Interpreting coefficients from a VECM (Vector Error Correction Model)

Question

I would like to ask a question about error correction terms from VECM if I may. I am currently working on a lot of time-series data and one of the questions I would like to address is whether there is some relationship between different time-series. Reading around the subject it seemed to me that testing for cointegration would be a good way of showing that two or more time-series were in a long run equilibrium. However, before embarking on such procedures I wanted to be clear on a number of things.

Firstly, (assuming there is a cointegrating vector) I have been trying to work out how to interpret the error correction terms from a VECM. I have been using the vars package in R, which provides the error correction terms in the summary table for a vecm model. Now, as I understand it the error correction terms describe how the time-series adjust to disequilibrium.

I was wondering what the best way to interpret negative and positive error correction terms was?

Given two time-series Xt and Yt, from what I have read so far it seems that negative error correction terms would mean that when Yt-1 is above its long-run level then ΔY*t* will be negative, pulling Y back towards its long-run relationship with X.

On the other hand, I am less sure on the interpretation of a positive error correction term and I haven't been able to find a simple description.

Finally, I have been trying to discover how one could interpret ECTs when two or more cointegrating vectors exist. So far, the only thing I have found in the papers I have searched is that its very difficult.

Thank you for help, any advice, clarification etc. would be much appreciated.

Answer 1

After much researching I the following reference was the most useful to me when trying to interpret the findings of a vecm:

Helmut Lütkepohl, Markus Krätzig

Structural Vector Autoregressive Modeling and Impulse Responses pp. 159-196. In: Applied time-series economics.

A link to the chapter is given below:

http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511606885&cid=CBO9780511606885A036

Answer 2

ECT is consider good if the range between 0 ~ 1 but not more than 2. ECT should be in negative number and if positive value means explosive and not reasonable. For example, if the ECT(-1) estimated coefficient is -0.87 (The estimated coefficient indicates that about 87 per cent of this disequilibrium is corrected between 1 year (if annually data)). But if the ECT(-1) are -1.07 as an example (The estimated coefficient indicates that about 107 per cent of this disequilibrium is corrected between 1 year - and this does not make sense).