.30</td><td>97.5</td><td>n</td><td>158</td></tr><tr><td>Within</td><td></td><td>11.93</td><td>12.20</td><td>101.07</td><td>T</td><td>3.65</td></tr><tr><td rowspan="3">LNGDP</td><td>Overall</td><td>8.19</td><td>1.07</td><td>5.77</td><td>10.69</td><td>N</td><td>1082</td></tr><tr><td>Between</td><td></td><td>0.99</td><td>6.25</td><td>10.03</td><td>n</td><td>146</td></tr><tr><td>Within</td><td></td><td>0.32</td><td>6.87</td><td>9.35</td><td>T</td><td>7.41</td></tr><tr><td rowspan="3">ADEDU</td><td>Overall</td><td>4.60</td><td>2.83</td><td>0.04</td><td>12.25</td><td>N</td><td>1048</td></tr><tr><td>Between</td><td></td><td>2.48</td><td>0.41</td><td>10.86</td><td>n</td><td>169</td></tr><tr><td>Within</td><td></td><td>1.05</td><td>0.85</td><td>8.15</td><td>T</td><td>6.20</td></tr><tr><td rowspan="3">TEAPRI</td><td>Overall</td><td>31.72</td><td>12.95</td><td>6.10</td><td>95.3</td><td>N</td><td>1296</td></tr><tr><td>Between</td><td></td><td>11.61</td><td>13.40</td><td>73.07</td><td>n</td><td>176</td></tr><tr><td>Within</td><td></td><td>5.93</td><td>10.89</td><td>56.77</td><td>T</td><td>7.36</td></tr><tr><td rowspan="3">TEASEC</td><td>Overall</td><td>19.36</td><td>7.12</td><td>6</td><td>64</td><td>N</td><td>1149</td></tr><tr><td>Between</td><td></td><td>6.01</td><td>8</td><td>45.5</td><td>n</td><td>176</td></tr><tr><td>Within</td><td></td><td>4.27</td><td>-2.21</td><td>45.79</td><td>T</td><td>6.53</td></tr><tr><td rowspan="3">SHPUPP</td><td>Overall</td><td>14.22</td><td>9.19</td><td>0.95</td><td>77.80</td><td>N</td><td>845</td></tr><tr><td>Between</td><td></td><td>9.43</td><td>2.27</td><td>49.76</td><td>n</td><td>156</td></tr><tr><td>Within</td><td></td><td>5.49</td><td>-10.39</td><td>54.64</td><td>T</td><td>5.42</td></tr><tr><td rowspan="3">SHPUPS</td><td>Overall</td><td>39.08</td><td>60.86</td><td>2.1</td><td>693.8</td><td>N</td><td>816</td></tr><tr><td>Between</td><td></td><td>46.09</td><td>4.83</td><td>275.83</td><td>n</td><td>154</td></tr><tr><td>Within</td><td></td><td>40.52</td><td>-119.12</td><td>460.91</td><td>T</td><td>5.30</td></tr><tr><td rowspan="3">EXPGNP</td><td>Overall</td><td>4.40</td><td>1.97</td><td>0</td><td>13.3</td><td>N</td><td>831</td></tr><tr><td>Between</td><td></td><td>1.87</td><td>0.78</td><td>13.3</td><td>n</td><td>174</td></tr><tr><td>Within</td><td></td><td>1.04</td><td>-0.45</td><td>9.33</td><td>T</td><td>4.78</td></tr><tr><td rowspan="3">SHSALP</td><td>Overall</td><td>354.88</td><td>278.40</td><td>40</td><td>2684</td><td>N</td><td>714</td></tr><tr><td>Between</td><td></td><td>232.26</td><td>40</td><td>1396.25</td><td>n</td><td>145</td></tr><tr><td>Within</td><td></td><td>153.71</td><td>-431.38</td><td>1642.63</td><td>T</td><td>4.92</td></tr><tr><td rowspan="3">REPPRI</td><td>Overall</td><td>10.36</td><td>9.28</td><td>0</td><td>47.5</td><td>N</td><td>996</td></tr><tr><td>Between</td><td></td><td>8.63</td><td>0</td><td>34.15</td><td>n</td><td>174</td></tr><tr><td>Within</td><td></td><td>3.50</td><td>-4.83</td><td>25.76</td><td>T</td><td>5.72</td></tr><tr><td rowspan="3">REPSEC</td><td>Overall</td><td>9.54</td><td>8.24</td><td>0</td><td>46</td><td>N</td><td>819</td></tr><tr><td>Between</td><td></td><td>7.15</td><td>0</td><td>31.2</td><td>n</td><td>156</td></tr><tr><td>Within</td><td></td><td>3.95</td><td>-8.06</td><td>28.47</td><td>T</td><td>5.25</td></tr><tr><td rowspan="3">INEDU</td><td>Overall</td><td>44.01</td><td>25.63</td><td>4.41</td><td>98.97</td><td>N</td><td>925</td></tr><tr><td>Between</td><td></td><td>24.62</td><td>7.13</td><td>92.27</td><td>n</td><td>109</td></tr><tr><td>Within</td><td></td><td>7.75</td><td>16.93</td><td>67.42</td><td>T</td><td>8.49</td></tr></tbody></table>

Note: For the abbreviations, see Table 1.
<table><caption>Table 4 – Random-effects estimation</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th><th>(10)</th><th>(11)</th><th>(12)</th></tr></thead><tbody><tr><td>Dependent variable</td><td colspan="5">Quality of education in mathematics at secondary level</td><td colspan="5">Net enrollment rate at secondary level</td></tr><tr><td>Education of adults <sub>t-1</sub></td><td>1.101<sup>*</sup><br>(0.367)</td><td>1.730<sup>*</sup><br>(0.461)</td><td>0.831<sup>‡</sup><br>(0.473)</td><td>1.486<sup>*</sup><br>(0.453)</td><td>1.710<sup>*</sup><br>(0.532)</td><td>1.024<sup>‡</sup><br>(0.623)</td><td>7.902<sup>*</sup><br>(0.463)</td><td>7.991<sup>*</sup><br>(0.531)</td><td>7.846<sup>*</sup><br>(0.589)</td><td>7.856<sup>*</sup><br>(0.536)</td><td>7.856<sup>*</sup><br>(0.536)</td><td>8.591<sup>*</sup><br>(0.511)</td></tr><tr><td>Educational spending<sup>(1)</sup> <sub>t-1</sub></td><td>0.037<br>(0.092)</td><td></td><td></td><td></td><td></td><td></td><td>-0.122<sup>*</sup><br>(0.049)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Educational spending<sup>(2)</sup> <sub>t-1</sub></td><td></td><td>-0.366<br>(0.493)</td><td></td><td></td><td></td><td></td><td></td><td>0.936<br>(0.740)</td><td></td><td></td><td></td><td></td></tr><tr><td>Teachers' pay <sub>t-1</sub></td><td></td><td></td><td>-0.009<br>(0.012)</td><td></td><td></td><td></td><td></td><td></td><td>-0.018<sup>†</sup><br>(0.008)</td><td></td><td></td><td></td></tr><tr><td>Class size <sub>t-1</sub></td><td></td><td></td><td></td><td>-0.167<br>(0.206)</td><td></td><td></td><td></td><td></td><td></td><td>-0.410<sup>†</sup><br>(0.172)</td><td></td><td></td></tr><tr><td>Repetition rates <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td>-0.065<br>(0.165)</td><td></td><td></td><td></td><td></td><td></td><td>-0.410<sup>†</sup><br>(0.172)</td><td></td></tr><tr><td>Educational inequalities <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td></td><td>-0.102<br>(0.109)</td><td></td><td></td><td></td><td></td><td></td><td>-0.031<br>(0.148)</td></tr><tr><td>F Test for time dummies</td><td>[0.00]</td><td>[0.00]</td><td>[0.01]</td><td>[0.00]</td><td>[0.04]</td><td>[0.00]</td><td>[0.00]</td><td>[0.01]</td><td>[0.02]</td><td>[0.00]</td><td>[0.00]</td><td>[0.01]</td></tr><tr><td>Observations</td><td>156</td><td>148</td><td>119</td><td>143</td><td>117</td><td>161</td><td>373</td><td>388</td><td>308</td><td>420</td><td>420</td><td>352</td></tr><tr><td>Country</td><td>58</td><td>63</td><td>41</td><td>60</td><td>55</td><td>54</td><td>117</td><td>126</td><td>112</td><td>133</td><td>133</td><td>121</td></tr><tr><td>R<sup>2</sup></td><td>0.47</td><td>0.31</td><td>0.49</td><td>0.47</td><td>0.48</td><td>0.44</td><td>0.75</td><td>0.71</td><td>0.76</td><td>0.73</td><td>0.73</td><td>0.69</td></tr></tbody></table>

Levels of significance: *1%. †5%. ‡10%. The numbers between brackets represent standard errors.

(1) Educational spending per student at secondary level as percentage of GDP per capita.

(2) Educational spending as percentage of GNP.
<table><caption>Table 5 – Fixed-effects estimation</caption><thead><tr><th rowspan="2">Dependent variable</th><th colspan="8">Quality of education in mathematics at secondary level</th><th colspan="5">Net enrollment rate at secondary level</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th><th>(10)</th><th>(11)</th><th>(12)</th></tr></thead><tbody><tr><td>Education of adults <sub>t-1</sub></td><td>1.776<br>(1.284)</td><td>0.288<br>(1.111)</td><td>1.931<br>(1.399)</td><td>0.637<br>(1.350)</td><td>2.194<br>(1.721)</td><td>1.378<br>(1.244)</td><td>3.129<sup>†</sup><br>(1.361)</td><td>1.279<br>(1.514)</td><td>3.105<sup>‡</sup><br>(1.850)</td><td>2.564<sup>‡</sup><br>(1.369)</td><td>1.910<br>(1.822)</td><td>1.261<br>(1.246)</td></tr><tr><td>Educational spending<sup>(1)</sup> <sub>t-1</sub></td><td>0.002<br>(0.115)</td><td></td><td></td><td></td><td></td><td></td><td>-0.052<br>(0.066)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Educational spending<sup>(2)</sup> <sub>t-1</sub></td><td></td><td>0.967<br>(0.655)</td><td></td><td></td><td></td><td></td><td></td><td>0.742<br>(0.815)</td><td></td><td></td><td></td><td></td></tr><tr><td>Teachers' pay <sub>t-1</sub></td><td></td><td></td><td>0.007<br>(0.010)</td><td></td><td></td><td></td><td></td><td></td><td>0.008<br>(0.007)</td><td></td><td></td><td></td></tr><tr><td>Class size <sub>t-1</sub></td><td></td><td></td><td></td><td>-0.137<br>(0.327)</td><td></td><td></td><td></td><td></td><td></td><td>0.191<br>(0.201)</td><td></td><td></td></tr><tr><td>Repetition rates <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td>0.038<br>(0.290)</td><td></td><td></td><td></td><td></td><td></td><td>0.176<br>(0.323)</td><td></td></tr><tr><td>Educational inequalities <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td></td><td>0.166<br>(0.200)</td><td></td><td></td><td></td><td></td><td></td><td>-0.485*<br>(0.146)</td></tr><tr><td>F Test for time dummies</td><td>[0.53]</td><td>[0.69]</td><td>[0.33]</td><td>[0.82]</td><td>[0.24]</td><td>[0.00]</td><td>[0.00]</td><td>[0.00]</td><td>[0.01]</td><td>[0.00]</td><td>[0.00]</td><td>[0.00]</td></tr><tr><td>Observations</td><td>156</td><td>148</td><td>119</td><td>143</td><td>117</td><td>161</td><td>373</td><td>388</td><td>308</td><td>420</td><td>352</td><td>416</td></tr><tr><td>Countries</td><td>58</td><td>63</td><td>41</td><td>60</td><td>55</td><td>54</td><td>117</td><td>126</td><td>112</td><td>133</td><td>121</td><td>96</td></tr><tr><td>R<sup>2</sup></td><td>0.91</td><td>0.31</td><td>0.91</td><td>0.47</td><td>0.94</td><td>0.92</td><td>0.96</td><td>0.95</td><td>0.96</td><td>0.73</td><td>0.94</td><td>0.95</td></tr></tbody></table>

Levels of significance: *1%. †5%. ‡10%. The numbers between brackets represent the standard errors. The independent variables are lagged for a period of 5 years.

(1) Educational spending per student at secondary level as percentage of GDP per capita.

(2) Educational spending as percentage of GNP.
<table><caption>Table 6 - Estimation with GMM system</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th><th>(10)</th><th>(11)</th><th>(12)</th></tr></thead><tbody><tr><td>Dependent variable</td><td colspan="5">Quality of education in mathematics at secondary level</td><td colspan="5">Net enrollment rate at secondary level</td></tr><tr><td>Education of adults <sub>t-1</sub></td><td>2.222*<br>(0.854)</td><td>2.053†<br>(0.857)</td><td>1.932‡<br>(1.092)</td><td>2.775*<br>(0.935)</td><td>1.735‡<br>(0.936)</td><td>2.991†<br>(1.218)</td><td>7.632*<br>(0.752)</td><td>7.210*<br>(0.885)</td><td>8.932*<br>(0.856)</td><td>9.044*<br>(0.866)</td><td>8.742*<br>(0.740)</td><td>3.398†<br>(1.485)</td></tr><tr><td>Educational spending<sup>(1)</sup> <sub>t-1</sub></td><td>-0.036<br>(0.167)</td><td></td><td></td><td></td><td></td><td></td><td>-0.118†<br>(0.050)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Educational spending<sup>(2)</sup> <sub>t-1</sub></td><td></td><td>-0.495<br>(1.154)</td><td></td><td></td><td></td><td></td><td></td><td>-1.444<br>(1.040)</td><td></td><td></td><td></td><td></td></tr><tr><td>Teachers' pay <sub>t-1</sub></td><td></td><td></td><td>-0.011<br>(0.016)</td><td></td><td></td><td></td><td></td><td></td><td>-0.022*<br>(0.009)</td><td></td><td></td><td></td></tr><tr><td>Class size <sub>t-1</sub></td><td></td><td></td><td></td><td>-0.122<br>(0.370)</td><td></td><td></td><td></td><td></td><td></td><td>-0.226<br>(0.220)</td><td></td><td></td></tr><tr><td>Repetition rates <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td>0.181<br>(0.181)</td><td></td><td></td><td></td><td></td><td></td><td>0.064<br>(0.181)</td><td></td></tr><tr><td>Educational inequalities <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td></td><td>0.232<br>(0.252)</td><td></td><td></td><td></td><td></td><td></td><td>-0.690*<br>(0.223)</td></tr><tr><td>F Test for time dummies</td><td>[0.00]</td><td>[0.01]</td><td>[0.00]</td><td>[0.00]</td><td>[0.04]</td><td>[0.01]</td><td>[0.00]</td><td>[0.01]</td><td>[0.07]</td><td>[0.00]</td><td>[0.04]</td><td>[0.00]</td></tr><tr><td>Hansen's test</td><td>[0.32]</td><td>[0.22]</td><td>[0.36]</td><td>[0.18]</td><td>[0.47]</td><td>[0.24]</td><td>[0.80]</td><td>[0.41]</td><td>[0.96]</td><td>[0.24]</td><td>[0.29]</td><td>[0.54]</td></tr><tr><td>AR(2) test</td><td>[0.23]</td><td>[0.20]</td><td>[0.19]</td><td>[0.76]</td><td>[0.34]</td><td>[0.74]</td><td>[0.72]</td><td>[0.76]</td><td>[0.23]</td><td>[0.26]</td><td>[0.25]</td><td>[0.21]</td></tr><tr><td>Observations</td><td>156</td><td>148</td><td>119</td><td>143</td><td>117</td><td>161</td><td>373</td><td>388</td><td>308</td><td>420</td><td>352</td><td>416</td></tr><tr><td>Countries</td><td>58</td><td>63</td><td>41</td><td>60</td><td>55</td><td>54</td><td>117</td><td>126</td><td>112</td><td>133</td><td>94</td><td>96</td></tr></tbody></table>

Levels of significance: *1%. †5%. ‡10%. The numbers between brackets represent the standard errors. The independent variables are lagged for a period of 5 years.

(1) Educational spending per student at secondary level as percentage of GDP per capita.

(2) Educational spending as percentage of GNP.
<table><caption>Table 7 - Estimation with test scores, sub-samples</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th><th>(10)</th><th>(11)</th><th>(12)</th></tr></thead><tbody><tr><td>Dependent variable</td><td colspan="13">Quality of education in mathematics at secondary level</td></tr><tr><td>Sample</td><td colspan="5">OECD countries</td><td colspan="8">Non-OECD countries</td></tr><tr><td>Education of adults <sub>t-1</sub></td><td>1.259<br>(1.064)</td><td>-0.099<br>(0.980)</td><td>1.091<br>(0.855)</td><td>1.052<br>(0.762)</td><td>-0.965<br>(1.655)</td><td>0.433<br>(1.228)</td><td>1.668<br>(1.232)</td><td>1.783<sup>†</sup><br>(0.871)</td><td>1.204<br>(1.363)</td><td>0.864<br>(1.278)</td><td>1.501<sup>†</sup><br>(0.752)</td><td>2.651<br>(1.849)</td></tr><tr><td>Educational spending<sup>(1)</sup> <sub>t-1</sub></td><td>0.031<br>(0.149)</td><td></td><td></td><td></td><td></td><td></td><td>0.085<br>(0.220)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Educational spending<sup>(2)</sup> <sub>t-1</sub></td><td></td><td>0.127<br>(0.923)</td><td></td><td></td><td></td><td></td><td></td><td>-0.362<br>(1.080)</td><td></td><td></td><td></td><td></td></tr><tr><td>Teachers' pay <sub>t-1</sub></td><td></td><td></td><td>-0.003<br>(0.018)</td><td></td><td></td><td></td><td></td><td></td><td>-0.055<sup>‡</sup><br>(0.031)</td><td></td><td></td><td></td></tr><tr><td>Class size <sub>t-1</sub></td><td></td><td></td><td></td><td>0.407<sup>‡</sup><br>(0.211)</td><td></td><td></td><td></td><td></td><td></td><td>-0.472<br>(0.426)</td><td></td><td></td></tr><tr><td>Repetition rates <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td>0.419<br>(0.397)</td><td></td><td></td><td></td><td></td><td></td><td>-0.837<sup>‡</sup><br>(0.493)</td><td></td></tr><tr><td>Educational inequalities <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td></td><td>-0.072<br>(0.198)</td><td></td><td></td><td></td><td></td><td></td><td>0.048<br>(0.364)</td></tr><tr><td>F Test for time dummies</td><td>[0.11]</td><td>[0.03]</td><td>[0.12]</td><td>[0.01]</td><td>[0.03]</td><td>[0.07]</td><td>[0.00]</td><td>[0.09]</td><td>[0.00]</td><td>[0.00]</td><td>[0.00]</td><td>[0.01]</td></tr><tr><td>Hansen's test</td><td>[0.57]</td><td>[0.35]</td><td>[0.27]</td><td>[0.40]</td><td>[0.83]</td><td>[0.38]</td><td>[0.34]</td><td>[0.78]</td><td>[0.99]</td><td>[0.64]</td><td>[0.62]</td><td>[0.52]</td></tr><tr><td>AR(2) Test</td><td>[0.87]</td><td>[0.79]</td><td>[0.79]</td><td>[0.68]</td><td>[0.57]</td><td>[0.67]</td><td>[0.30]</td><td>[0.79]</td><td>-</td><td>[0.67]</td><td>[0.60]</td><td>[0.76]</td></tr><tr><td>Observations</td><td>106</td><td>91</td><td>90</td><td>88</td><td>67</td><td>111</td><td>50</td><td>57</td><td>29</td><td>55</td><td>50</td><td>50</td></tr><tr><td>Countries</td><td>22</td><td>28</td><td>22</td><td>28</td><td>24</td><td>28</td><td>29</td><td>35</td><td>16</td><td>32</td><td>31</td><td>26</td></tr></tbody></table>

Levels of significance: *1%. †5%. ‡10%. The numbers between brackets represent the standard errors. The independent variables are lagged for a period of 5 years.

(1) Educational spending per student at secondary level as percentage of GDP per capita.

(2) Educational spending as percentage of GNP.
<table><caption>Table 8 - Estimation with net enrollment rate, sub-samples</caption><thead><tr><th rowspan="2">Sample</th><th colspan="12">System GMM</th></tr><tr><th colspan="6">OECD countries</th><th colspan="6">Non-OECD countries</th></tr></thead><tbody><tr><td>Education of adults <sub>t-1</sub></td><td>4.547<sup>*</sup><br>(1.190)</td><td>1.726<sup>‡</sup><br>(0.967)</td><td>6.154<sup>*</sup><br>(1.469)</td><td>5.343<sup>*</sup><br>(1.388)</td><td>3.009<sup>†</sup><br>(1.313)</td><td>1.848<br>(2.034)</td><td>6.205<sup>*</sup><br>(2.513)</td><td>8.516<sup>*</sup><br>(2.552)</td><td>6.145<sup>*</sup><br>(2.161)</td><td>8.051<sup>*</sup><br>(2.134)</td><td>5.771<sup>†</sup><br>(2.902)</td><td>8.080<sup>*</sup><br>(2.388)</td></tr><tr><td>Educational spending<sup>(1)</sup> <sub>t-1</sub></td><td>0.431<sup>‡</sup><br>(0.218)</td><td></td><td></td><td></td><td></td><td></td><td>-0.093<br>(0.063)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Educational spending<sup>(2)</sup> <sub>t-1</sub></td><td></td><td>0.308<br>(1.382)</td><td></td><td></td><td></td><td></td><td></td><td>-1.807<sup>‡</sup><br>(1.114)</td><td></td><td></td><td></td><td></td></tr><tr><td>Teachers' pay <sub>t-1</sub></td><td></td><td></td><td>-0.015<br>(0.016)</td><td></td><td></td><td></td><td></td><td></td><td>-0.007<br>(0.016)</td><td></td><td></td><td></td></tr><tr><td>Class size <sub>t-1</sub></td><td></td><td></td><td></td><td>-0.431<br>(0.614)</td><td></td><td></td><td></td><td></td><td></td><td>-0.261<br>(0.266)</td><td></td><td></td></tr><tr><td>Repetition rates <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td>0.245<sup>*</sup><br>(0.061)</td><td></td><td></td><td></td><td></td><td></td><td>0.594<br>(0.674)</td><td></td></tr><tr><td>Educational inequalities <sub>t-1</sub></td><td></td><td></td><td></td><td></td><td></td><td>-0.421<br>(0.364)</td><td></td><td></td><td></td><td></td><td></td><td>-0.464<br>(0.339)</td></tr><tr><td>F Test for time dummies</td><td>[0.00]</td><td>[0.00]</td><td>[0.07]</td><td>[0.00]</td><td>[0.00]</td><td>[0.00]</td><td>[0.00]</td><td>[0.57]</td><td>[0.05]</td><td>[0.10]</td><td>[0.05]</td><td>[0.15]</td></tr><tr><td>Hansen's test</td><td>[0.31]</td><td>[0.48]</td><td>[0.18]</td><td>[0.60]</td><td>[0.63]</td><td>[0.31]</td><td>[0.16]</td><td>[0.61]</td><td>[0.25]</td><td>[0.16]</td><td>[0.38]</td><td>[0.82]</td></tr><tr><td>AR(2) Test</td><td>[0.18]</td><td>[0.47]</td><td>[0.12]</td><td>[0.96]</td><td>[0.76]</td><td>[0.47]</td><td>[0.41]</td><td>[0.92]</td><td>[0.23]</td><td>[0.21]</td><td>[0.55]</td><td>[0.18]</td></tr><tr><td>Observations</td><td>146</td><td>133</td><td>126</td><td>129</td><td>89</td><td>158</td><td>227</td><td>255</td><td>182</td><td>291</td><td>263</td><td>258</td></tr><tr><td>Countries</td><td>27</td><td>28</td><td>27</td><td>28</td><td>26</td><td>27</td><td>26</td><td>98</td><td>85</td><td>105</td><td>95</td><td>69</td></tr></tbody></table>

Levels of significance: *1%. †5%. ‡10%. The numbers between brackets represent the standard errors. The independent variables are lagged for a period of 5 years.

(1) Educational spending per student at secondary level as percentage of GDP per capita.

(2) Educational spending as percentage of GNP.