## ARDL Substituted Coefficients

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Posts: 5
Joined: Thu Sep 12, 2013 10:35 am

### ARDL Substituted Coefficients

I have a question related to the substituted coefficient in an ARDL estimation.

I use the following file (http://www.stern.nyu.edu/~wgreene/Text/ ... leF5-2.txt) to estimate the most simple ARDL(1,1) model.

EViews displays the following specification :

***********************************************************************************************************************************************************************************

Substituted Coefficients:
=========================
REALCONS = 0.940663367262*REALCONS(-1) + 0.35122309101*REALGDP - 0.306997295848*REALGDP(-1) - 11.0441854096

Cointegrating Equation:
D(REALCONS) = -0.059336632737*REALCONS(-1) + 0.044225795161*(REALCONS - (0.74533712*REALGDP(-1) -186.12760617 ) + 0.351223091007*D(REALGDP) )

***********************************************************************************************************************************************************************************

But, according to the ARDL representation, the Cointegration Equation should be represented like this :

***********************************************************************************************************************************************************************************

Cointegrating Equation:
D(REALCONS) = -0.059336632737*( 0.74533712*REALGDP(-1) -186.12760617 ) + 0.351223091007*D(REALGDP)

***********************************************************************************************************************************************************************************

Maybe I missed something. I would be very interested by your answer.

Kind regards,

EViews Mirza
Posts: 46
Joined: Sat Apr 22, 2017 8:23 pm

### Re: ARDL Substituted Coefficients

Hi Jamel,

I'm not entirely sure how you're obtaining that output, but when I run the estimation on my end, the output I receive is:

----------
Estimation Command:
=========================
ARDL @FL(REALCONS,1) @FL(REALGDP,1) @

Estimation Equation:
=========================
REALCONS = C(1)*REALCONS(-1) + C(2)*REALGDP + C(3)*REALGDP(-1) + C(4)

Substituted Coefficients:
=========================
REALCONS = 0.940663367262*REALCONS(-1) + 0.35122309101*REALGDP - 0.306997295848*REALGDP(-1) - 11.0441854096

Cointegrating Equation:
D(REALCONS) = -11.044185409502 -0.059336632737*REALCONS(-1) + 0.044225795161*(REALCONS - (0.74533712*REALGDP(-1) -186.12760617 ) + 0.351223091007*D(REALGDP) )
----------

Clearly, our cointegrating equations are not the same. What version of EViews are you running?

Posts: 5
Joined: Thu Sep 12, 2013 10:35 am

### Re: ARDL Substituted Coefficients

Hi EViews Mirza,

I am using EViews 10+ (March 18 2019 build).

Our cointegration regressions are the same and it was a mistake in the previous message :

******************************************************************************************************************
Estimation Command:
=========================
ARDL(FIXED, DEPLAGS=1, REGLAGS=1, COV=HAC) REALCONS REALGDP @

Estimation Equation:
=========================
REALCONS = C(1)*REALCONS(-1) + C(2)*REALGDP + C(3)*REALGDP(-1) + C(4)

Forecasting Equation:
=========================
REALCONS = C(1)*REALCONS(-1) + C(2)*REALGDP + C(3)*REALGDP(-1) + C(4)

Substituted Coefficients:
=========================
REALCONS = 0.940663367262*REALCONS(-1) + 0.35122309101*REALGDP - 0.306997295848*REALGDP(-1) - 11.0441854096

Cointegrating Equation:
D(REALCONS) = -11.044185409502 -0.059336632737*REALCONS(-1) + 0.044225795161*(REALCONS - (0.74533712*REALGDP(-1) -186.12760617 ) + 0.351223091007*D(REALGDP) )

******************************************************************************************************************

However, I still think that the cointegration regression should be written as follow in order to revert to the original ARDL(1,1) model:

***********************************************************************************************************************************************************************************

Cointegrating Equation:
D(REALCONS) = -0.059336632737*( 0.74533712*REALGDP(-1) -186.12760617 ) + 0.351223091007*D(REALGDP)

***********************************************************************************************************************************************************************************

Maybe the cointegration equation is written in order to stabilize the REALCONS in the long rung.

Kind regards,

EViews Mirza
Posts: 46
Joined: Sat Apr 22, 2017 8:23 pm

### Re: ARDL Substituted Coefficients

Ah! I think I understand your point now. What you are claiming is "incorrect" is in fact the Error Correction Form (ECM) of the ARDL model. And you are right! The ECM is NOT equal to the cointegrating equation that we display in the outputs we have pasted earlier, namely.

Cointegrating Equation:
D(REALCONS) = -11.044185409502 -0.059336632737*REALCONS(-1) + 0.044225795161*(REALCONS - (0.74533712*REALGDP(-1) -186.12760617 ) + 0.351223091007*D(REALGDP) )

What we refer to as the "Cointegrating Equation" there is in fact the Conditional Error Correction equation in the View\Coefficient Diagnostics\Long Run Form and Bounds Test Form output. In particular:

[img]CECM.png[/img]

However, if you go to View\Coefficient Diagnostics\Error Correction Form, then you will see that we correctly display the ECM as you expect it to be displayed. Namely:

[img]ECM.png[/img]

Note that the images are added as attachments. In any case, I suppose we can look into relabeling the original output that brought confusion. I hope this clarifies things.
Attachments
ECM.PNG (15.01 KiB) Viewed 152 times
CECM.PNG (8.49 KiB) Viewed 152 times

Posts: 5
Joined: Thu Sep 12, 2013 10:35 am

### Re: ARDL Substituted Coefficients

Thank you for this reply, I think I understand the causes of my confusion.

Indeed, I wrote to the Error Correction Form (ECM) form of the ARDL model in my previous messages.

I think it would be more simple to understand if we write the Conditional Error Correction Regression in this way :

*********************************************************************************************************************************************
CECR

[img]
table_longrunform.png
[/img]

Cointegrating Equation:
D(REALCONS) = -11.044185409502 -0.059336632737*REALCONS(-1) + 0.044225795161*REALGDP(-1)
+ 0.351223091007*D(REALGDP)

*********************************************************************************************************************************************
ECM

[img]
table_ecm.png
[/img]

Model:

D(REALCONS) = -0.059336632737*( REALCONS(-1) - 0.74533712*REALGDP(-1) + 186.12760617 ) + 0.351223091007*D(REALGDP)

Cointegrating Equation:
REALCONS(-1) = 0.74533712*REALGDP(-1) - 186.12760617

*********************************************************************************************************************************************

In order to switch between the CECR and the ECM more easily. But, it is just a suggestion.

Thank you again for your help.

Kind regards,