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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: [email protected]

Estefanía Mourelle: [email protected]

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.

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-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

https://www.mecd.gob.es/servicios-al-ciudadano-mecd/estadisticas/educacion/recursos-economicos/gasto-publico.html

https://www.mecd.gob.es/servicios-al-ciudadano-mecd/estadisticas/educacion/recursos-economicos/gasto-publico.html

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-1


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


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


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


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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31

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



Proportion of population with tertiary education


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)


Physical capital (PHY)

Real Gross Fixed Capital Formation



Government expenditure (EXP)

Government expenditure on education (as a percentage of GDP)



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

34

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

35

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