VECM - Allowing Constant in both Long-Run and Cointegrating Equation

[jamesrobinsonjnr]

Hello Matthieu,

In a research paper that uses the VECM function from tsDyn to discover the equilibrium path for residential housing prices within a specific real-estate market, I realize that there seems to be a restriction in this function that limits the researcher to use a constant in only one of the equations (LR or SR) at a time. However, when estimated in Eviews, a constant is allowed in both the LR and SR equations. Could you say why such a restriction may exist or what can be done to include the constant in both?

[MatthieuStigler]

Hi James

Someone asked the same question in the (ow to be deprecated) google groups. It has been a long time I worked on that, but in my memory, I thought the two parameters could not be identified simultaneously? Maybe Eviews is using applying some normalization to permit identifcation?

[jamesrobinsonjnr]

Hello Matthieu. Thanks for the feedback. I've been searching around on this issue as well. I find MathWorks' exposition on VECM in Matlab interesting. Recognizing that a VECM is essentially adding the Error Correction term to a VAR in differences, the resulting Cointegrated VAR may include exogenous variables, whereby a constant term actually represents a deterministic linear trend in levels. I do recall that when exogenous variables are included in EVIEWS, a constant is included by default. Based on my reading of MathWorks, it could potentially represent a deterministic trend, whereas the constant in the LR equation is in its truest sense, a constant in levels. I welcome your feedback. https://www.mathworks.com/help/econ/introduction-to-cointegration-analysis.html

[MatthieuStigler]

I think you are making a right point about the (complicated) interpretation of the parameters.

But what about the more basic question of identification? It seems to me having a constant in both the LR and ST term amounts to having a final model with two constants? Note identification in VECM is complicated already, likfe the case for the alpha and beta terms (see ?tsDyn::coefB), and hence there is a normalization done there. But what is the normalization for those two intercepts? Did you find anything in Johansen 1995, hamilton 1994 or Juselius 2006?