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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
Services for Science and Education – United Kingdom
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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Archives of Business Research (ABR) Vol. 9, Issue 12, December-2021
Services for Science and Education – United Kingdom
volume in the long-run. The study also found that depreciating the currency value of the home
country negatively affected exports in the short run and a direct effect in the long run.
Obinwata et al. (2018) investigated the pattern between exchange rate and export output in
Nigeria. They used descriptive method of analysis. The findings showed that exchange rate
fluctuations had an enormous impact on the output of export demand volume.
Vinh and Duong-Trinh (2018) studied the effect of Exchange Rate Fluctuations on Exports in
Vietnam (2000 – 2014). The analysis used the autoregressive distributed lag (ARDL) (ARDL).
The results showed that exchange rate volatility negatively affected the export volume in the
long run.
Sugiharso (2017) analyzed the effects of exchange rate fluctuations on the export of Indonesia
to the US, China and Japan. The study used Ordinary Least Squares Regression analysis in
characterizing the relationship of the disturbances through the equations in the study. The
results of the study showed that exchange rate volatility negatively impacts export but the
impacts differed among the countries under study.
Dominic (2017) examined the effect of the exchange rate on cocoa export in Nigeria (1980 –
2013). The research used the error correction model. The unit root test and the co-integration
test were conducted. The ADF stationarity test results indicate that all study variables – cocoa
export, agricultural export, exchange rate trade openness and world cocoa price were
stationary at order one I(1). The Johansen co-integration revealed 2 co-integrating equations
suggesting the presence of a long-run relationship between the variables. The t-test showed a
direct relationship between Exchange rate and cocoa export, an inverse relationship between
trade openness and world cocoa price.
Musibau et al (2017) examined exchange rate volatility and Non-oil Exports in Nigeria (1986 –
2014). The study adopted the Error Correction Model. The findings showed presence of
volatility in exchange rate. The findings also showed that exchange rate volatility has an indirect
and significant effect on non-oil export in Nigeria.
Odili (2015) studied the short-run and long run impact of real exchange rates volatility and
level of economic improvement on international trade (exports and imports) in Nigeria (1971
- 2011). The study used the vector error correction model. The result showed that imports and
exports were affected by the real exchange rate, exchange rate volatility, foreign income, gross
domestic product in the short run and long run,. The findings also showed that in the long run,
exchange rate negativel affected export and import. The pairwise Granger Causality test
showed unidirectional Causality running from exchange rate to import, from export to
exchange rate volatility, and. Also, from real GDP to import and export.
Nyeadi et al. (2014) studied the effects of exchange rate movement on the growth of Ghana's
export. The study utilized the Ordinary Least Square estimation technique. They discovered
from their findings that in Ghana, exports was not significantly affected by the exchange rate.
Olufayo and Fagile (2014) examined the influence of exchange rate volatility on Nigeria’s export
sectors performance (1980 to 2011). They adopted the econometrics method of Seemingly