Post on 14-Mar-2020
EDUCATION AS ABSORPTIVE CAPACITY AND ITS ROLE FOR
ECONOMIC GROWTH: AN ASSESSMENT OF THE ECOLOGICAL
FALLACY
Authors and e-mails of them:
Laura Márquez-Ramos: laura.marquez-ramos@adelaide.edu.au
Estefanía Mourelle: estefania.mourelle@udc.es
Department:
Laura Márquez-Ramos: Institute for International Trade.
Estefanía Mourelle: Economics.
University:
Laura Márquez-Ramos: The University of Adelaide (Australia).
Estefanía Mourelle: Universidade da Coruña (Spain).
Subject area: Growth, development, competitiveness.
Abstract:
Might economic growth behave in a different manner depending on the evolution of
absorptive capacity? In this research, we consider education as a channel for economic
growth since it is a key element for a country’s absorptive capacity. Additionally,
education is a relevant topic in the decentralization debate such that analyzing the
aggregate link between absorptive capacity and economic growth may lead to an
ecological fallacy. Therefore, we carry out both an aggregate (country level) and a
disaggregated (regional level) analysis to study the role of absorptive capacity in
economic growth.
We hypothesize the existence of a threshold for absorptive capacity, so that once it is
exceeded, economic growth shows different characteristics. Addressing this question
requires moving from a linear framework to a nonlinear one, and we resort to Smooth
Transition specifications. This is relevant because economic growth presents
asymmetries (and, subsequently, nonlinearities) that are not able to be considered in
linear specifications. Our empirical analysis for Spain points to the existence of
nonlinearities in the relationship between absorptive capacity and economic growth at
country level. This asymmetric evolution is clearly appreciated in the two dimensions of
absorptive capacity taken into account (i.e., secondary and tertiary education). Next, as
different solutions emerge in different regions, we provide a regional analysis for a
number of representative Spanish regions. Our evidence provides important insights for
education such as the fact that both secondary and tertiary education matter for
economic growth and that nonlinearities of this relationship should be taken on board.
Keywords: education; absorptive capacity; economic growth; nonlinearities; regions;
ecological fallacy.
JEL codes: C32, I25, R11, R15.
1. Introduction
The objective of the present paper is to analyze the relationship between education and
economic growth from a new perspective. Specifically, we understand that a country
with a population able to exploit new knowledge will perform better. Therefore,
education is considered as a channel for economic growth since it constitutes an
intrinsic mechanism of knowledge absorption1 and then, it is a key element for a
country’s absorptive capacity.
Following Cohen and Levinthal (1990), Zahra and George (2002), and Márquez-Ramos
and Martínez-Zarzoso (2010), we consider absorptive capacity as the ability to put
information from abroad into practice, which plays a key role in economic development.
At aggregate (country) level, Márquez-Ramos and Martínez-Zarzoso (2010)
distinguished between potential absorptive capacity, a function of the acquisition and
assimilation capacities of a country, whereas realized absorptive capacity was
considered as a function of transformation and exploitation capabilities. In this vein, we
focus on exploitation capabilities and examine their role in economic growth. In other
words, education is considered as a channel for economic growth since it is a key
1 See, for example, the illustration of the role of education in the aerospace sector for establishing sufficient levels of absorptive capacity in Asia (van der Heiden et al., 2015).
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element for a country’s absorptive capacity and then, we hypothesize that gross
enrollment ratios are good proxies for absorptive capacity.
It is well known from the growth, the education, and the development literature that
primary education has a relatively higher impact on individual wages than secondary
education and tertiary education (i.e., over certain domains there are decreasing returns
to education). Thus, it is also well know that nonlinearities exist on the micro level, and
macro literature has also explored diverse effects. For example, previous studies have
shown that country-heterogeneity exists, and that estimated returns to education are, in
general, higher in developing countries than in developed countries (Duflo, 2001).
Moreover, there is a very large macro (cross-country and panel) literature analyzing the
relevance of education and economic growth which has focused on different types of
education. However, the results obtained at macroeconomic level are contradictory
(Krueger and Lindahl, 2001; Armellini, 2012).
In this research, we are interested in absorptive capacity, which has a different
interpretation and links the existing brands of the literature to the fields of dynamic
capability, organizational learning and knowledge management (Cohen and Levintahl,
1990; Easterby-Smith et al. 2008). As a consequence, our interest goes beyond the
consideration of years of schooling as a potential determinant of economic growth: we
generalize to countries’ exploitation capabilities and explore the inherent nonlinearities
in the absorptive capacity-economic growth relationship. This is relevant because
absorptive capacity can be seen as a process and organizations do not absorb
information without effort (Easterby-Smith et al. 2008). Therefore, a context that
supports education organizations to generate both “users” and “creators” of those tools
required for processing innovation and creation will play a key role in the relationship
economic growth-absorptive capacity. This is especially important in a context
characterized by uncertainty about how the future scenario will be in the educational
system (Márquez-Ramos and Mourelle, 2016).
This research has a bearing in the literature of education and economic growth, which
has analyzed the causal effect of education on countries’ economic performance using a
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variety of measures and quantitative tools for cross-country, time series and panel data.
In this brand of the existing literature, Hanushek and Wößmann (2010) highlighted that
economic growth is affected by the knowledge of people.
The importance of nonlinearities has previously been identified. As Krueger and
Lindahl (2001) pointed out: “It is common in the empirical growth literature to assume
that the initial level of education has a linear effect on sub-sequent GDP growth (…)
that linearity is unlikely to hold. The importance of the linearity assumption has not
been explored extensively in growth models” (pp. 1129-1130). Surprisingly, more than
a decade after this claim was made, linearity is usually assumed in this field of the
literature (see, for example, Self and Grabowski, 2004; Cohen and Soto, 2007; Afzal et
al., 2011; Armellini, 2012; Jalil and Idrees, 2013). However, economic growth presents
asymmetries and, as a consequence, nonlinearities, that cannot be considered in linear
specifications.
The present paper brings into question the linearity assumption by using time series
techniques for 1971-2013 in Spain, as we believe that the role of absorptive capacity
can be that of a force driving a possible nonlinear behavior in the economic growth.
Spain is an interesting country to be explored because of its high degree of
decentralization, through which different solutions emerge in different regions.
Therefore, heterogeneity in Spain among regions should matter a great deal for obtained
results. Indeed, education is a relevant topic in the decentralization debate such that
analyzing the aggregate link between absorptive capacity and economic growth may
lead to an ecological fallacy: Existing analyses in the education-economic growth
literature are ecological studies that make large scale comparisons between groups of
people, i.e. the effect of the education status of countries on economic growth.
However, ecological studies do not allow examination of individuals and then, they are
open to bias (see, for example, Sedgwick 2011).
In our empirical analysis, we incorporate a number of additional controls that are
closely related to both absorptive capacity and economic growth, as they also affect this
relationship; based on the applied literature, we account for the potential effects that the
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physical capital, the labor force and the public expenditure on education may have on
the economic activity. Although there are a number of studies that have considered a
setting of time series to analyze the relationship between education and economic
growth (see, for example, Self and Grabowski, 2004, for India, and Afzal et al., 2011,
for Pakistan), they do not understand education as absorptive capacity. Additionally,
focusing on the case of Spain is of great interest, mainly because Spain is a country with
a solid trajectory in its education system and it is also a developed economy that is
representative of a large number of countries. In this case study, we are able to provide
evidence of the nonlinear relationship between absorptive capacity and economic
growth at both country and regional level. This analysis will also help us to shed light
on the question posed by the existing literature about the positive, although still without
consensus, impact of education on economic growth.
The paper is organized as follows. Section 2 presents the methodology employed.
Section 3 explains the empirical results obtained at country-level, whereas Section 4
presents the results at regional level and tests the ecological fallacy. Finally, Section 5
presents the conclusions and discussion.
2. Methodology
2.1. The model
One common assumption when analyzing the relationship between two variables is that
of linearity. Actually, the majority of empirical papers centered on the education-
economic growth link are grounded on the linear consideration. Nevertheless, this
assumption is too strong if what we aim to analyze is the relationship between
absorptive capacity and economic growth, as this would mean that the parameters in the
relationship do not change over time. This is, however, unrealistic as it would reflect
that learning and innovation processes are linear (Márquez-Ramos and Mourelle, 2016).
We consider that a nonlinear modelling is more appropriate and, by using Smooth
Transition Regression (STR) models, we allow for the parameters to change depending
on a shock, which is defined on an ad hoc basis. This framework provides us with more
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flexibility when studying the dynamics of economic growth and other variables related
to absorptive capacity. The reason for selecting this type of models is in line with the
idea of the potential existence of a threshold that determines the behavior of the
economic growth according to some variable.
Smooth Transition (ST) models belong to the family of state-dependent models where
the data-generating process is linear but switches between a certain number of regimes
according to some rule. This parameterization allows for capturing different types of
behavior that a linear model cannot appropriately characterize; once the state is given,
the model is locally linear, involving an easy interpretation of the local dynamics. In
contrast to other regime-switching models (such as Markov-Switching or threshold
models), STs consider that the change between regimes is smooth over time, rather than
abrupt, which is normally a more realistic situation; in any case, STs nest some
threshold models as particular cases.
STs have been popular in the last decades in economic time series, proving good
performance in capturing cyclical behavior in macroeconomic variables (see Teräsvirta
and Anderson, 1992; Mejía-Reyes et al., 2010; and Cuestas and Mourelle, 2011, among
others). For further details on these models, see Teräsvirta (1994, 1998) and van Dijk et
al. (2002).
In this paper we resort to the most general ST model, the STR, as it permits the
incorporation of exogenous variables in addition to the endogenous structure. Let yt be a
stationary, ergodic process and, without loss of generality, only one exogenous variable
xt. The model is given by:
y t=w t' π+(w t
' θ ) F ( st ; γ , c )+ut, (1)
where w t= (1 , y t−1, …, y t−p 1 ;x t , x t−1 ,…,x t−p 2) ' is a vector of regressors;
π=( π0 , π1 , …, π p ) ' and θ=(θ0 , θ1 ,…,θp ) ' are parameter vectors (p=p1+p2+1); and ut is
an error process, ut Niid (0, 2). Likewise, F(.) is a transition function customarily
bounded between 0 and 1, implying that the STR coefficients vary between j and j + j
(j = 0, ..., p), respectively. The regime at each t is determined by the transition variable,
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st, and the associated value F(st); the transition variable can be a lagged endogenous
variable, an exogenous variable or just another variable. Finally, the slope parameter γ
defines the smoothness of the transition, so that the higher it is, the more rapid the
change; the location parameter c indicates the threshold between the two regimes.
In its basic version, the regime-switching STR specification considers two distinct
regimes corresponding to F=0 and F=1, and the transition from one regime to the other
is smooth over time, meaning that parameters in (1) gradually change with the transition
variable. Two formulations are mainly used for F: the logistic and the exponential
function. In the logistic model the extreme regimes are associated with st values far
above or below c, where dynamics may be different; otherwise, in the exponential case
the extreme regimes are related to low and high absolute values of s t, with rather similar
dynamics, which can be different in the transition period. According to these
definitions, intuitively speaking, the logistic transition appears to be the most suitable
for describing the relationship between absorptive capacity and economic growth, as
there is no reason to assume a similar effect for a positive and a negative variation in the
absorptive capacity of a country on its economic activity.
2.2. Modelling procedure
The STR modeling cycle has traditionally relied on the iterative methodology proposed
by Teräsvirta (1994) for the univariate case: specification, estimation and evaluation of
the model. The usual starting point is finding out the linear model that better
characterizes the behavior of the series under study; once this specification is obtained,
its adequacy to the relation being analyzed is tested. In case the null hypothesis of a
linear process against the alternative of a STR one is rejected, a preliminary
specification of the nonlinear model is defined. Then, the parameters of the STR
specification are estimated by nonlinear least squares.
Nevertheless, an important branch of the literature on this specification does not follow
that procedure in such a strict manner, as, among other issues, linearity tests suffer from
size and power problems under certain circumstances (see van Dijk et al., 2002, for
more information). In this sense, it is argued that it is possible to develop nonlinear
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formulations that improve the fit of the linear ones without having to do the previous
tests, i.e., the data itself would reveal the potential existence of nonlinearities; the
validation process will determine whether the model has correctly captured the
nonlinear behavior or not (Granger and Teräsvirta, 1993).
This alternative procedure is done by carrying out an extensive search of STR models
by defining a grid for (γ, c). This is the strategy proposed by several authors as Öcal and
Osborn (2000), or Sensier et al. (2002), among others, and the one we adopt in our
study; we try for different values of γ and use the sample mean of the transition variable
for c. Where parameter convergence is reached, models are subject to further
refinement; cross-parameter restrictions are evaluated in order to increase efficiency and
no significant coefficients are dropped to conserve degrees of freedom.
As aforementioned, less emphasis is given to the initial stages of the modelling process
in exchange for paying special attention to the validation of the estimated model, as it
will unveil any possible inadequacy of the specification (van Dijk et al. 2002). Most
part of the tests commonly applied to dynamic models are also valid in the STR
framework. Besides, STR estimation is based under the assumption of no residual
autocorrelation and parameter constancy; therefore, it is necessary to test these
hypotheses. Eitrheim and Teräsvirta (1996) develop several evaluation tests especially
derived for ST models, as the test of residual serial independence against processes of
different orders and the test of parameter constancy against changing parameters under
the alternative, which refer to the two previous assumptions. In addition, these authors
define the test of no remaining nonlinearity in the residuals.
In this paper, we use the following evaluation tests. As diagnostic statistics, we employ
the adjusted determination coefficient and we pay particular attention to the variance
ratio of the residuals from the nonlinear model and the best linear regression estimated
by Ordinary Least Squares (OLS), as it provides relevant information on the
explanatory power of both specifications. Regarding the misspecification tests, those
considered are the three already mentioned specific tests for STs. Finally, these
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evaluation tests are completed with an analysis of the estimated residuals in order to
describe the behavior of the STR model more in depth.
3. Empirical results at country-level
3.1. Data and preliminary analysis
As mentioned above, the data used for this empirical application is centered on the
Spanish case; we carry out both an aggregate study at country level and a disaggregated
analysis for a group of regions, so as to detect any evidence of ecological fallacy. Table
A.1 in the Appendix displays the variables used in the empirical analysis, their
definitions and sources.
GDP is traditionally considered for measuring economic activity. We measure
absorptive capacity by using enrollment ratios for secondary and tertiary education in
Spain (we denominate dimension 1 to our measure for secondary education and
dimension 2 to tertiary education). We define one proxy for labor force for each
educational level; in particular, we calculate the proportion of active population with
secondary (tertiary) education over total active population in Spain. In the context of our
research, these two variables proxy for the prior knowledge base in Spain. For the
physical capital, we use real Gross Fixed Capital Formation; we include investment as it
exerts a relevant indirect effect on education. Finally, we use the government
expenditure on education (as a percentage of GDP) as a control variable that allows to
isolate the relationship between absorptive capacity and economic growth. The sample
goes from 1971 to 2013 and data have annual frequency. All variables are used in their
logarithmic transformation.
Before focusing on the relationship between economic growth and absorptive capacity,
a statistical processing of the information is required, with the aim of getting a suitable
form of the variables taken into account. In particular, one assumption of ST models is
that all the variables involved in the study must be stationary. In this paper, we have
applied the Ng and Perron (2001) unit root tests to analyze the order of integration of
our variables. These authors propose several unit root tests (MZα, MZt, MSB and MPt) 9
with the aim of improving the performance of existing ones, in particular regarding size
and power features. In this paper, the Ng-Perron tests include intercept and linear trend
as deterministic components, and the lag length has been selected by means of the
modified Akaike Information Criterion proposed by the authors. The null hypothesis is
the existence of unit roots. The test statistics are displayed in Table 1.
TABLE 1
Ng-Perron unit root test results
Variable MZα MZt MSB MPt
lGDPt -12.764 -2.482 0.194 7.382
lENRSt -4.395 -1.464 0.333 20.569
lENRTt -3.210 -1.065 0.332 24.209
lPHYt -18.808 -2.948 0.157 5.550
lLABSt -12.312 -2.283 0.185 8.436
lLABTt -5.759 -1.696 0.295 15.822
lEXPt -2.645 -0.910 0.344 26.870
Note: l stands for the logarithm. The asymptotic critical values are:
Significance level MZα MZt MSB MPt
1% -23.8000 -3.42000 0.14300 4.03000
5% -17.3000 -2.91000 0.16800 5.48000
10% -14.2000 -2.62000 0.18500 6.67000
Considering the asymptotic critical values defined in Ng and Perron (2001), all the
variables considered in the study are unit root processes. These results point out the
need for applying regular differences in all (the logarithms of) our variables.
Finally, so as to provide an overview of the selected magnitudes in Spain, we display
their evolution in differences in Figures 1 and 2.
10
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011
GDP ENRS PHY LABS EXP
FIGURE 1. Evolution of the selected variables over time, in differences (secondary education)
Notes. ENRS denotes enrollment ratio secondary education; PHY: physical capital; LABS: labor force with secondary education; EXP: government expenditure on education.
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011
GDP ENRT PHY LABT EXP
FIGURE 2. Evolution of the selected variables over time, in differences (tertiary education)
Notes. ENRT: enrollment ratio tertiary education; PHY: physical capital; LABT: labor force with tertiary education; EXP: government expenditure on education.
From these graphs we can highlight several features. The proxies used for exploitation
capability show a satisfactory evolution over time. This is especially remarkable for
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tertiary education, which increases at a higher speed than secondary education; the latter
even experiences negative variations in a number of periods. In general, all variables
display a favorable evolution in recent decades, in particular after the dictatorship
period and the economic crisis of the 70’s. Thus, mid 70’s is a crucial period for public
government expenditure on education and labor force with tertiary education starting to
rise; the growth rates for labor force with secondary education show an almost
continuous downward trend. In the 80’s, the physical capital experiences a great
increase until the breakout of the last economic crisis. The good evolution of the GDP is
accompanied by a good evolution of the remaining variables.
3.2. Main results
Three main aspects must be remarked. First, as specific data regarding enrollment and
active population ratios for secondary and tertiary education is available, the estimation
process has two branches that allow for distinguishing two dimensions of absorptive
capacity, one for each level of education. Second, four explanatory variables are
initially included in the analysis for each branch: education, physical capital, labor
force, and public government expenditure on education. Third, we consider up to two
lags of the variables in the regression analysis, so as to account for the effect of their
most recent history on economic growth.
The role of linearity tests is more that of a tool for specifying the model rather than
strictly testing a theory in this paper (see Teräsvirta, 1998, and Skalin and Teräsvirta,
2002); as stated previously in section 2, the core part of our modelling process is the
validation stage. At this point we should account for the fact that our sample could be
affected by the “baby boom” process experienced in Spain in the 60’s (and potentially
reflected in the enrollment ratios). Usual linearity tests (Teräsvirta, 1994, 1998) can be
misleading in the presence of outliers. van Dijk et al. (1999) advocate linearity tests that
display a better level and power behavior than the standard ones in case outliers are
present. We carried out these tests robust to outliers with the transition variable assumed
to be the difference of (the logarithm of) the gross enrollment ratio up to two lags. Table
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2 presents the results, where the null hypothesis is a linear behavior of the variable
under study.
TABLE 2
Linearity tests against logistic smooth transition regression (p-values). Country-level analysis
Transition variable Secondary education Tertiary education
ΔlENRS/Tt 0.0038 0.0022
ΔlENRS/Tt-1 0.5345 0.0382
ΔlENRS/Tt-2 0.7189 0.1960
Note. Δ denotes first differences.
Rejection of linearity is evidenced in half the cases. We should highlight the fact that
these tests involve working with a great number of cross products and our sample size is
not very high, so the obtained results must be taken with caution. Thus, as the results are
not conclusive for the two educational levels, we follow the aforementioned strategy of
an extensive search of STR models.
The starting point of the modelling procedure consists of finding out the linear
specification that would best describe the behavior of the series under study. OLS
estimation is carried out; all parameters are introduced initially, but then those no
significant at a 0.05 level are successively excluded.2 The next stage focuses on the
estimation of the nonlinear models. We achieve valid STR specifications for secondary
and tertiary education.
As our main purpose is to study the impact of absorptive capacity on economic growth,
the decision on the transition variable is clear: the enrollment ratio. Then, this variable
plays a double role in the explanation of the economic growth dynamics. On the one
hand, it represents the source of nonlinearities in the evolution of the economic growth;
on the other hand, it is also a determining factor of the dynamics of GDP growth. The
2 The resulting models are not reported, but are available from the authors upon request.13
estimated models are presented in Table 3, along with several diagnostic statistics and
misspecification tests.
TABLE 3
Estimated STR models. Country-level analysis
Secondary education Tertiary educationTransition variable: ΔlENRSt-1 Transition variable: ΔlENRTt-2
Linear part Nonlinear part Linear part Nonlinear part
ΔlGDPt-1 -1.31 (0.26) 3.97 (1.38) 0.66 (0.15) -1.35 (0.28)ΔlGDPt-2 1.43 (0.25) -2.66 (0.80) 0.32 (0.14)ΔlENRTt 0.18 (0.06) -0.34 (0.12)ΔlENRTt-1 -0.50 (0.12) 0.67 (0.14)ΔlENRTt-2
ΔlPHYt 0.56 (0.14) 0.23 (0.03)ΔlPHYt-1 0.56 (0.07) -1.51 (0.48) 0.18 (0.07)ΔlPHYt-2 -0.48 (0.13) 0.83 (0.27) -0.18 (0.07) 0.22 (0.07)ΔlLABS/Tt -0.85 (0.32) 1.26 (0.53) 0.07 (0.03) 0.07 (0.03)ΔlLABS/Tt-1 1.07 (0.36) -1.76 (0.62) 0.17 (0.05)ΔlLABSt-2 0.16 (0.09)ΔlEXPt 0.08 (0.04)ΔlEXPt-1 0.21 (0.08) -0.15 (0.08)ΔlEXPt-2 -0.08 (0.04)γ 2.17 (1.00) 66.65 (375.65)c 0.01 (0.01) 0.05 (0.00)
R2 0.92 0.87
s2/s2L 0.25 0.33
AUTO 2.89 (0.08) 3.52 (0.06)NL 2.60 (0.23) 2.50 (0.32)PC 1.40 (0.38) 1.09 (0.55)
Notes. Δ denotes first differences. Values after regression coefficients are SEs of the estimates; R2is the adjusted determination coefficient; s2/s2
L is the variance ratio of the residuals from the STR model and the linear regression; AUTO is the test for residual autocorrelation of order 2; NL is the test for no remaining nonlinearity; PC is the general parameter constancy test. Numbers in parentheses after evaluation statistics are p-values.
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Going first into detail on the dimension 1 of exploitation capabilities (i.e., secondary
education), we appreciate how the estimated model exhibits notably significant
coefficients that highlight the dependence of the economic growth on its own recent
history, as well as on physical capital, labor force and public government expenditure
on education. As observed, according to our results, this first dimension of absorptive
capacity is not a significant factor determining the economic activity. Figure 3 depicts
the estimated transition functions; each dot represents one observation in the sample.
FIGURE 3. Estimated transition functions. Country-level analysis
Regarding the secondary education case, the transition between regimes is logistic and
smooth, according to the value of γ, and the delay is one year. We can define a lower
extreme regime, covering from negative growth to 1.5% variation in the enrollment
ratio, and an upper extreme regime, for variations greater than 1.5%. In other words, the
Spanish economic activity will exhibit different dynamics when the enrollment ratio
grows above 1.5% than when it goes at slower pace, that is, below that threshold. This
function has a wide variation range, allowing more flexibility in the dynamics of
economic growth. The estimated value for the threshold is slightly below the enrollment
ratio mean (2%), so that the left side of the logistic function contains a lower number of
observations (66% of the total).
Based on the evaluation tests, the model presents no evidence of misspecification. The
specific tests do not detect serial dependence in the estimated residuals, there is no need
for a second transition function and parameter constancy is demonstrated. A fact to
emphasize is the high explanatory power of this model compared to the corresponding
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linear specification: according to the variance ratio, the STR model explains 75% of the
residual variance of the linear regression.
Turning now to the second dimension of exploitation capabilities (tertiary education),
results from Table 3 indicate that the estimated parameters are again highly significant.
In this case, recent history of economic growth has a significant effect on its current
state, as well as enrollment ratio, physical capital, labor force and government
expenditure on education. In contrast to the previous dimension, the enrollment ratio in
the tertiary level is a significant determinant for the economic growth dynamics in
Spain. This result indicates that higher education is a key factor for economic
development and, in terms of absorptive capacity, we interpret that it is very important
for economic growth that people in a country are “creators” of those tools required for
processing innovation and creation. According to the results obtained in our aggregate
analysis, absorptive exploitation capacity makes a difference: a higher number of
“creators” in Spain increases the country’s potential to put new information and
knowledge into practice by developing new products and processes that conduct to
economic growth.
With regard to the estimated transition function, another difference with secondary
education is the features of the transition from one regime to the other: now it is quite
abrupt (due to the large value of γ) and the delay is two years instead of one. In fact,
these extremely rapid regime changes suggest the need for threshold specifications,
strengthening the importance of using STR models (this model resembles a pure
threshold one). Therefore, economic growth appears to evolve more rapidly from one
extreme regime to the other when considering the second dimension of absorptive
capacity (i.e., tertiary education); that is, economic growth reacts in a more immediate
way to shocks in tertiary education than to shocks in secondary education. A possible
cause can be found in the high weight traditionally given to pursuing a university degree
in Spain; a historical and sociological background points to a more rooted character of
higher education in Spain than in other similar countries.
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Two regimes arise from this model: a lower extreme regime, which ranges from
negative growth to 5.2% variation in the enrollment ratio, and an upper extreme regime,
for variations greater than 5.2%. The value for the location parameter is remarkably
close to the mean of the transition variable (5.7%), so there exists a near equal
distribution between the left and the right sides of the logistic function. In addition,
there are no indications of misspecification in the model, so one may conclude that the
proposed STR is adequate, as it occurred in secondary education. Once again, this
model shows greater explanatory power than the linear formulation: the STR model
explains 67% of the residual variance of the linear regression.
In order to describe the behavior of the STR models more in depth, an analysis of the
estimated residuals has been carried out. It compares the residuals of the linear and
nonlinear specifications for secondary and tertiary education. Figure A.1 in the
Appendix is an illustrative one for this purpose, as it depicts the differences, in absolute
values, between the residuals from the linear model and the STR specification over
time. In both cases, the residuals of the STR model are lower (in absolute value) than
those of the linear regression; in particular, the nonlinear model globally lessens the
highest residuals of the linear specification in a sensible way. Moreover, divergences
between residuals are mainly positive, which favors the STR specification. These signs
reinforce the better behavior of the nonlinear model, a fact that the variance ratio had
already pointed out.
4. Testing the existence of the ecological fallacy in the education-economic growth
relationship: Results at regional level
In a first step, we construct a classification matrix to choose a representative sample of
Spanish regions for the analysis. Classifications by regional income per capita and by
regional government expenditure per capita are considered. Information in Table A.2 in
the Appendix is used to determine whether the different Spanish regions in the country
are above or below the average in both income and government expenditure in
education. For example, when income per capita in a specific region is above the
17
average over the period taken into account for all regions, then this region is considered
to be in a different cell of the classification matrix that a region that is below the
average. A representative region is selected from each of the four groups of regions
constructed (in bold in Table A.2).
Two issues must be remarked regarding data at regional level. First, as gross enrolment
ratios are not available for the Spanish regions, we use a proxy variable proposed by de
la Fuente & Doménech (2015) that is constructed as the proportion of the population for
which the maximum level of education achieved is either secondary or tertiary. Second,
with respect to government expenditure on education, we combine the government
expenditure as a percentage of GDP and the weight of each region’s GDP over the total
Spanish GDP3. In addition, the sample ranges from 1971 to 2013 except for the proxy
for absorptive capacity, which goes from 1971 to 2011, and for labor force, which starts
in 1977 (until 2013). Data have annual frequency in all cases. All variables are used in
their logarithmic transformation.
Following the preliminary analysis, we carry out the Ng-Perron unit root tests for the
different variables at regional level. As for the aggregate, all variables will be used in
their first differences.4 In a second step, we test the linearity assumption and we run the
corresponding analysis for the four regions selected. Tables A.3.A and A.3.B in the
Appendix present the results of the linearity tests, which mainly support the existence of
nonlinearities in the regions under study. In any case, to preserve the consistency with
the aggregate analysis regarding the modelling procedure, we develop an extensive
search of STRs at regional level.
The estimated STR models for the dimension of secondary and tertiary education are
presented in tables 4 and 5, respectively.
3 Note that we considered a more accurate proxy for regional public spending in education by considering the series provided by the Ministry of Education (“Recursos económicos. Gasto Público”, available at https://www.mecd.gob.es/servicios-al-ciudadano-mecd/estadisticas/educacion/recursos-economicos/gasto-publico.html). However, due to the limitation of the available time series, we rely on the constructed alternative proxy.4 The results from the tests are not reported to save space, but are available from the authors upon request.
18
TABLE 4
Estimated STR models for the first dimension of exploitation capabilities (secondary education). Regional analysis
CASTILLA Y LEÓN
CATALUÑA COMUNIDAD VALENCIANA
PAÍS VASCO
Transition variable: ΔlENRSt
Transition variable: ΔlENRSt
Transition variable: ΔlENRSt-1
Transition variable: ΔlENRSt
Linear p. Nonlin. p. Linear p. Nonlin. p. Linear p. Nonlin. p. Linear p. Nonlin. p.
ΔlGDPt-1 1.07 (0.28)
-1.20 (0.40)
-0.46 (0.10)
0.47 (0.18)
-0.63 (0.16)
0.63 (0.21)
ΔlGDPt-2 2.14 (0.35)
-0.77 (0.22)
-1.57 (0.38)
ΔlENRSt 0.40 (0.15)
-0.44 (0.16)
5.86 (1.72)
-5.66 (1.70)
-1.73 (0.26)
1.24 (0.36)
-1.80 (0.54)
ΔlENRSt-1 -0.51 (0.28)
0.74 (0.16)
-1.27 (0.42)
ΔlENRSt-2 0.16 (0.05)
0.16 (0.05)
ΔlPHYt 0.10 (0.02)
-0.39 (0.07)
0.06 (0.02)
0.10 (0.02)
-0.21 (0.04)
ΔlPHYt-1 -0.09 (0.01)
-0.09 (0.01)
0.39 (0.10)
-0.37 (0.10)
0.15 (0.04)
ΔlPHYt-2 0.10 (0.02)
ΔlLABSt 0.72 (0.14)
ΔlLABSt-1 -0.57 (0.13)
0.11 (0.03)
0.11 (0.03)
ΔlLABSt-2 -0.36 (0.17)
0.48 (0.20)
0.25 (0.06)
0.95 (0.22)
ΔlEXPt 0.46 (0.06)
-0.46 (0.06)
0.22 (0.07)
0.59 (0.06)
0.80 (0.08)
ΔlEXPt-1 0.20 (0.07)
-1.23 (0.41)
1.42 (0.44)
ΔlEXPt-2 -0.25 (0.04)
-0.25 (0.04)
-0.43 (0.07)
0.51 (0.14)
-0.31 (0.07)
0.63 (0.18)
γ 5.37 (2.01) 4.60 (2.21) 8.99 (3.64) 12.88 (5.02)19
c 0.06 (0.00) 0.03 (0.01) 0.06 (0.00) 0.05 (0.00)
R2 0.89 0.87 0.94 0.85
s2/s2L 0.12 0.16 0.08 0.13
AUTO 3.00 (0.10) 5.87 (0.03) 3.24 (0.10) 2.47 (0.14)
NL 0.23 (0.93) 0.28 (0.96) 0.33 (0.89) 1.85 (0.40)
PC 0.87 (0.64) 1.78 (0.54) 0.62 (0.74) 2.87 (0.21)
Notes. ‘Linear p.’ and ‘Nonlin p.’ stand for the linear part and the nonlinear part of the model. Δ denotes first differences. Values after regression coefficients are SEs of the estimates; R2is the adjusted determination coefficient; s2/s2
L is the variance ratio of the residuals from the STR model and the linear regression; AUTO is the test for residual autocorrelation of order 1; NL is the test for no remaining nonlinearity; PC is the general parameter constancy test. Numbers in parentheses after evaluation statistics are p-values.
20
TABLE 5
Estimated STR models for the second dimension of exploitation capabilities (tertiary education). Regional analysis
CASTILLA Y LEÓN
CATALUÑA COMUNIDAD VALENCIANA
PAÍS VASCO
Transition variable: ΔlENRTt-2
Transition variable: ΔlENRTt-1
Transition variable: ΔlENRTt
Transition variable: ΔlENRTt-1
Linear p. Nonlin. p. Linear p. Nonlin. p. Linear p. Nonlin. p. Linear p. Nonlin. p.
ΔlGDPt-1 0.98 (0.21)
-0.70 (0.14)
-0.47 (0.13)
ΔlGDPt-2 -1.21 (0.20)
0.69 (0.22)
0.24 (0.11)
0.24 (0.11)
-0.36 (0.11)
ΔlENRTt 0.37 (0.13)
-1.65 (0.72)
-0.47 (0.27)
0.96 (0.31)
1.14 (0.13)
-0.50 (0.12)
-0.71 (0.26)
ΔlENRTt-1 -0.91 (0.19)
2.38 (0.72)
-0.70 (0.07)
-0.70 (0.07)
0.75 (0.34)
-2.49 (0.53)
ΔlENRTt-2 0.69 (0.37)
-0.69 (0.37)
ΔlPHYt 0.04 (0.02)
-0.09 (0.04)
0.07 (0.03)
-0.07 (0.03)
0.15 (0.01)
0.07 (0.02)
0.17 (0.06)
ΔlPHYt-1 -0.11 (0.02)
0.25 (0.04)
0.05 (0.02)
0.05 (0.02)
0.07 (0.01)
0.09 (0.03)
ΔlPHYt-2 0.06 (0.02)
-0.19 (0.05)
-0.26 (0.06)
0.04 (0.02)
0.17 (0.02)
0.09 (0.02)
ΔlLABTt -0.15 (0.08)
0.21 (0.10)
0.09 (0.01)
0.09 (0.01)
ΔlLABTt-1 -0.16 (0.03)
0.21 (0.05)
0.06 (0.02)
0.10 (0.02)
0.10 (0.02)
ΔlLABTt-2 0.06 (0.01)
0.06 (0.01)
0.30 (0.05)
ΔlEXPt 0.33 (0.04)
0.33 (0.04)
0.24 (0.04)
0.11 (0.04)
0.59 (0.10)
0.25 (0.07)
0.93 (0.22)
ΔlEXPt-1 0.53 (0.09)
-0.96 (0.10)
-0.25 (0.04)
0.58 (0.08)
0.36 (0.16)
ΔlEXPt-2 -0.46 (0.12)
0.19 (0.03)
-0.37 (0.08)
0.63 (0.19)
21
γ 12.67 (5.67) 22.16 (20.26) 5.71 (1.31) 5.38 (1.29)
c 0.04 (0.00) 0.04 (0.00) 0.04 (0.00) 0.04 (0.00)
R2 0.94 0.82 0.98 0.90
s2/s2L 0.08 0.39 0.06 0.17
AUTO 4.63 (0.06) 2.67 (0.12) 2.13 (0.18) 0.85 (0.38)
NL 1.42 (0.48) 0.37 (0.88) 0.58 (0.78) 0.46 (0.83)
PC 3.00 (0.28) 3.31 (0.26) 4.80 (0.34) 0.50 (0.82)
Notes. ‘Linear p.’ and ‘Nonlin p.’ stand for the linear part and the nonlinear part of the model. Δ denotes first differences. Values after regression coefficients are SEs of the estimates; R2is the adjusted determination coefficient; s2/s2
L is the variance ratio of the residuals from the STR model and the linear regression; AUTO is the test for residual autocorrelation of order 1; NL is the test for no remaining nonlinearity; PC is the general parameter constancy test. Numbers in parentheses after evaluation statistics are p-values.
Regarding the first dimension of exploitation capabilities (secondary education), we
observe how the estimated models reflect the dependence of the economic growth on its
own past, educational level of the population, physical capital, labor force and
government (regional) expenditure on education. As in the country-level analysis, the
proxy for absorptive capacity plays the double role of being a determining factor of the
economic growth evolution as well as the force driving its nonlinear behavior. As
opposed to the results for the Spanish aggregate, however, two issues arise in the
regional analysis for secondary education. Firstly, the first dimension of absorptive
capacity is found to be a significant factor for the economic activity at regional level in
Spain, while it was not statistically significant at country level. Secondly, overall, the
variable of labor force does not seem to exert the same influence on economic growth at
regional level as it does at country level. The observable relevance of other factors like
physical capital or public expenditure on education might be diminishing the effect of
labor force. Importantly, the different relevance of a number of factors in the aggregated
and in the disaggregated analyses supposes evidence in line of ecological fallacy.
Figure 5 presents the estimated transition functions for the first dimension of
exploitation capability.
22
Castilla y León Cataluña
Comunidad Valenciana País Vasco
FIGURE 5. Estimated transition functions for the first dimension of exploitation capability. Regional analysis
One remarkable difference from the aggregate analysis for secondary education is the
estimated value for the slope parameter. At regional level, the transition between the
lower and the upper regime takes place at a higher speed compared to the analysis at
country level. The location parameters that determine the thresholds between the
extreme regimes are remarkably close to the mean of the transition variable (5-6%),
except for Cataluña. Finally, the estimated functions generally display a wide variation
range (except for Cataluña), which permits more flexibility in the dynamics of economic
growth.
The evaluation of the four regional models for secondary education is satisfactory
regarding the validation tests, as they do not show evidence of misspecification. As it
occurred with the aggregate analysis, the STR models show an outstanding explanatory
23
power compared to the linear ones. Following the variance ratios, the regional STR
models for secondary education explain from 84% to 92% of the residual variance of the
corresponding linear regressions.
Turning to the second dimension of exploitation capabilities (tertiary education), all the
variables considered are relevant factors explaining regional economic growth. As in the
previous analysis, the estimated coefficients are statistically significant, and once more
the educational level plays a key role acting as the transition variable as well as a
relevant factor explaining the economic growth in Spain.
One aspect shared by both the first and the second dimension of exploitation capability
is the remarkable influence of physical capital, which is often present in all models,
while human capital appears as an explanatory variable to a higher extent in the
aggregate than in the disaggregated analysis. Otherwise, public spending in education
appears in a higher number of cases as an explanatory variable at regional level than at
country level. One explanation might be that the analysis using the aggregated data
might be masking the importance of public spending in education for economic growth
in Spain. In the case of education, regions depend on both regional and state funding,
making it a factor that economy and education ministries have to pay special attention.
Regarding tertiary education, the transition between the extreme regimes is smoother at
regional than at country level (see Figure 6). Nevertheless, the values for the slope
parameter are not low; quite the contrary, the changes between regimes occur at a
notable speed. The estimated thresholds between the extreme regimes range from 3% to
6%; these values are extremely close to the respective enrollment ration means (mainly
around 4%). Thus, there exists a quite balanced situation between the left and the right
side of the logistic function regarding the number of observations. As observed in the
secondary education case, the variation range for the estimated transition functions is
wide, involving a more flexible dynamics for economic growth.
24
Castilla y León Cataluña
Comunidad Valenciana País Vasco
FIGURE 6. Estimated transition functions for the second dimension of exploitation capability. Regional analysis
Focusing on the evaluation stage, the estimated models for the four regions present no
evidence of misspecification following the diagnostic statistics. Furthermore, and as it
has been previously noted, the explanatory power of the nonlinear models outstandingly
surpasses the linear specifications. According to the variance ratios, the regional STR
models for tertiary education explain from 61% to 94% of the residual variance of the
corresponding linear regressions.
It is worth mentioning the relatively high speed in the transition between the extreme
regimes we observe in the regional analysis; even though the slope parameters do not
reach the value for the aggregate in tertiary education, the estimated figures indicate
notable regime changes. As it has been already noted, this fact points out the need for
threshold specifications, thus strengthening the relevance of STR models.
25
Finally, as we also carried out for the aggregate analysis, the residuals of both linear and
STR models have been examined for the four regions under study. Figures A.2.A and
A.2.B in the Appendix display the results obtained. Figure A.2.A depicts the differences
between the absolute values of the estimated residuals derived from the linear and the
STR models corresponding to each region for secondary education; while Figure A.2.B
is for the case of tertiary education. According to the results obtained, the pattern of
behavior at regional level resembles the one observed for the aggregate, although in
some regions the evidence in favor of the nonlinear model is even more remarkable (see
the case of Comunidad Valenciana and, at some extent, Castilla y León). One aspect to
highlight is that the Spanish economy experienced several turbulent phases over the
sample period (1992-1993 and 2008-on, for example) and that, unlike the country level,
most nonlinear models for the regions seem to offer a better adequacy - by generating
lower residuals - than the linear specification in those periods. As the characterization of
this kind of periods is not straightforward, the pre-eminence of the STR model justifies
its utility by itself. The evidence provided by the validation tests showing that the STR
model captures all the existing nonlinearity strengthens this determination.
In sum, according to the obtained results in both the country and the regional analysis,
we find evidence of the existence of ecological fallacy: although, overall, both the
aggregate and disaggregated analyses lead to consistent and coherent results, which are
in line with the expectations, we observe a number of differences regarding the
importance of secondary education as an explanatory variable, as well as the role of
other regressors of interest. Indeed, there are some variables that might seem of higher
relevance than really are as a consequence of statistical aggregation (e.g. human capital,
once education is controlled for), while others might seem of lower relevance (e.g.
public spending in education).
Overall, regarding the dimension of secondary education, it seems that in the analysis at
regional level the slope parameter is higher than that obtained in the country-level
analysis. This result indicates that the change between regimes at the regional level is
more abrupt than at country level. The opposite occurs in tertiary education, although,
as in the aggregated analysis, there is a rapid transition. We consider that one possible 26
explanation for the more rapid reaction of economic growth to shocks in secondary
education than to shocks in tertiary education at regional level may rest on certain
intrinsic features; secondary education is normally attended “at home”, that is, close to
the family residence due to the age of the students, but tertiary education allows for
mobility among regions (if not countries), so that any sort of impact on secondary
education would be more severe at regional level than at country level, and also higher
than an impact on higher education.
Both secondary and tertiary education dimensions, i.e., those related to the number of
“users” and that related to the number of “creators” of technology, are relevant for
economic growth; however, the results support the idea that there is not a particular
direction on the bias arisen as a consequence of aggregating the statistical data in the
absorptive capacity-economic growth relationship. Obtained results are in line with the
need of using a nonlinear model, as there are abrupt shifts between regimes.
5. Conclusions and discussion
In this paper the traditional linearity assumption in the relationship between education
and economic growth is brought into question. As we understand education as
absorptive capacity, we analyze the nonlinear relationship between absorptive capacity
and economic growth. As analyzing the aggregate link between absorptive capacity and
growth may lead to an ecological fallacy, our study aims to test whether conclusions
achieved at country-level also hold for regions.
In our empirical analysis, we proceed in two stages. Firstly, we focus on the role of
secondary and tertiary enrollment in economic growth in Spain (aggregated or country-
level analysis). Secondly, as different solutions emerge in different regions, we perform
our nonlinear analysis for a number of representative Spanish regions (disaggregated or
regional analysis).
The empirical framework chosen is that of time series (from year 1971 to 2013) and,
more specifically, we estimate Smooth Transition Regression (STR) models, which are
able to explain our relationship of interest in a satisfactory manner. The estimated 27
models reflect how the variation of the enrollment ratio (contemporary or one or two
periods ago) generates nonlinear effects on the economic growth at present time. We
consider that a country’s and a region’s absorptive capacity are at the origin of the
observed nonlinearities. Then, the asymmetric evolution of economic growth is clearly
observable in the two dimensions of absorptive capacity taken on board (secondary and
tertiary education).
This research proves the crucial relevance of education in Spain. An important
conclusion that we can draw from the analysis is that in order to economically succeed,
it seems necessary that countries and regions maintain and foster their level of
absorptive capacity, not only by maintaining (or increasing) their achieved number of
“users” of those tools required, but also by increasing the number of “creators”.
Therefore, under the contemporaneous societal changes that we are experiencing
worldwide, going from an industrial society, to a knowledge society and, finally, to a
network society (Castells, 2010 and 2016), the future role of universities and other
higher education organizations should be a priority for the development of countries and
regions. In sum, our main policy implication is that national and regional governments
must care for their educational system, not only for its intrinsic importance, but also for
its effects on economic growth.
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Appendix
Table A.1. Dataset description
Variable name Definition Source
Spain Regions
Gross Domestic Product (GDP)
Real Gross Domestic Product
International Monetary Fund’s International Financial Statistics (IFS) database
FEDEA, reference: de la Fuente (2017)
Absorptive capacity, secondary education (ENRS)
Gross Enrollment Ratios for secondary education
World Development Indicators, World Bank
Proportion of population with secondary education
FEDEA, reference: de la Fuente & Doménech (2015)
Absorptive capacity, tertiary education (ENRT)
Gross Enrollment Ratios for tertiary education
World Development Indicators, World Bank
FEDEA, reference: de la Fuente & Doménech (2015)
Proportion of population with tertiary education
FEDEA, reference: de la Fuente & Doménech (2015)
Human capital (LABS, LABT)
Proportion of active population with secondary (tertiary) education over total active population
The Valencian Institute of Economic Research (IVIE, in its Spanish acronym)
The Valencian Institute of Economic Research (IVIE, in its Spanish acronym)
Physical capital (PHY)
Real Gross Fixed Capital Formation
The Valencian Institute of Economic Research (IVIE, in its Spanish acronym)
The Valencian Institute of Economic Research (IVIE, in its Spanish acronym)
Government expenditure (EXP)
Government expenditure on education (as a percentage of GDP)
World Development Indicators, World Bank
World Development Indicators, World Bank
32
Government expenditure on education in real 2010 terms
Own calculation using World Development Indicators (World Bank) & FEDEA
Table A.2. Classification matrix
Low government expenditure per capita
High government expenditure per capita
Low income per capita
Andalucía
Galicia
Castilla-la-Mancha
Castilla y León
Asturias
Canarias
Extremadura
Cantabria
Comunidad Valenciana
Murcia
High income per capita
Aragón
La Rioja
Madrid
Cataluña
Baleares
Navarra
País Vasco
Note. Regions are classified in four groups as follows: regions are ordered from higher to lower income levels (GDP per capita, average 2000-2013) and from higher to lower government expenditure in education per capita (average 2000-2013), then a threshold for both GDP and government expenditure is composed by calculating the average of the sample in each magnitude.
Table A.3.A. Linearity tests against logistic smooth transition regression (p-values). Regional analysis: secondary education
Transition variable
Castilla y León Cataluña Comunidad Valenciana
País Vasco
ΔlENRSt
ΔlENRSt-1
ΔlENRSt-2
0.0072
0.0030
0.0112
0.0189
0.0400
0.0098
0.0003
0.0005
0.0132
0.0107
0.0006
0.0000
33
Table A.3.B. Linearity tests against logistic smooth transition regression (p-values). Regional analysis: tertiary education
Transition variable
Castilla y León Cataluña Comunidad Valenciana
País Vasco
ΔlENRSt
ΔlENRSt-1
ΔlENRSt-2
0.0001
0.0030
0.0150
0.1523
0.0440
0.0740
-
-
-
0.0873
0.0178
0.0247
Note. The test for Comunidad Valenciana presents size problems due to the characteristics of the linear model.
FIGURE A.1. Differences between the absolute values of the estimated residuals (linear and STR model). Country-level analysis
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FIGURE A.2.A. Differences between the absolute values of the estimated residuals (linear and STR model). Regional analysis: secondary education
FIGURE A.2.B. Differences between the absolute values of the estimated residuals (linear and STR model). Regional analysis: tertiary education
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