Estimating Error Correction Model (ECM) with Stata (Time Series)

If the variable are cointegrated (i.e, if the null hypothesis of no cointegration is rejected), the residuals from the equilibrium regression can be used to estimate the ECM.

From our discussion in cointegration test before, if x and y are cointegrated, the two variables have the error-correction form;

From the cointegration test before, the value of residual

estimates the deviation from long-run equilibrium in period (t - 1)

Hence, it is possible to use the saved residuals  obtained in Step 2 as an instrument for the expression   in Eq (1) and (2) above.

Thus using the saved residuals from the estimation of the long-run equilibrium relationship, we can estimate the ECM as;

Other than the error correction term , Eq(3) and Eq(4) constitute VAR in first difference.

To generate ECM model for Eq(3);

egranger y x,ecm

The results show that the coefficients value for the ECM is 0.0167 and its not significantly. 

That means, there is no short-run adjustment to make the model in Eq(3) is in equilibrium condition in the long run.