Can I use a VAR in first differences despite having co-integrated data? I have two variables. Both are I(1), so non-stationary in levels but stationary in first differences.
However, having run some tests, I find that both are co-integrated. Based on my statistics classes, I'm led to believe I should then use an ECM. However, I want to instead use first differences and estimate a VAR so that I can estimate IRFs.
Is this okay? Or should I not do this given the co-integrated nature of the variables? Or is it possible to somehow run an IRF from the ECM?
 A: Hi: ( Note that below considers the bivariate case but same type of discussion holds in general for $n > 2$ ).
The impulse response function using the var in differences will not be correct because it will not include the effect of the two levels of the variables being tied together in the long run. It is possible to calculate the IRF using the ECM but the response ( in the bivariate case ) results in both variables moving, rather than the standard impulse response where one moves.  I can't do the explanation justice here, even if I had more space, but it is explained very nicely ( albeit briefly. banerjee's textbook is old but nice. johansen and juselius have another and there's another by Lutkepohl ) ) in the document below. So, the short non-detailed answer is that, if you use a var in first differences to generate the IRF when the two series are cointegrated, you won't be getting the correct impulse response. I hope below helps. If it's not detailed enough, check out the textbooks that I mentioned.
http://jerrydwyer.com/pdf/topic5.pdf
