ARDL model

[challenges]

Dear Rats users,
I would like to estimate an Unrestricted Error Correction Model (UECM) based on an ARDL (1,0) of the form: yt=cst+yt-1+xt. Could you please help me to reparametrize the ARDL (1,0) in an UECM in such a way that one could distinguish this UECM from an UECM based on an ARDL (1,1) of the form: yt=cst+yt-1+xt+xt-1.
Thank you in advance for your help.

[TomDoan]

The whole point of an ARDL is to get something that can be run by linear regression. So to distinguish the two, just don't include the lagged X in your regressors on the LINREG.

[challenges]

Dear Tom,

Thank you a lot for your answer, however I do not understand what is precisely the econometric form of the UECM based on the ARDL(1,0).
Could you please explain it to me? Thank you for your help.

[TomDoan]

Error correction models are generally written in terms of first differences everywhere but in the error correction term, which usually is put in as a lag. The Pesaran-Shin method is to estimate dy on lagged y, lagged x and lags of dy and dx, with the cointegrating vector estimated as

y+(coefficient on x{1}/coefficient on y{1})x

That's used to create the error correction variable xi and the regression is then rerun with

dy on lagged xi + lagged dx and lagged dy

All the regressions can be done with LINREG. The different "ARDL"'s are created by altering the number of lags in the dy and dx polynomials.

[challenges]

Dear Tom,

Thank you for your quick reply. I suppose that my question was not very clear, as it is precisely the UECM based on the ARDL (1,0) that is problematic to me.
In the ARDL(1,1) framework, the UECM has the form: dyt=cst+b0*dxt+(a1-1)*yt-1+(b0+b1)*xt-1, where dyt=yt-yt-1 and dxt=xt-xt-1. The F-test for cointegration assessment is carried on the yt-1 and xt-1.
In the ARDL(1,0), the reparametrization would give: dyt=cst+b0*xt+(a1-1)*yt-1. The problem is that I need an UECM to perform the cointegration test. What is in the case of an ARDL (1,0) the appropriate UECM ? Thank you in advance for your advice.

[TomDoan]

With your definitions, an ARDL(1,0) can't be written in error correction form since it doesn't have rich enough dynamics for the X variable.