The Engle-Granger Technique for testing CointegrationThis is NOT done automatically in Eviews. First, run the cointegrating regression. Next, save theresiduals. Finally, use the ADF test to determine whether the null of NO cointegration can berejected. Note that all the issues concerning unit root testing apply here as well. In addition,however, one has to consider whether the constant, trend, or both are in the cointegrating vectorand/or the error correction term.In the example below I look at whether US real GDP (from file us1.wf1) is cointegrated with theTreasury bill rate.

First, I open the equation consisting of LGDP and TBILL.

After estimating the equation, I save the residuals. This is the error correction term. Note that inthe Engle-Granger framework you either have cointegration or you don’t.

The Johansen Cointegration Test

In the present case one has to estimate a VAR. For this example, I add the log of M1 (LM1).Recall that cointegration, if it exists, presumes that two or more series have a unit root.

First, you need to estimate the VAR. All the considerations we discussed earlier (i.e., choice foflag length) matter but the ORDER in which the variables enter does NOT, at least not at thisstage. This issue matters later.

Now comes the difficult part. Deciding whether the cointegrating vector has a constant, trend, orboth. Recall the point made earlier about what it means to have a trend, for example, in thecointegrating vector as opposed to the error correction model. The default in Eviews is usually agood choice but ultimately the choice depends on your priors, the nature of the data, and theparticular hypotheses about the long-run that you wish to test.

The top portion of the outpu t tells you whether there is cointegration and the number ofcointegrating vectors. Here one cannot reject the null of a single cointegrating vector using theTRACE test. We saw in class the differences between the TRACE and MAXIMALEIGENVALUE tests. The latter can be evaluated from the column of eigenvalues provided.

Depending on how much cointegration there is, one has to look at estimates of the normalizedcointegrating vector(s) to see estimates of the long-run relationship between the series. Here Ideliberately chose real GDP as the dependent variable to see if there is a long-run link betweenmoney and output. However, if I were estimating a money demand function I would have set the(real) money supply as the first variable. Nevertheless, it is not necessary to re-estimate the VARsince Eviews provides the non-normalized estimates. To normalize on the appropriate“dependent” variable you simply have to divide the estimate by itself and estomates of the othercoefficients in the cointegrating vector by the estimates of the “dependent” variable. In the aboveexample Eviews automatically divides all the estimates by the one for LGDP.

The final step in the estimation process consists in estimating a vector error correction model.You need to select how the cointegrating vector is structured, the lag length for the dynamicterms in the VECM and the number of cointegrating vectors. To obtain this window, you clickOBJECTS and then VECTOR ERROR CORRECTION in the VAR estimation window.

All VECM estimates will show estimates, standard errors and t-stats for the cointegratingvector(s) – here it was assumed there is only 1 vector. The next picture shows the rest of theoutput which estimates the dynamic terms in the VECM (i.e., the lagged variables in firstdifference form).