I am running a time series specification with investment being determined by GDP and lagged value of investment. These variables are cointegrated in the long run. I wonder whether I also need to include both variables in the short run part of the model, e.g. in difference form?
I suggest as long as you have confirmed existence of long run relationship between the two variables proceed with next step.
Long run relationship means the two variables tend to move together towards to a steady state and any deviations because of shock the system will have tendency to restore back.
Note Cointegration equation normally contains both shortrun and longrun estimates/ coefficients,
You can also visit on you you tube and have some video lectures about cointergration model STATA. or EVIEWS by Hossain. hope it will help you.
Dear Erasmus,
thank you for your quick answer. I also came across Eviews tutorials by Hossain. My question, however, relates to your third paragraph. You mention that cointegration normally contains both shortrun and longrun estimates / coefficients.
That is exactly my question. If I have GDP and Investment cointegrated, do both variables also need to be part of the short run relationship?
Thank you.
Yes, once you have a long-term co-integrating relationship it must enter the ECM with both short and long-term dynamics. If there is no co-integration the ECM includes only short-term dynamics.
Dear Thomas
Since your series are co-integrated, you need to proceed with the Error Correction Model (ECM) which includes the variables in difference form plus the error correction term (ECT) to capture the speed of the adjustment to the equilibrium.
Thank you for your answers, they are very helpful. Dear Paul, according to your answer I presume that if there is cointegration between GDP (Y) and Investment (I) I would need to include both (Y) and (I) in difference form as well? Hence, I could not just take one of them, e.g. (I), in difference form, is that correct?
You will include the lags of both variables depending on the appropriate number of lags. It also depends on the model (VECM, ARDL…) you selected for your analysis
As (log)GDP is unlikely to be weakly exogenous you would probably be better estimating a VECM for (log)GDP and (log)Investment. At least then you will be able to test for weak exogeneity and various reions on the system.
I would think that the equilibrium level of investment is determined by many other factors other than GDP. The impact of your formalisation is that all these other factors have no impact on long run investment.
Dear John, thank you for this answer.
I just mentioned GDP and Investment as an example. My main concern was (and still is) whether I need to integrate all variables that are part of the long run (e.g. logGDP and logInvestment) also to be in differenced form in the same specification, e.g. log(I) = log(Y) + log(I) + dlog(I) + dlog(Y), "d" stands for difference form.
Using another example, if I find cointegration among GDP, Investment, and Profits would it be ok to just have GDP and Investment in differenced form or do all three variables need to be part of the short run part of the model too?
I am not using a VAR model, but error correction tests by Banerjee et al. (1998) in a single equation framework. Hope this makes it clearer now.
I presume your reference is to Banerjee, Dolado and Mestre (1998), Error-correction Mechanism Tests for Cointegration in a Single-equation Framework, Journal of Time Series Analysis. I am sorry but I do not have access to this publication. As far as I can see none of the authors include it in their IDEAS listings and do not have a corresponding working paper mentioned on their web sites.
To return to your question I think that your initial model should be sufficiently general to give you clean residuals. You may then use your test procedures to eliminate insignificant variables. A survey of this type of modelling is available at http://www.federalreserve.gov/pubs/ifdp/2005/838/ifdp838.pdf . You might also find Chapter 9 of Banerjee, Dolado, Galbraith and Hendry (1993), Co-integration, error correction, and the econometric analysis of non-stationary data, Cambridge University Press useful.
Superb! Thank you very much for this. Yes that is the correct reference.. It should be available here: https://www.researchgate.net/profile/Anindya_Banerjee/publication/46431618_Error-correction_Mechanism_Tests_for_Cointegration_in_a_Single-equation_Framework/links/54d899b40cf2970e4e78220b.pdf/
Thank you for the literature references, This is exactly what we do, general to specific. Hence, I was wondering "how far" one can go in eliminating insignificant variables in the difference form.
Best
Thomas
Article Error-Correction Mechanism Tests for Cointegration in Single...
If your variables cointegrated, then proceed with ECM. All the Econometrics Softwares including E-views include these tests. In the ECM you need to include the first differences of your variables to account for the short run dynamics. You can also run bounds test of Peseran et al whether or not your variables are I(1) or I(0).
Good luck.
Dear Thomas,
You need to include the differenced variables in the short run model plus the lag of the residual from the long run equation which measures the speed of adjustment. I hope this helps and all the best
I have a Question about the ECM result. Like I took 5 variables to show the Long-run effect. In the ECM result I got 3 variables result but in the Long Run form I got all the variables outcome. Now if any variable missing in the ECM result, is there any problem for the model??
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