Specifying Vector Error Correction Models

So, what do you understand by vector error correction model (VECM)? You may say any of the following: that it is a system having a vector of two or more variables that all the variables in a VECM are endogenous there are no exogenous variables VECM is constructed only if the variables are cointegrated cointegration implies evidence of a long-run relationship among the variables it is a restricted VAR model with cointegrating restrictions built into the specification constructed to examine long- and short-run dynamics of the cointegrated series restricts the long-run behaviour of endogenous variables to converge to their cointegrating relationships that the cointegrating term is known as the error correction term it is a representation of cointegrated VAR (courtesy of granger’s representation theorem) and that the resulting VAR from VECM representation has more efficient coefficient estimates. Also, note that VAR specified in differences is a mis-specification while VECM is obtained by differencing a VAR, hence losing a lag. So, you construct a VECM with a (p-1) lag lengths for all the variables in the system. These are the basic steps required to estimating a VECM. (1) series must be stationary (integrated of same order) (2) determine optimal lag length for the model (3) perform Johansen cointegration test (4) if there is no cointegration, estimate the unrestricted VAR model (5) but if there is cointegration, then specify the restricted VAR model (i.e. VECM). In this video, I show you the rudiments of the VECM specification. Kindly check my channel and playlist for all simple and exciting hands-on tutorials using EViews, Stata and Excel applications:
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[@CrunchEconometrix]

KZbin recently changed the way my content will be monetised. My channel now needs 1,000 subscribers. So it would be amazing if you show your support by both watching my videos and subscribing to my channel if you haven’t done so already. Monetising my videos allows me to invest back into the channel with some new equipment so this small gesture from you will be extremely huge for me. Many thanks for your support….CrunchEconometrix loves to teach, support my Channel with your subscription and sharing my videos with your cohorts.

[@wanjadouglas3058]

Beautiful work Doc. You're amazing at what you do.

[@CrunchEconometrix]

Thanks so much for your encouraging feedback, Sir 😊

[@alfredphillips08]

Hello, many thanks for your videos and clear explanations.

[@CrunchEconometrix]

Thanks for the encouraging feedback, Philip. Deeply appreciated! Please may I know from where (location) you are reaching me?

[@surojitdey574]

Respected madam your videos informative and helpul for us.

[@CrunchEconometrix]

Hi Surojit, thanks for the encouraging feedback. Deeply appreciated! 🙏 ❤️

[@surojitdey574]

Madam I respect u as my professor. I follow your work and exactly do the same in my thesis. It is now submitted. Waiting for award. The day day I received my award after my supervisor I will tell u.🙏🙏🙏🙏🙏 Lots of respect madam from INDIA. UNIVERSITY OF CALCUTTA.

[@CrunchEconometrix]

Thumbs up, Surojit. Well done and congrats in advance! 😊

[@ViruFX]

Great explanations, Kudos. I learned a lot!!

[@CrunchEconometrix]

Thanks Precious, for the positive feedback...may I know from where (location) you are reaching me?

[@ViruFX]

I'm from Malawi. @@CrunchEconometrix

[@CrunchEconometrix]

Awesome Precious! My love to all Malawians please spread the word about my YT Channel...thanks!😀

[@ViruFX]

Most definitely, I will @@CrunchEconometrix

[@oblivious1545]

Amazing work, thank you. Was wondering what the σ, a and d represent in the VAR specification?

[@CrunchEconometrix]

These parameters are clearly explained in the video. Kindly re-watch and also take down some notes. Thanks.

[@wanjadouglas3058]

The best teacher

[@CrunchEconometrix]

Thanks for the encouraging feedback, Sir!

[@zanyatwa]

Thanks for the presentation! I just want to know if one can use Johansen test before estimating ECM?

[@CrunchEconometrix]

Thanks for the positive feedback, William. You engage JCT then VECM...not ECM.

[@yogeshmalhotra9120]

Nice and well-described video. I have one doubt about the coefficient sign of ECT. What if it is positive and negative as well as about the magnitude of it.

[@CrunchEconometrix]

I explained that in my videos on interpretations. Kindly watch them, thanks.

[@yogeshmalhotra9120]

@@CrunchEconometrix Thanks and I will watch them sure.

[@subhasishdas9045]

Thank you so much for this valuable lesson. Could you please refer any book or paper for this?

[@CrunchEconometrix]

Thanks, Subhasish for the positive feedback. Deeply appreciated! You can do a Google search for online resources.

[@868jjm8]

Can you use vecm with the Engle Granger method of cointegration?

[@CrunchEconometrix]

I'm not familiar with Engle-Granger cointegration. Never used it.

[@chisalamukonde4348]

What regression equations can be derived from the error correction term?

[@CrunchEconometrix]

Hi Chisala, what is your query about?

[@chisalamukonde4348]

Thank you for the feedback. My question is pertaining to the error correction term... Are there any equations can be represented by the error correction term "The epsilon t-1"?

[@choladakittipittayakorn4829]

Thank you so much for the excellent video tutorial😍🙏. I have a question regarding the VECM. If all the time series variables are not stationary at the first differencing but they are cointegrated at the first differencing. Can I still use the VECM for analysis?

[@CrunchEconometrix]

Watch my ARDL videos for series integrated at different orders.

[@choladakittipittayakorn4829]

@@CrunchEconometrix Thank you so so much! You’re the best! Love love from Sweden.❤️❤️❤️❤️

[@felmetaolkeba]

What we can say when optimal lag length is one, as there is a need to deduct one from it when running VECM?

[@CrunchEconometrix]

That'll be an exception. So, use 1 lag since VECM cannot be a static model.

[@felmetaolkeba]

@@CrunchEconometrix Tnx alot. The other issue challenged me is how can we test the Granger causality test under VECM among the following options: 1. Opening the data at level as group (non stationary) and looking for Granger causality 2. Opening VAR and looking for Granger causality 3. Running VECM and finding the Granger causality 4. Opening the data at a given order of integration i.e differencing to make stationary, then opening as a group and testing for causality TNX in advance for your cooperation.

[@CrunchEconometrix]

@@felmetaolkeba I have well-explained videos on these procedures. Kindly search through my Playlists. Thanks.

[@vaneberlot]

Hi madam, can you please cite reference literature for VECM model specification? I don't find anything similar to your formulas in econometric literature. thanks

[@CrunchEconometrix]

Hi Vane, kindly do a Google search and you will have access to tons of publications on the VECM procedure. I also listed textbook references at the end of this video too. Thanks.

[@simaykzlkaya9078]

Hello, thank you for the information given. I would like to ask a question. I perform dickey-fuller test on my logged variables and one of them struggles from non-stationarity. I take first differences of the variables and again it presents non-stationarity. How can I solve this kind of problem? Thank you in advance. I am going to use VECM or if you advice any model.

[@CrunchEconometrix]

Hi Simay, thanks for the positive feedback. Deeply appreciated! You'll have to change the variable to a closer proxy because you can't use an I(2) series for VECM. Please may I know from where (location) you are reaching me?

[@simaykzlkaya9078]

My feedback is not even close to your contributions! I appreciate that. I am reaching you from Turkey. By the way, what if I use the log versions of variables which are I(0) and take the first difference of related I(2) variable to make it I(0)?

[@CrunchEconometrix]

@@simaykzlkaya9078 Nah, from the little I know, you can't use I(2) series in VAR/VECM analysis. Do further enquiries. Hopefully, you may find a better solution😊. I'll appreciate it if you can share the link to my KZbin Channel with your friends and academic community in Turkey 🇹🇷. They will find the content helpful too 😊.

[@simaykzlkaya9078]

CrunchEconometrix I am also phD candidate and research assistant. Every one in my institution knows you :) but I will share your account's link. Note: I will use ARDL model if it is possible(with the suggestion of a professor) with the help of your videos. Best wishes 🧡

[@CrunchEconometrix]

@@simaykzlkaya9078...and your Institution is?

[@nausheensodhi803]

if I have 4 variables where two variables are I(0) and two are I(1), do I use VECM for the 4 variables? Since, there is only 1 cointegrating relation out of 4 variables, does that change anything in the estimation of VECM for me? Any input on this is appreciated. Thanks

[@CrunchEconometrix]

Hi Nausheen, using VECM depends on your analytical approach (system of equation OR single equation model).

[@nausheensodhi803]

I intend to use 4 simultaneous equations for VECM. But my question was whether I can use this exact method you explained in the video if I have two variables that are I(1) and two variables that are I(0)

[@CrunchEconometrix]

No, you cannot. All variables must be I(1) to use VECM.

[@nausheensodhi803]

I see! Thank you so much for clarifying. Big help 🙏🏻🙏🏻

[@rinawelly5221]

Hi Mam..can we do var and vecm analysis with data I (0) or it must I(1)...tengkyu

[@CrunchEconometrix]

Hi Rina, NO. Watch my video on VAR specification. Please may I know from where (location) you are reaching me?

[@rinawelly5221]

@@CrunchEconometrix oke mam, i'm from indonesia,

[@CrunchEconometrix]

@@rinawelly5221 Awesome! I'll appreciate it if you can share the link to my KZbin Channel with your students and academic community in Indonesia 🇮🇩. May God bless you as you do, amen 🙏

[@aliefimei6509]

It is necessary to perform Parsimonious Model in VECM approach? Help me Dr

[@CrunchEconometrix]

Hi Alief, not necessary.

[@aliefimei6509]

@@CrunchEconometrix thank Dr. A lot of love😍

[@zuzekandovela3872]

Crunch family please assist with the video that follows this one.

[@CrunchEconometrix]

Hi Zuzeka, depending on if you are using Stata or EViews, kindly search their Time Series Playlists for VECM ESTIMATION. Thanks.

[@zuzekandovela3872]

@@CrunchEconometrix thank you so much for your response Doc ❤️. Just one last question, if I have panel data are the steps still the same?

[@CrunchEconometrix]

Should be. Except that I've not done PVAR and/or PVECM before. You may want to check out other online resources for more constructive feedback. Thanks 💖

[@greenwoodsewanimanda2858]

Is it OK for a var model to be run on a lin-log basis?

[@CrunchEconometrix]

Hi Sewani, I don't know what you mean by "lin-log" but if you imply a log-linear VAR model where all the variables in the system are expressed in logs, then yes it is ok.

[@greenwoodsewanimanda2858]

Thanks madam. I meant, can the dependent variable be left unlogged while logging the independent variables. I say this because my model only becomes stable when my dependent variable is not logged.

[@CrunchEconometrix]

@@greenwoodsewanimanda2858 You are estimating a VAR model. Hence, all variables must be in the same form.

[@hogrideeeeer]

What is the i=0? Thanks for the video?

[@CrunchEconometrix]

Akdas, it means the TIME is contemporaneous.

[@hogrideeeeer]

@@CrunchEconometrix hi, thanks for the reply! One more thing I don't understand, in the video you show the VECM equation at levels but shouldn't it operate under first difference? I am specifying a vecm for my bachelor work, should i show the model under level or 1st difference? You have been really helpful for me !!!

[@CrunchEconometrix]

Akdas, I specified the VECM in 1st difference. Look at it again but it should have been I=1 and not I=0. That is a typo. Thanks.

[@hogrideeeeer]

@@CrunchEconometrix i see thank you. So in the case of the model should i write dLnGDP instead of LnGDP?

[@CrunchEconometrix]

Akdas, VAR and VECM specifications are not the same. Obviously, you didn't watch the clip to the end. My advice: Watch, jot down notes and PAY attention to my explanations. You will find these tips helpful. Thanks.