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Dear all,

I have questions about cointegration test.

I am doing cointegration test between two variables, Government Revenue and Expenditure. I use the Engle & Granger cointegration test, by following the steps from Walter Enders (2004) book "Applied Econometric Time Series".

Basically what I have done are the following:
1. Check each variable's order of integration --> I found that both variables are I(1).
2. Estimate the long run equation, and get the residual.
3. Check the property of residual --> I found that the residual is stationary. ( I used critical value from MacKinnon's - 1991, "Critical Values for Cointegration Tests")
4. Estimate the short run dynamic by Vector Error Correction Model --> I found that the Error Correction Terms are not significant.

My question is how should I interpret this result? Are the variables cointegrated?

By definition, two variables are cointegrated when linear combination of nonstationary variables is stationary. I have found that both variables are nonstationary - I(1), and the linear combination is stationary. So, my result basically satisfies the cointegration definition. However, the error correction terms from short run dynamic are not significant.

Is significance in error correction term also a necessary condition for cointegration?

Thank you.

Regards,
Cahya

Dear Cahya,

If still relevant: I guess that your variables are cointegrated in the long run but the relationship is insignificant in the short run.

Dear Cahya,

1. Don't worry, your estimation step and critical values used for Engle-Granger cointegration test is correct. Why your one period lagged error-correction term, ECT(-1) is insignificant because I suspect that you have used the long run coefficient provided by Johansen test - VECM. Because there is a function of VECM in Eview.

2. Run the long run coefficient with OLS, save the residuals and rename it as ECT or other name you like. Then run the error-correction model (ECM) with ECT(-1) and determine a proper lag order using AIC or SBC. If your both the ECTs(-1) are insignificant in the two ECM equations. Then your cointegration result may be spurious.

Good luck..

Warmest regards,
tcfoon

how we can determine the order of integeration series

If the series is stationary - I(0)
If the first difference is stationary - I(1)
if the second difference is stationary - I(2)
etc.

BTW there is an easier way to preform the EG cointegration test that is built in Eviews. Simply take the variables of the long run eq and open them as a group. Then press view-->cointegration test-->single equation cointegration test. The output show the results of stationary tests on the residuals from n equations (n=number of variables in the group) when each time it substitutes the LHS variable.