Spillover of Ideas and Regional Growth in Brazil
Ronaldo A. Arraes
Vladimir Kühl Teles**
The main focus of this paper is to provide better empirical comprehension of the income
differential among brazilian regions. In the scope of the endogenous growth models
framework, recent theoretical debates have relied on neo-schumpeterian models where
technological innovation has provided strong evidence toward positive externalities on
growth. Econometric models provide the measuring of spillovers of ideas, not only over time
but also across regions, in the process of generating externalities. Two distinct conclusions
were drawn from the results. First, there is evidence of a strong feedback in the R&D toward
spillover over time with increasing returns in production. Secondly, it is verified a significant
regionally negative spillover effect, which indicates that the production of ideas is
competitive among regions, therefore, there must have comparative advantage in the regional
income distribution.
Key-words: Regional Growth in Brazil, Technological Innovation, Production Function of
Ideas.
JEL: R11, O18, O32

Graduate Program in Economics (CAEN), Federal University of Ceará, Brazil. [email protected]
** University of Brasilia, Brazil
2
Spillover of Ideas and Regional Growth in Brazil
1. Introduction
Can the exponential growth be sustainable? If so, what will determine the dynamics of
long-term growth? Also, what type of policies can be implemented to promote progresses in
the levels of well being of the population? Such remark questions addressed a main concern
in growth studies of in the 50’s and 60’s decades, which have been brought up recently by
new models of endogenous growth.
Two facts motivated the recent contributions to the growth theory. Firstly, the growth
of the product supplanted the population growth continually during the last two centuries.
Secondly, different countries and regions presented a persistent discrepancy in their growth
rate relative to more developed countries and regions. Cross-sectional and time series data
have presented a significant correlation between national/regional growth and several
variables of economic, social and political-institutional characteristics, many of them guided
directly by government politics. These observations led to the formulation of a new
generation of economic growth models, which establish that the growth of income of local
and global economies is a consequence of the performance of several factors of political and
structural grounds.
Although the motivating facts and intentions seem to be similar, it is possible to verify
partitions within the recent theory of endogenous growth itself. Under that aspect, a stream of
theorists understand the capital accumulation (physical and/or human 1) as the driving force
for economic growth (e.g. Jones and Manuelli, 1990; King and Rebelo, 1990; Rebelo, 1991).
It states that firms accumulate capital continuously in perfectly competitive market with
constant returns to scale. Since capital is paid off by marginal product, the only innovation of
such models refers to the imposition of an inferior limit to the private return of capital as a
property of the aggregate production function in order to assure profitability of the
investment.
On the other hand, another approach frequently observed in the same theoretical
framework is the insertion of capital external effects on production, so that as individuals
accumulate capital, they contribute unwarily to the productivity of others. These spillovers are
modeled, naturally, under the perspectives of both physical capital (Arrow, 1962; Romer,
1986), and the human capital (Lucas, 1988). In that stream of thought, if the spillovers are
sufficiently strong, the capital marginal product can be kept continuously under the discount
rate, so that growth can be maintained by a continuous accumulation of such inputs that
generate positive externalities.
These two approaches offer coherent explanations for stylized facts of economic
growth. However, the approach on the models of endogenous growth has been the one that
support the neo-schumpterian models of economic growth, where the main mechanism to that
moves the economic growth process is the technological innovation. Such perspective, first
theorized by Schumpeter (1934), is applied to endogenous models through a linear differential
1
It is worth pointing out here that models as the one of Mankiw et. al. (1992) establish clear that human capital
can be seen as "anoother face" of the physical capital in the exogenous growth model without altering their main
conclusions. So that, it is not just the insertion of human capital itself that turn the endogenous models
innovative, but how this variable is treated in such models.
3
equation for the technological process. The theory is in agreement with Romer (1990),
Grossman and Helpman (1991) and Aghion and Howitt (1992), which states that the
economic growth is driven by the R&D sector, or sector of "ideas", of the economy.
However, the differential equation that expresses the technological production, that is,
the production function of ideas and inserted in these models requires a key hypothesis to
explain the exponential growth in the long run: exact linearity. In that way, the applicability
of those models for the explanation of the observed income differential between countries or
regions depends upon the truthfulness of this hypothesis. This opposes the hypothesis of
concavity of the ideas production function, as proposed by Jones (1995). This would imply
decreasing returns to the R&D sector, whose immediate consequence is to zero out the rate of
economic growth at the steady state, in the absence of a permanent growth of the number of
workers engaged in the sector.
It is based upon this theoretical motivation that this paper aims to contribute to a better
understanding of the income differential among the regions of a LDC country: the case of
Brazil. By estimating the regional production function of ideas, it would then become
available the estimates needed to turn out possible inferences on the linearity of such a
function and, consequently, on the applicability of the neo-schumpeterian models for the
Brazilian regions. To make it possible, we will propose alternative econometric models
seeking the estimate of the spillovers of ideas by means of panel data in order to capture
timely as well as the cross-sectional inter-regional effects, to test whether or not the
development of the R&D sector of a region can generate externalities on the others.
2. Theoretical Foundations
2.1. The Problem of Parameterization: Romer versus Jones
While the exogenous growth models considered that the technological progress was “a
gift from heaven”, recent growth models embodied a framework in the opposite direction,
where the technological progress should be understood throughout a production function of
ideas, represented by the following equation:
(1)
A   H A A
Where, A is the rate of technical progress, H A is the number of researchers engaged in the
production of ideas, and A is the stock of ideas of the economy. The seminal work of Romer
(1990) considered as hypothesis that     1 , which implies the exact linearity of the
production function of ideas. That means, an increase in the stock of ideas, or the number of
researchers, would bring about a perfectly proportional effect in the rate of technical progress
of the economy.
It is worthwhile pointing out that the magnitude of  becomes crucial for the overall
implications of the considered models. In this regard, if   0 , the hypothesis of fishing out in
the R&D sector could not be rejected, so that the number of ideas would be limited as the
number of fishes in the lake, and each new idea produced would raise the cost of an additional
new possible idea; likewise, the more fishes are caught, the less amount of fishes remain in
the lake. If 0    1 , the growth rate would tend asymptotically to zero. In the case if   1 ,
the growth rate would go up along the time, once A would tend to the infinite in a finite
amount of time.
4
It should be noted that the linearity hypothesis proposed by Romer (1990), and
according to equation (1) above, is expressed by,
A
(2)
 HA
A
In other words, the growth rate could be increased permanently while there was positive
variation of H A . In opposition, Jones (1995) rejects that and proposes his hypothesis as
  1 , meaning with this specification that the spillovers of ideas overtime are proportionally
lower and   1. This implies that the returns to research effort are subject to some type of
concavity. Under this approach, the growth rate of ideas would be given by,
A  H A
(3)

A A1
where, by taking logarithms and differentiating with respect to time, it follows that,
H
( A )
HA
A

(4)
A
1
In agreement with the expression (4), if the spillover of ideas is lower than what is
foreseen by Romer, the rate of economic growth of steady state will equal zero, as long as the
number of workers engaged in the R&D sector does not grow permanently. Therefore,
obtaining reliable estimates on the magnitudes of  and  is necessary to provide support to
the theoretical debate concerning the formulation of economic growth policies, either in the
national extent or in the regional context.
2.2. The Production Function of Ideas in the Regional Scheme
Currently, researchers have paid special attention to the fact that the production of
ideas in a country can affect the production of ideas in other countries through trading or by
mere imitation. It is then very plausible to expect that whichever the effect, it tends to be
much stronger in a regional space where there are no barriers to trading or mobility of
production inputs, once all regions are supposed to be regulated by the same legislation.
Furthermore, the implications of space spillovers of ideas have been a region of
intense research both in theoretical and empirical basis in the theory of the growth (e.g.
Grossman and Helpman, 1991; Rivera-Batiz and Romer, 1991; Griliches, 1992; Coe and
Helpman, 1995; Jones, 1995; Eaton and Kortum, 1996, 1998; Keller, 1997). The main
implications of these researches are that, under the hypothesis of equality of the factors prices,
which is a consequence of the spillovers of ideas, the rate of growth of backward regions is to
be larger than the one of the leaders regions, therefore the convergence of income among
regions is unavoidable (Abromowitz, 1986; Barro and Sala-i-Martin, 1992).
The production function of ideas can also be enriched by considering that, in the
regional scheme, the production of ideas in the national context promotes direct effects on the
domestic ideas production of a certain region, consequently, the production function takes the
following new version,
(5)
A j   H A Aj A j
where A j is the stock of ideas of region j , and A j is the stock of ideas of other regions in
the country. Thus, a positive value of  captures the possibility of inter-regional externality,
5
measuring the magnitude of complementarily between domestic and inter-regional
knowledge. It is evident, however, that the functional form of the relationship between the
productions of ideas of region j and the other regions can assume alternative formulations, as
for instance, the CES specification proposed by Porter and Stern (2000):
A j   H A ( A j   Aj  )
(5')
In that sense, they suggest that, although its computing is more complex, the
specification according to CES furnishes qualitatively more robust results. Therefore, it stands
clear that a model aiming to explain the dynamics of the R&D sector of a local economy, that
is, the path of ideas growing has to take into consideration the existent relationship with the
inter-regional production of ideas.
3. Empirical Tests for Brazil
3.1 Estimation
Econometric models will give support to the analysis by supplying estimates these will
generate inferences on the linearity of the production function of ideas for regions of Brazil. If
so, such models are constituted to estimate the parameters of the functions above discussed,
that is,
(6)
A   H A A
  

(7)
A j   H A A j A j
(8)
A   H  ( A    A   )
j
A
j
j
whose theoretical interpretations were detailed in section 2.
The estimation of equation (6) has as central objective to predict the dynamic
spillovers in the production of ideas inside of each state, while the estimations of equations
(7) and (8) aim the observation of the inter-state spillovers for idea production. Initially, two
estimation methods are proposed, the ordinary least square for equations (6) and (7) by
applying logarithm on both sides, and the second method is the two stage non-linear least
square for all three equations. Moreover, after testing for homoscedasticity, another method of
estimation – autoregressive model conditioned to heteroscedasticity – will be performed so
that to exhaust all necessary estimation possibilities, in order to obtain better reliability of the
results.
First the equations are estimated for a sample containing all of the Brazilian states, and
afterwards, separate estimates are accomplished for each aggregate region of the country. In
both cases, the procedure will deal with panel data, so that it will be able to test for spillovers
occurrence with different magnitudes, when considered the national and regional grounds in
separate forms. In doing so, it will be possible to withdraw information on convergence clubs
formation among regions.
3.2. Data
The proxy used for measuring the stock of ideas is the number of patents registered by
each state, where the main data source is the National Institute of Patents and Inventions
(NIPI). Concerning a proxy for the number of researchers producing ideas, several alternative
6
measures were tested, where the one chosen due to better adjustments to the models was the
average of schooling years of the population2.
Data are used in annually time series from 1979 to 1995. Since it is considered the
inexistence of depreciation of the stock of ideas, data for 1979 refer to the sum of the patents
registered in all of the previous periods, and for every year was added up the number of
registered patents, thus accumulating the stock of ideas of each state/region, so that the series
is non-decreasing. In this respect, the evolution of the frequency distribution of the stocks of
ideas is presented concisely in table 1.
Table 1
Frequency of the Stock of Ideas in Brazil, by Regions, 1979-1985
Regions
North
Northeast
Southeast
South
Mid-West
Years
1979
0,00
10,69
87,92
1,21
0,18
1985
0,00
20,69
77,87
1,35
0,09
1990
0,00
20,53
78,10
1,29
0,08
1995
0,03
9,44
88,17
2,31
0,05
Source: NIPI.
Table 2
Growth of the Stock of Ideas in Brazil by Regions
(base year: 1979=100)
Regions
North
Northeast
Southeast
South
Mid-West
Years
1979
100,00
100,00
100,00
100,00
100,00
1985
100,00
253,14
116,19
138,41
100,00
1990
100,00
277,88
128,55
144,85
100,00
1995
338,70
295,78
289,21
177,27
100,00
Source: NIPI
Two remarkable facts can be pointed out from the regional distribution of the stock of
ideas, in agreement with the results of table 1. First, there is strong evidence of centralization
of the stock of ideas in the Southeast, ranging from 75% to 90% of the total stock of ideas of
the country during the analyzed period. Second, the region closest to the Southeast in
producing ideas is the Northeast, which seemed to converge to the former region in the 80’s,
however it started a diverging process in the beginning of the next decade. The explanation
2
In view of unavailability of a source of information for the correct specification of the variable in the model
(H), number of producing of ideas, it is believed that the proxy here used keeps a high positive correlation with
the variable H.
7
for such divergence can be found in the economic opening by which the country passed
through the 90’s which could have promoted a more direct effect on the southeastern region,
the richest one.
Table 2 reinforces such facts, where an index is built for each region, with the purpose
of observing the dynamics of the stock of ideas growth in elapsing time. It is clear from such
data that no patent was registered in any state of the Mid-West in the whole period, the same
happening with the North during the 80´s. Besides, two periods stand out on the growth of the
stock of ideas in two regions; the beginning of the 80’s decade in the Northeast, and the
beginning of the 90’s decade in the Southeast. Therefore, in view of this characterization of
the data, the focus of regional analysis will be driven to the Southeast, Northeast, and
including the South for being the second most developed region. These regions account for
the almost totality of the stock of ideas of the country.
3.3. Estimates
Tables 3 to 5 present the results of the estimates of equations (6) to (8), respectively,
starting from the data contained in panel for all of the Brazilian states in the analyzed period,
by applying the methods of ordinary least squares (OLS), two stage non-linear least squares
(TSNLS) and autoregressive models conditioned to heteroscedasticity (ARCH)3.
Table 3
Estimations of Equation (6) – Brazil
Parameters



R2
F
OLS
-0,5831
(0,39)
0,6272*
(0,28)
0,9173*
(0,01)
0,85
1125,60
Models
TSNLS
0,9157*
(0,34)
1,0946*
(0,10)
0,8484*
(0,03)
0,84
1672,22
ARCH
-0,6945*
(0,40)
0,6659*
(0,29)
0,9295*
(0,04)
0,85
446,08
Notes: Values in parenthesis are standard errors..
(*) Significant up to 5%.
3
Although the OLS estimators are inefficient in the presence of heteroscedasticity, theirs estimates are kept
among the results just to illustrate such inefficiency.
8
Table 4
Estimations of Equation (7) – Brazil
Parameters




R2
F
OLS
8,9278*
(4,09)
0,6359*
(0,27)
0,9064*
(0,02)
-0,7767*
(0,33)
0,85
760,85
Models
TSNLS
59,0409
(48,97)
1,0339*
(0,11)
0,7467*
(0,03)
-0,2505*
(0,04)
0,85
1218,43
ARCH
14,0665*
(3,15)
0,6270*
(0,23)
0,9614*
(0,02)
-1,2220*
(0,24)
0,85
361,87
Notes: Values in parenthesis are standard errors.
(*) Significant up to 5%.
Table 5
Estimates of Equation (8) by TSNLS – BRASIL
Parameters
TSNLS

2,85E-05
(3,56E-05)
1,4401*
(0,15)
7,1752*
(1,10)
1,2359*
(0,12)
0,65
262,11



R2
F
Notes: Values in parenthesis are standard errors..
(*) Significant up to 5%.
The results presented in table (3) show inference on the parameters of the production
function of ideas according to the original theoretical model. The estimates from OLS and
TSNLS do not allow inferring about the linearity of such function. It indicates, however, a
strictly concave function, exhibiting decreasing marginal returns regarding the existent stock
of ideas, as the appropriate statistical tests are carried out, and the hypothesis that   1 cannot
be rejected for any one of the estimation methods, while the hypothesis that   1 the is
rejected at a significance level of up to 5% for both estimates.
9
However, it should be emphasized that the use of panel data itself already provides the
expectation for the heteroscedasticity occurrence, which might be confirmed by inspection of
the data disposition, especially regarding the variable number of researchers and, formally,
by performing White’s test. As so, it is expected that the estimates by OLS tend to present
some type of bias when accomplishing inferences on the parameters of the regression.
Therefore it is necessary to run estimations throughout autoregressive models conditioned to
heteroscedasticity. The results reached from this regression, unlike the previous ones, lead to
the non-rejection of the linearity of the production function of ideas, so that both  and  are
not statistically different from 1.
In other words, the empirical evidences obtained from the model corrected to
heteroscedasticity point for the non-rejection of the hypothesis proposed by Romer (1990),
Grossman and Helpman (1991), Aghion and Howitt (1992), regarding the scale effects of the
R&D sector as the main power for economic growth, whereas it is verified the dynamic
spillover effect of this sector for the Brazilian case. Nonetheless, it is yet to be tested for the
occurrence of regional spillovers of R&D, through the estimates of equations (7) and (8),
presented in tables 4 and 5.
The estimates shown in table 4 corroborate with the conclusions obtained from the
previous results, where the hypothesis that   1 cannot be rejected in none of the estimations
and the hypothesis that   1 cannot be rejected either, when the correction for
heteroscedasticity is accomplished. However, all of the estimates present a negative result in
accordance to the test of regional spillover in the sector of ideas. It indicates that, although the
innovations have a complementary characteristic with future innovations, they point for a
substitute scenario concerning innovations of other regions, endorsing, therefore, the
hypothesis of fishing out in the process of regional distribution of ideas.
These results are of extreme relevance on the theoretical discussion that involves the
convergence hypothesis, contrary to what is predicted thoroughly by convergence models,
(Barro and Sala-i-Martin (1995)), where regions possessing a research sector less developed
do not tend to approach their growth to those regions with research sector more developed.
This suggests an inter-regional competition in the R&D sector, so that development in a
certain region promotes an endogenous positive scale effect of it, but negative in relation to
the other regions.
A relevant question to be highlighted is: Under which regional extent the development
of the R&D sector does not generate positive externalities, turning to implicate in negative
externalidades on the sector of some other places? In order to shed light on this question, the
equation (7) has been reestimated to each one of the regions with the largest participations in
R&D of the country (Southeast, Northeast and South), generating estimates presented in
tables 6 to 8.
10
Table 6
Estimations of Equation (7) – Southeast
Parameters




R2
F
OLS
-0,0038
(0,04)
2,3418*
(0,57)
0,9418*
(0,02)
-0,4007*
(0,07)
0,95
3050,64
Models
TSNLS
0,0225
(0,01)
1,1702*
(0,17)
1,0352*
(0,03)
-0,4745*
(0,04)
0,95
1351,12
ARCH
0,0013
(0,96)
1,9623*
(0,22)
0,7325*
(0,01)
-0,5625*
(0,08)
0,92
846,62
Notes: Values in parenthesis are standard errors..
(*) Significant up to 1%.
Table 7
Estimations of Equation (7) – South
Parameters




R2
F
OLS
-0,0007
(0,02)
5,0534*
(0,60)
0,6213*
(0,02)
-0,4544*
(0,06)
0,95
2810,59
Notes: Values in parenthesis are standard errors..
(*) Significant up to 5%.
Models
TSNLS
55,0667
(40,24)
1,8116*
(0,15)
0,7703*
(0,04)
-0,4316*
(0,06)
0,95
2644,99
ARCH
0,0034
(1,005)
6,0814*
(0,54)
0,3458*
(0,01)
-0,4195*
(0,10)
0,92
795,5
11
Table 8
Estimations of Equation (7) – Northeast
Parameters




R2
F
OLS
0,0039
(0,07)
1,7640*
(0,37)
0,8571*
(0,02)
-0,1132*
(0,03)
0,86
845,56
Models
TSNLS
5527,57
(6153,33)
1,8080*
(0,19)
0,7183*
(0,04)
-0,6597*
(0,11)
0,84
719,23
ARCH
0,0120
(1,86)
2,7096*
(0,23)
0,5671*
(0,02)
-0,1096
(0,13)
0,80
265,74
Notes: Values in parenthesis are standard errors..
(*) Significant up to 5%.
The results observed in the tables 6 to 8 indicate to be relevant, since the inference on
the convergence of the sector of ideas cannot be verified, not even inside of a specific region,
which also rejects the hypothesis of convergence blocks. Another estimation procedure was
conducted, where the causal factor that dictates the existence cross-section spillover effect
was specified through iterative dummies variables for each region, so that it is assumed by
this formulation that the coefficients  ,  and  remain constant independently of the
considered region, thus testing the hypothesis that just the space spillover varies indeed from
region to region. The results of such model are presented in table 9.
As observed previously, the results presented in table 9 implicate a negative space
spillover in the R&D sector of any Brazilian region, corroborating the hypothesis of regional
fishing out. Such results meet the convergence theories based upon the arguments that the
cost of imitating a technology is lower than the cost of producing an innovation. On the other
hand, the results here found implicate that to each innovation, the innovative region generates
a scale effect on its future productivity, however it does not promote or obstruct the capacity
of innovation of the other regions, so that the regional convergence should be better
understood through the mobility of production factors than the mobility of ideas.
12
Table 9
Estimations of Equation (7) – Regional Effects
Parameters



 (North)
 (Northeast)
 (Southeast)
 (South)
 (Mid-West)
R2
F
Models
OLS
5,6285
(3,88)
2,2477*
(0,41)
0,7841*
(0,02)
-0,7962*
(0,32)
-0,5943*
(0,30)
-0,5875*
(0,32)
-0,6270*
(0,31)
-0,7850*
(0,32)
0,87
394,22
ARCH
12,4418*
(0,36)
1,7045*
(0,05)
0,7519*
(0,006)
-1,3167*
(0,03)
-1,1118*
(0,03)
-1,0669*
(0,03)
-1,0944*
(0,03)
-1,2285*
(0,03)
0,87
260,47
Notes: Values in parenthesis are standard errors..
(*) Significant up to 5%.
Conclusions
The central debate regarding the new theories of economic growth has been centering
on the rule of the sector of "ideas" of an economy. Under such aspect, the neo-shumpeterian
models of growth, as for instance, Romer (1993), Grossman and Helpman (1991) and Aghion
and Howitt (1992) suggest that the growth of the productivity is driven by a constant
allocation of resources for a producing sector of ideas, where such result critically depend
upon positive and especially strong dynamic spillovers, modeled through a production
function of ideas. Such an assessment has been under investigation, motivated by some
alternative models as that of Jones (1995), which inserts the hypothesis of decreasing returns
in the production function of ideas.
Within this debate, this paper aimed to contribute to the empirical understanding, still
not much explored, of the behavior of the production function of ideas in a developing
country – the case of Brazil – taking as central focus of analysis a regional overview. The
paper provided evidence for two main questioning. First, it is emphasized that the results
obtained from the estimates accomplished with data at state level support the existence of a
strong feedback in the R&D sector, as proposed by Romer (1990), being evidenced by the
linearity of the production function of ideas, and, therefore, the existence of a positive
dynamic spillover in the research activity.
Second, contrary to the dynamic approach, which investigated the existence of a
regional spillover of innovations in the R&D sector, it was also verified the existence of a
significant negative regional spillover, so that, while an innovation implicates in scale effects
13
in the sector of research within a specific region – assuming a complementary characteristic
with future research – it has an adverse impact on the sector of the other regions, assuming
substitute effect under the regional point of view. Such results allow inferring that innovations
might be considered specific assets to each place.
From the results obtained by estimation, and following the reasoning of Romer (1990),
among others, increasing returns seem to be a fact by nature. Ideas are a central factor in the
world we live. Under a time series standpoint, ideas are non-rivals, that implicates increasing
returns to scale naturally. On the other hand, under the cross section scenario, regions
compete in the production of ideas, which turn to implicate in the formation of comparative
advantages in the regional distribution of income. The conjugation of these results, in as much
as innovative, and relied on the statistical robustness of the estimates, it is an invitation to the
following questioning for the future: Can a practical theory of regional development abstain
from the comprehension of the creative-destructive lemma for ideas, and nevertheless obtain
success?
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