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I want to extend the standard VECM form:

Δx[t] = δ0 + ... + Π x[t-1] + Φ1 Δx[t-1] + Φ1 Δx[t-2] + ... + ε

to include exogenous variables (i.e. variables that are participant in describing the relationships amongst Δx[t], but are not in the dependent set Δx[t]). Let's call these new variables z. Would like to determine a MLE of the coefficients in the revised VECM:

Δx[t] = δ0 + ... + Π x[t-1] + Φ1 Δx[t-1] + ... + θ1 z[t-1] + ... +ε

I am familiar with the johansen method in determining the MLE coefficients for the 1st form. I'm not sure how can modify the method to determine the second form. Could use an optimiser to find the coefficients for VECM with exogenous vars, but thought there is probably a more direct approach.

chl
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Jonathan Shore
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1 Answers1

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In Johansen article VECM is specified with dummy variables. If your exogenous variables are strictly exogenous I see no reason why you cannot use original Johansen VECM, so look in the article how Johansen treats dummies.

R package vars implements Johansen approach, where you can supply the dummies.

mpiktas
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