# Using a VAR over a VECM (in spite of of existing cointegration)

Is there ever a reason to use a first differenced VAR over a VECM when all your variables are I(1) and co integration exists?

The reason why I ask is because I see in the most recent Bank of Canada Analytic note on the minimum wage increase (page 15) it seems that opt for a reduced form VAR over a VECM. $$\Delta \text{CPI}_t^p=\Sigma_{i=0}^4\eta_i \Delta\text{MW}_{t-i}+\Delta \alpha_1\text{CPI}_{t-1}^{p}+\alpha_2\Delta\text{UR}_t^p+\mu^m+\mu^y+\mu^p+\mathcal{E}_t$$

Is my understanding of the model correct? Is this theoretically sound?

The answer I got from the bank of Canada with regard to this question is the following:

Equation A1 (the equation in the question) is estimated with ordinary least squares (OLS). Data are pooled.

The equation above is neither a VAR or a VECM. It seems a little odd, but that is the model which is employed.

• @RichardHardy the answer seems legit. Im actually emailed the bank of canada regarding this result and am waiting a response – EconJohn Jan 22 '18 at 16:46
• I wonder if you got any response from them and whether it was in line with the answer. – Richard Hardy Feb 21 '18 at 11:16
• @RichardHardy I got an answer see the thread below. – EconJohn Feb 22 '18 at 17:27