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When estimating a Vector Error Correction (VEC) model in EViews, the resulting output always shows the error-correction terms together with standard errors and t-values for the included variables, and I was wondering if and how these numbers matter for the results?

In my understanding, the presence of cointegration among two or more variables is determined based on the Johansen Cointegration Trace/Eigenvalue test, and the error correction equation(s) are then retrieved by estimating a VEC model of the variables. Following this procedure, however, all variables included in the VEC estimation enter the error correction term, even though some of them may have no long-term relation with the other variables whatsoever, and their SE/t-values change depending on the ordering specified. Do SE/t-values actually play a role in determining the correct cointegrating relation(s)?

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Once you have an estimated model, the standard errors and the t-values characterize the model coefficients but not the regressors.

In a VECM the standard error associated with the error correction term (ECT) is the standard error of the corresponding estimated coefficient (the loading coefficient); it does not concern the ECT itself.

Estimating a VECM is already one step past the cointegration analysis (typically Johansen's procedure) that you seem to be interested in.

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  • $\begingroup$ If I am not mistaken, first the cointegrating vectors are estimated and the ECTs are formed. Only then (given the estimated ECTs) is VECM estimated. But I may be wrong about forming the ECTs before the VECM is being estimated... See also this post $\endgroup$
    – Richard Hardy
    Commented Jan 30, 2015 at 11:33

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