Medical, Pharma, Engineering, Science, Technology and Business

**Md. Arafat Rahman ^{1*}^{} and Tanvir Khan^{2}**

^{1}Research Student , Institute of Statistical Research and Training, University Of Dhaka

^{2}Research Student, Institute of Statistical Research and Training, University Of Dhaka. **E-mail:** [email protected]

- *Corresponding Author:
- Md. Arafat Rahman

Research Student

Institute of Statistical Research and Training

University Of Dhaka

**E-mail:**[email protected]

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International Journal of Economics & Management Sciences

Exports; Imports; Economic growth; Granger causality; Vector error correction model

With the introduction of globalization, international financial market has become wide open and the countries, specially the developing ones like Bangladesh is having a great opportunity to make some drastic positive change to its overall financial condition. Researchers are having great interest in analyzing the relationship between foreign trade and national income as both of them are very important components of economical growth of a country and a healthy balancing relationship should exist between them to make a country economically strong.

Whatever the condition of the economy of a country is, it always try to gain the trade balance, as well as to bring its national income to a balanced stage with the foreign trade. To investigate collective effect of many policies on international trade, one can look for the long-run equilibrium relationship between export and import. And if someone is interested in how the policies of in land economics is synchronizing with foreign trade policies to bring the county's overall economic status to a stable position, the analysis of long run equilibrium relationship among total exports, total imports and gross domestic product (GDP) might be of interest.

In this study the relationship between economic growth (GDP) and the components of foreign trade (total imports and total exports) is analyzed in context with long term relationship. We have tried to find whether these variables have long run equilibrium relationship or not and if they have, what are the nature of these relationship and how the short run dynamics are working. The response of shocks in one variable to the other variables are also analyzed and interpreted. Haydory Akbar Ahmed and Md. Gazi Salah Uddin (2009) investigates the causal nexus between export, import, remittance and GDP growth for Bangladesh using annual data from 1976 to 2005. The paper uses time series econometrics tools toinvestigate the relationship adding import and remittance in the model. Study finds limited support in favor of export-led growth hypothesis for Bangladesh as exports imports and remittance cause GDP growth only in the short run. Mamun and Nath (2005) examine time series evidence to investigate the link between exports and economic growth in Bangladesh. Using quarterly data for a period from 1976 to 2003, the article finds that industrial production and exports are cointegrated. The results of an error correction model (ECM) suggest that there is long-run unidirectional causality from exports to growth in Bangladesh. Shirazi and Manap (2005) examine the export-led growth (ELG) hypothesis for five South Asian countries including Bangladesh using cointegration and multivariate Granger Causality tests. They found feedback effects between exports and GDP and imports and GDP for Bangladesh. Hossain and Salim (2009) addressed the short run dynamics of long run relationship between export and economic growth in Bangladesh using annual time series data and found that export led growth and growth led exports were both valid for Bangladesh. Islam and Zaman (1996) found no significant relationship between exports and growth. The results cast considerable doubt as the time series used in the study was non-stationary. By adopting standard econometric techniques to analyse time series data for the period 1969-1991, Islam (1998) examines the nature and direction of causation between export expansionand growth for 15 Asian countries including Bangladesh. The estimation results show that export granger causes economic growth positively but not vice versa, in both the bivariate and error correction models. However, the multivariate Granger test shows no causality between the two. This study uses quarterly data for the considered time period, but did not provide any explanation of data generating process for Bangladesh.

2.1 *Data*

The variables used in this study of export, import economic growth (in terms of GDP) of Bangladesh are Exports of goods and services (constant 2000 US$), Imports s of goods and services (constant 2000 US$) and GDP (constant 2000 US$). The sample period covers annual data from 1960 to 2010. All the data is obtained from World Development Indicators, The World Bank.

2.2 *Data Description*

Exports of goods and services represent the value of al goods and other market services provided to the rest of the world. They include the value of merchandise, freight, insurance, transport, travel, royalties, license fees, and other services, such as communication, construction, financial, information, business, personal, and government services. They exclude compensation of employees and investment income (formerly called factor services) and transfer payments. Data are in constant 2000 U.S. dollars.Imports of goods and services represent the value of all goods and other market services received from the rest of the world. They include the value of merchandise, freight, insurance, transport, travel, royalties, license fees, and other services, such as communication, construction, financial, information, business, personal, and government services. They exclude compensation of employees and investment income (formerly called factor services) and transfer payments. Data are in constant 2000 U.S. dollars.GDP at purchaser's prices is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in constant 2000 U.S. dollars. Dollar figures for GDP are converted from domestic currencies using 2000 official exchange rates. For a few countries where the official exchange rate does not reflect the rate effectively applied to actual foreign exchange transactions, an alternative conversion factor is used.

2.3 *Unit Root Test*

Since macroeconomi c time-series data are usually non-stationary (Nelson and Plosser, 1982) and thus conducive to spurious regression, we test for stationary of a time series at the outset of cointegration analysis. For this purpose, we conduct an augmented Dickey-Fuller (ADF) test, which is based on the t-ratio of the parameter in the following regression.

(1)

where X is the variable under consideration, Δ is the first difference

It is essential at the onset of cointegration analysis, that we should solve the problem of optimal lag length because multivariate cointegration analysis which we are going to conduct in the study is very sensitive to lag length selection.

The most commonly used lag length selection criteria are the Final prediction error (FPE), Akaike's information criterion (AIC), Schwarz's Bayesian information criterion (SC), Hannan-Quinn Criterion (HQ)(Reference)

2.4 *Cointegration Test*

The econometric framework used for analysis in the study is the Johansen (1998) and Johansen and Juselius (1990) Maximum- Likelihood cointegration technique, which tests both the existence and the number of cointegration vectors. This multivariate cointegration test can be expressed as:

(2)

Where

Z_{t} = (EX , IM , GDP)

Z_{t} = a 3 x 1 vector of variables that are integrated of order one [i.e. *I* (1)]

EX, IM and GDP are exports, imports and real gross domestic product respectively

K = a 3 x 3 matrix of coefficients

Π = 3 x 3 matrix of parameters and

μ_{t} = a vector of normally and independently distributed error term.

The presence of r cointegrating vectors between the elements of Z implies that Π is of the rank r (0 < r < 2) .(less than equal)

To determine the number of cointegrating vectors, Johansen developed two likelihood ratio tests: Trace test (λtrace) and maximum eigenvalue test (λmax.).If there is any divergence of results between these two tests, it is advisable to rely on the evidence based on the λmax test because it is more reliable in small samples (see Dutta and Ahmed, 1997 and Odhiambo, 2005).

2.5 *Granger Causality*

If we exploit the idea that there may exist comovements among exports, imports and gdp and possibilities that they will trend together in finding a long run stable equilibrium, by the Granger representation theorem (Engle and Granger 1987), we may posit the following testing relationships, which constitute our vector error-correction model:

Where EX ,IM,GDP have been explained in section IV, Δ is a difference operator, ECT refers to the errorcorrection
term(s) derived from long run cointegrating relationship via the Johansen maximum likelihood
procedure, and ζit’s (for i = 1, 2, 3) are serially uncorrelated random error terms with mean zero. In our
case, equation 3 will be used to test causation from imports and GDP to exports. Equation 4 will be
used to test causality running from expor t s and GDP to imports whereas equation 5 will test causality
running from exports and imports to GDP. A consequence of relationships described by equations 3 to 5 is
that either ΔEX_{t}, ΔIM_{t}, ΔGDP_{t} or a combination of any them must be caused by ECT_{t-1} which is itself a
function of EX_{t-1}, IM_{t-1}, and GDP_{t-1}.

2.6* VEC model*

In a VAR model I have to include the variables which have bilateral causality with each other. A VAR model consists of a set of variables which can be represented as:

(6)

With Ai are (K×K) coefficient matrix for i=1, 2….p and μ_{t} is a K dimensional process with E(μ_{t}) = 0 and covariance matrix E (ut utT) = Σu. If Y_{t} ’s are cointegrated the VAR model can be rewritten as VECM:

(7)

where

If the coefficient matrix Π has reduced rank r < k, then
there exist k × r matrices and each with rank r such that Π = β΄ and β΄ Y_{t} is stationary. r is the number of
cointegrating relations and each column of β is the cointegrating vector.

2.7* Impulse Response Function*

The impulse response function of VEC is to analysis dynamic affects of the system when the model received the impulse. As our VER model, we have three variables. We can work the response between these variables.

3.1 *ADF Unit Root Tests*

Plots of the logarithms of the three time series are shown in **Figure 1**. From **Figure 1** it is clear that exports,
imports and GDP shows an upward trend and they have a tendency to move together, implying that they are
causally linked to each other.

The ADF test of unit root for the three variables of our concern, at suggested lag length three is presented below-

From the results shown in the above **table 1 **we can say that all the three variables are non stationary as we fail
to reject the null hypothesis of non stationary even at ten percent level of significance.

Variable | D statistic | P value |
---|---|---|

GDP | -0.4394 | 0.98 |

Import | -1.699 | 0.82 |

Export | -1.3918 | 0.70 |

**Table 1:** Augmented Dickey Fuller (ADF) Unit Root Tests

As the original variable are found to be non stationary, we difference them at order one and do ADF test again,
the results are shown below in **table 2**-

Variable | D statistic | P value |
---|---|---|

GDP (diff1) | -3.3209 | 0.08 |

Import (diff1) | -3.4403 | .06 |

Export (diff1) | -2.8062 | .252 |

**Table 2:** ADF tests after first difference

The results show that even after first differencing the variables remain non stationary. So, we difference them
again (at order tow). The results of ADF test at suggested lag length 3, on the second differenced variables are
given below in **Table 3**-

Variable | D statistic | P value |
---|---|---|

GDP (diff2) | -5.9131 | <0.01 |

Import (diff2) | -4.0381 | 0.015 |

Export (diff2) | -6.1316 | <0.01 |

**Table 3:** ADF tests after second difference

We can see that the null hypothesis that the variables are non stationary can now be rejected even at 1 percent level of significance for GDP and export and at 2 percent level of significance for the variable import.

3.2 *VAR Lag Order Selection*

Before fitting the model, we have to select the appropriate lag length of the vector error correction model. The value of different information criteria of the model at different lag length are given below-

The above **table 4** shows us that, both AIC and FPE are at their smallest values if we fit the model at lag 5, while
HQ gives smallest value at lag 3 and SC at lag 1. As FPE is considered as a more robust information criteria
than the others, we consider the model to be fitted best at lag 5.

IC | Lag 1 | Lag 2 | Lag 3 | Lag 4 | Lag 5 | Lag 6 |
---|---|---|---|---|---|---|

AIC | -13.96 | -14.17 | -14.65 | -14.54 | -14.80* | -14.72 |

HQ | -13.78 | -13.85 | -14.20* | -13.96 | -14.08 | -13.87 |

SC | -13.47* | -13.31 | -13.43 | -12.96 | -12.85 | -12.41 |

FPE | 8.69 | 7.10 | 4.45 | 5.09 | 4.14* | 4.83* |

*Indicates lag order selected by criterion

**Table 4:** Lag Length Criteria

*3.3 Johansen Co-integration Test*

Johansen cointegration test is conducted to check the existence of cointegration which is shown below in **Table
5 and Table 6**-

Null Hypothesis | Test Statistics | Critical Value at 10% | Critical Value at 5% | Critical Value at 1% |
---|---|---|---|---|

r<=2 | 8.07 | 7.52 | 9.24 | 12.97 |

r<=1 | 19.84 | 17.85 | 19.96 | 24.60 |

r=0 | 57.17 | 32.00 | 34.91 | 41.07 |

**Table 5:** Result of Johansen Contegration Test Based on Trace Statistics

Null Hypothesis | Test Statistics | Critical Value at 10% | Critical Value at 5% | Critical Value at 1% |
---|---|---|---|---|

r<=2 | 8.07 | 7.52 | 9.24 | 12.97 |

r<=1 | 11.76 | 13.75 | 15.67 | 20.20 |

r=0 | 37.34 | 19.77 | 22.00 | 26.81 |

**Table 6:** Result of Johansen Contegration Test Based on Maximum Eigen Value Statistics

From the above two table we can see that the null hypothesis that there is no cointegration relationship among the variables is rejected even at 1% level of significance and we fail to reject the null hypothesis that there is at most one conintegration relationship among the variable is failed to reject at 5% level of significance. Though we also fail to reject the null hypothesis about two such relationship inside the system, we ultimately come to the decision that the three variables of our concern has one cointegration relationship.

*3.4 Long Run Relationship*

The estimated value of conintegration vector β (normalized to the first variable) is presented in the following table-

According to the above **table 7** we can establish a equation among the three variables as-
GDP=.051 x Import-.69 x Export

Variable | Cointegration Coefficient |
---|---|

GDP | 1.00 |

Import | 0.051 |

Export | -0.69 |

**Table 7:** Estimating Long run Relationship

This equation gives us a clear indication that one unit increase in total imports of Bangladesh causes GDP of Bangladesh to increase by .051 unit on an average and one percent increase in total Export of Bangladesh causes GDP to decrease by .69 unit on an average.

*3.5 Short Run Analysis*

The value of the error correction terms of the vector error correction model is presented in the following table-

From the above **table 8** it can be seen that the error correction term for the equation GDP is negative and
statistically significant, that means the GDP of Bangladesh responds to deviations of the system in a balancing
manner. A value of -.098 for the coefficient of error means the Bangladeshi economy will converge towards its
long run equilibrium by a slow pace (9.8% per year) after any shock occur in the system.

Error Correction Term | Estimated Value | t statistic | P Value |
---|---|---|---|

For the equation of GDP | -.098 | -3.235 | 0.00283 ** |

For the equation of Import | .395 | 3.010 | 0.00507 ** |

For the equation of Export | -0.493 | -4.674 | 5.11e-05 *** |

** Significant for 1% level of significance

***** **Significant for 0.1% level of significance

**Table 8:** Summary result form VECM

The error correction term for the equation of exports is also negative and highly significant which suggests total exports of Bangladesh will converge to the equilibrium position at 49% per year after the system faces any deviation.

But the coefficient of the error correction term for total imports is positive and statistically significant, that means due to any disturbance in the system, divergence from equilibrium will take place at a very rapid pace (39.5% per year) and the system will be unstable.

*3.6 Granger Causality Test*

The result of multivariate Granger causality test of the three variables of our concern is given below in **Table 9**-

Null Hypothesis | F-Statistic | P-value |
---|---|---|

GDP doesn't Granger cause Import and Export | 4.1166 | 0.000116 |

Import doesn't Granger cause GDP and Export | 1.9703 | 0.0463 |

Export doesn't Granger cause GDP and Import | 3.1995 | 0.001527 |

**Table 9 :** Results of Ganger causality test

We can see that all the three variables granger causes each other at the system of our concern.

From the above **Figure 2** we can see that shocks in total yearly imports of Bangladesh have high positive
impacts on current and future values of total imports, a moderate to low positive impact on total exports and a
very low but positive impact on current and future values of GDP.

Again from the **figure 3** we can see that total imports of Bangladesh has no immediate reaction to the shock
occurring in total exports, though it will response positively in the future and the response will be highest three
and nine years after the shock. Total exports generally responses positively to one unit shock occurring in it and
the response is quite high and GDP responses very low and positively to the same shock.

From the above **figure 4** we can see that one standard deviation shock in GDP will cause immediate positive
response in total imports but it will eventually decrease. Total exports will have low positive response at
beginning but it will decrease and will remain almost zero up to the following three years and then will start
responding negatively and GDP will have a little positive response at the beginning but very soon (after seven
years) the effect of the shock will neutralize.

*3.7 Diagnostic Checks*

3.7.1 Portmanteau test

To check the adequacy of the model, the multivariate Portmanteau tests are conducted. Here the null hypothesis
is the residuals of the model are white noise. The value of the test statistic at lag 16 (about one third of the
length of the data set) and the corresponding P value are given below in **Table 10**-

Type of the test | Lag used | Value of the test statistic | DF | P value |
---|---|---|---|---|

Adjusted | 16 | 118.67 | 102 | 0.124 |

**Table 10:** Results of diagnostic checking

So, we fail to reject the null hypothesis even at ten percent level of significance. So, we can conclude that the errors of the VECM is not auto correlated

The long run relationship between total exports and total imports is of significant importance due to fact that it reflects the sustainability of foreign tradesituation of a country. The main objective of the study is to investigatethe long run relationship between Bangladesh’s exports, imports and GDP byapplying cointegration and vector error correction model techniques. We have used annual data for total exports, total imports and GDP for the period 1960 to 2010.

The results of the ADF unit root tests demonstrate that all series are non-stationary at their levels and become stationary after they are differenced at order one twice i.e. they all are I(2)(integrated of order two). Then we move forward by applyingthe Johansen multivariate cointegration test in order to investigating the long run relationship among exports, imports and GDP. The results indicate the existence of one cointegrating relationship among these variables. The cointegrating vector shows that total imports positively affect GDP while the effect of exports is negative.

Furthermore, we have tested the stability of the equilibrium using VECM. The results indicate that the coefficient of the error-correction term of export and GDP have the right sign (negative) and are statistically significant even at 0.1 percent level of significance. The value of coefficient of the error correction term of total exports is -0.49, that means in any case of disequilibrium in every year there will be 49 percent convergence for restoring the long run equilibrium position. The coefficient of the same term for GDP is -.098 which indicates almost 10 percent convergence every year to the long run equilibrium in case of any type of disturbance in the system. The coefficient of the error correction term of imports has positive sign and statistically significant even at 0.1 percent level of significance and depict divergence from the long run equilibrium in the system.

Multivariate Granger causality test shows that these three variables granger cause each other at our model and multivariate adjusted portmanteau test indicates the independence of the error terms of the model i.e. the adequacy of it.

The plots of impulse response function indicate shocks in total imports and exports affects positively on each other and also on themselves and the effects are moderate to high. These same shocks have positive but very low effect on GDP. Shocks in GDP have low positive effect on itself, moderate to high effect on imports and low positive effect at beginning but negative after three years on exports.

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