ï»¿ WPS6084
Policy Research Working Paper 6084
Decomposing the Increase in TIMSS Scores
in Ghana
2003â€“2007
Chris Sakellariou
The World Bank
Human Development Network
Education Unit
June 2012
Policy Research Working Paper 6084
Abstract
This paper attempts to explore certain aspects underlying the constant) dominate the effects of the coefficients.
the substantial improvement in 8th grade student One potentially important piece of information missing
performance in Ghana on the Trends in International from the Ghana data is whether a school is private or
Mathematics and Science Study from 2003 to 2007. public; this could potentially explain part of the over-
The improvement was largely heterogeneous; in time improvement. This is because over the short period
mathematics, performance improved more for students between the two surveys, there was a large increase in
already performing well, while the opposite was the the number of private schools in Ghana (by 36 percent
case for science, where students at the bottom of the between 2005/6 and 2007/8). Finally, an analysis of
score distribution experienced a spectacular increase the over-time change in the test score gap by location
in science scores. Most of the increase in scores for (between large and small communities) revealed that the
both mathematics and science is explained by over- gap became more heterogeneous, narrowing for worse
time changes in coefficients (and a smaller part by performing students and widening for better performing
improvements in characteristics). Contributors not students.
accounted for (and therefore captured by changes in
This paper is a product of the Education Unit, Human Development Network. It is part of a larger effort by the World
Bank to provide open access to its research and make a contribution to development policy discussions around the world.
Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted
at acsake@ntu.edu.sg.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
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names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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Decomposing the Increase in TIMSS Scores in Ghana: 2003-2007*
Chris Sakellariouâ€
JEL classification: I22, J3, J45
Keywords: Quantile regression, Oaxaca decomposition, learning outcomes, Ghana
Sector Board: Education
*
I am grateful for helpful comments to Peter Darvas, Kevin Macdonald and Harry Anthony Patrinos. All remaining
errors are mine. Research funded by the Bank-Netherlands Partnership Program.
â€
Division of Economics, Humanities and Social Sciences, Nanyang Technological University, Singapore (email:
acsake@ntu.edu.sg).
1. Introduction
1.1. Background
African countries are among countries with less than 50% of children achieving literacy,
numeracy and life skills mastery (Schaefer 2000). A large proportion of children do not have
basic functional skills to read, write and enumerate after year four of their educational
experience. The UNESCO (2005) report confirms these findings and shows that too many pupils
are leaving school without mastering a minimum set of cognitive and non-cognitive skills.
Ghana participated in the Trends in International Mathematics and Science Study (TIMSS) in
2003 and 2007. In 2003 Ghanaâ€™s score for mathematics at 276 was higher only compared to that
of South Africa among participating countries and much lower than the international average
score for mathematics (467), as well as the score for other African participating countries such as
Botswana (366) and Tunisia (410). In 2007, Ghana exhibited substantial improvement in the
mathematics score, which increased to 309 (a 12% increase), which is still one of the lowest
among the participating countries, ranking 47th among the 48 participants and lower than all the
African participating countries (South Africa did not participate in 2007). Similar improvements
were registered for science. The science score increased from 255 in 2003 to 303 in 2007, a 48
point increase (19%). Ghana is one of the countries in which boys perform significantly better
than girls. While the score increased significantly over time for both boys and girls, the gender
gap in 2007 stood at 22 points in mathematics and 28 points in science.
Table 1: Selected mathematics and science TIMSS scores
Mathematics Science
Countries 2003 2007 2003 3007
Singapore 605 593 578 567
Tunisia 410 420 404 445
Botswana 366 364 365 355
Ghana 276 309 255 303
International Average 467 500 474 500
Source: Anamuah-Mensah et al. (2008)
1.2. Challenges and problems
Ampiah (2010) outlined the problems and challenges that Ghana is faced in improving quality of
education. One challenge relates to trade-offs between rapid expansion of basic education
(towards universal access) and quality of education. In particular, if children attending are not
enabled to improve learning outcomes, especially in literacy and numeracy, access to education
is not meaningful. The authors feel that in the case of Ghana, quality of education seems to have
become subordinated to quantity of education as a priority and that in many cases, educational
expansion has come at the expense of quality.
The poor quality of teaching affects student learning, as most teachers lack the necessary
supervision and feedback on their instructional practices. In particular, supervision is weak and
2
school principals and teachers are present in school when they see fit, resulting in serious
problems of lateness and absenteeism and low teacher-pupil contact hours (MOESS, 2008).
As is the case in some other developing countries, the public perception is that private schools
have higher educational standards compared to public schools in both urban and rural areas; this
perception is reinforced by the better performing private school pupils at various assessments
such as the School Education Assessment (SEA), the National Education Assessment (NEA) and
the Basic Education Certificate Examination (BECE). In 2007/8, private school enrolment stood
at 24% of the total national enrolment, while the number of private schools increased by 36%
between 2005/6 and 2007/8 (from 2,990 to 4,068. The main advantage of private schools is that
they facilitate better English language skills; however, they also provide more access to extra
classes and special tuition to students (Ampiah, 2008; 2010).
Practices relating to language of instruction are also important. In Ghana, there are two
languages involved in basic education: the childâ€™s own vernacular as well as English language,
which is more widely used in education. From primary 4 onwards, the English language becomes
the medium of instruction (as well as a school subject). A relatively recent decision by the
Ministry of Education has been to develop quality bilingual literacy instruction in all primary
schools. However, implementation challenges remain, as some teachers are not functional in
local languages, most classes in urban areas are multilingual and textbooks, while written in
English are taught in the local language (Ampiah, 2010). Based on the outcome of TIMSS 2007,
the majority of the Ghanaian 8th grade students (66%) rarely spoke English at home â€“ if ever â€“
and the home language was found to be associated with lower achievement in both mathematics
and science (Anamuah-Mensah, Mereku and Ampiah 2008).
Finally, there are problems resulting from high proportions of untrained teachers in basic
education. Low retention and high attrition rates resulted in a discrepancy between trained
teachers in basic education and the output of the Teacher Training Colleges in Ghana. This
resulted in large numbers of untrained teachers filling teacher vacancies. In 2007, the proportion
of untrained teachers in Junior high school stood at 33% (MoESS 2007).
2. Methodology
2.1 General
Decomposition methods are frequently used in an attempt to answer important questions, such as
what accounts for pay differences between men and women, what is behind increases in wage
inequality in recent times, among others. They have also been applied in a variety of other
settings, including the study of gaps in test scores between schools (Krieg and Storer 2006), men
and women (Sohn 2008) and countries (McEwan and Marshal 2004; Ammermueller 2007).
In the last 10-15 years there has been an evolution and refinement of techniques used in
examining distributional issues, specifically in evaluating wage differentials between sub- groups
(and more generally the impacts of various programs) over the entire range of the earnings
distribution. These new techniques were first used to analyze gender earnings gaps (for example,
3
Albrecht et. al. 2003) and later to examine changes in wage distributions over time, where the
focal point is what contributes to the change in these distributions.
There are two types of decomposition which can be implemented using one of an increasing
number of methodological approaches. One is the aggregate decomposition of the outcome
variable into its two components â€“ the part due to differences in characteristics (composition
component) and that due to differences in coefficients. Going beyond Oaxaca-Blinder (1973)
decompositions at the mean, computing an aggregate decomposition of more general
distributional statistics is relatively straightforward, as there are several implementable
estimators with good asymptotics. Such parametric or semi-parametric approaches include those
proposed by Juhn, Murphy and Pierce (1993), Machado and Mata (2005) and Melly (2005).
There are also non-parametric approaches (such as the one by DiNardo, Fortin and Lemieux,
1996). Aggregate decomposition methods are closely linked to the treatment effects literature
and the identification assumptions involved generally carry over from this literature.
In an aggregate decomposition, the components of interest of the overall difference Î”ov in a
distributional statistic, v, are : 1) the component associated with differences in the distribution of
observable characteristics (what if everything except the distribution of X was the same); 2) the
component associated with the distribution of unobservable characteristics (what if everything
except the distribution of unobservables was the same); 3) the component of differences
associated with the return to observable characteristics, X, contained in the structural functions
(what if everything except the return to X was the same for the two groups); 4) the component
associated with differences in the return to unobservable characteristics in the structural
functions (what if everything except the return to unobservable characteristics was the same). In
practice, because of the presence of the components involving unobservables, one cannot
compute all 4 components, at least without additional assumptions.
Detailed decomposition methods, on the other hand, aim at deriving the effect of individual
covariates for a distributional statistic, and are more recent, less established and still evolving.
Machado and Mataâ€™s (2005) quantile regression and simulation based method can estimate only
the subcomponents of the coefficients structure component. DiNardo, Fortin and Lemieux (1996)
suggested a reweighting approach to derive the subcomponents of the composition effect, while
Altonji, Bharadwaj and Lange (2007) suggested a generalization of this approach. A weakness of
these methods is that they are path dependent - the decomposition depends on the order it is
performed (Fortin, Lemieux and Firpo 2010).
One recent method of implementing detailed decompositions which is gaining popularity
because it is close to the spirit of the Oaxaca-Blinder (OB) decomposition is that by Firpo, Fortin
and Lemieux (2009). This method, which is path independent, replaces the original left hand
side variable with the recentered influence function (RIF) of the distributional statistic and
estimates a RIF regression to derive coefficients which are in turn used to implement a detailed
decomposition. As suggested in Firpo, Fortin and Lemieux (2007), the best way to implement
this method is in two steps (a â€œhybridâ€? approach), whereby in the first step one derives the
aggregate components of the gap; for example one can use reweighting with appropriate
weighting functions. Since the major weakness of this method is its questionable accuracy (the
4
derived coefficients are only local approximations), the two-step approach helps assess how
accurate the approximation is.
In this study, we first choose an appropriate method to implement an aggregate decomposition of
the over-time change in the test score distribution in Ghana. The method used is an extension of
the Machado and Mata (2005) decomposition method, and decomposes differences in
distribution into three components â€“ characteristics, median coefficients and residuals â€“ as
outlined in Melly (2005). In the first step, the distribution of the dependent variable, TS (TIMSS
test score) conditional on the independent variables, X, is estimated using linear quantile
regression (see Koenker 2005). The conditional distribution of test scores (TS) is then integrated
over the independent variables to obtain the unconditional distribution. This procedure allows us
to estimate more precisely the unconditional distribution of TS by using the information
contained in the regressors. More importantly, this procedure allows for the estimation of
counterfactual unconditional distributions. This estimator is a special case of the class of
estimators discussed in Chernozhukov, Fernandez-Val and Melly (2009) and its statistical
properties as well as the validity of the bootstrap follow from their results. Additional advantages
of this methodology are that it accounts for heteroscedasticity, and is more efficient compared to
the Machado and Mata (2005) method.
Subsequently, we compute a detailed decomposition of the over-time change in test score
distributions in Ghana, using the Firpo, Fortin and Lemieux (2009) method (hereafter, FFL). As
is the case with other methods, the FFL method is not without problems. To estimate the effect
of changes in the distribution of X (with a functional of interest in mind), one uses a first order
linear approximation of the effect. The procedure results in two terms: the first order linear
approximation term and the remaining approximation error. The first order term is estimated
using a mean regression method which exploits the law of iterated expectations and the
assumption of linearity of the term. However, the estimand is still an approximation of the effect
and the approximation error does not vanish. Recently, Rothe (2010a) showed that the effect of
counterfactual changes (both fixed and infinitesimal) in the unconditional distribution of a single
covariate on the unconditional distribution of an outcome variable of interest are point identified
if the covariate affected is continuously distributed; on the other hand, if the distribution of the
covariate is discreet, the effects are only partially identified.
For the purposes of this study, the FFL method is an attractive option in deriving estimates of the
contribution of grouped characteristics (i.e., household, school, etc.) to supplement the results of
the aggregate decomposition, especially when implemented in its two-step (â€œhybridâ€?) version.
By comparing the estimates from aggregate decomposition to those from the RIF regression-OB
decomposition components, one can get a sense of the extent of the problem.
2.2 Aggregate decomposition of test score increase at percentiles
Starting with an independent sample from a population, where X is a vector of
characteristics and the Ï„th quantile of TS conditional on Xi given by:
,
while assuming a linear relationship between the dependent variable and the covariates
(household, school and teacher characteristics), the quantile regression coefficients can be
5
interpreted as the return to different characteristics (or more generally the effects on student
performance) at different points of the conditional distribution. Following Koenker and Bassett
(1978), the estimate of Î²(Ï„) is given by:
Î² Ï„
Î²(Ï„) is estimated separately for each Ï„, and the vector of all quantile regression coefficients is:
Î² Î² Ï„ . Given that this is a model for the conditional quantiles of TS, while the intention is to
estimate the unconditional quantiles of TS, one needs to integrate the conditional distribution
over the entire range of the distribution of Xs. Melly (2005) shows that one can overcome the
potential lack of monotonicity to derive the sample analogue of the Î¸th quantile as:
where the Î¸th quantile of the sample is estimated by weighing each observation by ;
under standard restrictions, is is a consistent and asymptotically normally distributed estimator.
In practice, if the sample is large (as in our case), a smaller number of quantile regressions are
estimated. Statistical inference can be conducted using bootstrapping.
Now consider distributions of two samples, 1 and 0, in our case one group in year 2007 and the
other in year 2003 (TIMSS 2007 and 2003). The aggregate decomposition is as follows:
where, m, and r refer to median coefficients and residuals respectively; , calculated
, and , is the quantile estimate of the distribution that
would have prevailed if the median return to characteristics had been the same as in sample 1 but
residuals had been distributed as in sample 0. Therefore, the first component measures the
residual effect, the second the coefficients structure effect and the last the composition effect.
2.3 Detailed decomposition: A â€œhybridâ€? approach
In implementing the detailed decomposition at percentiles, in a first step, a reweighting approach
is employed to derive estimates of the 2 components of the over-time changes in test score
distributions. Using weighting functions, one can transform features of the marginal distribution
of test scores into features of the conditional distribution of TS1 given and TS0 given
, as well as the features of the counterfactual distribution of TS0 given . In deriving
the re-weighting functions, the probability that a person belongs in group 1 conditional on X
(â€œpropensity scoreâ€?) is derived from a logit regression.
In the second step, we use FFLâ€™s unconditional quantile approach to derive the detailed
decomposition, by deriving the recentered influence function (RIF) of the dependent variable at
quantile Ï„,
where can be estimated by the sample quantile and can be estimated using Kernel
density. If the specification of the unconditional quantile regression is linear, i.e.,
6
, then the OLS estimate of Î² (namely, RIF-OLS estimator) provides a consistent
estimator of the marginal effect on the unconditional quantile of a small location shift in the
distribution of X, holding else constant. So, one can decompose any two distributions at
quantiles in a similar spirit as Oaxaca-Blinder approach. It is worth noting, however, that the
assumption of linearity used in implementing this detailed decomposition implies that the
outcome distribution depends on the marginal distribution of covariates only through their mean
(Rothe 2010b).
The decomposition of test score change over-time can be rewritten as3:
where and are approximation errors that appear because of the first order approximations
and the assumption of linear specification. They are calculated as differences between the
aggregate explained effect and the total composition effect: , and that between
unexplained component and the total coefficients structure effect: .
An identification problem exists in this sort of detailed decompositions as pointed out by Oaxaca
and Ransom (1999), as the coefficients effect is not invariant to the choice of reference group;
this problem has no easy solution. One approach is to derive results using more than one
alternative reference group. The other is to use one of the solutions suggested to deal with this
problem. We used the averaging approach proposed by Yun (2005).
3. Data and Summary Statistics
3.1. Data
We used the Trends in International Mathematics and Science Study (TIMSS) data for 8th grade
Ghanaian students. TIMSS is an international assessment conducted every four years in order to
generate information about trends in mathematics and science achievement in each country and
over time. The age of tested student population is 9 to10 years (4th grade) and 13 to 14 years (8th
grade) in more than 60 countries; the outcome is an extensive pool of data about the quantity,
quality, and content of teaching, which can be used by researchers to assess individual country
progress as well as to make comparisons among participating countries. Ghana participated in
the TIMSS assessment in 2003 and 2007, but only with 8th grade (JHS2) students.
Table A1 in the appendix gives the summary statistics for the student, household, school and
teacher characteristics used in the analysis. Notable over-time changes include, from student and
household characteristics: the substantial decline in the proportion of children with paid
employment (from 55% to 41%), an improvement of parentsâ€™ education qualifications (55% with
secondary or tertiary qualifications in 2007 compared to 43% in 2003), the decline in the
proportion of students who spent no time doing homework; from school characteristics: the
increase in average 8th grade student enrolment numbers, the large increase in the proportion of
students in small communities of less than 3,000 people (from 20% to 35%) and the substantial
decline in the proportion of schools with shortages in buildings and teachers; and from the
3
Since and , taking expectations on both sides yields .
So, .
7
teacher characteristics: the decline in the proportion of certified teachers (from 94% to 82%) and
the increase in the proportion of schools giving pay incentives to teachers (from 12% to 21%).
Further to the reported increase in the TIMSS mathematics and science scores from 2003 to 2007
(by 12% and 19% respectively), graphs A1 and A2 show the over-time changes in Kernel density
functions. For mathematics, the increase in scores is fairly similar across the score distribution;
for science, on the other hand, over-time the variance of the distribution decreased and the
increase in scores is smaller at higher points in the distribution of scores.
The above changes in distributions (especially for science) suggest that over-time changes in the
degree of inequality in student performance have taken place. Table 2 gives measures of student
performance inequality over-time. All estimates are consistent with a decrease in performance
inequality for both mathematics and science, but much more for science. Based on the Gini (as
well as the relative mean deviation and the coefficient of variation), inequality declined by about
8% for mathematics and by more than 22% for science. The decline in inequality is substantially
higher when based on Theilâ€™s entropy measure. In the case of science, percentile scores suggest
that the decline was more pronounced at the lower part of the distribution of scores.
Table 2: Inequality measures for Mathematics and Science scores and their over-time changes
2003 2007 Change (%)
Statistic Mathemati Science Mathemati Science Mathemati Science
cs cs cs
Relative mean deviation 0.115 0.173 0.105 0.131 -8.7 -24.3
Coefficient of variation 0.288 0.419 0.264 0.326 -8.3 -22.2
Gini coefficient 0.162 0.239 0.149 0.185 -8.0 -22.6
Theil entropy measure 0.042 0.094 0.035 0.056 -16.6 -40.4
p90/p10 2.14 3.50 2.04 2.58 -4.7 -26.3
p90/p50 1.42 1.60 1.38 1.47 -2.8 -8.1
p75/p25 1.50 1.95 1.43 1.60 -4.7 -17.9
p50/p10 1.51 2.19 1.47 1.75 -2.6 -20.1
Source: authorâ€™s calculations.
Prior to model estimation and derivation of results, we deal with the problem of missing
information. Several variables have missing values, as some students and school principals did
not answer parts of the questionnaires. The extent of missing values in the variables used in the
model ranges from 0 to about 10%. Data for missing responses were imputed using the method
of relating observations in the original data to a set of â€œfundamentalâ€? variables (see for example
Woessmann 2004). Such variables are: student age, student sex, parent education dummies and
dummies for community location of schools. As some of the â€œfundamentalâ€? variables had a very
small number of missing values, these values were imputed by the median category.
8
4. Results
4.1. The model
First, a cognitive achievement production function is specified. The model specification is as
follows:
TSija = TSa(Fija, Sija, TRija)+Îµija,
where TSija is the observed test score of student i in household j at time a (TIMSS year), Fija is a
vector of student and family inputs, Sija is a vector of school-related inputs, TRija is a vector of
teacher characteristics and Îµija is an additive error, which includes all of the omitted variables
including those that relate to the history of past inputs, and measurement error.
Issues of self-selection into schools are non-trivial, as they may have consequences on the
estimated relationships between various student, family, school and teacher characteristics and
student outcomes. One possible source of self-selection may result from households choosing
specific schools based on observed differences, such as cost and location. We control for a wide
range of student background characteristics in order to reduce the extent of such a potential bias.
Another source has to do with unobserved and hard to measure differences that can affect choice
of schools (Vegas 2002). If for example, more educated or more motivated parents
systematically choose certain type of schools, the results will overestimate the positive effects
associated with such schools. Yet another source of bias is possible, if families choose schools
based on their resources; however, in the case of Ghana one does not expect substantial
differences in resources between schools (compared to, say, the United States).
Since family income (or a similar measure) is not available in the data, the interpretation of
certain coefficients, such as those pertaining to the availability household resources (such as
number of books, having a desk, etc.) as well as combining paid work and study is less than
straightforward; such information is expected to at least partially capture the effect of family
wealth.
Another potentially important information which is not available in the Ghana data is the
identification of schools as public vs. private. As reported earlier, in 2007/8, private school
enrolment stood at 24% of the total national enrolment, while the number of private schools
increased by 36% between 2005/6 and 2007/8 (from 2,990 to 4,068). The main advantage of
private schools in Ghana is that they facilitate better English language skills; however, they also
provide more access to extra classes and special tuition to students.
4.2. Counterfactual decompositions
The decomposition of changes in mathematics and science scores can reveal whether the over-
time improvement in student performance in Ghana, as summarized by the increase in the mean
score applies to all 8th grade students, as opposed to the existence of significant heterogeneity in
performance improvement between high and low scoring pupils, as well as the relative
contribution of improved characteristics vs. changes in the effect of these characteristics on
performance across the score distribution. The decomposition results are given in tables 3a and
3b.
9
For both mathematics and science, the overall picture is not adequately described by the reported
changes at the mean. The improvement in performance is highly heterogeneous across the
distribution of scores and more so for science; however, the pattern is very different between
mathematics and science. For mathematics, the grade improvement increases at higher points in
the distribution, so that the increase for already well performing students is higher compared to
students who performed poorly. The p90/p10 ratio of score increase in mathematics is 1.35.
The opposite pattern is observed for science. The largest improvement applies to students at the
bottom decile of the score distribution - 62 points; this is an impressive increase at it amounts to
an improvement of about 50% within 4 years. The pattern of performance improvement declines
monotonically as one goes to higher points in the distribution and at the 90th percentile is
approximately 38 points (or by about 10%).
For mathematics as well as for science, the contribution of improved characteristics to the overall
increase in scores is rather small. At the median they contribute 17% and 21% to the overall
increase in scores in mathematics and science respectively. The contribution of improved
characteristics varies from 13% (19%) at the bottom decile to about 25% for both mathematics
and science at the top. Across the distribution, therefore, characteristics contribute more to
improved performance in the case of science compared to mathematics.
Table 3a: Decompositions of over-time change in Mathematics score at percentiles:
Ghana, 2003-07
Percentile Total change Characteristics Median Residuals
Coefficients
P10 30.85 4.36 32.96 -6.47
(1.56) (1.74) (2.18) (1.85)
P20 33.28 4.83 31.69 -3.24
(1.63) (1.79) (1.82) (1.53)
P30 34.49 5.28 30.44 -1.24
(1.61) (1.74) (1.77) (1.32)
P40 35.47 5.83 29.67 -0.03
(1.61) (1.74) (1.74) (1.15)
P50 36.14 6.29 29.35 0.49
(1.48) (1.66) (1.67) (1.19)
P60 36.82 6.70 29.03 1.09
(1.36) (1.73) (1.70) (1.38)
P70 38.00 7.27 28.97 1.76
(1.37) (1.79) (1.76) (1.56)
P80 39.99 8.46 28.89 2.64
(1.58) (1.84) (2.25) (1.74)
P90 41.59 10.22 28.30 3.07
(2.07) (2.09) (2.98) (2.09)
Standard errors in parentheses.
10
Table 3b: Decompositions of over-time change in Science score at percentiles:
Ghana, 2003-2007
Percentile Total change Characteristics Median Residuals
Coefficients
P10 62.36 11.56 46.50 4.30
(2.48) (1.85) (2.68) (2.54)
P20 59.79 11.57 43.89 4.33
(2.73) (1.66) (2.55) (1.90)
P30 56.81 10.90 42.31 3.59
(2.77) (1.68) (2.25) (1.72)
P40 53.67 10.65 40.85 2.17
(2.81) (1.76) (2.23) (1.67)
P50 49.98 10.39 39.49 0.10
(2.90) (1.95) (2.19) (1.87
P60 46.49 10.10 38.03 -1.64
(2.83) (2.00) (2.35) (2.31)
P70 43.16 10.12 35.94 -2.90
(1.78) (2.17) (2.53) (2.87)
P80 39.98 9.74 33.34 -3.11
(2.59) (2.50) (2.89) (3.49)
P90 38.61 9.84 29.80 -1.03
(2.18) (3.03) (3.53) (3.95)
Standard errors in parentheses.
The effect of included characteristics on test scores (median coefficients effect) is the largest
component of the over-time increase in tests scores in Ghana. This component contributed more
to the improvement in the performance of students at lower parts of the score distribution for
mathematics, while it generally had a uniformly positive effect on the improvement of science
scores. It accounted for more than 100% of the gross mathematics score improvement at the 10th
percentile and 68% at the 90th percentile. Similarly, it accounted for 75% and 77% of the gross
science score improvement at the 10th and 90th percentiles, respectively.
The second component of the increase in scores (due to improvement in characteristics) is
generally small for mathematics, but increases to about one-quarter of the total change at higher
points in the distribution of scores. In science the characteristics effect is larger, accounting for
20-25% of the total. The third component (residuals) had a small and generally not statistically
significant effect, especially around the middle of the distribution. Below the 20th percentile it
contributed negatively to the over-time change in the mathematics test scores, while it accounted
for a small part of the increase in science scores, only below the 30th percentile.
11
Graph 1: Mathematics: Components of the change in score over-time
Decomposition of differences in distribution
40
30
Log wage effects
20
10
0
-10
0 .2 .4 .6 .8 1
Quantile
Total differential Effects of residuals
Effects of median coefficients Effects of characteristics
Graph 2: Science: Components of the change in score over-time
12
Decomposition of differences in distribution
60
Log wage effects
40
20
0
0 .2 .4 .6 .8 1
Quantile
Total differential Effects of residuals
Effects of median coefficients Effects of characteristics
4.3. Decompositions by gender and location
Gender gap
The gender test score gap for 8th grade Ghanaian students is generally moderate and in favor of
boys, in both mathematics and science. In 2003, the gender gap in the mathematics score at the
mean was 17 points or 6% of the mean male score and was little changed at about 21 points or
6.4% of the male score in 2007. On the other hand, the gender gap in the science score declined
from 34.5 points or 12.7% of the mean male score to 29 points or 9.5% of the mean male score.
Tables A2a and A2b in the appendix give the decomposition results for the gender gap in
mathematics and science scores over the entire score distribution (see also charts 3a-3c). In 2003
the gender gap in the mathematics score, measured in points, was higher towards higher points in
the distribution, while remaining approximately constant as a proportion of the male score at any
particular percentile. In 2007, the gender gap generally increased (and more so below the
median), except at the top of the distribution where we observe a decline in the gender score gap.
Both the characteristics and the coefficients components contribute to the overtime change in the
gender gap.
Gender gaps in science scores are higher compared to mathematics, at about 30-35 points at the
median. This gap declined over time, and drastically so at the top quartile of the science score
distribution. The main contributor to this decline is associated with changes in the coefficients
component which favored of girls.
13
35
Chart 3a: Gender gap in Mathematics score at percentiles - 2003
30 vs. 2007
25
G
e 20
n
15 Math-2007
d
e Math-2003
10
r
5
G
a 0
p 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
14
10
Chart 3b: Characteristics component of the gender gap in
8
Mathematics score: 2003 vs. 2007
6
4
G
e 2
n 0
d Math-2007
-2 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
e Math-2003
r -4
-6
G
a -8
p -10
Percentile
35
Chart 3c: Coefficients component of the gender gap in
30 Mathematics score: 2003 vs. 2007
25
G
e 20
n
15 Math-2007
d
e Math-2003
10
r
5
G
a 0
p 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
15
45
Chart 4a: Gender gap in Science score at percentiles - 2003 vs.
40 2007
35
30
G
e 25
n 20
Sience-2007
d
15 Science-2003
e
r 10
5
G
a 0
p 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
10
Chart 4b: Characteristics component of the gender gap in
Science score: 2003 vs. 2007
5
G
0
e Sience-2007
n 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
d
Science-2003
-5
e
r
-10
G
a
-15
p Percentile
16
55
Chart 4c: Coefficients component of the gender gap in Science
score: 2003 vs. 2007
45
35
G
e
n 25
d Sience-2007
e 15 Science-2003
r
5
G
a
-5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
p
Percentile
Location gap
In the absence of information on urban vs. rural school location, information on the size of
community was used. In the data, size of community is grouped in four categories: under 3,000,
3,000-15,000, 15,000 to 500,000 and over 500,000. A dichotomous variable was created
whereby large communities are defined as those with population over 15,000 and small
communities those with population under 15,000. Approximately 46% of schools were located in
large communities in 2003 and 42% in 2007. Over time, mean mathematics scores increased by
12% in schools in large communities, vs. 14% in small communities; similarly, science scores
increased by 17% in large communities and 22% in small communities.
Estimates of the overtime change in the location gap over the entire distribution of scores are a
lot more revealing. They suggest that while in 2003 the location gap was of similar magnitude
across the distribution of scores (that is for both low and high performing students) at about 35
points for mathematics and between 30 and 50 points for science, in 2007 the location gap in
both mathematics and science increased monotonically as one goes to higher points in the
distribution of scores; for worse performing students it decreased drastically, while for better
performing students correspondingly increased.
Furthermore, the decomposition results reveal that the structure of the components of the
location gap have changed drastically for both mathematics and science. In 2003, most of the gap
in favor of large communities was due to better returns to characteristics in large compared to
small communities for the entire distribution of scores. In 2007, the narrowing of the gap among
worse performing pupils is due to the improvement in the return to the characteristics of pupils in
small communities compared to pupils in large communities. However, as one goes to higher
points in the distribution, a build-up of characteristics in favor of large communities appears to
have taken place over time. Above the median, the substantial increase in the characteristics
component, along with an increasing coefficients component led to a widening of the location
gap among well performing pupils.
17
Over time, therefore, the location gap became more heterogeneous, decreasing among worse
performing pupils and increasing among better performing students. The increase in the
characteristics component of the location gap, especially at the upper part of the distribution was
crucial in this development. One could speculate that the apparent improvement in quality of
characteristics for pupils in schools in large communities compared to small communities may
be related to the overtime growth in the proportion of private schools, given that most such
schools tend to be located in urban areas.
18
65
Chart 5a: Mathematics: Test score gap at percentiles between
55
students in large vs. small communities - 2003 vs. 2007
L 45
o
c 35
a
t 25 Math-2007
i
Math-2003
o 15
n
5
G
a
-5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
p
Percentile
40
Chart 5b: Mathematics: Characteristics component of the test
35 score gap between students in large vs. small communities -
2003 vs. 2007
30
L
o 25
c
a 20
t Math-2007
15
i Math-2003
o 10
n
5
G
0
a
p 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
19
40
Chart 5c: Mathematics: Coefficients component of the test score
35 gap between students in large vs. small communities - 2003 vs.
2007
30
L
o 25
c
a 20
t Math-2007
i 15
Math-2003
o
10
n
5
G
a 0
p 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
70
Chart 6a: Science: Test score gap at percentiles between students
in large vs. small communities - 2003 vs. 2007
60
L 50
o
c 40
a
t 30 Science-2007
i
Science-2003
o 20
n
10
G
a 0
p 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
20
40
Chart 6b: Science: Characteristics component of the test score
35 gap between students in large vs. small communities - 2003 vs.
2007
30
L
o 25
c
20
a
t 15 Science-2007
i Science-2003
o 10
n 5
G 0
a 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
-5
p
Percentile
50
Chart 6c: Science: Coefficients component of the test score gap
between students in large vs. small communities - 2003 vs.
40 2007
L
o 30
c
G
a Science-2007
20
a
t Science-2003
p
i
o 10
n
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Percentile
4.4. Detailed decompositions
Tables 4a and 4b present the results of decomposing the over-time change in scores at the mean,
using a standard Oaxaca decomposition methodology; the coefficients used in the decomposition
were transformed using the deviation contrast transform procedure (see Yun 2005)4 in order to
deal with the well-known â€œidentificationâ€? problem associated with Oaxaca-type decompositions;
that is, the problem arising from the dependence of the coefficients effect on the choice of
reference group, when various groups of a categorical variable are involved.
Improved characteristics account for one-third of the increase in the mean mathematics score and
one-quarter of the increase in the science score. Main contributors include the lower incidence of
4
The basic idea of Yunâ€™s solution is to derive estimates for all possible reference groups and then derive the averaging
ones; fortunately the implementation doesnâ€™t necessarily involve tedious and repeated regressions for varying reference
groups. The STATA command Devcon is used for this purpose.
21
paid work, more homework time, increase in grade 8 enrolment5 and more pay incentives for
teachers. The coefficients component for the covariates used in the model is towards an over-
time decrease in both the mathematics and science scores; however, a large effect associated
with changes in the constants is the main contributor to the over-time increase in TIMSS scores
in Ghana.
Table 4a: Detailed decomposition of change in the 8th grade Mathematics score at the Mean
Mean prediction for 2003: 281.2
Mean prediction for 2007: 316.6 Characteristics Coefficients Total Change
Total change 12.27 23.19 35.46
(9.6) (14.5) (23.1)
Characteristics component
Student and household characteristics
Age -0.99 -0.28 -1.27
Gender of student -0.02 0.03 0.01
Speaks/not speak test language at home 0.05 0.29 0.34
Calculator at home 0.20 -0.04 0.16
Desk at home 0.00 -1.80 -1.80
Works/Not in paid job 2.90 0.18 3.08
Homework time 1.22 1.85 3.07
Highest education of parent -0.45 -1.62 -2.07
Both parents born/not born in country 0.46 0.43 0.89
Books at home 0.10 -0.16 -0.06
Total 3.47 -1.12 2.35
School characteristics
Total enrolment, grade 8 3.29 -5.79 -2.50
Community size 0.06 -1.76 -1.70
Proportion of disadvantaged students -0.16 2.18 2.02
Ability grouping yes/no -0.07 0.86 0.79
Remedial lesson in Math Yes/no 0.04 0.91 0.95
Severe absenteeism in school yes/no 0.68 4.50 5.18
Shortage of buildings yeas/no 0.53 -0.14 0.39
Shortage of teachers yeas/no 0.00 0.17 0.17
Index of good attendance -1.12 -3.18 -4.30
Total 3.25 -2.25 1.00
Teacher characteristics
Teacher age 0.41 -2.55 -2.96
Teacher gender 0.66 -0.40 0.26
Teacher years of experience 0.08 -11.02 -10.94
Teacher education 0.40 -3.25 -2.85
Teacher certificate yes/no 1.60 -0.26 1.34
Teacher feels safe/not safe 0.09 6.10 6.19
Teacher satisfaction 0.15 -1.98 -1.83
Pay incentives for teachers yes/no 2.16 -5.87 -3.71
Total 5.55 -19.23 -14.50
Constant - 45.80 45.80
N 11,892
2003: 5,100
2007: 6,792
z-values in parentheses.
5
Results show that higher enrolment is associated with higher scores in Ghana.
22
Table 4b: Detailed Oaxaca decomposition of change in the 8th grade Science score at the Mean
Mean prediction for 2003: 262.6
Mean prediction for 2007: 311.5 Characteristics Coefficients Total Change
Total change 11.71 37.13 48.83
(7.4) (18.2) (24.5)
Characteristics component
Student and household characteristics
Age -1.22 1.43 0.21
Gender of student -0.03 -0.34 -0.37
Speaks/not speak test language at home 0.00 1.12 1.12
Calculator at home -0.12 -0.12 -0.24
Desk at home -0.01 -1.61 -1.62
Works/Not in paid job 2.87 0.00 2.87
Homework time 1.66 1.95 3.61
Highest education of parent -0.67 -2.04 -2.71
Both parents born/not born in country 0.52 -5.62 -5.10
Books at home 0.11 0.01 0.12
Total 3.11 -5.22 -2.11
School characteristics
Total enrolment, grade 8 3.95 -9.03 -5.08
Community size -0.62 -1.21 -1.83
Proportion of disadvantaged students -0.25 3.05 2.80
Ability grouping yes/no -0.54 2.62 2.08
Remedial lesson in Math Yes/no -0.20 -1.12 -1.32
Severe absenteeism in school yes/no 0.90 5.13 6.03
Shortage of buildings yeas/no 0.50 -0.17 0.33
Shortage of teachers yeas/no -0.01 0.38 0.37
Index of good attendance -1.38 -1.04 -2.42
Total 2.35 -1.39 0.96
Teacher characteristics
Teacher age 0.61 -2.94 -2.33
Teacher gender 0.55 1.04 1.59
Teacher years of experience 0.03 -14.51 -14.48
Teacher education 0.66 -4.64 -3.98
Teacher certificate yes/no 1.41 3.00 4.41
Teacher feels safe/not safe 0.11 6.53 6.64
Teacher satisfaction -0.39 2.48 2.09
Pay incentives for teachers yes/no 2.62 -8.16 -5.54
Total 5.6 -17.2 -11.6
Constant - 60.95 60.95
N 11,892
2003: 5,100
2007: 6,792
z-values in parentheses.
23
4.5. Detailed decompositions at percentiles using a â€œhybridâ€? approach
Table A4a and A4b in the appendix contain the (transformed) RIF regression coefficients at
selected quantiles (10th, 50th and 90th). Students in the right age for 8th grade are associated with a
higher score, while the effect of being an overage student reduces scores and more so at higher
point in the score distribution. Speaking the test language at home seems beneficial to high
scoring students, but the opposite is the case below the median. The effect of books at home is
complex; high scoring student with the most books at home are associated with a higher score in
science; however, the pattern for mathematics is different, with students below the median
associated with a higher score in 2003, but a lower score in 2007. The effect of having a parent
with tertiary education is small for poorly performing students, but increases substantially at
higher points in the distribution, especially in science. Having both parents born in Ghana has a
strong positive association with scores in 2003 and less so in 2007. Two of the most powerful
regressors have to do with paid work and time spent on homework. At the median, a child in
combining paid work with study results in a decline in mathematics (science) score by 10 points
(18 points); likewise, spending no time on homework decreases scores by 13 (17) points.
Larger 8th grade enrolment is associated with higher scores.6 The association between
community size and performance is strong but heterogeneous. For example, in science there a
strong positive association between high performing students in large cities (>500,000) and
performance in 2003; for students below the median the positive association is strongest for
medium-size communities (15,000-500,000). However, small communities (<3,000) are
consistently associated with lower performance in both mathematics and science. In 2003,
students in schools with low proportion of disadvantaged students performed better; however,
this association seems to have disappeared or reversed in 2007. There is some evidence that
ability grouping by schools is negatively associated with performance, especially I science.
Students in schools with a severe absenteeism problem performed worse, while high performing
students in schools with high index of good attendance performed better.
Teacher age is negatively associated with student performance, while the opposite is the case for
teacher years of experience. Having a teacher with university education (ISCED 5A) results in a
significant increase in student scores (but mostly in science), and this effect increased in 2007
compared to 2003. Finally, the practice of pay incentives to teachers has a moderate by
consistently positive association with performance, and more so at higher points in the
distribution.
Decompositions results (given in tables 5a and 5b, with detailed results in tables A5a and A5b in
the appendix) are derived from the 2-step procedure outlined in the methodology section. In the
first step, the changes in score and its two constituent components are derived using re-
weighting, without imposing specific functional forms or parametric distributions when deriving
estimates of the total gap. In deriving the re-weighting functions, the probability that a person
belongs in the â€œyear 2003â€? group conditional on (propensity score) is estimated from a logit
regression. In the second step, estimates of the effects of each individual variable on the test
score gap are generated. The estimation of unconditional quantile regression involves deriving
6
The Ministry of Education (2004) of Ghana in its summary of its key findings on TIMSS 2003 found a positive
correlation between class size and student performance.
24
the Recentered Influence Function of the dependent variable and estimating an OLS regression
of the generated RIF variable on covariates. The estimated coefficients are in fact unconditional
partial effects of small location shifts of the covariates; therefore, the decomposition becomes
similar to decomposing the gap at the mean using the Oaxaca-Blinder method.
In tables 5a and 5b the contributors to the characteristics and coefficients effects are combined
into one group relating to student and family characteristics, another to school characteristics and
a third to teachers characteristics. Within the coefficients component, the effect associated with
changes in the constant is given separately. Finally, an approximation error/residual is involved;
this is due to the linearity assumption involved in estimating the RIF-OLS regressions and
because these estimated regression coefficients is only first-order approximations. In practice,
the error in the coefficients/characteristics effect can be estimated as the difference between the
estimate of the through re-weighting and the estimate obtained from the RIF-regression
procedure.
25
Table 5a: Decomposition of change in 8th grade Mathematics score at percentiles
Characteristics Coefficients Total change
P10
Student and household 1.01 -1.03 -0.02
Schools -0.50 4.35 3.85
Teachers 0.39 -3.91 -3.52
Constant - 26.16 26.16
Approximation error 2.03 -1.82 0.21
Total 2.94 23.75 26.69
P20
Student and household 0.99 6.56 7.55
Schools -0.02 13.63 13.61
Teachers 0.89 -8.10 -7.21
Constant - 17.47 17.47
Approximation error 1.35 -1.10 0.15
Total 3.20 28.45 31.65
P30
Student and household 1.32 17.67 18.99
Schools -1.35 21.50 20.15
Teachers 2.25 -12.64 -10.39
Constant - 5.22 5.22
Approximation error 2.07 -1.86 0.21
Total 4.28 29.89 34.17
P40
Student and household 0.50 -11.37 -10.87
Schools -1.08 7.29 6.21
Teachers 1.32 -5.25 -3.93
Constant - 42.11 41.11
Approximation error 2.72 -2.19 0.53
Total 3.46 30.60 34.06
P50
Student and household 0.88 7.96 8.84
Schools -2.67 18.55 15.88
Teachers 3.44 -19.21 -15.77
Constant - 24.58 24.58
Approximation error 0.69 -0.43 0.26
Total 2.33 31.45 33.78
P60
Student and household 0.23 17.40 17.63
Schools -2.16 3.94 1.78
Teachers 2.53 -13.86 -11.33
Constant - 57.93 57.93
Approximation error 3.23 -2.73 0.50
Total 3.84 27.87 31.71
P70
Student and household -0.06 -8.05 -8.11
Schools -1.45 4.94 3.49
Teachers 1.83 -5.84 -4.01
Constant - 39.49 39.49
Approximation error 3.72 -3.48 0.24
Total 4.04 27.05 31.09
P80
Student and household -0.35 -18.85 -18.50
Schools -1.03 -2.90 -3.93
Teachers 3.46 -9.21 -5.75
Constant - 63.65 63.65
Approximation error 5.24 -5.72 -0.48
Total 7.31 26.97 34.28
P90
Student and household 0.28 -9.28 -9.00
Schools -0.52 -6.80 -7.32
Teachers 1.41 1.09 2.50
Constant - 51.40 51.40
Approximation error 3.88 -4.35 -0.47
Total 5.05 32.06 37.11
N: 2003 5,100
N: 2007 6,792
26
40 Graph 7a: Mathematics: components of total score change
35
30
Total change
25
Characteristics
20 Coefficients
15
10
5
0
P10 P20 P30 P40 P50 P60 P70 P80 P90
Graph 7b: Mathematics: Major contributors to score increase
70
60
50
Student/
40 household
30 School
20 Teacher
10
Constant
0
-10 P10 P20 P30 P40 P50 P60 P70 P80 P90
-20
-30
The estimates of the total score change and the two components, while qualitatively similar to
those obtained using the aggregate decomposition (based on a different methodology), differ
substantially with respect to the size of the characteristics component (given the different
approaches used), and more so in the case of science. In the aggregate decomposition the
characteristics component constituted 15-25% of the total gap. Using Firpo et.al (2009) the
characteristics component is around zero or slightly negative.
While changes hidden behind the constant shaped the increase in scores between 2003 and 2007,
for students performing at the median and below in mathematics certain characteristics
controlled for contributed significantly, in particular school and student/family characteristics .
On the other hand, changes associated with teacher characteristics are generally towards
27
reducing scores. In science, changes in the constant overwhelmingly determine the observed
increase in scores, with the exception of the median, where school characteristics contributed as
much as changes in forces behind the constant.
28
Table 5b: Decomposition of change in 8th grade Science score at percentiles
Characteristics Coefficients Total change
P10
Student and household 1.10 -3.72 -2.62
Schools -0.52 4.91 4.39
Teachers -0.34 11.78 11.44
Constant - 37.83 37.83
Approximation error 0.22 0.61 0.83
Total 0.46 51.40 51.86
P20
Student and household 1.18 -16.58 -15.40
Schools -2.46 6.57 4.11
Teachers 0.48 5.65 6.13
Constant 60.33 60.33
Approximation error --0.66 1.40 0.74
Total -1.47 57.37 55.90
P30
Student and household 0.55 0.31 0.86
Schools -3.06 7.42 4.36
Teachers 0.84 -3.96 -3.12
Constant - 51.89 51.89
Approximation error -1.37 1.90 0.53
Total -3.04 57.56 54.52
P40
Student and household -0.12 -14.70 -14.82
Schools -4.06 10.64 6.58
Teachers 0.89 -0.24 0.65
Constant - 54.50 54.50
Approximation error -0.71 1.68 0.97
Total -4.00 51.87 47.87
P50
Student and household -1.07 4.81 3.74
Schools -6.25 31.22 24.97
Teachers 1.07 -5.47 -4.40
Constant - 15.10 15.10
Approximation error 1.04 -0.36 0.68
Total -5.21 45.29 40.08
P60
Student and household -0.69 -32.79 -32.10
Schools -1.98 -2.89 -4.87
Teachers 1.01 4.19 5.20
Constant - 67.73 67.73
Approximation error -3.09 4.24 1.15
Total -4.75 40.49 35.74
P70
Student and household -0.31 -0.08 -0.39
Schools -1.76 10.45 8.69
Teachers 2.51 -20.05 -17.54
Constant - 42.65 42.65
Approximation error -1.10 1.78 0.68
Total -0.66 34.75 34.09
P80
Student and household -0.47 -6.60 -7.07
Schools -0.11 1.20 1.09
Teachers 1.17 -10.87 -9.70
Constant - 44.62 44.62
Approximation error -0.30 0.55 0.25
Total 0.29 28.90 29.19
P90
Student and household -0.76 -21.75 -22.51
Schools 0.52 -15.53 -15.01
Teachers 2.51 -26.43 -23.92
Constant - 87.42 87.42
Approximation error 0.58 -0.11 0.47
Total 2.84 23.61 26.45
N: 2003 5,100
N: 2007 6,792
29
70
Graph 7c: Science: components of total score change
60
50
Total change
40
30 Characteristics
20 Coefficients
10
0
P10 P20 P30 P40 P50 P60 P70 P80 P90
-10
Graph 7d: Science: Major contributors to score increase
80
60
Student/
40 household
School
20 Teacher
0 Constant
P10 P20 P30 P40 P50 P60 P70 P80 P90
-20
-40
From the detailed decomposition results (see tables A5a and A5b), besides the dominant effect of
unaccounted forces behind the constant, one can single out certain individual contributors which
fairly consistently contribute either positively or negatively to the change in mathematics and
science scores. From the positive but small characteristics component, a moderate positive effect
is associated with students involved less in paid work and spending more time doing homework.
From the coefficients component, and starting with science, a performance improving effect is
associated with changes in coefficients associated with the proportion of disadvantaged students
in the school, variables relating to absenteeism, proportion of certified teachers and satisfied
teachers. On the other hand, a negative effect on scores is associated with changes in coefficients
30
relating to both parents born in Ghana, teacher experience (and occasionally teacher education
level) and larger enrolment in 8th grade. In mathematics, the most important contributors are
generally the same, along with a score increasing effect of the coefficients associated with more
homework for students below the median.
5. Conclusion
This paper brings to light certain factors underlying the substantial over-time performance
improvement in mathematics and science in Ghana. Performance improved more for better
performing students in mathematics, while the opposite was the case for science where students
at the bottom of the score distribution experienced a spectacular increase in science scores. More
specifically, inequality in scores decreased over time, mostly in science.7 Most of the increase in
scores is accounted by changes in coefficients (and a smaller part by improvements in
characteristics). Within the coefficients component, measured or unmeasured characteristics not
accounted for (and therefore captured by changes in the constant) dominate this effect. However,
for students below the median the effect associated with school and student characteristics is
substantial.
One could speculate that among the possible unaccounted characteristics, a school being private
vs. public could be of importance in accounting for the over-time increase in scores. This is
because a substantial proportion of grade 8 students attended private schools in 2007, private
schools are generally perceived to produce better performing students, and most importantly,
over the short period between the two TIMSS surveys there was a large increase in the number
of private schools in Ghana (by 36% only between 2005/6 and 2007/8). Evidence is also given
suggesting that the structure of the gap related to large vs. small communities changes
drastically; characteristics improved substantially for pupils in schools in large communities
relative to smaller communities.
7
On the other hand, standard inequality measures suggest a light decline in inequality in scores in mathematics as well.
31
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33
APPENDIX
.005
.004
.003 Graph A1a: Kernel densities for the Mathematics score by year
Density
.002
.001
0
0 200 400 600
score_math
score_2003 score_2007
34
Graph A1b: Kernel densities for the Science score by year
.004
.003
Density
.002
.001
0
0 200 400 600 800
score_science
score_2003 score_2007
35
Table A1: Weighted Mean Characteristics by Year
2003 2007
Mathematics score 280.8 307.6
Science score 261.7 316.6
Student and household characteristics
Age of student 15.65 15.71
Male student 54.99 54.65
Female student 45.01 45.35
Speaks Language of test at home: yes 32.78 33.19
Speaks Language of test at home: no 67.22 66.81
Calculator at home 50.09 54.30
No calculator at home 49.91 45.70
Desk at home 60.16 60.83
No desk at home 39.84 39.17
0-10 books at home 34.19 37.62
11-25 books at home 33.68 39.25
> 25 books at home 32.13 23.13
Works paid job: yes 54.53 40.87
Works paid job: no 45.47 59.13
Highest parentâ€™s education: primary or less 12.33 12.15
Highest parentâ€™s education: lower secondary 32.28 26.96
Highest parentâ€™s education: secondary 19.56 23.86
Highest parentâ€™s education: tertiary 23.43 30.80
Both parents born in country: yes 84.74 88.95
Both parents born in country: no 15.26 11.05
No time for homework 11.02 8.03
Homework < 1 hour per day 39.94 41.15
Homework 1-2 hours per day 26.02 26.80
Homework 2 or more hours per day 23.01 24.01
School characteristics
Total school enrolment: 8th grade 66.79 72.94
School community > 500,000 19.50 22.66
School community 15,000-500,000 25.84 16.27
School community 3,000-15,000 35.05 26.22
School community < 3,000 19.61 34.84
Proportion of disadvantaged pupils: 0-25% 11.35 14.63
Proportion of disadvantaged pupils: 26-50% 17.90 14.60
Proportion of disadvantaged pupils: > 50% 70.75 70.78
Ability grouping in Math: yes 19.95 23.78
Ability grouping in Math: no 80.05 76.22
Remedial lessons in Math: yes 76.83 77.60
Remedial lessons in Math: no 23.17 22.40
Ability grouping in Science: yes 17.19 24.80
Ability grouping in Science: no 82.81 75.20
Remedial lessons in Science: yes 71.79 77.39
Remedial lessons in Science: no 28.21 22.61
Severe absenteeism: yes 22.71 24.78
Severe absenteeism: no 77.29 75.22
Shortage buildings: yes 52.66 23.96
Shortage buildings: no 47.34 76.04
Shortage teachers: yes 62.17 16.49
Shortage teachers: no 37.83 83.51
Index of good attendance: high 8.08 5.26
Index of good attendance: medium 69.26 70.56
Index of good attendance: low 22.66 24.18
36
Teacher characteristics
Teacher age: < 25 12.12 15.35
Teacher age: 25-30 40.65 37.25
Teacher age: 30-40 24.81 30.03
Teacher age: > 40 22.42 17.37
Teacher male 91.62 90.87
Teacher female 8.38 9.13
Teacher education: Upper secondary 10.82 14.29
Teacher education: Post-sec. (non-tertiary) 67.72 63.04
Teacher education: Tertiary (ISCED 5B) 11.92 14.32
Teacher education: Tertiary (ISCED 5A) 9.54 8.35
Teacher certificate: yes 94.31 81.69
Teacher certificate: no 5.69 18.31
Teacher years of experience 7.86 7.53
Teacher feels safe: yes 76.48 73.67
Teacher feels safe: no 23.52 26.33
Teacher satisfaction high 52.62 57.51
Teacher satisfaction medium 30.88 21.00
Teacher satisfaction low 16.50 21.48
Pay incentives: yes 11.64 20.62
Pay incentives: no 88.36 79.38
N 5,100 6,792
37
Table A2a: Decomposition of the gender gap in Mathematics score at percentiles:
Ghana, 2003-2007
Gross gap Characteristics Median Residuals
Percentile Coefficients
2003 2007 2003 2007 2003 2007 2003 2007
P10 14.52 20.82 -4.40 -1.94 19.38 25.37 -0.45 -2.61
(1.30) (2.53) (1.92) (1.50) (2.16) (2.12) (1.89) (2.82)
P20 14.98 20.72 -5.72 -2.75 20.73 26.02 -0.03 -2.55
(1.45) (2.10) (1.76) (1.36) (2.12) (2.13) (1.84) (2.39)
P30 15.04 21.07 -6.73 -3.84 21.90 27.01 -0.13 -2.10
(1.92) (2.01) (1.91) (1.30) (2.16) (2.24) (1.86) (2.03)
P40 15.75 21.68 -6.93 -4.53 22.03 27.55 0.66 -1.34
(2.13) (2.02) (1.72) (1.29) (2.53) (2.26) (1.98) (1.69)
P50 16.50 21.56 -7.33 -5.31 22.30 27.67 1.53 -0.80
(2.54) (2.13) (1.67) (1.27) (2.55) (2.60) (1.84) (1.65)
P60 17.83 21.54 -7.15 -6.02 22.62 27.17 2.36 0.39
(2.99) (2.58) (1.77) (1.52) (2.87) (2.63) (2.11) (1.51)
P70 18.84 20.14 -7.44 -6.80 22.93 26.03 3.36 0.90
(3.51) (2.70) (1.64) (1.68) (3.23) (2.65) (2.42) (1.44)
P80 20.77 18.16 -7.25 -7.54 22.81 24.86 5.20 0.84
(3.86) (2.95) (1.77) (1.75) (3.49) (2.90) (2.71) (1.63)
P90 25.39 17.49 -6.01 -8.02 22.10 23.97 9.31 1.54
(3.83) (3.56) (2.07) (1.93) (3.85) (3.60) (3.14) (2.07)
Standard errors in parentheses.
38
Table A2b: Decomposition of the gender gap in Science score at percentiles:
Ghana, 2003-2007
Gross gap Characteristics Median Residuals
Percentile Coefficients
2003 2007 2003 2007 2003 2007 2003 2007
P10 30.00 23.81 -4.00 -3.08 40.86 34.71 -6.88 -7.82
(3.16) (3.18) (2.93) (1.30) (3.80) (2.72) (2.40) (3.33)
P20 33.05 27.39 -5.48 -4.38 42.38 37.09 -3.85 -5.32
(2.15) (2.18) (2.59) (1.15) (3.93) (2.75) (2.61) (2.95)
P30 34.50 30.64 -6.90 -4.87 42.79 38.90 -1.39 -3.39
(2.10) (1.97) (2.83) (1.45) (4.05) (2.80) (2.30) (2.36)
P40 35.57 32.21 -7.70 -5.80 42.54 39.45 -0.72 -1.44
(2.37) (1.59) (3.06) (1.37) (4.06) (2.91) (2.37) (2.16)
P50 36.47 33.27 -7.78 -6.33 42.37 39.63 1.82 -0.03
(2.44) (1.67) (2.92) (1.41) (4.21) (3.20) (2.28) (1.93)
P60 37.07 32.84 -8.01 -7.08 42.31 39.00 2.78 0.93
(2.28) (1.84) (2.94) (1.58) (4.59) (3.52) (2.56) (1.99)
P70 37.69 30.99 -8.23 -8.16 42.09 37.80 3.84 1.35
(2.41) (1.73) (2.99) (1.55) (4.39) (3.53) (2.72) (2.20)
P80 37.74 27.80 -7.38 -8.96 42.08 35.37 3.03 1.39
(2.99) (1.64) (2.68) (1.69) (4.70) (3.64) (3.39) (2.69)
P90 35.31 22.81 -5.84 -9.39 41.41 31.82 -0.26 0.38
(4.37) (1.60) (3.91) (1.65) (5.10) (3.97) (3.53) (3.29)
Standard errors in parentheses.
39
Table A3a: Mathematics: Decomposition of the test score gap by size of community at
percentiles: Ghana, 2003-2007
Gross gap Characteristics Median Residuals
Percentile Coefficients
2003 2007 2003 2007 2003 2007 2003 2007
P10 32.34 14.65 7.94 11.55 27.45 0.93 -3.05 2.17
(3.59) (2.42) (2.11) (1.30) (2.89) (2.26) (1.75) (1.63)
P20 34.90 19.63 8.89 13.97 27.50 3.18 -1.49 2.48
(3.29) (2.19) (2.70) (1.18) (3.05) (1.86) (1.33) (1.93)
P30 36.02 23.43 8.98 16.44 28.09 4.89 -1.05 2.09
(2.94) (2.05) (2.91) (1.52) (3.06) (1.59) (1.45) (1.95)
P40 36.97 27.38 8.78 18.62 28.54 6.72 -0.34 2.05
(2.84) (1.99) (2.04) (1.70) (2.90) (1.78) (1.55) (2.39)
P50 36.72 31.43 8.45 20.98 28.04 8.25 0.23 2.19
(2.71) (2.24) (3.46) (2.12) (2.78) (2.41) (1.31) (2.86)
P60 35.87 35.40 7.92 22.95 27.97 9.60 -0.02 2.85
(2.95) (2.45) (3.69) (2.79) (3.01) (2.99) (1.75) (2.92)
P70 34.18 39.51 6.20 23.64 28.54 13.02 -0.57 2.85
(3.20) (2.60) (4.15) (3.08) (3.28) (3.11) (1.95) (2.74)
P80 31.66 44.00 4.37 22.74 28.68 17.12 -1.39 4.14
(3.05) (2.99) (4.76) (4.25) (3.71) (3.34) (2.43) (2.27)
P90 30.18 49.25 1.60 19.15 29.27 23.42 -0.70 6.67
(1.52) (3.32) (5.09) (4.95) (5.65) (4.32) (3.01) (2.65)
Standard errors in parentheses.
40
Table A3b: Science: Decomposition of the test score gap by size of community at
percentiles: Ghana, 2003-2007
Gross gap Characteristics Median Residuals
Percentile Coefficients
2003 2007 2003 2007 2003 2007 2003 2007
P10 46.23 14.70 6.38 11.56 37.38 3.48 2.48 -0.35
(6.20) (4.07) (3.01) (3.73) (5.77) (5.10) (5.49) (3.95)
P20 47.74 25.22 7.69 15.33 35.69 5.45 4.35 4.43
(6.10) (3.56) (3.44) (3.01) (8.01) (4.28) (5.11) (1.33)
P30 47.82 31.32 9.14 18.33 33.57 7.94 5.11 5.05
(4.99) (2.07) (3.16) (2.60) (7.55) (3.18) (4.44) (1.22)
P40 47.54 35.42 9.44 21.22 33.15 10.06 4.95 4.14
(3.94) (2.79) (3.08) (2.34) (7.37) (2.41) (3.63) (1.41)
P50 46.21 39.32 9.62 23.38 31.83 11.71 4.76 4.22
(3.19) (3.26) (2.85) (1.91) (6.74) (1.71) (4.09) (1.96)
P60 45.02 43.41 9.25 25.40 31.77 13.43 4.00 4.28
(2.55) (3.58) (3.24) (1.78) (5.75) (0.88) (4.12) (2.15)
P70 43.79 47.50 8.83 27.92 31.61 15.60 3.35 3.98
(2.79) (4.06) (3.21) (2.08) (4.67) (2.17) (4.27) (3.17)
P80 41.33 52.21 7.59 30.18 32.77 19.00 0.97 3.03
(2.27) (4.72) (3.36) (1.65) (4.77) (2.98) (4.08) (4.30)
P90 35.38 56.74 3.68 29.94 33.96 25.51 -2.27 1.30
(2.39) (3.74) (4.54) (2.54) (6.77) (2.52) (4.36) (4.08)
Standard errors in parentheses.
41
Table A4a: Transformed RIF-Regression coefficients at Quantiles by year: Mathematics
2003 2007
Q10 Q50 Q90 Q10 Q50 Q90
Age 13 0.83 3.46 15.22 0.7 -2.08 3.86
(0.2) (1.0) (2.0) (0.3) (0.3) (0.7)
Age 14 5.19 13.95 15.84 4.79 19.77 12.05
(2.5) (7.1) (3.8) (3.2) (5.5) (4.3)
Age 15 2.33 4.22 5.01 0.41 1.15 -0.42
(1.2) (2.5) (1.6) (0.3) (0.4) (0.2)
Age 16 -1.83 -2.61 -5.94 1.52 1.12 -5.08
(0.8) (1.4) (2.0) (1.0) (0.3) (2.8)
Age 17 -1.07 -7.68 -11.69 -4.86 -11.91 -3.74
(0.4) (3.7) (3.7) (3.2) (3.7) (2.0)
Age 18 -5.60 -11.34 -18.45 -2.22 -8.61 -6.68
(1.8) (5.2) (6.5) (1.0) (2.0) (3.3)
Male student 5.16 7.93 10.17 4.09 12.46 4.55
(5.0) (9.3) (6.6) (5.3) (8.6) (5.3)
Speaks test language at home -3.06 -2.94 2.34 -2.83 -4.81 1.64
(1.8) (3.3) (1.4) (3.4) (3.1) (1.7)
0-10 books -1.01 -3.41 -3.24 2.57 8.70 0.57
(0.6) (2.7) (1.6) (2.2) (4.1) (0.5)
11-25 books -2.16 -0.86 3.01 -0.47 -3.38 -0.65
(1.5) (0.7) (1.4) (0.5) (1.7) (0.5)
> 25 books 3.17 4.27 0.23 -2.10 -5.32 0.08
(2.2) (3.4) (0.1) (1.6) (2.4) (0.1)
Calculator at home 1.23 1.18 5.07 2.26 2.16 1.71
(1.1) (2.4) (3.4) (2.7) (1.4) (2.0)
Desk at home 3.60 8.33 7.03 0.51 4.90 0.45
(3.2) (1.1) (5.1) (0.6) (3.2) (0.5)
Parentâ€™s education tertiary 2.90 6.88 15.70 0.36 4.86 2.19
(1.7) (4.3) (4.9) (0.3) (2.1) (1.4)
Parentâ€™s education secondary 2.48 8.78 0.20 -1.78 0.80 -0.02
(1.4) (5.3) (0.1) (1.4) (0.3) (0.0)
Parentâ€™s education lower secondary -3.39 -5.69 -2.70 -1.57 -8.45 -0.081
(2.0) (4.2) (1.3) (1.5) (4.2) (1.5)
Parentâ€™s education primary or less -2.07 -9.98 -13.20 2.99 2.79 -0.36
(0.8) (4.8) (6.0) (1.8) (0.8) (0.2)
Both parents born in country 4.44 4.46 4.66 2.28 3.76 1.94
(2.7) (3.8) (2.6) (2.0) (1.8) (1.7)
Student works in paid job -5.88 -10.34 -14.14 -6.02 -18.27 -6.93
(5.5) (11.3) (9.6) (7.0) (11.8) (8.7)
Homework: no time -10.77 -13.12 -10.55 -12.20 -24.60 -4.79
(5.1) (9.9) (7.6) (5.9) (10.8) (6.2)
School enrolment: 8th grade 0.08 0.12 0.25 0.06 0.15 0.07
(4.3) (6.9) (6.0) (5.4) (6.4) (4.3)
Community: > 500,000 3.67 2.82 5.76 -3.79 0.45 -0.25
(1.7) (1.6) (1.8) (2.5) (0.2) (0.2)
Community: 15,000-500,000 10.21 17.86 10.90 2.74 2.57 2.85
(6.3) (10.7) (3.3) (1.8) (0.8) (1.2)
Community: 3,000-15,000 2.29 -4.89 -5.41 -0.46 0.00 -1.00
(1.3) (3.3) (2.4) (0.3) (0.0) (0.7)
Community: < 3,000 -16.17 -15.79 -11.26 1.50 -3.02 -1.60
(5.9) (8.4) (3.9) (1.0) (1.1) (1.1)
Proportion disadvantaged: 0-25% 3.32 10.75 16.04 0.43 -4.60 -1.03
(1.6) (5.7) (3.9) (0.3) (1.5) (0.5)
42
Proportion disadvantaged: 26-50% -0.87 -4.31 -19.50 -0.39 -0.19 0.62
(0.5) (2.4) (5.6) (0.3) (0.1) (0.3)
Proportion disadvantaged: > 50% -2.45 -6.44 3.45 0.083 4.79 0.41
(1.5) (4.7) (1.2) (0.7) (2.1) (0.3)
Ability grouping: yes 0.38 -2.84 -1.34 -2.05 -1.73 -3.46
(0.3) (2.2) (0.6) (2.0) (0.9) (3.6)
Remedial lessons: yes 3.53 -0.10 -0.48 1.22 6.73 2.65
(2.5) (0.1) (0.3) (1.2) (3.7) (2.6)
Severe absenteeism: yes 0.66 -5.13 -5.90 -3.98 -15.09 -9.01
(0.4) (3.7) (2.9) (3.0) (6.3) (7.8)
Shortage buildings: yes -0.21 -0.16 -0.70 1.92 2.54 -2.97
(0.2) (0.2) (0.4) (2.1) (1.3) (2.8)
Shortage teachers: yes -2.11 -3.37 0.65 -1.17 -0.18 2.06
(2.0) (3.6) (0.4) (1.5) (0.2) (2.3)
Index good attendance high -1.86 1.39 27.24 -5.39 8.21 14.13
(0.8) (0.7) (5.0) (2.4) (1.8) (3.2)
Index good attendance medium -0.25 -3.82 -12.36 3.42 -5.80 -11.84
(0.1) (2.6) (3.6) (2.3) (2.1) (5.2)
Index good attendance low 2.11 2.43 -14.88 1.97 -2.42 -2.29
(1.0) (1.2) (4.3) (1.0) (0.6) (0.8)
Teacher age: < 25 7.10 11.90 12.20 7.91 17.67 0.48
(2.5) (4.9) (2.6) (3.7) (4.1) (0.2)
Teacher age: 25-30 6.13 5.97 2.99 -2.17 -7.10 -7.04
(3.3) (3.7) (1.1) (1.3) (2.4) (4.1)
Teacher age: 31-40 -3.10 -7.91 -1.70 -1.66 -2.20 -1.11
(1.4) (4.6) (1.6) (1.2) (0.8) (0.7)
Teacher age: > 40 -10.13 -9.96 -13.50 -4.07 -8.38 7.67
(3.7) (4.1) (3.4) (1.4) (1.7) (2.2)
Teacher male 1.90 -0.26 -12.97 -3.55 -9.66 0.09
(1.0) (0.2) (4.0) (3.5) (4.1) (0.1)
Teacher education: < tertiary -4.81 -2.60 1.12 -2.59 -7.18 -4.45
(2.4) (1.6) (0.4) (2.0) (2.6) (2.4)
Teacher education: Tertiary (5B) 4.18 2.72 1.60 -1.70 7.82 0.14
(2.0) (1.3) (0.4) (1.2) (2.6) (0.1)
Teacher education: Tertiary (5A) 0.63 -0.12 -2.72 4.29 -0.63 4.31
(0.2) (0.1) (0.7) (3.6) (0.2) (1.6)
Teacher experience 0.55 0.94 1.34 0.17 0.58 0.00
(3.0) (5.5) (4.0) (1.1) (2.0) (0.0)
Teacher certificate: yes 0.52 -3.16 -9.72 0.23 -2.98 -4.46
(0.3) (1.6) (2.2) (0.2) (1.3) (3.0)
Teacher feels safe 0.10 -0.01 -3.68 2.34 6.63 3.13
(0.1) (0.0) (2.1) (2.4) (3.5) (3.6)
Teacher satisfaction low 2.75 -0.56 -5.73 -2.52 0.07 0.00
(1.7) (0.4) (2.7) (2.2) (0.0) (0.0)
Pay incentives: yes 1.62 1.28 3.71 2.36 10.05 4.06
(1.0) (0.8) (1.4) (2.2) (4.8) (2.9)
Constant 160.1 245.1 366.3 186.7 270.7 416.2
(28.0) (55.3) (47.2) (53.2) (42.9) (92.8)
R-squared 0.095 0.273 0.163 0.102 0.207 0.161
N 5,100 6,792
43
Table A4b: Transformed RIF-Regression coefficients at Quantiles by year: Science
2003 2007
Q10 Q50 Q90 Q10 Q50 Q90
Age 13 -5.77 5.25 53.67 -2.73 5.34 19.91
(0.6) (1.1) (3.1) (0.5) (0.6) (1.7)
Age 14 6.78 16.43 9.36 4.22 20.08 19.66
(1.5) (5.8) (1.1) (1.6) (4.3) (3.6)
Age 15 0.48 1.39 2.99 1.79 0.84 -2.82
(0.1) (0.6) (0.4) (0.8) (0.3) (0.8)
Age 16 -2.85 -0.59 -20.98 5.20 1.21 -9.43
(0.6) (0.2) (3.0) (2.1) (0.3) (2.4)
Age 17 -1.05 -`0.45 -11.65 -2.38 -15.12 -12.67
(0.2) (3.5) (1.5) (0.8) (3.7) (3.6)
Age 18 3.36 -12.03 -33.39 -6.11 -12.36 -14.64
(0.6) (3.6) (4.4) (1.5) (2.4) (3.5)
Male student 13.31 14.61 27.74 5.75 19.42 11.30
(6.1) (11.8) (8.0) (4.7) (11.0) (6.7)
Speaks test language at home -0.62 -0.53 10.89 -3.31 -2.79 6.29
(0.3) (0.4) (2.9) (2.5) (1.5) (3.3)
0-10 books 4.93 -1.08 0.83 8.11 3.89 -0.50
(1.5) (0.6) (0.2) (4.4) (1.4) (0.2)
11-25 books -4.74 -0.91 -12.02 -0.15 1.05 -4.59
(1.6) (0.5) (2.6) (0.1) (0.4) (2.0)
> 25 books 0.19 1.99 11.20 -7.95 -4.94 5.09
(0.1) (1.1) (2.1) (3.6) (1.8) (1.7)
Calculator at home -0.26 2.33 4.24 0.73 -2.23 0.50
(0.1) (1.8) (1.3) (0.6) (1.2) (0.3)
Desk at home 3.08 8.42 13.52 2.55 5.61 3.52
(1.3) (6.4) (4.0) (2.0) (3.0) (2.1)
Parentâ€™s education tertiary 8.35 12.45 28.93 2.72 9.98 7.08
(2.2) (5.4) (4.0) (1.7) (3.4) (2.3)
Parentâ€™s education secondary 7.01 7.32 1.99 1.24 2.59 2.22
(1.9) (3.0) (0.3) (1.7) (0.8) (0.7)
Parentâ€™s education lower secondary -6.01 -9.45 -11.82 -8.53 -15.62 -5.05
(1.8) (4.8) (2.4) (5.5) (6.2) (2.1)
Parentâ€™s education primary or less -9.35 -10.31 -19.10 4.58 3.05 -4.25
(1.6) (3.4) (3.0) (2.0) (0.7) (1.2)
Both parents born in country 11.58 12.36 17.59 3.42 1.07 1.76
(3.4) (7.4) (4.8) (1.9) (0.4) (0.7)
Student works in paid job -14.25 -18.29 -33.89 -10.75 -20.48 -15.16
(6.3) (13.5) (10.1) (8.0) (10.9) (9.7)
Homework: no time -22.89 -17.18 -25.61 -26.57 -35.38 -8.82
(5.1) (8.8) (8.1) (7.8) (14.0) (5.1)
School enrolment: 8th grade 0.14 0.17 0.53 0.05 0.22 0.18
(3.6) (7.1) (5.6) (2.7) (7.3) (6.1)
Community: > 500,000 5.34 -1.66 34.52 -4.32 3.54 4.89
(1.2) (0.7) (4.5) (1.9) (1.1) (1.5)
Community: 15,000-500,000 20.27 22.05 -8.70 2.77 5.94 -1.50
(5.9) (9.2) (1.6) (1.2) (1.5) (0.3)
Community: 3,000-15,000 -2.67 -3.74 -8.70 1.96 7.80 1.98
(0.7) (1.7) (1.6) (0.9) (2.5) (0.7)
Community: < 3,000 -22.94 -16.65 -32.66 -0.40 -17.29 -5.36
(4.3) (5.9) (5.2) (0.2) (5.0) (1.8)
Proportion disadvantaged: 0-25% 9.92 13.67 18.34 0.10 -4.83 -6.87
(2.3) (4.9) (2.2) (0.0) (1.3) (2.0)
44
Proportion disadvantaged: 26-50% -4.52 -5.54 -36.44 -0.36 -3.15 6.30
(1.2) (2.1) (4.7) (0.2) (0.9) (1.7)
Proportion disadvantaged: > 50% -5.41 -8.03 18.10 0.46 7.98 0.56
(1.6) (3.9) (2.9) (0.3) (2.8) (0.2)
Ability grouping: yes -2.77 -1.90 -8.03 0.09 -7.28 -7.41
(0.9) (1.0) (1.6) (0.1) (3.3) (3.7)
Remedial lessons: yes 4.35 -0.11 -4.44 4.02 0.44 3.35
(1.6) (0.1) (1.1) (2.3) (0.2) (1.7)
Severe absenteeism: yes 0.28 -5.56 -11.42 -6.61 -22.97 -15.73
(0.1) (2.8) (2.2) (3.3) (7.7) (6.0)
Shortage buildings: yes 0.33 0.40 -0.08 2.20 0.79 -8.10
(0.1) (0.3) (0.0) (1.4) (0.3) (4.1)
Shortage teachers: yes -4.87 -5.45 -12.74 -1.97 1.24 0.98
(2.2) (4.0) (3.2) (1.5) (0.7) (0.6)
Index good attendance high 11.63 9.47 49.65 -7.89 7.95 28.37
(2.9) (3.1) (4.3) (2.1) (1.3) (3.7)
Index good attendance medium -5.34 -9.85 -32.65 0.90 -7.52 -22.78
(1.6) (4.5) (4.2) (0.4) (2.2) (5.6)
Index good attendance low -6.29 0.37 -17.00 6.99 -0.42 -5.59
(1.4) (0.1) (2.0) (2.2) (0.1) (1.0)
Teacher age: < 25 9.30 17.07 13.62 8.19 16.02 -4.25
(1.7) (4.8) (1.3) (2.4) (3.1) (0.8)
Teacher age: 25-30 5.67 7.32 14.33 -2.85 -8.44 -5.63
(1.6) (3.1) (2.1) (1.2) (2.2) (1.7)
Teacher age: 31-40 -9.32 -7.74 -2.56 -2.29 -1.58 3.68
(2.0) (3.0) (0.4) (1.0) (0.5) (1.2)
Teacher age: > 40 -5.65 -16.65 -25.38 -3.04 -5.99 6.20
(1.1) (4.7) (2.5) (0.8) (0.9) (1.0)
Teacher male -1.13 -0.15 -15.52 -3.27 -5.82 2.83
(0.3) (0.1) (2.3) (2.2) (2.0) (0.9)
Teacher education: < tertiary -2.44 -5.35 -3.68 -3.77 -12.24 -15.67
(0.6) (2.1) (0.5) (1.8) (3.6) (4.1)
Teacher education: Tertiary (5B) 1.07 -1.84 1.57 -2.17 4.46 -0.92
(0.2) (0.6) (0.2) (1.0) (1.2) (0.2)
Teacher education: Tertiary (5A) 1.36 7.19 2.11 5.94 7.77 16.59
(0.2) (2.1) (0.2) (2.9) (1.8) (3.0)
Teacher experience 0.37 1.21 3.07 0.31 0.16 0.22
(1.0) (4.7) (3.7) (1.5) (0.5) (0.5)
Teacher certificate: yes -4.84 -7.92 0.32 2.97 0.96 -6.98
(1.2) (2.8) (0.0) (1.5) (0.3) (2.4)
Teacher feels safe -2.38 2.15 2.16 5.82 10.27 2.80
(0.9) (1.4) (0.5) (3.5) (4.6) (1.5)
Teacher satisfaction low 6.06 4.75 -13.56 -4.44 -7.41 -2.31
(1.90) (2.3) (2.8) (2.6) (3.3) (1.2)
Pay incentives: yes 2.26 1.06 13.70 4.87 8.71 8.21
(0.7) (0.5) (2.2) (3.5) (3.5) (2.9)
Constant 94.57 229.8 338.2 132.4 244.8 425.6
(8.2) (35.6) (20.2) (24.1) (30.9) (50.1)
R-squared 0.083 0.257 0.139 0.134 0.224 0.164
N 5,100 6,792
45
Table A5a: Detailed decomposition of change in 8th grade Mathematics score at percentiles:
Ghana 2003-2007
Percentile/Characteristic Characteristics Coefficients Total change
P10
Age of student -0.40 -0.03 -0.43
Gender of student -0.03 -0.11 -0.14
Language of test at home -0.01 -0.08 -0.09
Books 0.26 0.18 0.44
Calculator at home 0.19 0.00 0.19
Desk at home 0.01 -0.62 -0.61
Parentsâ€™ education -0.44 -0.01 -0.45
Parents born/not born in country -0.03 -1.48 -1.51
Paid work 0.75 0.00 0.75
Homework 0.73 1.11 1.84
Total school enrolment 0.36 -1.45 -1.09
School community -0.07 -1.03 -1.10
School: % disadvantaged students -0.03 2.07 2.04
Ability grouping -0.17 1.48 1.31
Remedial lessons 0.11 -1.23 -1.12
Severe absenteeism -0.11 2.49 2.38
Shortage buildings -0.91 -0.10 -1.01
Shortage teachers 0.11 0.08 0.19
Index of good attendance 0.27 2.19 2.46
Teacher age 0.40 -1.46 -1.06
Teacher gender 0.09 -4.55 -4.46
Teacher experience -0.05 -3.03 -3.08
Teacher education -0.04 1.25 1.21
Teacher certification -0.06 -0.25 -0.31
Teacher feels safe/unsafe -0.13 1.18 1.05
Teacher satisfaction -0.26 3.52 3.26
Pay incentives 0.43 -0.56 -0.13
Approximation error 2.03 -1.82 0.21
Constant - 26.16 26.16
Total 2.94 23.75 26.69
P20
Age of student -0.64 0.45 -0.19
Gender of student -0.05 0.25 0.20
Language of test at home -0.01 0.22 0.21
Books 0.62 0.08 0.70
Calculator at home 0.18 0.00 0.18
Desk at home 0.02 -0.50 -0.48
Parentsâ€™ education -1.43 -0.50 -1.93
Parents born/not born in country -0.04 -1.41 -1.45
Paid work 1.18 0.12 1.30
Homework 1.17 7.84 9.01
Total school enrolment 0.69 2.45 3.14
School community -0.40 -0.61 -1.01
School: % disadvantaged students -0.03 3.69 3.66
Ability grouping -0.05 0.90 0.85
Remedial lessons 0.05 0.20 0.25
Severe absenteeism -0.19 3.37 3.18
Shortage buildings -0.42 -0.03 -0.45
Shortage teachers 0.12 0.08 0.20
Index of good attendance 0.26 3.77 4.03
Teacher age 0.59 -1.51 -0.92
46
Teacher gender 0.14 -6.08 -5.94
Teacher experience -0.06 -2.07 -2.13
Teacher education -0.04 -2.38 -2.42
Teacher certification 0.15 0.45 0.60
Teacher feels safe/unsafe -0.23 2.25 2.02
Teacher satisfaction -0.22 2.73 2.51
Pay incentives 0.56 -1.48 -0.92
Approximation error 1.35 -1.10 0.25
Constant - 17.47 17.47
Total 3.20 28.45 31.65
P30
Age of student -1.08 1.14 0.06
Gender of student -0.08 0.68 0.60
Language of test at home -0.02 0.90 0.88
Books 0.61 0.10 0.71
Calculator at home 0.26 0.00 0.26
Desk at home 0.04 -0.07 -0.03
Parentsâ€™ education -2.18 -1.36 -3.54
Parents born/not born in country -0.06 0.47 0.41
Paid work 2.07 0.34 2.41
Homework 1.76 15.48 17.24
Total school enrolment 1.05 6.43 7.48
School community -0.36 -0.76 -1.12
School: % disadvantaged students -0.04 4.32 4.28
Ability grouping -0.22 1.68 1.46
Remedial lessons 0.10 2.65 2.75
Severe absenteeism -0.32 4.82 4.50
Shortage buildings -1.11 -0.07 -1.18
Shortage teachers -0.05 0.23 0.18
Index of good attendance -0.04 1.86 1.82
Teacher age 0.99 -2.53 -1.54
Teacher gender 0.22 -7.58 -7.36
Teacher experience -0.10 -2.05 -2.15
Teacher education 0.01 -1.90 -1.89
Teacher certification 0.55 -0.13 0.42
Teacher feels safe/unsafe -0.32 3.10 2.78
Teacher satisfaction -0.25 2.23 1.98
Pay incentives 1.15 -3.78 -2.63
Approximation error 2.07 -1.86 0.21
Constant - 5.22 5.22
Total 4.29 29.89 34.18
P40
Age of student -0.57 -1.12 -1.69
Gender of student -0.04 -0.52 -0.56
Language of test at home -0.01 -1.15 -1.16
Books 0.28 0.08 0.36
Calculator at home 0.12 0.00 0.12
Desk at home 0.02 -1.80 -1.78
Parentsâ€™ education -1.22 -0.52 -1.74
Parents born/not born in country -0.03 -1.86 -1.89
Paid work 1.08 -0.14 0.94
Homework 0.85 -4.32 -3.47
Total school enrolment 0.52 -3.38 -2.86
School community -0.46 -0.34 -0.80
School: % disadvantaged students -0.06 7.86 7.80
Ability grouping -0.08 -0.40 -0.48
47
Remedial lessons 0.05 1.75 1.80
Severe absenteeism -0.19 0.69 0.50
Shortage buildings -0.58 0.01 -0.57
Shortage teachers 0.01 0.32 0.33
Index of good attendance -0.09 1.41 1.32
Teacher age 0.56 -0.58 -0.02
Teacher gender 0.11 -4.33 -4.22
Teacher experience -0.09 -7.10 -7.19
Teacher education 0.04 -1.05 -1.01
Teacher certification 0.37 3.96 4.33
Teacher feels safe/unsafe -0.22 -1.95 -2.17
Teacher satisfaction -0.10 1.25 1.15
Pay incentives 0.65 0.67 1.32
Approximation error 2.72 -2.18 0.54
Constant - 42.11 42.11
Total 3.46 30.60 34.06
P50
Age of student -0.99 0.53 -0.46
Gender of student -0.08 0.45 0.37
Language of test at home -0.02 0.64 0.62
Books 0.67 0.08 0.75
Calculator at home 0.18 0.00 0.18
Desk at home 0.04 -0.70 -0.66
Parentsâ€™ education -2.62 -1.67 -4.29
Parents born/not born in country -0.05 -0.41 -0.46
Paid work 2.28 0.25 2.53
Homework 1.47 8.78 10.25
Total school enrolment 0.99 2.53 3.52
School community -0.68 0.16 -0.52
School: % disadvantaged students -0.28 7.19 6.91
Ability grouping -0.15 0.25 0.10
Remedial lessons 0.10 4.34 4.44
Severe absenteeism -0.43 5.28 4.85
Shortage buildings -1.10 -0.14 -1.24
Shortage teachers 0.02 0.27 0.29
Index of good attendance -0.41 -2.16 -2.57
Teacher age 0.99 -2.66 -1.67
Teacher gender 0.25 -7.92 -7.67
Teacher experience -0.17 -2.79 -2.96
Teacher education 0.14 -2.95 -2.81
Teacher certification 0.74 0.93 1.67
Teacher feels safe/unsafe -0.36 3.54 3.18
Teacher satisfaction 0.01 -0.52 -0.51
Pay incentives 1.84 -6.85 -5.01
Approximation error 0.69 -0.43 0.26
Constant - 24.58 24.58
Total 2.33 31.44 33.77
P60
Age of student -0.87 0.05 -0.82
Gender of student -0.07 -0.65 -0.72
Language of test at home -0.01 -1.01 -1.02
Books 0.48 0.16 0.64
Calculator at home 0.12 0.00 0.12
Desk at home 0.03 -2.66 -2.63
Parentsâ€™ education -2.47 -1.80 -4.27
Parents born/not born in country -0.04 -4.41 -4.45
48
Paid work 1.96 -0.24 1.72
Homework 1.08 -6.84 -5.76
Total school enrolment 0.82 -12.26 -11.44
School community -0.98 -0.18 -1.16
School: % disadvantaged students -0.30 7.00 6.70
Ability grouping -0.04 -0.92 -0.96
Remedial lessons 0.08 7.21 7.29
Severe absenteeism -0.38 2.94 2.56
Shortage buildings -0.18 -0.11 -0.29
Shortage teachers 0.10 0.42 0.52
Index of good attendance -0.70 -0.63 -1.33
Teacher age 0.40 -2.93 -2.53
Teacher gender 0.17 -4.58 -4.41
Teacher experience -0.07 -13.07 -13.14
Teacher education 0.07 1.34 1.41
Teacher certification 0.98 9.57 10.55
Teacher feels safe/unsafe -0.24 2.87 2.63
Teacher satisfaction -0.14 -2.50 -2.64
Pay incentives 1.36 -4.56 -3.20
Approximation error 3.23 -2.73 0.50
Constant - 57.93 57.93
Total 3.84 27.87 31.71
P70
Age of student -0.50 -0.54 -1.04
Gender of student -0.04 -0.13 -0.17
Language of test at home 0.00 -0.02 -0.02
Books 0.21 0.05 0.26
Calculator at home 0.10 0.00 0.10
Desk at home 0.03 -1.25 -1.22
Parentsâ€™ education -1.65 -1.23 -2.88
Parents born/not born in country -0.02 -2.25 -2.27
Paid work 1.21 -0.09 1.12
Homework 0.61 -2.59 -1.98
Total school enrolment 0.56 -4.85 -4.29
School community -0.77 0.36 -0.41
School: % disadvantaged students -0.19 4.02 3.83
Ability grouping -0.11 -0.61 -0.72
Remedial lessons 0.06 4.00 4.06
Severe absenteeism -0.28 3.25 2.97
Shortage buildings 0.41 -0.02 0.39
Shortage teachers 0.00 0.27 0.27
Index of good attendance -0.67 -2.07 -2.74
Teacher age 0.25 -1.70 -1.45
Teacher gender 0.08 -0.06 0.02
Teacher experience -0.09 -5.89 -5.98
Teacher education 0.04 -1.43 -1.39
Teacher certification 0.78 4.74 5.52
Teacher feels safe/unsafe -0.17 2.42 2.25
Teacher satisfaction -0.08 -0.69 -0.77
Pay incentives 1.01 -3.23 -2.22
Approximation error 3.72 -3.48 024
Constant - 39.39 39.39
Total 4.04 27.05 31.09
P80
Age of student -0.95 1.31 0.36
Gender of student -0.06 -0.96 -1.02
49
Language of test at home 0.00 -0.08 -0.08
Books 0.06 0.04 0.10
Calculator at home 0.17 -0.01 0.16
Desk at home 0.03 -2.25 -2.22
Parentsâ€™ education -2.16 -2.20 -4.36
Parents born/not born in country -0.01 -6.11 -6.12
Paid work 1.85 -0.33 1.52
Homework 0.70 -8.25 -7.55
Total school enrolment 0.83 -17.33 -16.50
School community -0.23 -0.06 -0.29
School: % disadvantaged students -0.33 3.71 3.38
Ability grouping -0.06 -0.99 -1.05
Remedial lessons 0.06 6.16 6.22
Severe absenteeism -0.54 6.91 6.37
Shortage buildings 1.42 -0.05 1.37
Shortage teachers -0.06 0.21 0.15
Index of good attendance -1.29 -2.46 -3.75
Teacher age 0.35 -3.32 -2.97
Teacher gender 0.07 6.17 6.24
Teacher experience -0.14 -18.34 -18.48
Teacher education 0.06 -6.17 -6.11
Teacher certification 1.59 14.29 15.88
Teacher feels safe/unsafe -0.27 5.55 5.28
Teacher satisfaction 0.12 -5.00 -4.88
Pay incentives 1.68 -2.40 -0.72
Approximation error 5.24 -5.72 -0.48
Constant - 63.65 63.65
Total 7.31 26.97 34.28
P90
Age of student -0.32 0.39 0.07
Gender of student -0.03 -0.55 -0.58
Language of test at home 0.01 0.19 0.20
Books -0.02 -0.16 -0.18
Calculator at home 0.14 0.00 0.14
Desk at home 0.00 -1.34 -1.34
Parentsâ€™ education -0.62 -1.26 -1.88
Parents born/not born in country -0.03 -1.84 -1.87
Paid work 0.86 -0.23 0.63
Homework 0.28 -4.48 -4.2
Total school enrolment 0.46 -12.14 -11.68
School community -0.05 0.38 0.33
School: % disadvantaged students -0.09 -0.56 -0.65
Ability grouping -0.09 -0.19 -0.28
Remedial lessons 0.04 1.68 1.72
Severe absenteeism -0.26 1.66 1.40
Shortage buildings 0.88 0.05 0.93
Shortage teachers -0.13 0.06 -0.07
Index of good attendance -0.76 1.25 0.49
Teacher age -0.09 -0.65 -0.74
Teacher gender -0.01 11.07 11.06
Teacher experience -0.03 -9.77 -9.80
Teacher education 0.00 -3.77 -3.77
Teacher certification 0.92 5.33 6.25
Teacher feels safe/unsafe -0.17 3.59 3.42
Teacher satisfaction 0.09 -4.42 -4.33
Pay incentives 0.70 -0.08 0.62
50
Approximation error 3.88 -4.35 -0.47
Constant - 51.40 51.40
Total 5.05 32.06 37.11
N 11,892
2003: 5,100
2007: 6,792
51
Table A5b: Detailed decomposition of change in 8th grade Science score at percentiles:
Ghana 2003-2007
Percentile/Characteristic Characteristics Coefficients Total Change
P10
Age of student -0.18 0.61 0.43
Gender of student -0.04 -0.75 -0.79
Language of test at home -0.01 0.90 0.89
Books 0.97 0.35 1.32
Calculator at home 0.06 0.00 0.06
Desk at home 0.02 -0.11 -0.09
Parentsâ€™ education -2.61 -1.86 -4.47
Parents born/not born in country -0.05 -5.62 -5.67
Paid work 1.34 -0.11 1.23
Homework 1.58 2.85 4.43
Total school enrolment 0.30 -6.03 -5.73
School community -0.74 0.03 -0.71
School: % disadvantaged students -0.01 3.92 3.91
Ability grouping 0.02 -1.91 -1.89
Remedial lessons 0.43 -0.14 0.29
Severe absenteeism -0.19 3.69 3.50
Shortage buildings -1.04 -0.09 -1.23
Shortage teachers 0.19 0.26 0.45
Index of good attendance 0.38 5.65 6.03
Teacher age 0.34 -1.15 -0.81
Teacher gender 0.09 -1.78 -1.69
Teacher experience -0.09 -0.48 -0.57
Teacher education -0.06 -1.05 -1.11
Teacher certification -0.73 6.93 6.20
Teacher feels safe/unsafe -0.32 4.29 3.97
Teacher satisfaction -0.45 7.03 6.58
Pay incentives 0.89 -2.00 -1.11
Approximation error 0.22 0.61 0.83
Constant - 37.83 37.83
Total 0.46 51.40 51.86
P20
Age of student -0.40 0.39 -0.01
Gender of student -0.05 -1.15 -1.20
Language of test at home -0.01 1.42 1.41
Books 0.89 0.20 1.09
Calculator at home 0.03 0.00 0.03
Desk at home 0.03 -0.61 -0.58
Parentsâ€™ education -2.03 -1.00 -2.03
Parents born/not born in country -0.02 -11.70 -11.72
Paid work 1.38 -0.17 1.21
Homework 1.36 -3.95 -2.59
Total school enrolment 0.36 -7.72 -7.36
School community -1.61 -0.60 -2.21
School: % disadvantaged students 0.11 5.10 5.21
Ability grouping -0.53 -0.21 -0.74
Remedial lessons 0.31 -0.50 -0.19
Severe absenteeism -0.22 3.53 3.31
Shortage buildings -1.22 -0.07 -1.29
Shortage teachers 0.12 0.31 0.43
Index of good attendance 0.19 7.10 7.29
Teacher age 0.60 -2.20 -1.60
52
Teacher gender 0.07 -1.09 -1.02
Teacher experience -0.11 -2.22 -2.33
Teacher education -0.04 -1.67 -1.71
Teacher certification -0.07 5.62 5.55
Teacher feels safe/unsafe -0.31 1.01 0.70
Teacher satisfaction -0.31 6.33 6.02
Pay incentives 0.65 -0.15 0.50
Approximation error -0.66 1.40 0.74
Constant - 60.33 60.33
Total -1.47 57.37 55.90
P30
Age of student -0.79 1.38 0.59
Gender of student -0.08 -0.22 -0.30
Language of test at home -0.02 1.76 1.74
Books 1.02 0.25 1.27
Calculator at home -0.11 0.00 -0.11
Desk at home 0.05 -0.34 -0.29
Parentsâ€™ education -2.87 -1.20 -4.07
Parents born/not born in country -0.01 -8.93 -8.94
Paid work 1.64 -0.08 1.56
Homework 1.71 7.70 9.41
Total school enrolment 0.81 -1.67 -0.86
School community -1.80 -0.21 -2.01
School: % disadvantaged students 0.01 6.48 6.49
Ability grouping -0.39 -1.18 -1.57
Remedial lessons 0.00 -1.73 -1.73
Severe absenteeism -0.31 2.85 2.54
Shortage buildings -1.43 -0.15 -1.58
Shortage teachers 0.17 0.28 0.45
Index of good attendance -0.04 2.61 2.57
Teacher age 0.62 -1.29 -0.67
Teacher gender 0.15 -4.22 -4.07
Teacher experience -0.09 -3.72 -3.81
Teacher education -0.01 -4.75 -4.76
Teacher certification 0.09 3.35 3.44
Teacher feels safe/unsafe -0.46 3.21 2.75
Teacher satisfaction -0.22 5.32 5.10
Pay incentives 0.76 -1.85 -1.09
Approximation error -1.37 1.90 0.53
Constant - 51.89 51.89
Total -3.05 57.56 54.51
P40
Age of student -0.93 0.20 -0.73
Gender of student -0.10 -0.84 -0.94
Language of test at home -0.01 0.68 0.67
Books 0.86 0.32 1.18
Calculator at home -0.16 0.00 -0.16
Desk at home 0.05 -1.47 -1.42
Parentsâ€™ education -3.53 -0.95 -5.00
Parents born/not born in country -0.03 -13.20 -13.23
Paid work 1.88 -0.44 1.44
Homework 1.86 1.00 2.86
Total school enrolment 1.03 -8.56 -7.53
School community -2.55 0.14 -2.41
School: % disadvantaged students -0.17 10.71 10.54
Ability grouping -0.79 -0.87 -1.66
53
Remedial lessons -0.13 -1.38 -1.51
Severe absenteeism -0.45 2.55 2.10
Shortage buildings -0.71 0.00 -0.71
Shortage teachers 0.03 0.66 0.69
Index of good attendance -0.17 7.15 6.98
Teacher age 0.69 -1.65 -0.96
Teacher gender 0.17 -2.88 -2.71
Teacher experience -0.02 -12.24 -12.26
Teacher education -0.02 -2.87 -2.89
Teacher certification -0.01 7.69 7.68
Teacher feels safe/unsafe -0.50 3.73 3.23
Teacher satisfaction -0.50 10.59 10.09
Pay incentives 1.07 -2.63 -1.56
Approximation error -0.71 1.68 0.97
Constant - 54.50 54.50
Total -4.00 51.87 46.87
P50
Age of student -1.15 0.14 -1.01
Gender of student -0.13 0.48 0.35
Language of test at home -0.01 0.76 0.75
Books 0.60 0.22 0.82
Calculator at home -0.19 0.00 -0.19
Desk at home 0.05 -0.56 -0.51
Parentsâ€™ education -4.89 -2.61 -7.5
Parents born/not born in country -0.01 -7.77 -7.78
Paid work 2.55 0.07 2.62
Homework 2.11 14.09 16.20
Total school enrolment 1.39 3.06 4.45
School community -4.24 1.63 -2.61
School: % disadvantaged students -0.29 10.16 9.87
Ability grouping -1.21 3.58 2.37
Remedial lessons 0.04 0.24 0.28
Severe absenteeism -0.66 9.34 8.68
Shortage buildings -0.37 -0.02 -0.39
Shortage teachers -0.12 0.60 0.48
Index of good attendance -0.40 1.29 0.89
Teacher age 0.88 -2.42 -1.54
Teacher gender 0.15 -4.73 -4.58
Teacher experience -0.05 -8.26 -8.31
Teacher education 0.05 -4.43 -4.38
Teacher certification -0.24 7.88 7.64
Teacher feels safe/unsafe -0.57 4.25 3.68
Teacher satisfaction -0.76 8.14 7.38
Pay incentives 1.59 -5.89 -4.30
Approximation error 1.04 -0.36 0.68
Constant - 15.10 15.10
Total -5.21 45.29 40.08
P60
Age of student -0.43 0.30 -0.13
Gender of student -0.05 -1.64 -1.69
Language of test at home 0.00 -0.04 -0.04
Books 0.09 0.42 0.51
Calculator at home -0.02 0.00 -0.02
Desk at home 0.02 -3.06 -3.04
Parentsâ€™ education -2.12 -1.03 -3.15
Parents born/not born in country -0.01 -14.32 -14.33
54
Paid work 1.13 -0.72 0.41
Homework 0.71 -12.69 -11.98
Total school enrolment 0.57 -17.66 -17.09
School community -1.32 -0.16 -1.48
School: % disadvantaged students 0.01 6.64 6.65
Ability grouping -0.58 -1.60 -2.18
Remedial lessons 0.13 0.46 0.59
Severe absenteeism -0.30 0.73 0.43
Shortage buildings 0.14 -0.01 0.13
Shortage teachers -0.09 1.05 0.96
Index of good attendance -0.37 7.56 7.19
Teacher age 0.03 -1.44 -1.41
Teacher gender 0.08 0.72 0.80
Teacher experience 0.03 -15.21 -15.18
Teacher education 0.02 1.93 1.95
Teacher certification 0.33 13.57 13.90
Teacher feels safe/unsafe -0.22 0.73 0.51
Teacher satisfaction -0.23 4.41 4.18
Pay incentives 0.96 -0.51 0.45
Approximation error -3.09 4.24 1.15
Constant - 67.73 67.73
Total -4.75 40.49 35.74
P70
Age of student -0.69 -1.47 -2.16
Gender of student -0.08 0.29 0.21
Language of test at home 0.00 0.50 0.50
Books 0.04 0.07 0.11
Calculator at home 0.05 0.00 0.05
Desk at home 0.04 -0.32 -0.28
Parentsâ€™ education -2.44 -1.72 -4.16
Parents born/not born in country -0.02 -3.53 -3.55
Paid work 1.86 0.14 2.00
Homework 0.93 5.97 6.90
Total school enrolment 0.92 -0.04 0.88
School community -0.92 0.31 -0.61
School: % disadvantaged students -0.04 3.19 3.15
Ability grouping -1.11 3.38 2.27
Remedial lessons 0.07 0.58 0.65
Severe absenteeism -0.43 6.23 5.80
Shortage buildings 1.08 0.02 1.10
Shortage teachers -0.15 0.47 0.32
Index of good attendance -0.85 -4.80 -5.65
Teacher age -0.25 -1.65 -1.90
Teacher gender 0.10 -1.61 -1.51
Teacher experience 0.10 -9.41 -9.31
Teacher education -0.01 -4.19 -4.20
Teacher certification 1.41 -0.19 1.22
Teacher feels safe/unsafe -0.34 3.38 3.04
Teacher satisfaction -0.29 1.26 0.97
Pay incentives 1.79 -8.02 -6.23
Approximation error -1.10 1.78 0.68
Constant - 42.64 42.64
Total -0.67 34.75 34.08
P80
Age of student -0.44 0.62 0.18
Gender of student -0.04 -0.26 -0.30
55
Language of test at home 0.00 0.35 0.35
Books -0.14 0.02 -0.12
Calculator at home 0.01 0.00 0.01
Desk at home 0.02 -0.77 -0.75
Parentsâ€™ education -1.09 -0.73 -1.82
Parents born/not born in country -0.02 -4.10 -4.12
Paid work 0.89 -0.13 0.76
Homework 0.34 -1.59 -1.25
Total school enrolment 0.44 -7.41 -6.97
School community -0.35 0.22 -0.13
School: % disadvantaged students -0.19 0.38 0.19
Ability grouping -0.51 0.69 0.18
Remedial lessons 0.09 1.29 1.38
Severe absenteeism -0.21 2.48 2.27
Shortage buildings 1.28 0.09 1.37
Shortage teachers -0.08 0.42 0.34
Index of good attendance -0.40 2.49 2.09
Teacher age -0.07 -0.47 -0.54
Teacher gender 0.03 1.23 1.26
Teacher experience 0.03 -9.08 -9.05
Teacher education 0.00 -1.68 -1.68
Teacher certification 0.45 2.89 3.34
Teacher feels safe/unsafe -0.10 1.01 0.91
Teacher satisfaction -0.10 -1.91 -2.01
Pay incentives 0.93 -2.86 -1.93
Approximation error -0.30 0.55 0.25
Constant - 44.62 44.62
Total 0.29 28.90 29.19
P90
Age of student -0.90 4.61 3.71
Gender of student -0.08 -1.64 -1.72
Language of test at home 0.02 1.54 1.56
Books -0.59 0.45 -0.14
Calculator at home 0.04 0.00 0.04
Desk at home 0.03 2.00 2.03
Parentsâ€™ education -1.68 -0.22 -1.90
Parents born/not born in country -0.02 -10.89 -10.91
Paid work 1.89 -0.59 1.30
Homework 0.53 -13.00 -12.47
Total school enrolment 1.19 -23.48 -22.29
School community -0.82 0.30 -0.52
School: % disadvantaged students -0.42 -8.37 -8.79
Ability grouping -1.23 -0.41 -1.64
Remedial lessons 0.36 3.44 3.80
Severe absenteeism -0.45 2.31 1.86
Shortage buildings 3.83 0.38 4.21
Shortage teachers -0.10 1.23 1.13
Index of good attendance -1.41 7.57 6.16
Teacher age -0.13 -1.45 -1.58
Teacher gender -0.07 15.30 15.23
Teacher experience -0.07 -22.52 -22.59
Teacher education -0.07 -8.31 -8.38
Teacher certification 1.74 -6.47 -4.73
Teacher feels safe/unsafe -0.15 0.34 0.19
Teacher satisfaction -0.24 -7.53 -7.77
Pay incentives 1.50 4.23 5.73
56
Approximation error 0.58 -0.10 0.48
Constant - 87.42 87.42
Total 2.84 23.61 26.45
N
2003: 5,100
2007: 6,792
57
Graph A2a: Mathematics: Characteristics component
Effects of characteristics
30
20
Log wage effects
10
0
0 .2 .4 .6 .8 1
Quantile
Graph A2b: Mathematics: Median Coefficients
Effects of median coefficients
40
35
Log wage effects
30
25
20
15
0 .2 .4 .6 .8 1
Quantile
58
Graph A2c: Mathematics: Residuals
Effects of residuals
10
0
Log wage effects
-10
-20
0 .2 .4 .6 .8 1
Quantile
Graph A2d: Science: Coefficients component
Effects of characteristics
30
Log wage effects
20
10
0
0 .2 .4 .6 .8 1
Quantile
59
Graph A2e: Science: Median Coefficients
Effects of median coefficients
60
40
Log wage effects
20
0
0 .2 .4 .6 .8 1
Quantile
Graph A2f: Science: Residuals
Effects of residuals
20
10
Log wage effects
0
-10
-20
0 .2 .4 .6 .8 1
Quantile
60