ARDL/ECM Question

[mickeykozzi]

ARDL/ECM Question

Hello. When I run the Error Correction Form in Eviews, it produces the ECM/ARDL parsimonious model.

When I then run the residual diagnostic tests (as pictured) for Normality, Serial Correlation and Heteroskedasticity, and CUSUM, are the results from the ECM/ARDL Model or the original ARDL model given when first running the ARDL Model? Can I use these results for my ECM/ARDL Model?
Collecting Residual results are obviously very important. Thank you.

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[EViews Gareth]

Original ARDL

[mickeykozzi]

Hi,
So how do I find the residual results for the ECM/ARDL?
Bth the original ARDL and the parsimonious ECM/ARDL use the same seated mod, so I'm guessing they have the same residual result???

[EViews Mirza]

Hi,
So how do I find the residual results for the ECM/ARDL?
Bth the original ARDL and the parsimonious ECM/ARDL use the same seated mod, so I'm guessing they have the same residual result???

The residuals from the contemporaneous and the ECM model are identical. All inferences on the residuals generated internally hold true regardless of the model transformation. Remember, the ECM is just a re-expression of the contemporaneous ARDL form. You can also verify this with a simple program I've attached below.

Code: Select all

wfcreate a 1901 2000

'make some data
series y = @rnorm
series x = @rnorm
series z = @rnorm

'estimate ardl with fixed lags (so we can more easily grab substituted coefficient specification below)
equation eq.ardl @fl(y,1) @fl(x,2) @fl(z,3)

'make ardl residuals (not from ecm regression)
eq.makeresids rez_ardl

'make and freeze the ecm output (since we can't grab ecm coefficients otherwise)
freeze(ecm) eq.ecreg

'make cointegration vector called "coint"
eq.makecoint coint

'grab substituted coefficient spec from ecm table
%scoef = ""

for !k = 1 to 6
   if (!k < 6) then
      %scoef = %scoef +  ecm(13 + !k, 2) + "*" + ecm(13 + !k,1) + "+"
   else
      %scoef = %scoef +  ecm(13 + !k, 2)  + "*coint(-1)" 'replace the "CointEq(-1)" instance with "coint(-1)"
   endif
next

'replace any "+-" instance with "-"
%scoef = @replace(%scoef, "+-", "-")

'make ecm residuals
series rez_ecm = d(y)-({%scoef})

'show difference between ardl and ecm residuals
show rez_ardl-rez_ecm

'you can see that the residuals are virtually identical


[mickeykozzi]

Thank you Mirza.
I had a feeling that this was the case, as I noticed the ARDL selection model was the same for the ARDL and then the ECM Model (that is parsimoniously selected).You are saying that model transformation does not change the residuals (I thought this might be the case).

I have another question for you as well.

There appears to be 2 methods in finding ARDL and ECM:

1) The Eviews method
2) OLS method

I notice that some Youtube Instruction videos (from Drs of Economics) use the OLS ARDL method, that is they creaet a long run model (such as: GDP C CON EXP NE) My supervisor says creating a longrun model from a simple OLS is incorrect.

So why are there 2 methods of creating an ARDL and ECM? WHy do people use both?

Thanks :)

[EViews Mirza]

There appears to be 2 methods in finding ARDL and ECM...

I'm not aware that there are multiple approaches to expressing the contemporaneous ARDL form into its EC equivalent. They are both equivalent representations of the same underlying structure. However, the ARDL model is typically estimated via OLS, and that is correct. Namely, the estimation doesn't require anything more than OLS.

You should check out our blog series on ARDL models which goes into significant detail (more than you'll typically need) on building, manipulating, and estimating ARDL models.

http://blog.eviews.com/2017/04/autoregressive-distributed-lag-ardl.html
http://blog.eviews.com/2017/05/autoregressive-distributed-lag-ardl_8.html
http://blog.eviews.com/2017/05/autoregressive-distributed-lag-ardl.html

[mickeykozzi]

Thank you EViews Mirza, I have read these and they are very helpful.

The example I refer to can be found in this youtube example by Crunch Economics.
Many other authors on youtube follow the same method

https://www.youtube.com/watch?v=2F1OY_1X8A0.

In explaining it simply, I have added photors:

Photo 1: Shows the short-run and long-run model specifications used in the LS - Least Squares method.
Photo 2: Using the long-run specification, you create the ECM series. Then you place in the LS equations (short run and long run) and run the model
Photo 3: You run the short run and long run (EMC model) with the LS method. The ARDL-ECM model is then displayed

As you can see, this is a different method used.
Are you able to tell me why authors use this method?
My supervisor seems to think that the long-run model is not specified properly here.

If you did this method and compared it to the Eviews method (that we have spoken about), the long run model and ARDL contain different coefficients completely.

What are you thoughts?

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[mickeykozzi]

Hello EViews Mirza,

How are you?
Have you had a chance to take a look at this one?
its an interesting question with a lot of views! :)

Cheers

[igor]

What is presented on the slide (last two lines) is nothing more than Engle-Granger procedure without testing for cointegration at the first stage (static long-run equation). I highly recommend not only watching videos on the Internet, but also reading original papers on the subject, as well as an exhaustive Eviews blog on the ARDL modeling.

[mickeykozzi]

Hello
I dont really understand what you mean.
What original works? What blogs?

Cheers

[igor]

If you cannot understand this and about trend specification, you have to learn econometrics diligently
What blog: Eviews Blog on the first page of this site, and use Search then. By the way, Mirza has provided the links above.
What papers: start, for instance, with Pesaran et al (2001) paper in Journal of Applied Econometrics on Bounds testing.
https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.616

Good luck!

[mickeykozzi]

Hi
Thanks I guess. I'll keep searching

[EnjoFaes]

What is presented on the slide (last two lines) is nothing more than Engle-Granger procedure without testing for cointegration at the first stage (static long-run equation). I highly recommend not only watching videos on the Internet, but also reading original papers on the subject, as well as an exhaustive Eviews blog on the ARDL modeling.

The Engle Granger method is totally different from the method to do ARDL estimation when variables are of mixed order of integration. While Engle Granger is only allowed for I(1) variables.. However what Michael is trying to ask is, whether this method is correct... OLS estimation, to see wether all variables are statistically significant + then you can display the key statistics of the long run relationship (because this isn't given by eviews).

Given that the long run relationship is not equal to the eviews levels equation this must be incorrect. However in Eviews there is no possibility to choose a case where AND a constant in the levels (long run) equation is given AND a constant in the EC-model, while most papers like for example the good author Narayan (2005), best in the field, does display both..

[igor]

Once again: Long-run model specification and error correction model specification on the slide are not directly related to ARDL Bounds test. Long-run model specification is like the static level equation in Engle-Granger method. The error correction model specification is like second stage dynamic equation in Engle-Grander method. Definitely, OLS is correct here, see Nobel-price paper in Econometrica. Generally, the results will not coincide with ARDL model since it takes into account dynamics while estimating the long-run. So what is your question about? Eviews ARDL Bounds test is implementation of Pesaran et al procedure and nothing more (Eviews makes this even better than original paper and Microfit). All deterministic terms specifications in Eviews are strictly the same as in Pesaran et al (2001). What Narayan (2005) had added to this?

[EnjoFaes]

The question consists out of 2 parts.

Most papers do report a constant in the EC-model, as well as in the long run.

While estimating a 7 variable ARDL (similar to Michael's research), some variables are fluctuating around 0, but some (macro-economic) variables keep increasing. When then applying a co-integration test like PSS and Narayan proposed to see if there is co-integration between the variables, the only possibility is the Bounds test because the model should include all variables. However, in eviews there are 2 cases that could be of interest: restricted constant and unrestricted constant. The choice between case 2 or case 3 doesn't seem obvious, however if you estimate it. The results are almost identical, with a small difference in the F-bounds statistic.

The question by Michael, is related, I presume, to the model specification that can be done in OLS. The procedure is correct, however it is maybe less correct when estimating ARDL, because the results of the long run levels equation that come with the bounds test =/= the long run equation via OLS. Because when estimating in OLS, you can choose your variables and a constant. Thus, what are therefore obliged to use a mixture of case 2 for a constant in the Long run relationship & case 3 for a constant in the ECM? Again, like all papers do...