The Regional Dynamics of Economic Growth: Evidence
from GMM Estimation in Brazil
Osvaldo Ignácio baptista
Insper Learning Institution, Brazil
Abstract
A relevant topic in the recent economic debate, the discussion about the
determinants of regional economic growth gains great relevance. After all, what
makes some regions achieve greater economic growth than others? This study
investigates the potential determinants of regional economic growth in the
context of the 27 states of the Brazilian economy. In this regard, we analyze the
impact of human capital, research and development, exports, tax collection,
inflation and unemployment on the regional income of the 27 Brazilian
federation units in the period 2012-2018. This study is based on the article by
Gömleksiz and Özsahin (2019), The Regional Dynamics of Economic Growth:
Evidence from GMM Estimation in Turkey.
Introduction
The causes of disparities in regional growth have demanded great attention
from researchers and policy makers. Given this situation, several fields of
economics have been studying this spatial aspect of the regional economy.
Empirical results, such as Karlsson et al., 2001 and p. 3; Crespo-Cuaresma et
al., 2011, p. 810, show that national economic growth depends mainly on the
dynamics of regional economies. Regional economies can be characterized by
macroeconomic, microeconomic, structural and institutional factors; and most of
these factors interact with each other (OECD, 2009, p. 3; Pires Manso et al.,
2015, p. 11).
The Brazilian economy has different characteristics at a regional level, whether
due to geographic differences in a continental country or due to the historical
heritage of each region since colonization.
Since 1970, Brazil has been divided into 5 geographic regions (North,
Northeast, Midwest, Southeast and South) and is also regionalized into 3
economic macro-regions (Center-South, Amazon and Northeast). While the
Center-South region has the best economic and social indicators, it has a
diversified economy and most of the country's industries are concentrated in
this region; the Amazon region (comprised of almost all the states covered by
Amazonian vegetation) is less densely populated and has a more restricted
industrial activity, with worse access to social, education and infrastructure and
worse economic development (economic and social indicators) . The Northeast
region, where the semi-arid climate prevails, was highly explored in the colonial
period, leaving behind a region with serious economic, social and structural
problems.
In this context, the objective is to investigate the set of factors that may be
relevant to explain the differences in regional growth in Brazil. On potential
determinants of regional economic growth, we are going to analyze human
capital, research and development (R&D), exports, tax collection, inflation and
unemployment in all 27 units of the federation (UF) of Brazil. In this study, we
will use the difference GMM estimation method (Arellano and Bond, 1991) to
control the potential problem of endogeneity in the estimates, by combining
endogenous growth factors with fundamental structural factors. The data used
in the analysis did not come from the Brazilian Institute of Geography and
Statistics (IBGE), the National Institute of Industrial Property (INPI), the National
Institute of Educational Studies and Research Anísio Teixeira (INEP) and the
Ministry of Economy. In the remainder of the paper, section 2 discusses the
factors that affect regional growth, section 3 presents the dataset and the
econometric model used in the analysis, section 4 summarizes the empirical
results, and section 5 concludes the article.
Dynamics of regional economic growth and empirical literature
In the economic literature, economic growth and its determinants have been
analyzed from different perspectives and, although there is no consensus on its
main determinants, we will continue in line with the determinants postulated by
Gömleksiz and Özsahin (2019). In this context, human capital is defined as the
accumulation of time spent on education and training, this indirectly contributed
to productivity and growth through learning and increased level of skill and
talent (Mathur, 1999, p. 210). According to (Farole, 2013, p. 22) international
trade is also an important engine of growth in the short and long term. These
contacts on education and international trade are supported by empirical
studies such as Soukiazis and Antunes (2011) which show that human capital
and exports are relevant factors in explaining regional growth and convergence
in Portuguese regions in the period 1996-2005. The formation of R&D also
comes from the combination of physical and human capital is considered
another determining factor of economic growth through innovations (RodríguezPose and Crescenzi, 2008, p. 53), Pakes (1985) also shows that current and
past changes in R&D has a significant effect on US patent application counts in
the 1968-1975 period and Kaldei and Walz (2001) indicate a significant positive
relationship between the average growth rate of GDP per capita and patent
applications for 11 EU regions analyzed . Another factor that can be important
in economic growth is related to public intervention, Hirschman (1958) assesses
that the government has a positive impact on the economy through the
allocation of resources in areas such as education, infrastructure, health and
investments. Thus, the allocation of resources and the size of the government
budget can induce the economic efficiency of a UF, in this context Mıhçı and
Köksal (2010) conclude that public investment has a negative impact on
regional growth per capita in a study covering the 65 provinces of the Turkey in
the period 1980-2000, a result that diverges from the study by Önder et al
(2010) in the context of the 26 NUTS 2 regions of Turkey for the same period.
Unemployment is another factor whose link to economic growth is much
debated, as high unemployment can be considered as one of the main causes
of poverty and also indicates an inefficient use of resources, thus Reinstadler
and Ray (2010) note that unemployment at the regional level it probably
negatively affects individuals with low income levels due to the decrease in work
and pressure on wages, empirically Bere et al (2014) conclude by examining
Romanian cities in the period 1996-2010 that unemployment has a negative
impact on the GDP per capita, while spending on R&D positively affects
economic growth. Inflation, on the other hand, can also have a negative effect
on well-being and economic growth according to Friedman (1977), Fischer
(1993) also states that inflation hinders growth by reducing investment and
productivity, Shevchuk (2014) investigates the determinants of growth in 26
Ukrainian regions in the period 2002-2012 and its results point to a significantly
negative effect of inflation on per capita production (although this same study
concluded that per capita exports also have a negative effect).
Dataset and Econometric Model
In this study we used the Difference GMM (Generalized Method of Moments)
dynamic panel estimation method (Arellano and Bond, 1991) in order to
investigate the dynamics of regional growth in Brazil. Estimates were performed
with robust standard errors against the potential endogeneity problem.
The data set used in the study consists of data from 27 states (26 states and
the Federal District) in the period 2012-2018. Data are obtained at the regional
level and used in a logarithmic way. In table 1, GDP per capita is expressed in
Reais (R$). In relation to R&D, we consider the statistics of invention patents,
utility model and industrial design registration in line with the empirical literature
that postulates that patents are considered as one of the main results of R&D
(Pakes, 1985). In the case of human capital, there are controversies about the
best measure and we will follow according to Gömleksiz and Özsahin (2019)
and we will use the percentage of graduates in each region. In the case of
inflation, we will measure this variable through the IPCA, which is I calculate for
the IBGE for a set of capitals and metropolitan regions and we are considering
the inflation of each capital or metropolitan region as representative for the
entire state. In the case of states other than whose capital is not included in the
IPCA survey, we will consider the IPCA of the nearest metropolitan region. As
far as international trade is concerned, we will use the volume of exports per
capita by region. We will use the IGBE unemployment statistics to calculate the
unemployment rate and finally, we will measure the tax collection of each state
through the Ministry of Economy's data on the collection of each UF.
lpcgdpit = α0 + α1lpcgdpi,t-1 + α2lrdit + α3lhumit + α4lexit + α5ltrit + α6linfit +
α7lunmpit + ηi + μt + εit
In the above equation, ηi is the specific individual effect that takes the
unobservable heterogeneity between the cross section units into account, μt is
the time specific effect. While i denotes the cross section units, t represents the
time dimension and εit is o error term. lpcgdpi,t-1 is one year behind GDP per
capita in logarithmic form. This variable is also included in the long-term
equation as the instrumental variable to eliminate the problem of endogeneity in
the regression. In the analysis, we used the xtabond2 command in STATA.
Variable
Economic Growth
Research and Development
Human Capital
Exports
Tax Revenue
Inflation
Unemployment
Table 1. Definitions and Sources of Variables
Abbreviation Indicator
Source
lpcgdp
Real GDP per capita
IBGE (2018)
Patent Applications per
lrd
INPI (2018)
100,000 persons
Share of tertiary
lhum
education graduates in
INEP (2018)
total population
lex
Total volume exports
Ministério da Economia (2018)
ltr
Per capita tax revenue
Ministério da Economia (2018)
linf
IPCA
IBGE (2018)
lunmp
Unemployment rate
IBGE (2018)
As (Guetat and Sridi, 2017, p. 91), in dynamic panel analysis, estimators require
the use of instruments as a lagged form of endogenous variables. These
estimators are a good choice if there is a functional relationship between the
variables, or the present value of a variable of the dependent variable depends
on its past values, or when the independent variables are not strictly exogenous
(Roodman, 2009, p. 86). A method that proposes to solve these problems is
Arellano and Bond (1991), this method considers the unobserved heterogeneity
and predetermined regressors. In this method, it first takes into account the first
difference of the equation in order to eliminate specific unobserved effects in the
long-term regression. This method performs well when the cross section is
relatively larger than the time dimension (Moral-Benito et al., 2017, p. 7-8).
Applying the difference or 1-step difference GMM method (Arellano and Bond)
to the dynamic growth model as a first difference regression:
lpcgdpit - lpcgdpi,t-1= μt - μt-1 + α1lpcgdpi,t-1 + α2lrdit + α3lhumit + α4lexit +
α5ltrit + α6linfit + α7lunmpit + εit
However, this method is criticized as it has some biased results in small
samples. When variables approach a random walk, lagged levels often turn out
to be weak instruments for first difference. To overcome these problems, the
GMM system estimator was developed (Arellano and Bover, 1995; Blundell and
Bond, 1998), this method includes some additional moment conditions based
on two equations (the ―original equation‖ and the ―transformed into differences‖).
These methods are called two-step difference GMM. Bond et al. (2001) argue
that in case the time series is persistent and the number of observations in the
time series is small, the GMM difference is poorly behaved, however the two
methods are asymptotically equivalent. Despite the advantages, especially of
the GMM system, they have the disadvantage of converging to their asymptotic
form slowly compared to Monte's experiments (Carlo Bond et al., 2001, p. 3-18).
The GMM system allows more instrumental variables than the GMM difference,
improving the estimation power (Roodman, 2009, p. 86). The first equation of
the GMM system is the same equation as the first step of the GMM difference,
the level equation is given by the equation below:
lpcgdpit = α1lpcgdpi,t-1 + α2lrdit + α3lhumit + α4lexit + α5ltrit + α6linfit +
α7lunmpit + ηi + μt + νit
We will evaluate the consistency of the results through two tests, firstly to
assess the existence of first and second order autocorrelation, and additionally
we will check if there is a problem of overidentification (Hansen test). In the
case of the autocorrelation problem, (Mileva, 2007) observes that the difference
of the GMM method often rejects the null hypothesis that the first residual
differences are serially uncorrelated in the AR(1) process and considering the
consistency of the estimator GMM, it is suggested that the first residue
differences are not correlated in the AR process (2) (Hou and Chen, 2013, p.
188).
Empirical Results
In the table 2 we can see the results of the estimates of the GMM difference.
With the exception of the first lag of GDP itself, all other explanatory variables
had their relevance rejected (with 95% confidence), although for the model the
F test rejects the null hypothesis with 95% confidence. Autocorrelation and
Hansen tests show that there are no autocorrelation and overidentification
problems in the model, indicating, to some extent, the robustness of the model.
lpcgdpi,t-1
lrdit
lhumit
lexit
ltrit
linfit
lunmpit
Table 2. Results of Panel GMM
Arellano and
Bond (1991)
Corrected
[95% conf.
t
P>|t|
The Difference Std. Error
interval]
GMM
0.643
0.284
2.270 0.032 0.060 1.227
0.001
0.019
0.040 0.970 0.039 0.041
0.232
0.496
0.470 0.645 0.788 1.252
0.010
0.027
0.360 0.720 0.046 0.066
-0.005
0.088
0.060 0.956 0.186 0.176
0.007
0.021
0.320 0.748 0.036 0.050
0.001
0.042
0.030 0.974 0.086 0.089
AR(1)
AR(2)
-1.26(0.206)
-0.68(0.496)
Hansen test
19.31(1.000)
Let's now analyze the estimates according to the GMM system approach, for
this case we chose STATA's xtdpdsys function. xtdpdsys fits dynamic panel
data estimators with the Arellano – Bover / Blundell – Bond system. After testing
several functional forms, we identified that from the third lag of explanatory
variables onwards, we were able to reject the self-relationship hypothesis
through the Arellano-Bond test. In this model, we have reasons to suspect that
the strict exogeneity hypothesis is very strong, so we will weaken it to the
hypothesis that the variables are only predetermined, that is, the error term of
period t is not affected by the explanatory variables of period ts, for every 1 ≤ s.
In the table 3 we can evaluate the results obtained. In this case, we were able
to reject the null hypothesis for all explanatory variables, with the exception of
inflation. This exception may come from the fact that we do not have the IPCA
value for capitals of all states (in this case we had to consider the inflation of the
closest capital in the case of states not included in the IPCA survey), this
hypothesis may have reduced the IPCA variability across states, leaving us with
no evidence to reject the null hypothesis. Also in System GMM, the
autocorrelation tests indicate that there is no evidence of a specification
problem, thus supporting the robustness of the model.
lpcgdpi,t-1
lrdit
lhumit
lexit
ltrit
linfit
lunmpit
AR(1)
AR(2)
Table 3. Results of Panel GMM
Arellano and Bover
(1995),
Corrected
z
Blundell and Bond (1998) Std. Error
The System GMM
0.883
0.054
16.27
0.027
0.014
2.02
1.207
0.555
2.17
0.048
0.022
2.17
0.433
0.173
2.51
0.000
0.019
-0.02
-0.083
0.051
-1.64
P>|z|
0.000
0.043
0.030
0.030
0.012
0.984
0.101
[95% conf.
interval]
0.776
0.001
0.119
0.005
0.095
-0.038
-0.183
0.989
0.054
2.295
0.092
0.772
0.037
0.016
-1.79(0.730)
1.0162(0.309)
The Difference GMM ended up not being able to verify the relevance of the
analyzed variables as potential determinants for the dynamics of regional
growth, however, when we weakened the hypothesis of strict exogeneity for
predetermined variables and used the System GMM, which behaves better in
smaller samples, we found that the unemployment has a negative impact on
economic growth, while inflation varied in sign according to the estimation
method used, but in neither case was it relevant. The other variables: R&D,
education, foreign trade and tax collection affect regional economic growth. This
result is in line with most of the results obtained in the work by Gömleksiz and
Özsahin (2019), on which this paper is based, with two exceptions: for data
from Turkey, the results show inflation as a variable, different from that obtained
for Brazil, the limited availability of IPCA data for Brazil is a possible explanation
for this difference. On the other hand, for data from Brazil, the results show
relevance of R&D for regional economic growth, while for data from Turkey this
variable was not significant.
Final remarks
In this study, we could verify that regional economic growth in Brazil has been
negatively affected by unemployment and positively affected by human capital,
R&D, international trade and tax collection in each unit of the federation. These
factors emerge as potential determinants to explain economic disparities
between different regions of Brazil. Human capital is shown to be a crucial
element for economic growth in Brazil and, not surprisingly, in line with the
result obtained by Gömleksiz and Özsahin (2019) for data from Turkey. In this
way, we can see the dynamizing effect of human capital on economic growth as
emphasized in endogenous growth models. The relevance of R&D to regional
economic growth also sheds light on the potential combination of human capital
and learning, which can leverage R&D training and thus a greater stock of
knowledge at a regional level (Gömleksiz and Özsahin, 2019).
The System GMM results also indicate the relevance of international trade for
economic growth. This allows for economies of scale, allowing the production of
more competitive goods and technology transfer (Gömleksiz and Özsahin,
2019). The results of the study also indicate the contractionary effect on the
regional per capita in the System GMM, thus a high rate of unemployment can
also harm the efficient use of resources and disfavor regional production.
Finally, another variable that proved to be relevant in the Brazilian context was
tax collection. It is worth noting in this case, in the study by Gömleksiz and
Özsahin (2019), the variable considered was public investment. Unfortunately,
this information at regional level is only available in the period from 2017
onwards, making a robust model unfeasible. Faced with this impossibility, we
tested a series of proxies, such as total collection per UF per capita (adding tax
collection and transfers received), but the results proved contradictory.
Investigating further, we find that the states that receive the most transfers per
capita are the poorest states, while a rich state like São Paulo is the second that
received the least transfers in 2018 for example. Thus, we had the sum of two
variables that vary divergently with economic growth: while per capita transfers
vary negatively with each state's GDP per capita, it is to be expected that tax
revenue will grow with the increase in GDP. Thus, the inclusion of tax collection
alone as a proxy has shown to have greater potential, and it is to be expected
that a state with a higher budget per inhabitant will allocate a greater amount to
public investment (although this is not necessarily true if we analyze the
proportion budget allocated to public investment).
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