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Archives of Business Research – Vol. 9, No. 12
Publication Date: December 25, 2021
DOI:10.14738/abr.912.11328.
Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence Between International Trade and Macroeconomic
Stability in Nigeria: A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
Services for Science and Education – United Kingdom
Dynamic Linear Interdependence between International Trade
and Macroeconomic Stability in Nigeria: A Vector Error
Correction Modelling
Tuaneh, Godwin Lebari
Dept. of Agricultural and Applied Economics
Rivers State University, PMB 5080, Port Harcourt, Nigeria
Essi, Isaac Didi
Department of Mathematics, Rivers State University
PMB 5080, Port Harcourt, Nigeria
Ozigbu, C. Johnbosco
Department of Economics, Rivers State University
PMB 5080, Port Harcourt, Nigeria
ABSTRACT
Causal relationships are often treated erroneously in isolation as a single equation
without the consideration of the endogeneity of right-hand side variables and also
without recourse to the presence of co-integration. This study modelled and
estimated the dynamic linear interdependence between international trade and
macroeconomic stability in Nigeria. The specific objectives were to, establish the
trend of the study variables, model and estimate the interdependence existing
among total export, total import, exchange rate, and inflation rate, determine the
significant causalities and summarize the causal channels among the study
variables. The study used the quasi-experimental design. Monthly time series data
on all the variables, which spanned from January, 2000 to June, 2019 were sourced
from the Central Bank of Nigeria Statistical Bulletin. Appropriate models were
specified in line with the objectives. The study used the Vector Error Correction
Models, the pre and post-diagnostic tests were also conducted. The unit root test
results showed that the variables were integrated of order one [I(1)]. The co- integration test results showed 1 co-integrating equation and VAR lag length
selection criteria choose lag 3. The Vector Error Correction Result showed that
inflation rate was the most explained by variations in the independent variables (R2
=73.4%) while exchange Rate was the least explained (R2 =18.8%), the total export
model had R2 = 53.8% and total import model had (R2 =59.2%. Significant bi- directional causality was found between total export and inflation rate, and also
between total import and inflation rate. There was also significant joint causality on
total import and also on exchange rate. The post test showed that the models were
stable. It was recommended that the right-hand side variables should be tested for
endogeneity before concluding on single or system equation. It was also
recommended that policies to check inflation rate should consider possibility of
shocks to international trade.
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Archives of Business Research (ABR) Vol. 9, Issue 12, December-2021
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Keywords: Vector Error Correction Model (VECM), International Trade, Export, Import,
Exchange Rate, Inflation Rate, Macroeconomic Stability, Nigeria.
INTRODUCTION
The relationships among variables are often measured using the correlation analysis. The
correlation analysis also measures, strength, significance and the direction of the relationship.
However, it does not answer the question of cause or effect. The effects of one or more variables
on the other are determined using the regression analysis. The most common among the
regression tools is the Ordinary Least Squares (OLS). One often violated assumption of the OLS
is the true exogeneity of the right-hand side variables. Tuaneh and Essi (2017) recommended
in their study on simultaneous equation models that models should be tested for exogeneity of
the right-hand side variables before concluding on the statistical tools to use. According to
Koutsoyiannis (2003), the application of least squares in a single equation assumes among
other things that the explanatory variables are truly exogenous. Consequently, there should be
one-way causation between the dependent and the independent variables. Essi et al. (2010)
explained that using OLS in estimating an equation gives an inconsistent estimate because of
the existing relationships between independent variable and the stochastic disturbance. Brooks
(2008), Tuaneh and Essi (2017) among other studies asserted that the application of OLS to a
structural equation which is part of a simultaneous system will lead to biased coefficient
estimate known as simultaneity bias. Gujarati (2001) reported that ‘According to Sims,
variables should be viewed on equal basis (endogenous) when true simultaneity exist between
set of variables. On this consideration, Sims built the Variance Autoregressive (VAR) model’.
Simultaneity Bias
Note that Yt = βXt + Ut (1.1)
and �" = (Xt
1Xt)-1 Xt
1Yt (1.2)
Where; Yt = Dependent Variable, Xt = Independent variable, β = regression coefficient, Ut = Error
term. Putting equation 1.1 in equation 1.2,
�" = (Xt
1Xt)-1 Xt
1(βXt + Ut) (1.3)
�" = (Xt
1Xt)-1 Xt
1Xtβ + (Xt
1Xt)-1 Xt
1Ut (1.4)
�" = β + (Xt
1Xt)-1 Xt
1Ut (1.5)
Following from equation 1.5 above, if E(Ut) = 0, it implies therefore that E(�") = β, ie �" becomes
the unbiased estimator of β and the application of the OLS holds, but when the assumption is
violated [E(Ut) ≠ 0], and the E(�") ≠ β because the last term in equation 1.5 will not vanish, as a
result, it is erroneous to treated the model in isolation as a single equation model.
VAR is one of the few statistical tools used in addressing issues of simultaneity bias. VAR is a
system (multi-equation) in which all the variables are viewed as endogenous (dependent)
consequently, each variable is a dependent variable in the system of equation. VAR is
a stochastic process model used to capture the linear interdependencies or dynamic
interrelationship among multiple time series. It is a known time-series modelling technique
which has earned so much popularity since Sims introduced it in 1980. For the Analysis of
multivariate time series, VAR model is one of the most efficient models, scalable and easy to
model, it has been successfully utilized for explaining the complexity and dynamic behavior of
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
financial and economic time series and for forecasting. VAR is a multivariate time series
modification of the single variable autoregressive (AR) model to.
A VAR system includes a set of m variables and each one along with an error term is represented
as a linear p lag function of itself and the other m – 1 variables. This implies that the right-hand
side of each equation contains lagged values of the endogenous variables of the system in the
reduced form.
A VAR model is basically a multivariate linear autoregressive time series model, the general
form is; Yt = ψ! + ∑ ψ"Yt-i + εt
#
$%& (1.6)
Where; Yt = A set of endogenous time series variables (Yt1, Yt2, ...., Ytn), and it is nx1 Vector,
ψ! = A KX1 vector of intercepts, ψ" = Full rank m by m matrix of coefficients, and i = 1, 2,
3,..., p, εt = Ut1, Ut2, ..., Unt are ~ iid ~ mean 0, error term (white noise).
However, VAR assumed that there is no cointegration between the variables. The analysis
changes when there is cointegration amongst the I(1) variables. The first difference is that the
summative model becomes Error Correction (VECM) Model. More explicitly, when variables in
the study are co-integrated or found to have one or more cointegrating vectors, then a suitable
estimation technique is the Vector Error Correction Model (VECM) because it can corrects the
short-run and long run deviations from equilibrium.
The general form of the VECM is;
∆Yt = �! + α&ECM'(& + ∑ βi∆Yt-i + εt
#
$%& (1.7)
ECMt-1 is known as the Error correction term. It measures the speed of adjustment to
equilibrium.
Aim and Objectives
The study applied Vector Error Correction in modelling and estimating the dynamic
interdependence among international trade and macroeconomic stability. The study adopted
the measures used by Tuaneh and Essi (2021) who used total export and total import as proxies
for international trade while exchange rate and inflation rate were used as proxies for
macroeconomic stability. The specific objective therefore; (i) ascertained the trend of the study
variables, (ii) modelled and estimated the interdependence existing among total export, total
import, exchange rate, and inflation rate in Nigeria. (iii) determined the direction of causality,
the significance of the causality and also summarize the causal channels among total export,
total import, exchange rate, and inflation rate. (iv) ascertained the fraction in each variable
explains by the innovations in the other variables.
LITERATURE
Export and Exchange Rate
Thuy & Thuy (2019) analyzed the effects of exchange rate fluctuations on exports in Vietnam
using quarterly data from 2000- 2014. The analysis utilized the autoregressive distributed lag
model. The findings showed that exchange rate fluctuations negatively influenced export
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
Unrelated Regression (SUR) and the generalized autoregressive conditional heteroskedasticity
(GARCH) in testing the volatility of the exchange rate. The result showed the presence of
volatility in the exchange rate. The findings also established the negative relationship between
the exchange volatility and export performance of oil and non-oil sectors.
Elif & Oksan (2014) studied the influence of exchange rate on import and export. The study
used the panel co-integration analysis and found out that a long-run co-integrated relationship
existed between effective exchange rates, imports and exports of emerging economies.
Muhammed (2014) studied whether exchange rate instability in Pakistan affects import,
export, trade balance, foreign exchange reserve and GDP. He used yearly data from 1952 to
2010. The researcher conducted the granger causality test and found out that depreciation of
exchange rate had a positive effect on exports.
Gherman, Ştefan, & Filip (2013) examined exchange rate volatility effects on export
competitiveness of the economy of Romania. The study used the simple regression analysis.
Their findings showed that export responded to exchange rate fluctuations which implied that
a depreciation of the Romanian currency affected export positively.
Zukarnain (2013) studied the association between exchange rate volatility and export in the
Malaysian economy. The study utilized regression analysis while also adopting the Generalized
Autoregressive Conditional Heteroscedasticity (GARCH(1,1)) Model in accounting for volatility
in exchange rate within the period under study (2000-2012). The result indicated that exports
from Malaysia to Japan and the US were related to exchange rate volatility. However, the
association between Malaysia exchange rate of and export to the USA was found to be negative
while that of Japan was positive. On the other hand, Malaysia's export to Singapore and the
United Kingdom was insignificantly related to the volatility in the exchange rates.
Erdal et al. (2012) carried out a pragmatic study on the effects of Real Effective Exchange Rate
Volatility on Agricultural Export and Agricultural Import in Turkey. The work span through
1995-2007. It adopted the Generalized Autoregressive Conditional Heteroscedasticity model.
The long-term equilibrium relationship between variables was also ascertained using the
Johansen co-integration test. The pairwise Granger causality established the direction of the
relationship. The findings showed that there was a direct and significant long-term relationship
between real exchange rate and Agricultural Export.
Import and Exchange Rate
Oyelade (2018) explored the determinants of import in Nigeria. The analysis employed the
autoregressive distributed lag process. The results indicated that domestic wages, import rates,
and index of openness exerted a direct and significant effect on import in the short-run, while
domestic interest rate imposed a long-run significant and negative effect on the import of goods
and services in Nigeria.
Muhia (2018) examined the impact of exchange rates fluctuations on imports and exports
(1980-2015) using a log-linear multiple regression model. The findings show that the
fluctuations of the real exchange rate significantly affected imports and exports. Also, the rise
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in exchange rate volatility has had long-term adverse effects on exports but does not impact
imports.
Oloyede and Essi (2017) analyzed the Impact of the Exchange Rate on Imports and Exports in
Nigeria from January 1996 to June 2015. The analysis used the vector auto-regression (VAR),
model. The results indicates that exchange rates had a positive and insignificant impact on
imports, a negative and insignificant effect on exports at lag 1 and a positive and insignificant
effect at lag 2. Exports were also found to influence exchange rates negatively while imports
affect exchange rates positively. The above result, therefore, indicates that the exchange rate in
Nigeria was not significantly affected by the activities of imports and exports. Neither does the
exchange rate impact on the imports and exports in Nigeria.
Isnowati (2015) studied the impact of the exchange rate, national income and inflation on the
import price in Indonesia. The research used the Error Correction Model (ECM) (ECM). The
findings exposed that the exchange rate had a positive impact on import. The result also showed
that the inflation rate had a positive and important impact on import in the short and long run.
Godfrey and Cosmas (2014) examined the effect of exchange rates on exports, imports and
national production in Tanzania from 1990–2011. The study followed the Vector Error
correction model, Variance Decomposition, Impulse Response Function, and Time-series
Simulation. The findings showed that variables had a long-run association with the exchange
rate but a lower long-run effect on and export and import.
Export and Inflation
Evans et al. (2017) studied the association between exports and inflation in Kenya: for the
period 2005–2015. The study used Vector autoregression (VAR) analytical techniques,
Johansen cointegration, Granger causality,.VECM hence explained the variance decomposition
and impulse response function result. The results showed that inflation has a significant
positive long-run association with total exports. This is a conclusion supported by variance
decomposition and impulse analysis with a coefficient of 1.39 at 5% level of significance
Kiganda et al. (2017) examined the relationship between exports and inflation in Kenya. The
study adopted the VECM, variance decomposition, impulse response and Granger causality. The
findings revealed that in the long-run, inflation had a direct and significant relationship with
total exports.
Thorvaldur (1998) investigated the determinants of export using regression analysis. The
study covering 160 countries use a cross-sectional data the result showed an indirect link
between inflation and export during the period under study.
Import and Inflation
Volkan & Ergün (2017) analyzed the connection between the import volume and inflation rate
in Turkey. The research employed an error correction model and the Granger causality
technique. The findings from the study showed that there was indeed a long term and short
term co-integrating correlation existed between inflation and import volume in the Turkish
economy.
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
Dewan and Shafiullah (2014) studied the relationship between inflation, import and export in
Bangladesh. The research used monthly time series data from 1994-2011. The research used
the Cointegration and Error Correction Model and Variance Decomposition and Granger
causality test. By using the Cointegration technique. The result showed that in the long run, a
one per cent rise in import and export contributes to a 3.21 per cent increase and a 1.91 per
cent decrease in inflation respectively. The results of variance decompositions showed that
export had the highest shock effect on inflation. The Granger causality result of the study
indicated a unidirectional causality running from Inflation to import and the presence of
bidirectional causality between inflation and export.
Ariful (2013) researched the effect of inflation on import in Bangladesh, using correlation
analysis. The findings showed that there was a direct and insignificant link between inflation
and import trade in Bangladesh.
Ofori et al. (2015) examined the relationship between import and inflation in the economy of
Ghana. They followed the Autoregressive Distributed Lag Model (ARDL) co-integration process.
The findings showed a significant co-integrating association between inflation and import. The
result also showed that import was negatively linked to inflation and, negligible in the long run
while there existed an inverse but significant association between inflation and import in the
short run. The study subsequently concluded that import was not inflationary during the time
of the study (1960-2012).
METHODOLOGY
This section presents the research design, types and sources of data, data collection methods,
methods of data analysis and model specification.
Research Design
The quasi-experimental design was used. This was owing to the fact that the study determined
the causes and effects relationship of the variables
Types and Sources of Data
The study used monthly time series data on exchange rate, inflation rate total import, and total
export, spanning from January 2000 to June 2019. The data were obtained from the Central
Bank of Nigeria (CBN) Statistical Bulletin 2019.
Methods of Data Analysis
The study adopted the Vector Error Correction Model (VECM) a linear modelling technique.
However, pre-test particularly the unit root tests and the co-integration tests were conducted
to ascertain the stationarity status and long term equilibrium relationship among the study
variables.
The Vector Error Correction Model: This was required for the estimation of the specified
models n line with the stated objectives. The choice of the VECM was driven by the popularity
of non-stationary time series and a common existence of cointegrating equations among related
series. Ankargren & Lyhagen (2018) speculates that the VECM provides the most popular ways
to model macroeconomic variables. VECM estimates the short term effects and the long-run
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return to equilibrium. The direction and significance of causalities among the study variables
were also examined using Granger causality/block exogeneity test.
Pre-estimation Tests: These are tests conducted by subjecting the study data to scientific
inquiry about certain characteristics of the data. The first-order diagnostics econometric tests
carried out before using the VECM were the (i) Unit Root Test and (ii) the co-integration test
The Unit Root Test
The study used the Augumented Dickey Fuller and the Phillips-Perron Unit Root test. The null
hypothesis of non-stationary series is rejected in favour of the stationary alternative in each
case if the test statistic is more negative than the critical value or the probability value is less
than 0.05. A rejection of the null hypothesis means that the series does not have a unit root.
The Co-integration Test
The study employed the Johansen maximum likelihood approach. Washall and Sauders (2000)
as reported by Tuaneh (2019) stated that Trace statistics is more robust to skewness and excess
kurtosis in residuals than the Maximum Eigen test, the Maximum Eigen approach is said to be
more preferable due to its properties. The researcher, however, used both Maximum Eigen
statistics and the Trace statistics
Model Specification
The models stated in this section will be used to evaluate the interdependence between
variables that served as proxies for international trade and macroeconomic stability indicators.
VAR Model
A functional K-dimension VAR(p) process as given in 1.6 can also be written as;
Yt = Ω! + Ω&Y'(& + Ω)Y'() + ⋯ + Ω*Y'(* + ��' + �' (3.1)
Where;
Yt = (Y1t, Y2t, Y3t, ... Ykt,) is a KX 1 Vector of the endogenous variable
Xt = (X1t, X2t, X3t, ... Xdt,) is a dX 1Vector of exogenous variable
Ω1 - Ωp are KXK matrix of the lag coefficient to be estimated
C is dXd matrix of the coefficient of the exogenous variable to be estimated
εt = (εt1, εt2, ... , εkt) is white noise innovation process with E(ε') = 0, E(ε'ε'′) = ∑,
The vector of innovations are contemporaneously related to the full rank matrix Σ" but are
uncorrelated with their leads and lags of the innovations and are assumed to be uncorrelated
with all of the right-hand side variables
VECM Models
The above VAR(p) process is on the assumption that there is no cointegration between the
variables. When the I(1) variables have one or more cointegrating vectors, then the appropriate
estimation technique is the Vector Error Correction Model. The short run changes and
deviations from equilibrium is adjusted in VECM.
The general form of the VECM as shown in 1.7 as
∆Yt = �! + α&ECt'(& + ∑ βi∆Yt-i + εt
#
$%& (3.2)
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
With the ECT-1 as the term depicting Error Correction, the VECM involving the four variables is
presented in its framework as:
∆TEX = ECT(,(&) + ∑ �&," ∆ ���'(" + *
"(& ∑ �&," ∆ ���'(" + *
"(& ∑ Γ&," ∆ ���'(" + *
"(&
∑ �&" ∆ ���'("
*
"(& + �& + �',& (3.3)
∆TIM = ECT(,(&) + ∑ �)," ∆ ���'(" + *
"(& ∑ �)," ∆ ���'(" + *
"(& ∑ Γ)," ∆ ���'(" + *
"(&
∑ �)," ∆ ���'("
*
"(& + �) + �',) (3.4)
∆EXR = ECT(,(&) ∑ �/," ∆ ���'(" + *
"(& ∑ �/," ∆ ���'(" + ∑ Γ/," ∆ ���'(" + *
"(&
*
"(&
∑ �/," ∆ ���'("
*
"(& + �/ + �',/ (3.5)
∆INR = ECT(,(&) + ∑ �0," ∆ ���'(" � + *
"(& ∑ �0," ∆ ���'(" + *
"(& ∑ Γ0," ∆ ���'("
*
"(& +
∑ �0," ∆ ���'("
*
"(& �0 + �',0 (3.6)
Where:
TEX = Total Export,
TIM = Total Import,
EXR = Exchange Rate, Vector of endogenous variables
INR = Inflation Rate,
ECT = Error Correction Term,
Δ = difference operator,
∑ = summation,
C1 - C4 = Intercepts,
�&,", �0,", Γ&,", ω&," = Matrix of Autoregressive parameter
�',& − �',0 = Stochastic term (white noise Innovations)
p = Maximum Lag Length
Lag length Selection Criteria
Understanding that too few lags may result in auto-correlated errors whereas too many lags
may result in over fitting and consequently, increase means square forecast error (MSFE) of the
VAR model. The lag length selection uses information criteria to minimize these errors. The
commonly used information criteria are: Akaike Information Criteria (AIC), Hanna Quinn
Information Criteria (HQ) and Schwartz Information Criteria (SC). The lag length selection
result indicated that a lag length of 3 was chosen by most information criteria, however, the
researcher adopted the Akaike Information Criteria which also selected lag length 3, and this
informed specifying the model below with lag length 2 and subsequent estimation was done
using 2 lags. Note the loss of one lag in the Error Correction Models.
Model Specification with the appropriate lag length
∆TEX = �&,!ECT(,(&) + �&,& ∆ ���'(& + �&,) ∆ ���'() + �&,& ∆ ���'(& + �&,) ∆ ���'() +
Γ&,& ∆ ���'(& + Γ&,) ∆ ���'() + ω&,& ∆ ���'(& + ω&,) ∆ ���'() + �&1 + �',& (3.7)
∆TIM = �),!ECT(,(&) + �),& ∆ ���'(& + �),) ∆ ���'() + �),& ∆ ���'(& + �),) ∆ ���'() +
Γ),& ∆ ���'(& + Γ),) ∆ ���'() + ω),& ∆ ���'(& + ω),) ∆ ���'() +�)1 + �',) (3.8)
∆EXR = �/,!ECT(,(&) + �/,& ∆ ���'(& + �/,) ∆ ���'() + �/,& ∆ ���'(& + �/,) ∆ ���'() +
Γ/,& ∆ ���'(& + Γ/,) ∆ ���'() + ω/,& ∆ ���'(& + ω/,) ∆ ���'() +�/1 + �',/ (3.9)
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∆INR = �0,!ECT(,(&) + �0,& ∆ ���'(& + �0,) ∆ ���'() + �0,& ∆ ���'(& + �0,) ∆ ���'() +
Γ0,& ∆ ���'(& + Γ0,) ∆ ���'() + ω0,& ∆ ���'(& + ω0,) ∆ ���'() + �01 + �',0 (3.10)
Where;
�&,! − �0,! = Coefficient of the Error correction Term
C19 – C49 = Intercept
�&,&- �0,&, �&,&- �0,&, Γ&,&- Γ0,&, ω&,&- ω0,&, = Matrix of Autoregressive parameter
RESULTS
Descriptive Analysis
Table 1: Summary of Descriptive Statistics on all Variables of the Study
Statistics TEX TIM EXR INR
Mean 796297.82 551256.95 172.59 12.13
Median 738424.37 524811.90 149.74 11.65
Maximum 1937959.02 1969117.79 381.86 28.21
Minimum 113942.12 32366.88 98.78 -2.49
Std. Dev. 448614.56 402520.19 78.50 4.87
Skewness 0.26 0.57 1.66 0.25
Kurtosis 2.06 2.97 4.33 3.84
Jarque-Bera 11.140 12.533 125.226 9.418
Probability 0.004 0.002 0.000 0.009
Sum 186333688.7 128994125.3
Sum Sq. Dev. 4.68924E+13 3.77512E+13
Observations 234 234 234 234
The descriptive statistics in Table 1 indicated that within the period covered, total export (TEX)
was 186 trillion Naira, with an average of 796.3 billion Naira and a standard deviation of 448.6
billion Naira while. Total import (TIM) was 129 trillion Naira with an average of 551.3 billion
Naira and a standard deviation of 402.5 billion Naira within the period of the study. Total export
(TEX) had a maximum value of 1.93 trillion obtained in April 2019 and a minimum value of 113
billion obtained in February 2002. The maximum of total export (TEX) was 1.96 trillion
obtained in January 2019 and a minimum value of 32.36 billion obtained in January 2000.
The exchange rate on the other hand had an average of 172.59 Naira per dollar with a standard
deviation of 78.70 Naira per dollar. The maximum was 381.86 naira per dollar obtained in May
2017 and the minimum was 98.78 naira per dollar obtained in January 2000. The descriptive
statistics in Table 1 also revealed that inflation rate had an average of 12.13% with a standard
deviation of 4.87%. The maximum was 28.21% obtained in August 2005 and the lowest was -
2.49% attained in January 2000.
Trend Analysis of all Variables
Time plot and trend analysis were conducted and the results presented in Figures 1 - 4.
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
Trend of Total Export
Figure 1 Time Plot and fitted/trend analysis of Total Export (TEX),
TEX = -132013788.11 + 181.02*T
A cursory look at Figure 1 shows that there was a fluctuation in total export throughout the
period of the study. The trend equation on total export above shows that for every additional
month, total export would increase by 181.02 million. The positive slope of the trend line in
Figure 1 typically indicated an upward trend over the duration considered as also indicated by
the positive sign of the parameter of Time period (T) in the TEX trend equation above.
Trend of Total Import
Figure 2 Time Plot and fitted/trend analysis of Total Import (IIM),
TIM = -130000000 + 177.77*T
The time plot on total import in Figure 2 shows that there was a fluctuation in total export over
the period of the study. However, one can also deduce a positive trend from the time plot. The
positive slope of the trend line in Figure 3 largely displayed upward trend of total import over
the period of the study as also indicated by the positive sign of the coefficient of T in the TIM
trend equation above. The trend equation on total import above shows that for every additional
month, total import would increase by 177.77 million.
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Trend of Exchange Rate
Figure 3 Time Plot and fitted/trend analysis of Exchange Rate (EXR),
EXR = -21891.52 + 0.03*T
The time plot on the exchange rate in Figure 3 indicates fluctuation over the period of the study.
However, there is an observable positive trend from the time plot. The positive slope of the
trend line in Figure 3 generally showed upward trend of the exchange rate over the period of
the study as also indicated by the positive sign of the coefficient of T in the EXR trend equation
above. The trend equation on exchange rate above shows that for every additional month, total
import would increase by 0.03 dollar/ naira.
Trend of Inflation Rate
Figure 4 Time Plot and fitted/trend analysis of Inflation Rate (INR),
INR = 140.44 - 0.0002*T
The time plot on inflation rate in Figure 4 indicates fluctuation over the duration of the study.
However, there is a noticeable negative trend from the time plot. The negative slope of the trend
line in Figure 4.8 generally showed downward trend of inflation rate over the period of the
study as also indicated by the positive sign of the coefficient of T in the INR trend equation
above. The trend equation on inflation rate above indicates that for every added month,
inflation would decrease by 0.0002 per cent
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
Pre-estimation Diagnosis
Table 2: Unit Root Test Results
Vari
able
ADF Phillips-Perron ADF Phillips-Perron Order of
Levels Sig Levels Sig 1st Diff Sig 1st Diff Sig integration
TEX -2.670 0.247 -1.633 0.463 -7.66*** 0.000 -22.86*** 0.000 I(1)
TIM -0.100 0.946 -3.366 0.056 -11.66*** 0.000 -82.88*** 0.000 I(1)
EXR -0.995 0.941 -0.842 0.959 -12.68*** 0.000 -12.51*** 0.000 I(1)
INR -0.974 0.294 -1.081 0.252 -13.48*** 0.000 -13.46*** 0.000 I(1)
The study adopted the Augmented Dickey-Fuller and the Phillips-Perron unit root tests. Data
on the study variables were tested for unit root to guide against the problem of spurious
regression as explained in the methodology. The Augmented Dickey-Fuller (ADF) and the
Phillips-perron (PP) statistics tested the null hypothesis of a non-stationarity. The result of the
test as shown in Table 2 shows that at all variables were stationary at first difference. Both
Augmented Dickey-Fuller and the Phillips-Perron unit root tests showed that the variables
were stationary after first difference. More so, while the time plots and the trend plots
respectively showed obvious fluctuation and an identified pattern of movement of the the
series, the plots of the series at first difference as shown in Figure 5 were de-trended.
Figure 5
It was necessary to perform the cointegration test to establish the presence or absence of long- run relationship among the study variables, nevertheless, owing to the fact that the stationarity
test results indicated I(1), the Johansen method of cointegration was effective and was
conducted and presented below:
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Table 3: Johansen Co-integration Test
Hypothesiz
ed No. of
CE(s)
Eigen
value
Trace
Statistic
0.05
Critical
Value Prob.**
Max- Eigen
Statistic
0.05
Critical
Value Prob.**
None * 0.1269 58.843 47.856 0.003 31.08408 27.584 0.017
At most 1 0.0877 27.759 29.797 0.084 21.02599 21.131 0.051
At most 2 0.0242 6.733 15.495 0.609 5.611327 14.265 0.663
At most 3 0.0048 1.122 3.841 0.290 1.121722 3.841 0.290
The Trace test and the Max-eigenvalue test showed 1 cointegrating equationat the 0.05 level of
significance. The normalized cointegrating equation is:
EXR = 28.27903INR – 0.00039TEX + 0.00067TIM
(5.61597) (0.00013) 0.00015)
The long-run combination of stationary processes can be non-stationary, cointegration exists if
long-run or equilibrium relationship exists between them. The study employed the Johansen
maximum likelihood approach and the results as presented in Table 3 indicates from the Trace
statistics that the null hypothesis of no cointegrating relationship was rejected in favour of at
most 1 cointegrating relationship (Trace statistics = 58.84 > 47.85 critical value and a
probability 0.017). More so, from the Maximum Eigen statistics, the null hypothesis of no
cointegrating relationship was rejected in favour of a cointegrating relationship (Max-Eigen
statistics 31.08 > 27.58 critical value and a probability 0.017), therefore, there exists a long-run
relationship among the variables. This agrees with Elif & Oksan (2014) who found out from the
panel co-integration analysis of their study that a long-run co-integration related existed
between effective exchange rates, imports and exports. Given the existence of co-integrating
equations, the estimation of the vector error correction model was necessary.
The Interdependence Existing among Total Export, Total Import, Exchange Rate, and
Inflation Rate
The results of the cointegration analysis indicated the presence of cointegrating relationship,
consequently, the Vector Error Correction Model (VECM) was preferred to the Vector Auto- regression (VAR) as explained in the methodology. The VECM was estimated in the differenced
form through the period January 2000 to June 2019. The period showed a fairly lengthy time
dimension and as such there was sufficient information for parameter estimation.
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The error correction term explains the speed with which the model returns to equilibrium
following an external shock. It is often indirectly signed depicting a backward movement
towards equilibrium, a positive sign on the other hand would mean a movement away from
equilibrium. The error correction as shown in short-run result in Table 4 shows that the error
correction term was negative (correctly signed) and significant at 5% level of significance (t = -
2.093). The result implied that the previous period’s deviation from long-run equilibrium was
corrected in the subsequent period at 8.7% speed of adjustment. The short-run result in Table
4 also showed that only the first lag of total export (t = -12.664), second lag of total export (t =
-6.537), and first lag of inflation rate ((t = 2.147) had significant effects on total export at 0.05
level of significance.
Effects of Total Export, Exchange Rate, and Inflation Rate on Total Import
Table 5: Vector Error Correction Model (DTIM as Dependent Variables)
Cointegrating Eq:
Exogenous
variables Coefficient Standard
error t-stat
TIM(-1) -0.815 0.20588 -3.956**
EXR(-1) -0.386 1.01768 -0.379
INR(-1) 1.572 0.11335 13.866***
C -0.006
Error Correction:
Exogenous
variables Coefficient Standard
error t-stat
ECM(-1) 0.177 0.067 2.650**
DTEX(-1) -0.037 0.108 -0.341
DTEX(-2) -0.036 0.100 -0.357
DTIM(-1) -0.877 0.071 -
12.299***
DTIM(-2) -0.397 0.062 -6.418***
DEXR(-1) 0.142 0.604 0.235
DEXR(-2) -0.077 0.602 -0.128
DINR(-1) -0.288 0.082 -3.512**
DINR(-2) -0.119 0.053 -2.225**
C -0.002 0.020 -0.090
R2 0.592
�"! 0.576
Note: * = significant at 10%, ** = significant at 5%, and *** = significant at 1%
ECTt-1 = 1.000TEX(t-1) - 0.815*TIM(t-1) - 0.386*EXR(t-1) + 1.572*INR(t-1) - 0.006
D(TIM) = 0.177*ECT(t-1) - 0.037*D(TEX)(t-1) - 0.0358*D(TEX)(t-2) - 0.877*D(TIM)(t-1) -
0.397*D(TIM)(t-2) + 0.142*D(EXR)(t-1) - 0.077*D(EXR)(t-2) - 0.288*D(INR)(t-1) - 0.119*D(INR(t-2) -
0.002
The v result presented in Table 5 above revealed that(�P)) was 0.576. This implied that 57.6%
variation in total import is explained by the changes in total export, exchange rate and inflation
rate, the remaining 42.4% are explained by other variables not include in the model. The error
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
correction result in Table 5 indicates that the error correction term was signed correctly
(negative) and statistically significant (t = -2.650) at 5% level of significance. The error
coefficient of -0.177 implied an adjustment speed of 17.7%. This means that the long run
deviation from equilibrium in previous period was corrected in the current period at an
adjustment speed of 17.7%. The short run result in Table 5 also showed that the first lag of total
import (t = -12.299), second lag of total import (t = -6.418), first lag of inflation rate (t = -3.511),
and the second lag of inflation rate (t = -2.225) had significant effects on total import at 0.05
level of significance.
Effects of Total Export, Total Import, and Inflation Rate on Exchange Rate
Table 6: Vector Error Correction Model (DEXR as Dependent Variables)
Cointegrating Eq:
Exogenous variables Coefficient Standard error t- stat
TEX(-1) -0.815 0.20588 -3.956**
EXR(-1) -0.386 1.01768 -0.379
INR(-1) 1.571708 0.11335 13.866***
C -0.006
Error Correction:
Exogenous
variables Coefficient Standard
error t-stat
ECM(-1) -0.008 0.007 -1.076
DTEX(-1) 0.001 0.012 0.097
DTEX(-2) -0.010 0.011 -0.952
DTIM(-1) -0.004 0.008 -0.550
DTIM(-2) -0.006 0.007 -0.985
DEXR(-1) -0.397 0.064 -6.181***
DEXR(-2) -0.269 0.064 -4.200**
DINR(-1) 0.012 0.009 1.365
DINR(-2) 0.011 0.006 1.906
C 0.000 0.002 -0.016
R2 0.188
�"! 0.155
Note: * = significant at 10%, ** = significant at 5%, and *** = significant at 1%
ECTt-1 = 1.000TEX(t-1) - 0.815*TIM(t-1) - 0.386*EXR(t-1) + 1.572*INR(t-1) - 0.006
D(EXR) = - 0.008*ECM(t-1) + 0.001*D(TEX)(t-1) - 0.010*D(TEX)(t-2) - 0.004*D(TIM)(t-1) -
0.006*D(TIM)(t-2) - 0.397*D(EXR)(t-1) - 0.269*D(EXR)(t-2) + 0.012*D(INR)(t-1) + 0.011*D(INR(t-2) –
0.000033
Table 6 revealed an adjusted (R2) of 0.155. This implied that 15.5% variation in exchange rate
is explained by variations in total import, total export, and inflation rate, the remaining 84.5%
were explained by other variables not include in the model. This does not show a good fit. The
error correction result in Table 6 shows that the error correction term was correctly signed
(negative) and was not statistically significant at 5% level of significance (t = -1.076). The error
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correction coefficient of -0.008 showed that the previous period’s deviation from long run
equilibrium was corrected in the current period at an adjustment speed of 0.8%. The short run
result in Table 6 showed that only the first and second lag of total import (t = -6.181) and (t = -
4.200) respectively had significant effects on exchange rate at 0.05 level of significance.
Effects of Total Export, Total Import, and Exchange Rate on Inflation Rate
Table 7: Vector Error Correction Model (DINR as Dependent Variables)
Cointegrating Eq:
Exogenous
variables Coefficient Standard
error t-stat
TEX(-1) -0.815 0.20588 -3.956**
EXR(-1) -0.386 1.01768 -0.379
INR(-1) 1.572 0.11335 13.866***
C -0.006
Error Correction:
Exogenous
variables Coefficient Standard
error t-stat
ECM(-1) -0.900 0.066 -13.565***
DTEX(-1) 0.457 0.107 4.264**
DTEX(-2) 0.067 0.099 0.676
DTIM(-1) -0.472 0.071 -6.677***
DTIM(-2) -0.232 0.061 -3.795**
DEXR(-1) -0.331 0.598 -0.553
DEXR(-2) -0.460 0.597 -0.770
DINR(-1) 0.165 0.081 2.029**
DINR(-2) 0.044 0.053 0.835
C 0.015 0.020 0.785
R2 0.734
�"! 0.723
Note: * = significant at 10%, ** = significant at 5%, and *** = significant at 1%
ECTt-1 = 1.000TEX(t-1) - 0.815*TIM(t-1) - 0.386*EXR(t-1) + 1.572*INR(t-1) - 0.006
D(INR) = - 0.900*ECM(t-1)0.457*D(TEX)(t-1) + 0.067*D(TEX)(t-2) - 0.472*D(TIM)(t-1) -
0.232*D(TIM)(t-2) - 0.331*D(EXR)(t-1) - 0.460*D(EXR)(t-2) + 0.165*D(INR)(t-1) + 0.044*D(INR)(t-2) +
0.015
Table 7 showed that the adjusted coefficient of determination(�P) ) is 0.723. Thus 72.3%
variation in inflation rate is explained by variations in total import, total export, and exchange
rate. This shows good fit, the remaining 27.3% were explained by other variables not included
in the model. The error correction result shows that the error correction term was signed
correctly and was also statistically significant at 5% level of significance (t = -13.565). The error
coefficient of -0.900 showed that the deviation from long-run equilibrium in the previous
period was corrected in the current period at an adjustment speed of 0.8%. The short-run result
in Table 7 showed that; the first lag of total export (t = 2.64), first and second lag of total import
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
(t = -6.677) and (t = -3.795) respectively had the first leg of exchange rate had significant effects
on inflation rate at 0.05 level of significance.
The significance of the Causality, Direction of Causality, and Summary of the Causal
Channels among Total Export, Total Import, Exchange Rate, and Inflation Rate
Direction of Causality and Causal Channels
The direction of causality amongst the series in the model was captured using the Granger
causality test. The test was carried out at 5% level of significance and the results summarized
in Table 9.
Figure 6: Causal Channels among Variables
The arrows in Figure 6 were indications of the direction of the causality, a single arrow
indicated unidirectional causality while the double arrow indicated bidirectional causality. The
broken lines indicated insignificant causality implying that the broken line between the
exchange rate and inflation rate was not significant. The thick lines, on the other hand, indicated
a significant causality hence the thick lines between export and inflation rate means that a
significant relationship exists between them, the double-headed arrow implied a bidirectional
relationship from export to the inflation rate and from inflation rate to export. This was also the
case in the relationship between import and inflation rate. Hence, significant bidirectional
causality was found between total export and inflation rate and also between total import and
inflation rate. This is depicted in the causal channels among variables in Figure 6.
Significance of Causality (Discussion of the Test of Hypotheses Results)
Apart from the tests of the significance of joint causality on each variable, 60% of the
hypotheses was to ascertain the significance of bidirectional causality between pairs of the
study variables.
Total Export
Total Import
Exchange
Rate
Inflation
Rate
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Table 8: Summary of Bidirectional Causality Test Results
Direction of
causality
Chi-square (X2)
calculated
P-value Remark
D(TIM) ® D(TEX) 0.962 0.618 Insignificant causality
D(TEX) ® D(TIM) 0.147 0.929 Insignificant causality
D(TEX) ® D(EXR) 1.820 0.402 Insignificant causality
D(EXR) ® D(TEX) 2.391 0.303 Insignificant causality
D(INR) ® D(TEX) 6.446** 0.040 Significant Bi- D(TEX) ® D(INR) 26.101*** 0.000 directional causality
D(EXR) ® D(TIM) 0.101 0.951 Insignificant causality
D(TIM) ® D(EXR) 1.007 0.604 Insignificant causality
D(INR) ® D(TIM) 12.819*** 0.002 Significant Bi- D(TIM) ® D(INR) 46.036*** 0.000 directional causality
D(INR) ® D(EXR) 3.652 0.161 Insignificant causality
D(EXR) ® D(INR) 0.699 0.705 Insignificant causality
All ® D(TEX) 11.969 0.063 Insignificant causality
All ® D(EXR) 5.955 0.428 Insignificant causality
All ® D(TIM) 13.695** 0.033 Significant Joint
causality
All ® D(INR) 58.436*** 0.000 Significant Joint
causality
Null Hypothesis (H0): No bidirectional causality between each pair of variable
The causality from total export to total import was determined with the granger causality test
conducted and presented in Table 8. The results showed that there is no significant
bidirectional relationship between total export and total import. showed a chi-square of 0.147
and a corresponding PV = 0.929 > 0.05, therefore, there was no significant unidirectional
relationship from total export to total import. The direction from total export to total import
showed a chi-square of 0.962 and a corresponding PV = 0.618 > 0.05 therefore there was no
significant unidirectional relationship from total import to total export. Overall, there was no
enough evidence to conclude that a significant bidirectional relationship between total export
and total import.
On the direction of causality from total export to exchange rate, the granger causality test
conducted and presented in Table 9 showed a chi-square of 1.820 and a corresponding PV =
0.402 > 0.05, hence there was no significant unidirectional relationship from total export to
exchange rate. The direction from total export to exchange rate showed a chi-square of 2.391
and a corresponding PV = 0.303 > 0.05therefore there was no significant unidirectional
relationship from total export to exchange rate. Accordingly, there is no enough evidence to
conclude a significant bidirectional relationship between total export and exchange rate. This
negates the findings of Odili (2015) who found out significant unidirectional relationship
running from exchange rate to import. It however agree with the findings of Nyeadi et al.(2014)
who found out that exports was not significantly affected by the exchange rate in Ghana. In the
same manner.
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
The causality from total export to the inflation rate as shown in Table 8 indicates a chi-square
of 26.101 and a corresponding PV = 0.000 < 0.05, therefore, there was a significant
unidirectional relationship from total export to the inflation rate. The direction from inflation
rate to total export showed a chi-square of 6.446 and a corresponding PV = 0.040 < 0.05
therefore there was a significant unidirectional relationship from inflation rate to total export.
Overall, there was a significant bidirectional relationship between total export and inflation
rate. This agreed with Dewan and Shafiullah (2014) who found out significant bidirectional
causality between inflation and export. Evans et al. (2017) also found out from their study on
the association between exports and inflation in Kenya that inflation has a significant positive
long-run association with total exports. The result is also supported by findings of Kiganda et
al. (1998).
The causality from total import to the inflation rate as shown in Table 8 indicates a chi-square
of 46.036 and a corresponding PV = 0.000 < 0.05, therefore, there was a significant
unidirectional relationship from total import to the inflation rate. The causality from inflation
rate to total import showed a chi-square of 12.819, PV = 0.040 < 0.05 therefore there was a
significant unidirectional relationship from inflation rate to total import. Overall, it was
therefore concluded that there is a significant bidirectional relationship between total import
and inflation rate. This result agreed with Dewan and Shafiullah (2014) who found significant
unidirectional causality running from Inflation to import. Ofori, Richardson, & Asuamah (2015)
also significant cointegrating association between inflation and import.
The joint causality from all variables (total import, inflation rate, and exchange rate) to total
export as presented in Table 8 showed a chi-square of 11.969, PV = 0.0.063 > 0.05.
Consequently, there is no enough evidence to a significant joint causality on total export.
The joint causality on exchange rate as presented in Table 8 showed a chi-square of 5.955, PV
= 0.428 > 0.05, an insignificant jointly on exchange rate was thus concluded.
The post estimation test conducted showed that the model had no serial correlation at lag 1 and
2, (Rao F Stat = 0.596, PV = 0.888 > 0.05), and (Rao F Stat = 0.745, PV = 0.748 > 0.05)
respectively. The result also showed that the residuals were multivariate normal on the total
export and the total import components. The heteroskedasticity revealed that the residual was
homoscedastic. The stability test conducted also showed that all roots lie inside the unit root
circle and the detailed result showed that all modulus were less than one, consequently, the
estimated VECM was stable.
Fraction in each Variable Explained by the Innovations in the other Variables
The Impulse Response Function
The VAR model allows the effects of shocks in other variables to be seen. This also holds for
shocks to endogenous variables. Shocks to endogenous variables do not only directly impact an
endogenous variable but are also transmitted to other endogenous variables via the dynamic
(lag) structure of the VAR. To assess the effect of a one-time shock on the current and future
values of the endogenous variables, the impulse response is utilized. The dynamics of the model
as shown in Table 10. This study revealed four fundamental innovations: I a shock to total
export; (ii) a shock to total import; (iii) a shock to the exchange rate; and (iv) shock to inflation;
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both shocks are one standard deviation (or sigma) apart from the respective series' first
difference.
Variance Decomposition
One of the methods used in the study of the dynamic interaction among the variables that occur
after the data is post-sampled is the variance decomposition. It was also important to isolate
the variance in an endogenous variable into the effects of the shocks on the system. The
variance decomposition was used to calculate this. Variance decomposition gives information
about the comparative significance of each random innovation as it affects variables in the
system differently.
Table 9: Table of Variance Decomposition
Variance Decomposition of
DTEX:
Period S.E. DTEX DTIM DEXR DINR
1 0.186291 100.0000 0.000000 0.000000 0.000000
2 0.188685 98.32728 1.140108 0.349941 0.182668
3 0.211410 96.84030 0.922513 0.869077 1.368111
. . . .
12 0.325247 96.52775 1.048431 0.958577 1.465237
Variance Decomposition of DTIM:
1 0.299982 4.073184 95.92682 0.000000 0.000000
2 0.301135 4.742794 95.24305 0.006445 0.007715
3 0.341606 4.359388 93.53092 0.032332 2.077356
. . . .
12 0.496676 6.129508 91.44833 0.025649 2.396516
Variance Decomposition of DEXR:
1 0.031926 0.413148 0.156053 99.43080 0.000000
2 0.037302 0.304269 0.116185 99.57942 0.000125
3 0.040534 0.481630 0.177106 99.33634 0.004927
. . . .
. . . .
12 0.070838 0.190078 0.094261 99.33993 0.375729
Variance Decomposition of DINR:
1 0.297410 0.422409 2.048180 0.098247 97.43116
2 0.319417 4.114530 6.057634 0.093166 89.73467
3 0.324792 5.630672 7.242001 0.146126 86.98120
. . . .
. . . .
12 0.382886 10.93763 24.21248 0.118508 64.73138
Cholesky Ordering: DTEX DTIM DEXR DINR
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Tuaneh, G. L., Essi, I. D., & Ozigbu, C. J. (2021). Dynamic Linear Interdependence between International Trade and Macroeconomic Stability in Nigeria:
A Vector Error Correction Modelling. Archives of Business Research, 9(12). 65-90.
URL: http://dx.doi.org/10.14738/abr.912.11328
Figure 7: Variance Decomposition Graph
Variance Decomposition of Total Export
The percentage of the forecast error variance as shown Table 9 revealed that in the short run,
100% forecast variance in total export is self-explained. Total import, exchange rate, and
inflation rate, however, showed very weak influence in predicting total export hence they are
strongly exogenous. Total export decreases while total import, exchange rate, and inflation rate,
increased as we move into the future but were not strongly exogenous as the percentage
forecast variance of total export was 96.52% in the long run while the percentage forecast
variance of total import, exchange rates and inflation rates, in the long run, were 1.05%, 0.96%,
and 1.46% respectively.
Variance Decomposition of Total Import
Table 9 showed that 95.92% of the forecast error variance of total import in the short run was
explained by its shock. Total export exchange rate and inflation rate, however, showed very
weak influence in predicting total import hence they are strongly exogenous. In the long run,
however, total import decreases while total export, exchange rate, and inflation rate increases
as we move into the future but at a very slow rate and were not strongly exogenous The
percentage forecast variance of total import was 91.44% in the long run while total import,
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12
DTEX DTIM
DEXR DINR
Variance Decomposition of DTEX
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12
DTEX DTIM
DEXR DINR
Variance Decomposition of DTIM
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12
DTEX DTIM
DEXR DINR
Variance Decomposition of DEXR
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12
DTEX DTIM
DEXR DINR
Variance Decomposition of DINR
Variance Decomposition using Cholesky (d.f. adjusted) Factors
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exchange rates and inflation rates, in the long run, were 4.36%, 0.030%, and 2.30%
respectively.
Variance Decomposition of Exchange Rate
The percentage of the forecast error variance as shown in Table 9 revealed that in the short
run, 99.43% forecast variance in the exchange rate is self-explained. Total import, total export,
exchange rate, and inflation rate showed very weak influence in predicting exchange rate hence
they are strongly exogenous. In the long run, exchange rate decreased while total export, the
total import and inflation rate increased as we move into the future but we're still not strongly
exogenous as the percentage forecast variance of the exchange rate was 99.34% in while the
percentage forecast variance of total import, exchange rates and inflation rates, in the long run,
were 0.19%, 0.19%, and 0.005% respectively.
Variance Decomposition of the Inflation Rate
Table 9 showed that 97.43% of the forecast error variance of inflation rate in the short run was
explained by its own shock. Total export, total import, and exchange rate a showed very weak
influence in predicting inflation rate hence they are strongly exogenous. In the long run,
however, inflation rate decreases while total export, total import, and exchange rate increased
as we move into the future but at a very slow rate and were not strongly exogenous The
percentage forecast variance of inflation rate was 64.73% in the long run while total export,
total import, exchange rates, and inflation rates, in the long run, were 10.93%, 24.21%, and
0.11% respectively.
Historical Decomposition
Historical decomposition measures the contribution of uncertainty shocks to the variables from
their respective baseline projection. It displays the cumulative effects of structural shocks. The
actual change equals baseline forecast + shock1 + shock 2 + shock 3 + ... Baseline forecast refers
to the dynamic forecast of each endogenous variable generated from the VAR model.
Conclusion and Recommendations
Exogeneity test should be key component of pre-estimation diagnosis before concluding on a
single equation or system equation estimation. Having seen that inflation was the most affected
by the dynamic behaviour of all the variables in the system, policies to regulate the inflation
rate must consider activities or dynamic behaviour of international trade varaiabls.
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