Cointegration with I(0) Dependent Variable-ARDL

[Muhammad Azam]

I am told that cointegration can not be checked when the Dependent Variable is I(0) in case of ARDL. However the Independent Variables / Regressors can be a mix of I(0) and I(1). Does anybody agree with this?

[Sebastian Kripfganz]

Cointegration can only exist between variables that are all individually I(1). If the dependent variable is I(0), then there can only exist a long-run relationship with other I(1) variables if the latter are cointegrated among themselves.

More on ARDL in Stata:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Muhammad Azam]

Cointegration can only exist between variables that are all individually I(1). If the dependent variable is I(0), then there can only exist a long-run relationship with other I(1) variables if the latter are cointegrated among themselves.

More on ARDL in Stata:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

I wrote to Dr. Pesaran and his colleague responded that it is OK to have an I(0) Dependent variable in ARDL Bounds testing approach, did not mention any other condition for that. But if my model's bound test shows cointegration then it means the independents must be cointegrated among themselves, am I right?

[Sebastian Kripfganz]

Yes, you can apply the bounds test when the dependent variable is I(0).

No, the bounds test does not indicate "cointegration" in that case. It indicates the existence of a long-run relationship. This is a more general concept than cointegration. Cointegration can only be present among I(1) variables.

The bounds test does not directly indicate cointegration among the independent variables themselves. A rejection of the bounds test null hypothesis always means that there is evidence for a long-run relationship including the dependent variable. However, if some of the independent variables in the long-run relationship are I(1) and they have a statistically significant long-run coefficient, but the dependent variable is I(0), those I(1) variables must be cointegrated among themselves. Otherwise, the long-run relationship would not be balanced in terms of the integration order. This is an indirect reasoning that is not directly tested by the bounds test.

[Muhammad Azam]

Great. If we conclude that there exists a long run relationship but not Cointegration then can we go for running an Error Correction Model ? Can you refer to some literature on long-run relationship in the absence of cointegration, any tests.

[Sebastian Kripfganz]

As a start, you might find the following paper helpful. You can then continue with further references given therein:

• Kripfganz, S. and D. C. Schneider (2020). Response Surface Regressions for Critical Value Bounds and Approximate p‐values in Equilibrium Correction Models. Oxford Bulletin of Economics and Statistics 82 (6), 1456-1481.

[Eyup TANIL]

Is there anyone who can answer this question?