I've attached results obtained from VECM. As, I have two cointegration equations. My prime objective is to estimates effects of these variables on TFP, in both long and short run. I was advised to run VECM to check if long-run relationship exists among variables.
1) Now, I am seeking guidance on results obtained from VECM. How to interpret and write them in my paper. ( how do VECM define long-run and short run relationship?)
2) Do I need to do further analysis; like FMOLS, to estimate TFP?
When you use VECMs on your cointegrating vectors you adjust to both short run change and deviations from equilibrium.
You have to keep in mind that although your series do appear to move together, the relationship is not that. The error term reflect the meaning of the estimated adjustment parameters.
For Ex : (X0+aX1-bX2-c = error) if the error>0
→situation in X0 can be seeing as being above the equilibrium the same for the situation in X1.
→ but for the situation in X2 is below equilibrium.
So,if you want to reduce your error term the situation in X2 have to change.
If you have negative parameters, I suggest you to make a chi test to check whether each variable plays a significant role in your equations.These tests may help you to establish a sensible causal ordering.
You have to assume that your adjusted parameter are properly autoregressive lag 1. Otherwise you have to make a test to check a long run relationship between your paremeter before testing for the order of covariance stationarity, that you're talking.
I hope you find this interesting
Hi,
First of all, you need to decide which tool is more appropriate, VECM or VAR. If all the variables are I(1) and there is cointegration, the appropriate model is VECM. Otherwise, you can use VAR model. When presenting VAR/VECM results, it is very important to do an Impulse response analysis using IRF or OIRF. This sheds lights on the research question in hand. You can do this using both table and graphical method. Since both methods use a system of equations, you need to carefully see the significant relationships between DVs and IVs.
If you are using STATA, there are many useful tools and commands in it such as IRF, OIRF, system stability check etc. In addition to these, there are user-made commands such outreg2 to report the results in a journal-type way.
Kind regards
Thushara
As simple example will show how to interpret the cointegration equation.
For example, supoose that you obtained the followin cointegration equation between the LOG(GDP) and LOG(NO_STUDENTS) (the logarithm of GDP and the logarithm of the number of students)
LOG_GDP=20.5+0.23*LOG_NO_STUD
This means that a 1% increase in thenumber of students leads to a 0.23% increase in GDP.
The adjustment coefficient is intrepreted like this:
- A negative value of the adjustment coefficient(s) indicate that your model is dynamically stable.. The adjustement coefficient is computed by most of the econometric software packages.
See for example Walter Enders, Applied Econometric Time Series, Wiley and Sons, 1994. You can find some scanned pdfs of this book on the Internet (I don't know if it is legal or not, but google returns some links to pdf files).
regards,
Bogdan
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