y out unit root tests for all the variables present in equation (1).
On conducting the unit root tests to check for the series to be stationary we find that all three variables at non- stationary in their levels. However, volume of imports, gdp and the relative prices are stationary in their first differences. This means that each of them is an I (1) process with a single unit root.
To check for cointegration the Engle- Granger's Residual based ADF test and the Johansen Cointegration test have been used. First, equation (1) has been estimated using the OLS method. Next it was checked if the residuals are stationary through the ADF test similar to the ones conducted above. The result shows that F statistic is -4.76 which can be rejected at 5% significance level. Thus, the null hypothesis of non- cointegration is rejected. The volume of imports, real GDP, and relative prices are cointegrated that is the disequilibrium error in equation (1) forms a stationary I(0) time series.
To check for multivariate cointegration we use the Johansen Cointegration test. We estimate a VAR equation for all three variables and check for cointegration between volume of imports, prices of imports and GDP. We find a single cointegration vector (result in Appendix). Cointegration among variables implies that the variable cannot move 'too far away' in the long run. That is, the long run relationship is stable.
The final step in the analysis is estimating an error correction model (ECM). As the variables in equation (1) are cointegrated we use an error correction mechanism which combines both long term equilibrium relationship and short term adjustment dynamics. Through ECM we explain short run discrepancy from long term behaviour in the adjustment process. The model consists of one- period lagged values of logs of volume of imports, price of imports and GDP and difference terms of all three variables with four lagged periods.
The equation for the Error Correction Model is as follows:
†lnvolimpt = α0 + α1aˆ†lngdpt + α2 aˆ†lngdpt-1 + α3 aˆ†lngdpt-2
+ α4ˆ†lngdpt-3 + α5 aˆ†lngdpt-4 + Î20 aˆ†lnprt + Î21 aˆ†lnprt-1 + Î22 aˆ†lnprt-2
+ Î23 ˆ†lnprt-3 + Î24 aˆ†lnprt-4 + Î30 aˆ†lnvolimpt-1 + Î31 aˆ†lnvolimpt-2
+ Î32 ˆ†lnvolimpt-3 + Î33 aˆ†lnvolimpt-4 + Î′lnvolimpt-1 + ηlngdpt-1
+ λlnprt-1 + et (2)
The results of the above regression are in the appendix. For the above equation we conduct the following tests:
ARCH test for homoskedasticity. We find that the F statistic is 0.175 ruling out the possibility of heteroskedasticity.
Breusch- Godfrey serial correlation LM test for serial correlation gives F statistic 0.58. Again we cannot reject the null hypothesis and see that there is no serial correlation.
The error correction model can be modified by eliminating individual variables whose t ratios are insignificant. However, these variables might jointly be significant and to find evidence of this we conduct the Wald test to see that all the coefficients of the variables put together are insignificant. That is in the modified equation
