Ceará’s lobster exports: an approach by autoregressive
vectors – VAR
1Professor at the Department of Economics at the Regional University of Cariri – URCA. Researcher
at the Directorate of Regional, Urban, and Environmental Studies – DIRUR of the Institute of Applied
Economic Research – IPEA. Correo electrónico: luis.abel@urca.br. Orcid: https://orcid.org/0000-
0002-7453-1678.
3
Undergraduate in Economics at the Regional University of Cariri – URCA. Correo electrónico:
cosmorenanrl@gmail.com. Orcid: https://orcid.org/0009-0002-8234-8331.
2
PhD candidate in Economics at the Federal University of Paraíba – UFPB. Correo electrónico:
edcleutsonsouza@gmail.com. Orcid: https://orcid.org/0000-0003-3193-8520.
Las exportaciones de langosta del Ceará: un enfoque por vectores
autorregresivos - VAR
L u i s A b e l d a S i l v a F i l h o
C o s m o R e n a n d a S i l v a S o u z a
E d c l e u t s o n d e S o u z a S i l v a
Yu r i C é s a r d e L i m a e S i l v a
1
2
3
Submission date: August 29, 2024
Approval date: October 18, 2024
4
Professor at the Department of Economics at the Federal University of Roraima – UFRR Planning
and Budget Analyst at the Planning and Budget Secretariat of Roraima. Correo electrónico:
yuricesar@hotmail.com. Orcid: https://orcid.org/0000-0002-2110-6256.
4
Abstract
Animal protein consumption has been growing worldwide with the advancement of
globalization in trade, and it is sensitive to exchange rate changes and domestic product
prices. Brazil stands out as one of the world's largest exporters of protein commodities,
and Ceará is one of Brazil's largest fish exporters. Therefore, this study aims to analyze
how exchange rate changes and changes in lobster prices affect the volume of lobster
exported by the State of Ceará (the largest lobster exporter in the country). The selected
period covers 2002 to 2022, and the analysis will be conducted using the Vector
Autoregressive (VAR) approach. The results show that there is no long-term relationship
between the variables and that the dynamics of lobster exports from Ceará can be
explained much more by factors inherent and subjective to the supply and demand for the
product rather than by macroeconomic variables commonly used in studies of this nature.
Keywords: Exports, Ceará, fish, lobsters.
Resumen
El consumo de proteína animal ha ido creciendo en todo el mundo, con el avance de la
globalización comercial, siendo sensible a las variaciones del tipo de cambio y de los
precios de los productos internos. Brasil se destaca como uno de los mayores exportadores
de productos proteicos del mundo y Ceará es uno de los mayores exportadores de pescado
de Brasil. Por lo tanto, este estudio tiene como objetivo analizar cómo las variaciones del
tipo de cambio y los precios de la langosta afectan el volumen exportado por el Estado de
Ceará (mayor exportador de langosta del país). El período seleccionado abarca los años
2000 a agosto de 2023, y el análisis se realizará mediante el enfoque Vector Autoregresivo
(VAR). Los resultados muestran que no existe una relación de largo plazo entre las
variables y que la dinámica de las exportaciones de langosta de Ceará puede explicarse
mucho más por factores inherentes y subjetivos a la oferta y demanda del producto, que
por variables macroeconómicas comúnmente utilizadas en estudios de esta naturaleza.
Palabras clave: Exportaciones, Ceará, pescado, langostas.
1. Initial Considerations
The demand for fish consumption per capita is proliferating worldwide. This increase is
particularly significant in low-income countries, were population growth and rapid
urbanization drive animal product consumption, including fisheries.
Despite the growth of the fishing market in recent years, there are still obstacles to
international production distribution. According to Valdimarsson (2003), fishing faces
significant challenges due to the high import taxes charged by some developing countries,
which hinder the entry of raw materials and negatively impact the local market. However,
according to Subasinghe et al. (2009), the increased demand for fish meat has driven the
growth of fish farming, which has proven to be a promising solution to meet global
consumption needs. Raising fish in captivity has reduced production costs and increased
competitiveness through prices. As a result, in four decades, aquaculture has come to
represent 45% of the world’s production of fish for consumption.
Production performance, combined with demand and trade in fish, has driven the global
fish market, making it one of the most traded food commodities. Fish trade increasingly
improves food systems, benefiting local economies and importing countries. In this
context, developing countries generally export high-value fish to developed markets, with
lobster standing out in this category of high-value products (Tran et al., 2019).
With vast fishing potential along its coastline, Latin America has adopted aquaculture in
its territories. Hernández-Rodríguez et al. (2001) report that aquaculture began in the
region in the 1940s, initially intending to populate local ecosystems. It was only in the
1960s and 1970s that Latin American countries began to develop aquaculture to produce
food for domestic consumption and export, marking a modernization process in the
region's fishing economy.
The prospect of modernizing and overcoming challenges in the fishing sector is essential
for Brazilian states that depend heavily on this economic activity to develop and increase
their export competitiveness. Brazil has two strands of the fishing industry, each with
distinct and complementary economic roles. Although aquaculture is one of the fastest-
growing economic activities in the country's food sector, marine extractive fishing stands
out on the national agenda due to capturing species with high commercial value. It is
important to emphasize that even though aquaculture is one of the fastest-growing
economic activities in the Brazilian food sector, the most important fish on the national
agenda is lobster, a type of crustacean caught by marine extractive fishing that has high
commercial value (Farias & Farias, 2018).
However, this segment of Brazilian export trade has faced growth difficulties due to
overfishing and the devaluation of the product's price on the international market
(Almeida et al., 2021). This makes the locations that depend on this trade vulnerable,
depending on both a price recovery and a favorable exchange rate to make exports viable.
In the lobster fishing segment, the state of Ceará stands out. In this state, fish is of great
relevance to the trade balance, in addition to being the state that exported the most fish in
the country in 2022 among Brazilian states, with 25.19% of the country's total exports. In
this state, the fishing market generates around 57 thousand jobs (Ramos et al., 2023).
In this sense, this article seeks to answer the question: Are lobster exports in Ceará
affected by price changes and the exchange rate?
To answer this question, we used the vector autoregressive (VAR) model, which has been
used recurrently in the literature to study the commodity market in general and the price
dynamics of diverse types of fish. Mafimisebi (2012), for example, uses a VAR model to
analyze the price dynamics in the dried fish market in Nigeria, revealing that 59.1% of
the markets are spatially integrated in the long term.
Fernández-Polanco (2021) uses VAR to analyze the price dynamics of the sea bream
(Sparus) market. Murata) in Spain. In short, the authors conclude that prices are
transmitted from retailers and wholesalers to farmers in the domestic value chain.
Likewise, García-Del-Hoyo (2023) uses the VAR model to analyze the transmission of
price volatility of fresh anchovies in Spain between markets in the value chain. The results
achieved allow us to infer that the market with the most terrific price volatility is the one
where the product is passed on to large traders (first-hand sales), followed by the
wholesale market and, finally, the retail market.
As highlighted in the literature, this model has proven effective in analyzing price
volatility in the fish market. It is frequently used in empirical studies demonstrating its
ability to capture complex price dynamics and macroeconomic variables. Thus, its
approach in this study is justified.
Thus, in addition to this introduction, the second section presents the methodological
procedures, the third section presents the results and discussions, and the fourth section
presents the final considerations.
2. Methodological procedures
This section will present the methodological procedures adopted in this study. The
purpose is to answer the research question and help understand the study object analyzed
here.
2.1. Variables and database
To meet the objective proposed in this study, monthly data were selected from January
2000 to August 2023. Table 1 below shows the variables used in this study, with their
respective data sources and expected results.
Table 1: Variables used in the study, definition of variables, and source of available
public data.
Variable
Definition
Source
valuefobuss
Revenue from lobster exports
MDIC
exchange rate
Exchange rate
BACEN
premeditation
Average price of lobster on the international market
MDIC
Source: own elaboration
The vector autoregressive (VAR) econometric model is widely used in the literature on
international commodity trade (Felipe, 2013; Castro et al., 2018; Aidar & Deus, 2019;
Fernandez, 2020). There is consensus in the literature on the need to begin analytical
treatment through stationarity tests. From these tests, it is possible to identify whether the
variables have a unit root. These authors conclude that it is only possible to proceed with
the VAR if there is stationarity in all variables. Furthermore, after unit root tests, it is
necessary to carefully choose the number of lags present in the estimates to develop a
good model. However, the Akaike information criteria (AIC), Schwarz's Bayesian
criterion (BIC), and the Hannan -Quinn (HQ) become indispensable, and the results of
these tests will determine the number of lags that the VAR will have (Akaike, 1974;
Schwarz, 1978; Hannan & Quinn, 1979).
From the explanation for using the VAR model, it is possible to state that the model in
question meets the demands proposed for the objective proposed in this article since it
allows observing the dynamic interactions between the endogenous variables without an
immediate need to define causality between them. Prior to its application, the unit root
evaluates, and the cointegration test was performed (to define whether the VAR model or
the vector error correction model (VEC) will be used); and, after its application, the
Granger causality test, the impulse response function, and the variance decomposition
were performed. Finally, the forecasts were made using the VAR model.
2.2.Unit root test
The unit root test is a procedure that precedes the choice of the model and its application.
It is necessary to determine whether the time series is stationary.
The tests performed to determine whether there is stationarity in the time series were the
Dichey-Fuller, Augmented Dichey-Fuller (ADF), Elliot, Rothenberg, and Stock (ERS),
Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) and Phillips-Perron (PP) tests, as
shown in Table 2 below.
Table 2: Unit root tests applied to time series: Revenue from lobster exports, exchange
rate, and average price of lobster from Ceará on the international market
Test
Hypotheses
Author/article/journal/year
Dichey-Fuller
H0: The series is
non-stationary.
H1: The series is
stationary.
Dickey, DA; Fuller, W. A. (1979).
Distribution of the Estimators for
Autoregressive Time Series with a Unit Root.
Journal of the American Statistical
Association, vol. 74, no. 366, pp. 427–431,
1979.
Dichey-
Augmented
Fuller (ADF)
H0: The series is
non-stationary.
H1: The series is
stationary
Dickey, DA; Fuller, W. A. (1981).
Distribution of the Estimators for
Autoregressive Time Series with a Unit Root.
Econometrica, vol. 49, no. 4, pp. 1057-1072,
1981.
Elliot,
Rothenberg and
Stock (ERS)
H0: The series is
non-stationary.
H1: The series is
stationary
Elliott, G.; Rothenberg, T.J.; Stock JH (1996).
Efficient Tests for an Autoregressive Unit
Root, Econometrica, 64, 813-836, 1996.
Kwiatkowski,
Phillips, Schmidt
and Shin (KPSS)
H0: The series is
stationary.
H1: The series is not
stationary
Kwiatkowski, D., Phillips, P. C., Schmidt, P.,
& Shin, Y. (1992). Testing the null hypothesis
of stationarity against the alternative of a unit
root: How sure are we that economic time
series have a unit root? Journal of
econometrics, 54(1-3), 159-178.
Phillips- Perron
(PP)
H0: the series is
non-stationary; H1:
the series is
stationary.
Phillips, PCB; Perron, P. Testing for a unit root
in time series regression. Biometrika, Great
Britain, vol. 75, no. 2, p. 335-346. 1988.
Source: prepared by the authors
All these tests are used to verify whether the observed series is stationary, given models
in which the variables are generated by Autoregressive processes of order , the variables
may or may not have a unit root. In this way, it is possible to include the difference in the
lagged variable based on the test results, ensuring the preservation of the white noise
condition. The unit root tests were performed in the R software with the 'urca' package.
2.2.1. Dickey-Fuller test:
Dickey -Fuller test can be represented mathematically, according to equation 1, below:
Where: yₜ is the variable under study, Δyₜ is the first-order difference of the variable (yₜ -
yₜ₋₁), t is a time trend (optional), α and β are coefficients of the constant and the time trend,
respectively, γ is the coefficient associated with the level of the lagged series (checks if
the series has a unit root), εₜ is the random error term.
2.2.2. Dickey-Fuller Test (ADF):
The Dichey-Fuller (ADF) test is expressed by the following mathematical equations:
where: yₜ is the variable under study, Δyₜ is the first-order difference of the variable (yₜ -
yₜ₋₁), t is a time trend (optional), α and β are coefficients of the constant and the time trend,
respectively, γ is the coefficient associated with the level of the lagged series (checks if
the series has a unit root), δᵢ are the coefficients of the lagged differences of order i, εₜ is
the random error term.
2.2.3. Elliot, Rothenberg, and Stock Test (ERS):
The ERS test can be mathematically defined as in equations 5 and 6 below:
where: ₜ is the smoothed time series, λ is the chosen smoothing value (e.g. λ = 7 is a
common value), the remaining parameters are defined as in ADF.
2.2.4. Kwiatkowski, Phillips, Schmidt, and Shin Test (KPSS):
The KPSS test has its mathematical definition, according to the demonstration presented
in equation 7, below.
where: yₜ is the variable under study, α is the intercept (constant), βt is the time trend, rₜ
is a random walk with zero mean, εₜ is the error term.
2.2.5. Perron (PP) test:
The PP test can be mathematically defined as in equation 8 below:
where: yₜ is the variable under study, Δyₜ is the first-order difference of the variable (yₜ -
yₜ₋₁), t is a time trend (optional), α and β are coefficients of the constant and the time trend,
respectively, γ is the coefficient associated with the level of the lagged series (checks if
the series has a unit root), εₜ is the random error term.
2.3. Johansen cointegration test – Multivariate model
Based on the results presented by the unit root test, the next step was to apply tests that
show whether there is a long-term relationship between the variables in the model. To
obtain this result, it is necessary to apply for the cointegration test (Johansen, 1988). The
analysis aims to determine the presence or absence of multiple cointegration vectors in a
Vector Autoregressive (VAR) model. This model is used in conjunction with error
correction mechanisms, known as Vector Error Correction Models (VECM). The
mathematical representation of this model can be expressed by the following equations.
Let there be a VAR(p) model, where:
where: yₜ is a vector of n endogenous variables (nx 1), Aᵢ are coefficient matrices (nxn)
for each lag i, εₜ is an error vector (nx 1) that is considered white noise.
Error) Model Correction Model) can occur, according to the equation below:
where: Δyₜ represents the first differences of yₜ, Π is the long-term matrix (nxn) that
contains information about the cointegration between the variables, Γᵢ are the short-term
matrices (nxn) for each lag i, εₜ is the error vector (nx 1).
Thus, it is possible to perform the decomposition of Matrix Π, as follows:
where α (nxr) is the matrix of adjustment coefficients, representing the speed of
adjustment to long-term equilibrium, β (nxr) is the cointegration matrix, where each
column of β represents a cointegration vector, and r is the number of cointegration
relations.
Therefore, the Johansen Test can be defined in the two steps below:
Trace Test, according to the equation below:
for i = r+1 to n, and Maximum test Eigenvalue Test (Maximum Eigenvalue Test),
according to the equation:
where: T is the number of observations, λᵢ are the estimated eigenvalues of the matrix Π.
2.4.Granger Causality Test
As proposed in this article, the Granger test (Granger, 1969) will be performed. This test
is widely performed in econometric studies on time series. According to the author's
approach, correlation alone cannot necessarily imply causality. Granger (1969) explains
that the statistical discovery of the relationship between variables is not sufficient to
determine a cause-and-effect relationship. Thus, the author suggests that the possibility
of the existence of this cause and effect is only valid if past values represented by
collaborate in the prediction of present values . In other words, following Granger's
(1969) line of reasoning, a causal relationship between the series is necessary, which
cannot be determined solely by a statistical correlation relationship.
Therefore, the mathematical equations responsible for expressing the cause-and-effect
conditions can be expressed as follows.
The two equations above represent causality relationships in the Granger sense, , in
theory, incorporating uncorrelated noise. In equation (10), it is assumed that the current
values of the variable are linked to the past values of the variable , as well as to
the lagged values of the variable . In equation (11), represented by , a similar pattern
is reflected, where the current values of are related to the lagged values of the variable
, as well as to the lagged values of the first variable . Thus, Granger causality can
be identified in the series used in this work as unidirectional and bidirectional.
2.5.Impulse response function
The impulse response function is applied to time series to measure the effect that an
endogenous variable has on the other variables in the model. The shock can be applied to
any of the variables, the only condition being that it is endogenous to the model. Thus,
the result of this shock may affect all endogenous variables and the variable used to apply
the shock (Engle & Granger, 1987).
The impulse response function is as follows: The impulse is applied to an endogenous
variable in each period t. For example, if the shock is applied to the variable at time
t=0, even if it is applied to only one variable, it can affect all the other variables in the
model (Engle & Granger, 1987).
The mathematical representation is as follows, according to equation 12 below:
Where
represents i, j-th element multiplied by the matrix represented by expanded
from an impulse made at time t. It is important to emphasize that for this interpretation to
be valid it is necessary that the diagonal matrix where the elements related
to are not correlated.
2.6. Variance Decomposition of Forecast Error
Variance decomposition of forecast error is a primary test when using the VAR model
(Sims, 1980). According to Aidar and Deus (2019), analysis through variance
decomposition seeks to determine the percentage of forecast error variance attributable to
each endogenous variable.
For De Souza (2018), the decomposition of the variance of the forecast error and the
impulse response function allows us to assess the relevance of the effects of external
shocks on each of the variables in the model. It provides the percentage of the variance
of the forecast error of each variable in the different future periods that can be attributed
to each external shock.
The mathematical representation can be expressed as follows, according to equations 13
and 14, below:
Where,
is the variance of the shocks (or innovations) of the variable . In other
words, is the intrinsic variability of the shocks that affect ; (k) are the impulse
response coefficients. These coefficients measure the effect of a shock at x 1 at time t on
the variable in the subsequent periods t + k;
is the sum of the squares of the impulse response coefficients up to period
n-1 . The sum of squares is used to measure the cumulative contribution of an initial shock
over several periods; is the total variance of the forecast error of over the
horizon of n periods. This considers all sources of variability that affect the forecast of
over time.
2.7.Vector Autoregressive Model – VAR
After explaining the tests in the subsections above, once the VAR model has been
estimated, we now seek to apply the forecasts from the model. This model is widely used
in time series because it has the characteristic of capturing interrelated dynamic effects
simultaneously (at the same time) of the variables to be analyzed. The estimates are made
through Ordinary Least Quadratics – OLS and are represented by three independent and
interrelated equations (Sims, 1980).
VAR is represented mathematically as follows:
In matrix form, the VAR takes the following form:
In which represents an autoregressive vector (Nx1) of order ; is a vector (Nx1) of
intercepts; is a matrix of order parameters (nxn); and denotes the error term where
. Based on these settings, the VAR proves to be indispensable for the analysis
of the interactions proposed in this work, since it allows us to observe the dynamic
relationships between the endogenous variables considered, without the obligation to
define the causality between them previously. The following section addresses the results
of the analyses and estimates outlined in the methodological procedures presented in this
section.
After estimating the VAR Model, its stability test was performed, as shown in Figure 1
below.
Figure 1: VAR model stability test
According to figure 1, all eigenvalues are stable and are within the unitary cycle, showing
that there are no problems.
3. Econometric results for lobster exports from Ceará 2002-2023.
Table 1 shows the values of the logarithm of the exchange rate, average price and revenue
from lobster exports. According to the results shown in the Table, the minimum values
for the exchange rate, average price and export value were 0.4418; 1.204 and 6.377, while
the average values were 10.144; 2.274 and 14.657 and the maximum values of the
logarithm were 1.7529; 3.828 and 16.494 respectively.
Table 1: Descriptive statistics of the logarithm of the exchange rate, average lobster
price and export revenue (U$S)
Measures
exchange rate
premeditation
valuefobuss
Min.
0.4418
1,204
6,377
1st Thu.
0.7038
2,033
13,983
Median
0.9381
3,073
15,411
Mean
1.0144
2,774
14,657
3rd Quarter.
1,294
3,394
15,798
Max.
1,7529
3,828
16494
Source: prepared by the author, 2024.
One result that draws attention is the logarithm of the value of exports, as it presents a
large discrepancy regarding its maximum and minimum values. This may have caused
more significant variability throughout the series treated in this study.
The time series analyzed covers the period from January 2000 to August 2023. This
period comprises the equivalent of 272 observations, which can be considered a good
number of observations for using econometrics in time series.
Graph 1: Differentiated series – exchange rate, the average price of lobster exports and
export revenues (US$)
As we can see, Graph 1 shows that the logarithm of the exchange rate has a movement
like the logarithm of the average price of lobster. By preliminary analysis of the series, it
is possible to see that as the logarithm of the exchange rate increases, the average price
falls. Likewise, the average price increases when the exchange rate decreases, suggesting
a possible inverse relationship between the two variables. When analyzing the third graph
referring to the average revenue from exports, we notice a relationship of minor
sensitivity up to the observation number 100, and from there, more significant oscillations
are observed, suggesting a more contemporary relationship with the other variables.
According to Panisson (2018), to estimate the VAR model, it is necessary to perform the
unit root test to confirm whether the series in question is stationary or not. The most
widely used test to find out whether the series has stationarity is the Dickey-Fuller (ADF)
test. However, to ensure greater security in the results, the Dickey-Fuller augmented GLS
(DF-GSL) test, Elliott-Rothenberg-Stock test - with constant, Kwiatkowski -Phillips-
Schmidt-Shin test - KPSS - with constant and the Phillips- Perron (PP) Unit Root Test
were also performed.
Table 2 below shows the results found for the variables' logarithms from the tests
mentioned in the previous paragraph for a confidence interval of 1%, 5%, and 10%.
Table 2: Unit Root Tests applied to the series in differences: exchange rate, average
lobster price, and revenue from sales in dollars.
Dickey-Fuller test
Variables
1pct
5pct
10pct
The value of test-statistic
is:
Significanc
e
txcambio_tau1
-2.58
-1.95
-1.62
-10,145
***
precomedio_tau1
-2.58
-1.95
-1.62
-14,327
***
valuefobuss_tau1
-2.58
-1.95
-1.62
-12,519
***
Dickey-Fuller Test _Augmented
Trend = an intercept and a trend are added
trend_txcambio_tau3
-3.98
-3.42
-3.13
-10,193
***
trend_txcambio_phi2
6.15
4.71
4.05
34,633
***
trend_txcambio_phi3
8.34
6.3
5.36
51,948
***
trend_precomedio_tau
3
-3.98
-3.42
-3.13
-14,282
***
trend_precomedio_phi
2
6.15
4.71
4.05
68,006
***
trend_precomedio_phi
3
8.34
6.3
5.36
102,007
***
trend_valorfobuss_tau
3
-3.98
-3.42
-3.13
-12,474
***
trend_valuefobuss_phi
2
6.15
4.71
4.05
51,874
***
trend_valuefobuss_phi
3
8.34
6.3
5.36
77,811
***
Drift = an added intercept
drift_txcambio_tau2
-3.44
-2.87
-2.57
-10,208
***
drift_txcambio_phi1
6.47
4.61
3.79
52,108
***
drift_precomedio_tau2
-3.44
-2.87
-2.57
-14,306
***
drift_precomedia_phi1
6.47
4.61
3.79
102,336
***
drift_valueofbuss_tau2
-3.44
-2.87
-2.57
-12,497
***
drift_valuefobuss_phi
1
6.47
4.61
3.79
78.09
***
No intercept and no trend
none_txcambio_tau1
-2.58
-1.95
-1.62
-10,145
***
none_precomedio_tau
1
-2.58
-1.95
-1.62
-14,327
***
none_valuefobuss_tau
1
-2.58
-1.95
-1.62
-12,519
***
Elliott-Rothenberg-Stock Test - with constant
exchange rate
-2.57
-1.94
-1.62
-8,666
***
premeditation
-2.57
-1.94
-1.62
-2.37
***
valuefobuss
-2.57
-1.94
-1.62
-6,879
***
Kwiatkowski-Phillips-Schmidt-Shin test - KPSS - with constant
exchange rate
0.739
0.463
0.347
0.105
***
premeditation
0.739
0.463
0.347
0.033
***
valuefobuss
0.739
0.463
0.347
0.01
***
Phillips-Perron Unit Root Test
exchange rate
-324.82
***
premeditation
-295.27
***
valuefobuss
-259
***
Source: prepared by the author, 2024.
It is important to highlight that the null hypothesis of the ADF, PP, DF-GLS, and ERS
tests is the presence of a unit root in the series, which indicates that the series is not
stationary. In contrast, the KPSS test assumes as a null hypothesis that the series does not
have a unit root, which means that the series is stationary.
As can be seen, after the tests, the Dickey-Fuller test proved not to have a unit root in the
series since the values found for the variables exchange rate, average price, and value of
exports were lower than the critical values at 1%, 5%, and 10%. The Augmented Dickey-
Fuller test is nothing more than an extension of the previous test but more robust. After
the analysis, the stationarity of the residuals obtained by the Ordinary Least Squares
method was verified. The Tau statistic was used to test the slope, resulting in the rejection
of the null hypothesis, which indicates that the series does not have a unit root and,
therefore, is stationary.
The Elliott-Rothenberg-Stock tests also showed no unit root for the model. In this test,
attention is drawn to the values found for the exchange rate and the value of exports,
which were well away from zero, while the average price obtained a value closer to zero.
The Kwiatkowski -Phillips-Schmidt-Shin KPSS test had positive values between 0 and
1, confirming what was presented in the previous test. That is, there is no unit root in the
time series. Finally, the Phillips-Perron (PP) Unit Root Test showed negative parameters
smaller than zero, leading to rejecting the null hypothesis, as occurred in the ADF, DF-
GLS, and ERS tests.
After performing the stationarity tests, it is necessary to determine the order in which the
VAR model lags are chosen. The AIC (Akaike) and BIC (Bayesian) criteria were used.
Information Criterion) and HQ (Hannan -Quinn): These criteria define the appropriate
number of lags in the VAR model.
Table 3: Tests for determining the order and choosing the VAR model - AIC, BIC, HQ,
and M(p).
p
AIC
BIC
HQ
M(p)
p-value
0
-7,214
-7,214
-7,214
0.000
0.000
1
-7,261
-7,145
-7,214
29,193
0.001
2
-7,270
-7,038
-7,177
19,010
0.025
3
-7,295
-6,947
-7,156
22,841
0.007
4
-7,257
-6,794
-7.071
6,524
0.687
5
-7,288
-6,708
-7,055
23,656
0.005
6
-7,282
-6,586
-7,003
14,292
0.112
7
-7,347
-6,536
-7,022
31,753
0.000
8
-7,340
-6,412
-6.968
13,601
0.137
9
-7,531
-6,488
-7,113
61,106
0.000
10
-7.734
-6,574
-7,269
62,870
0.000
11
-7,908
-6.632
-7,396
55,481
0.000
12
-7,856
-6,465
-7,299
2,837
0.970
13
-7,854
-6,347
-7,249
13,862
0.127
14
-7,852
-6,229
-7,201
13,878
0.127
15
-7.861
-6,122
-7,164
16,100
0.065
Source: prepared by the authors, 2024.
Based on the values presented in Table 3, a VAR (11) model with 11 lags was selected
since the lowest values of the Akaike and Hannan -Quinn information criteria indicated
this specification.
3.1. Cointegration test result: trace and maximum eigenvalue tests
No unit root was found in the logarithm of the model's tested series, as shown in Table 2.
Therefore, the next step is the co-integration test. According to Sibin, Da Silva Filho, and
Ballini (2016), the stage begins with evaluating the proposed model through the first
difference analysis. This stage consists of examining the model's stability.
The Johansen co-integration test was performed to assess the existence of a long-term
relationship between the variables. Initially, the hypothesis r<=2 was considered,
analyzing the possibility of up to two cointegration vectors. Then, the hypothesis r<=1
was tested, considering the existence of a single cointegration vector. Finally, the null
hypothesis verified the presence of cointegration between the model variables, with
significance levels of 10%, 5%, and 1%.
Table 4: Result of the Johansen cointegration test: trace and maximum eigenvalue tests.
H0: rank = r
test
10pct
5pct
1pct
r <= 2 |
9.08
6.5
8.18
11.65
r <= 1 |
22.06
15.66
17.95
23.52
r = 0 |
38.94
28.71
31.52
37.22
Source: prepared by the author, 2024.
As can be seen in Table 4, the Johansen cointegration test showed that the series are
cointegrated with each other. Thus, we can conclude that, given the number of
cointegration vectors in the Table above, it is possible to see integration between the
model variables at 1%, 5%, and 10% significance. In other words, there is a possible long-
term relationship between them, so we used the VAR model to adjust the time series
proposed by this study.
3.2. VAR model stability test
In the context of the VAR model, it is vital to ensure the absence of residual correlation.
When examining the correlogram of the residuals of the VAR model, as shown in Figure
2, one observes the absence of residual correlation in the series. What is observed are
isolated occurrences. Therefore, rejecting the null hypothesis of the absence of correlation
in some specific lags is impossible. However, considering the lack of pattern among the
monthly periodicities of the series analyzed, it is interpreted that such correlations are
only due to the natural characteristics of time series of this nature.
Figure 2: Correlogram of residuals from the VAR model
Two more tests were applied to complement the correlogram to ensure no autocorrelation
in the model. The first test is the Portmanteau test, which has the non-existence of non-
contemporaneous autocorrelation as its null hypothesis. The LM test tests the null
hypothesis of the non-existence of serial correlation in the residuals of the first-order
model. Both tests confirmed the non-existence of residual autocorrelation.
3.3. Granger Causality Test
Granger (1969) developed a test known as the Granger causality test, which is based on
the premise that the future cannot influence the present or the past (Felipe, 2013). To
better understand whether α occurs after β, it is understood that α cannot cause β. In the
same way that if α happens before β, this does not necessarily imply that α is the cause or
influences β. It is necessary that regardless of whether α happens before β or after β or
both happen simultaneously, α does not influence β nor does β influence α.
As shown in Table 5 below, the Granger causality test was applied to the three variables
to verify their interdependence. The first analysis, which refers to the exchange rate
explained by two lags of the exchange rate plus two lags of the average price, results in a
P value associated with more than 5%, thus failing to reject the null hypothesis, indicating
that we cannot state that the exchange rate Granger causes the average price. In other
words, a shock in the lagged values of the exchange rate variable does not impact the
average price of lobster exports from Ceará. When an exchange rate shock is made
concerning the value of exports, we also have a P value associated with more than 5%.
Therefore, in this case, the null hypothesis is not rejected. That is, there is no causal
relationship, in the Granger sense, that the exchange rate causes revenue from lobster
exports to the international market.
Table 5: Granger causality test for the exchange rate, the average price of lobster
exports, and export revenues in US$
Model 1: (txcambio) ~ Lags ((txcambio), 1:2) + Lags (precomedio, 1:2)
Model 2: (txcambio) ~ Lags ((txcambio), 1:2)
Res.Df
Df
F
Pr(>F)
1 276
2 278
-2
2,8412
0.066
Model 1: (txcambio) ~ Lags ((txcambio), 1:2) + Lags (valorfobuss, 1:2)
Model 2: (txcambio) ~ Lags ((txcambio), 1:2)
Res.Df
Df
F
Pr(>F)
1 276
2 278
-2
1,5222
0.2201
Model 1: (precomedio) ~ Lags ((precomedio), 1:2) + Lags (txcambio, 1:2)
Model 2: (precomedio) ~ Lags ((precomediation), 1:2)
Res.Df
Df
F
Pr(>F)
1 276
2 278
-2
1.0063
0.3669
Model 1: (precomedio) ~ Lags ((precomedio), 1:2) + Lags (valorfobuss , 1:2)
Model 2: (precomedio) ~ Lags ((precomediation), 1:2)
Res.Df
Df
F
Pr(>F)
1 276
2 278
-2
1,205
0.3013
Model 1: (valorfobuss) ~ Lags ((valorfobuss), 1:2) + Lags (txcambio, 1:2)
Model 2: (valorfobuss) ~ Lags ((valorfobuss), 1:2)
Res.Df
Df
F
Pr(>F)
1 276
2 278
-2
1,3546
0.2598
Model 1: (valorfobuss) ~ Lags ((valorfobuss), 1:2) + Lags (precomedio, 1:2)
Model 2: (valorfobuss ) ~ Lags ((valorfobuss), 1:2)
Res.Df
Df
F
Pr(>F)
1 276
2 278
-2
1,0226
0.361
P=., sig 0.1; p=*, sig=0.05; p=**, sig=0.01, p=***, sig=0.001
Source: prepared by autoes, 2024.
When applying a shock using two lags of the average price variable together with two
lags of the exchange rate and, subsequently, with the value of exports, the result showed
that the p-value associated with the average price, both with the exchange rate and the
value of exports, was higher than the 5% significance level. This indicates that the null
hypothesis cannot be rejected. Thus, it can be concluded that the average price does not
Granger cause either the exchange rate or the value of exports, showing that a shock in
the lagged values of the average price variable does not impact the exchange rate or the
value of exports.
Finally, the impact of the export value variable on the number of lags with the exchange
rate and average price variables was analyzed. As a result, a p-value associated with
significance more significant than 5% was found for both variables. Furthermore, the null
hypothesis was not rejected, concluding that export revenue does not Granger cause the
exchange rate, as it does not Granger cause the average price. In other words, the export
value series has no temporal precedence regarding the exchange rate or the average price.
The results suggest that lobster exports from Ceará during the analyzed period are more
closely related to the supply and demand components than to the macroeconomic
variables tested. In other words, exports are random and more closely related to the
fishermen's supply capacity and the market's demand capacity.
3.4. Impulse response function
Next, the responses of each variable in the model to unexpected shocks on themselves
and the other variables were analyzed. Table 1A, in the appendix, shows numerically the
behavior of the three variables to the impulse response data on themselves and on the
other endogenous variables in the model over eleven periods. The same results can also
be visualized graphically in Figure 3.
Figure 3: Impulse Response Function for the variables, exchange rate, average price, and
export revenue.
As illustrated in Figure 3, a shock to the exchange rate generates an initial positive
response from the variable itself in the first few months, but this effect quickly dissipates.
This same shock, however, does not impact on the average price of lobster on the
international market, whose series remains stable. Similarly, export revenue reacts
negatively initially, but this influence diminishes rapidly over time. The results for the
exchange rate shock indicate that, initially, it exerts a minimal impact on the variable
itself and revenue from lobster exports. However, its influence on the variables is short-
lived.
A shock to the average price of lobster on the international market initially generates a
positive response only in the variable itself; however, this positive response soon
attenuates over time. On the other hand, the exchange rate and export revenue do not
significantly react to this shock. In short, an increase in the average price of lobster has a
positive impact only on the price itself, and, as a shock to the exchange rate, this influence
is short-lived.
Finally, a shock to lobster export revenue presents a response only in the variable itself,
with an initial positive effect in the first few months. However, this effect dissipates over
time as with the other shocks analyzed. The other variables do not present a significant
response to the shock to lobster export revenue. In short, a shock to lobster export revenue
exclusively affects the variable itself.
Therefore, it is concluded that the dynamics of lobster exports show a limited response to
shocks in international prices and the exchange rate, with responses being restricted to
the variable itself. The effects of these shocks are transitory and quickly dissipate over
time, indicating that volatility in lobster exports is not significantly transmitted to the
other economic variables analyzed. Thus, as in the Granger causality test, it leads to the
inference that the Brazilian lobster trade is more closely linked to supply and demand
than to the economic variables analyzed here.
After performing the impulse response function, the next step is to perform the variance
decomposition. Sibin, Da Silva Filho, and Ballini (2016) report that variance
decomposition makes it feasible to determine the proportion of the variance of forecast
errors that can be associated with unanticipated shocks of the variable in question and of
the other endogenous variables of the system on an individual basis.
3.5. Forecast Error Variance Decomposition
Table 1B, in the appendix, presents the results of the variance decomposition of the
forecast error for twelve periods for the variables exchange rate, average price, and export
revenue. In the exchange rate component, as expected, its decomposition explains 100%
of its forecast error. At the end of the period analyzed, this value remains high, falling
only to a percentage of 95.5%. The average price explains 0% in the first period and has
little influence over time, explaining only 3.5% of the exchange rate forecast error. On
the other hand, the value of exports has an even more negligible impact, causing less than
1% of the variance of the exchange rate forecast error.
The variance analysis applied to the average price component revealed very low
percentages over the 12 periods studied for the other variables. At the beginning of the
series, the exchange rate variable contributed only 0.4% of the average price forecast
error, increasing to 6.4% after 12 periods. The average price variable is responsible for
most of the forecast variance, accounting for 99.6% in the first period, and this percentage
decreases to 89% as the forecast horizon extends. In contrast, the value of exports initially
does not influence the average price forecast error, but this contribution increases to 4.6%
over the cycles.
The export value variable is the one that presents the most significant contribution of the
other variables in its variance forecast error at the end of the twelve periods compared to
the other variables. Initially, the export value explained 91.8% of its forecasts, while the
exchange rate and the average price contributed to 3.7% and 4.5%, respectively. After the
12 periods, the ability of the export value to explain its variance decreased by 7.9%,
falling to 83.9%. As expected, the other variables showed an increase: the exchange rate
rose to 6.2%, and the average price, which had the most significant increase, began to
explain 9.9% of the variance error of the export value.
Figure 4: Forecast Error Variance Decomposition
Figure 4 above shows how the variance decomposition of the forecast error is distributed.
As can be seen, of the three variables, the exchange rate is almost unaffected by the other
variables. The shock presented by the average price and the value of exports, added
together, explains only 5% of the forecast error of the variable analyzed. The shock in the
average price component shows a more significant impact than the previous variables
since it added to the exchange rate and the value of exports, which explains 11% of the
average price.
Of all the endogenous components presented, the value of exports was the one most
influenced by the other variables when analyzing the forecast error. At the end of the
period, this lost more than 15% of its explanatory capacity; this loss can be seen in Graph
3 of Figure 4.
3.6. VAR Predictions
After all the tests have been performed, we can proceed with the forecasts using the VAR
model. Table 1C in the appendix presents the estimates of each variable over 12 months.
As can be seen, the exchange rate has a forecast within the confidence interval, both in
the upper and lower bands, with a confidence level of 95%.
The VAR model also presents satisfactory results for the other two variables in the series,
with predictions within the 95% confidence interval in both the upper and lower bands.
This demonstrates the model's robustness for the variables analyzed.
Figure 5 shows how the forecasts are distributed in the VAR model, referring to Table
1C of the appendix. As can be seen in the first two graphs, which correspond to the
exchange rate and the average price, respectively, the blue dotted line behaves within the
red lines.
Figure 5: Forecasts for the impacts of the exchange rate on the price and the total value
of revenues from lobster exports from Ceará using the VAR model.
The blue line in the third graph in Figure 5 remains within the parameters, although it
presents more significant oscillations than the previous graphs. This indicates that, despite
the variations, the forecasts remain within a 95% confidence interval, demonstrating the
reliability of the estimate obtained from the VAR model.
4. FINAL CONSIDERATIONS
This article aimed to show the relationships between the variables exchange rate and the
average price and revenue from lobster exports in the State of Ceará. The study's
motivation was that Ceará is the largest lobster producer in Brazil. Thus, this ranking
justifies a study of this nature, given the importance of Ceará's exports in this sector for
both the country and the state. Furthermore, this analysis contributed to understanding
this sector in the fish export trade since it is little explored in the literature and never
addressed by the approach presented here.
The responses were obtained through the VAR model. However, before applying the data
to the VAR model's econometric modeling, tests were carried out to identify the existence
of interrelationships between the three components of the time series and to assess the
model's viability for carrying out the analyses.
The unit root test was applied, as suggested in the literature: Dickey-Fuller and
Augmented Dickey-Fuller, Elliott-Rothenberg-Stock, Kwiatkowski -Phillips-Schmidt-
Shin, and Phillip-Perron. Furthermore, the Johansen trace test was performed to identify
the variables' cointegration relationship and choose between the VAR and the VEC. After
choosing the VAR, the Granger causality test, the impulse response function, and the
forecast error variance decomposition were applied.
The AIC, BIC, and HQ criteria were used to determine the order of the model selection.
The AIC and HQ criteria indicated the same order; therefore, they were chosen. From
this, a VAR model with eleven lags was estimated.
It was not possible to identify Granger causality between the variables. The test indicated
no long-term dependence relationship between the three variables observed in the model.
Furthermore, based on the impulse response function, it is concluded that the dynamics
of lobster exports present a limited response to shocks in international prices and the
exchange rate, with responses being restricted to the variable itself. However, these
shocks are transitory and quickly dissipate over time, indicating that volatility in lobster
exports is not significantly transmitted to the other economic variables analyzed.
Thus, despite the economic potential of the lobster export sector to Ceará, it faces
significant challenges, such as overfishing, which affects the sustainability of catches and,
consequently, future exports of the goods. The results of this study suggest that the
dynamics of lobster exports from the State of Ceará seem to be more linked to issues
related to supply and demand rather than to the behavior of macroeconomic variables that
traditionally determine international trade. This conclusion points to the need for
strategies that promote sustainable fisheries management, ensuring the continuity of the
export sector and reducing vulnerability to fluctuations in supply, which are essential to
maintaining Ceará's competitiveness in the international lobster market. In addition,
promoting awareness about lobster marketing in the context of favorable exchange rates
and international prices is essential.
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Annexes
Table 1A : Coefficients of the Impulse Function Response to the Stimulus for the
variables exchange rate, average price and export revenue
Impulse/re
sponse
Impulse
response
coefficients$txcambio
Impulse
response
coefficients$precomedi
o
Impulse
response
coefficients$valuefobus
s
premeditati
on
valuefobu
ss
exchange
rate
valuefobu
ss
exchange
rate
premeditati
on
1
-0.0011
-0.2045
0.0000
0.1944
0.0000
0.0000
2
-0.0312
-0.1499
0.0003
0.0104
-0.0008
-0.0348
3
-0.0240
-0.2162
0.0051
-0.1843
-0.0002
-0.0540
4
0.0083
0.0250
0.0037
-0.0142
0.0014
-0.0515
5
-0.0108
0.0683
0.0025
-0.0456
0.0022
-0.0768
6
-0.0618
-0.0022
0.0065
-0.1256
0.0022
-0.0774
7
-0.0559
0.0216
0.0049
-0.1280
0.0034
-0.0646
8
-0.0391
0.0527
0.0021
-0.0534
0.0056
-0.0683
9
-0.0151
0.0703
0.0071
-0.1859
0.0095
-0.0786
10
-0.0323
0.0576
0.0089
-0.0393
0.0132
-0.0874
11
-0.0153
0.1558
0.0065
-0.0827
0.0111
-0.0376
Source: prepared by the authors, 2024.
Table 1B: variance decomposition of the forecast error for the exchange rate, average
price and revenue from exports of lobster from Ceará.
Mo
nths
Exchange
Average Price
USS Value
exchan
ge rate
premedi
tation
valofo
buss
exchan
ge rate
premedi
tation
valofo
buss
exchan
ge rate
premedi
tation
valofo
buss
1
1,000
0.000
0.000
0.004
0.996
0.000
0.037
0.045
0.918
2
0.999
0.000
0.001
0.010
0.983
0.007
0.030
0.048
0.921
3
0.992
0.007
0.001
0.010
0.981
0.009
0.031
0.073
0.897
4
0.984
0.014
0.001
0.016
0.973
0.011
0.050
0.078
0.872
5
0.982
0.017
0.001
0.020
0.967
0.013
0.051
0.079
0.870
6
0.982
0.017
0.001
0.043
0.944
0.013
0.052
0.080
0.868
7
0.977
0.021
0.002
0.043
0.940
0.017
0.052
0.079
0.869
8
0.971
0.027
0.002
0.045
0.938
0.017
0.052
0.079
0.869
9
0.967
0.030
0.003
0.049
0.934
0.017
0.051
0.086
0.863
10
0.966
0.030
0.005
0.051
0.932
0.017
0.050
0.091
0.859
11
0.959
0.032
0.008
0.052
0.911
0.037
0.055
0.091
0.854
12
0.955
0.036
0.008
0.064
0.890
0.046
0.062
0.099
0.839
Source: prepared by the authors, 2024.
Table 1C: Forecasts for the VAR model in a 12-month interval ahead of the analyzed
series
fvar [[" fcst " ]][ [" txcambio "]]
Time
fcst
lower
upper
CI
[1,]
1,595
1,562
1,627
0.033
[2,]
1,611
1,566
1,657
0.045
[3,]
1,619
1,561
1,678
0.059
[4,]
1,620
1,552
1,688
0.068
[5,]
1,620
1,544
1,696
0.076
[6,]
1,645
1,561
1,729
0.084
[7,]
1,657
1,566
1,749
0.092
[8,]
1,629
1,533
1,726
0.097
[9,]
1,654
1,552
1,756
0.102
[10,]
1,616
1,511
1,722
0.106
[11,]
1,656
1,547
1,766
0.109
[12,]
1,622
1,509
1,735
0.113
> fvar [[" fcst " ]][ [" precomedio "]]
Time
fcst
lower
upper
CI
[1,]
3,140
2,948
3,331
0.191
[2,]
3,314
3,100
3,529
0.215
[3,]
3,230
3,001
3,458
0.228
[4,]
3,466
3,233
3,699
0.233
[5,]
3,353
3,111
3,594
0.241
[6,]
3,240
2,989
3,491
0.251
[7,]
3,178
2,920
3,436
0.258
[8,]
3,283
3,020
3,547
0.264
[9,]
3,270
3,001
3,540
0.269
[10,]
3,408
3,130
3,685
0.277
[11,]
3,148
2,869
3,427
0.279
[12,]
3,246
2,959
3,532
0.287
fvar [[" fcst " ]][ [" valorfobuss "]]
Time
fcst
lower
upper
CI
[1,]
15,050
14,256
15,843
0.793
[2,]
15,667
14,809
16,524
0.857
[3,]
14,325
13,436
15,214
0.889
[4,]
15,762
14,872
16,651
0.889
[5,]
13,763
12,871
14,655
0.892
[6,]
14,113
13,214
15,011
0.899
[7,]
12,884
11,981
13,787
0.903
[8,]
12,785
11,873
13,697
0.912
[9,]
12,601
11,678
13,524
0.923
[10,]
15,061
14,135
15,988
0.926
[11,]
14,703
13,768
15,638
0.935
[12,]
15,392
14,449
16,336
0.944
Source: prepared by the authors, 2024.
