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Posted: **Sat Aug 01, 2020 7:09 am**

Hello. Estimation ARDL/ECM long term relationship

I have a question concerning the bounds test. When the F-value lies between the I(0) and I(1) value, the bounds test is inconclusive along Cruncheconometrix, I know referring to a youtuber is strange for a researcher, but in literature it is quite hard to find practical user guide for such tests.

What do I then do? Cruncheconometrix says to estimate the short term ARDL model. However a paper I found says the following:
If the calculated F statistics falls between the lower and upper bounds, it is inclusive. The alternative efficient
way of establishing cointegration is testing significant negative lagged error-correction term (Kremers et al.
1992; Bahmani-Oskooee, 2001; Iwata et al. 2012; Shahbaz et al. 2012b).

However looking at the ECT, means looking at the error correction form. Do I interprete the long term levels equation and use the Error correction form?

Is changing the Lag to automatic selection in ARDL a good other option? I had it now on 2 2, but changed it to 2 1
This gave a slightly better interpretation of the bounds test. With co-integration at 5% along the asymptotic PSS critical values and 10% along Narayan small sample by increments of 5.

Best regards,
Enjo

Posted: **Sat Aug 01, 2020 9:00 am**

The original authors of the ARDL bounds test, namely Pesaran, Shin and Smith (2001) (PSS henceforth) have the following advice in their paper:

Two sets of asymptotic critical values are provided for the two polar cases which assume that all
the regressors are, on the one hand, purely I(1) and, on the other, purely I(0). Since these two sets
of critical values provide critical value bounds for all classifications of the regressors into purely
I(1), purely I(0) or mutually cointegrated, we propose a bounds testing procedure. If the computed
Wald or F-statistic falls outside the critical value bounds, a conclusive inference can be drawn
without needing to know the integration/cointegration status of the underlying regressors. However,
if the Wald or F-statistic falls inside these bounds, inference is inconclusive and knowledge of the
order of the integration of the underlying variables is required before conclusive inferences can be
made. A bounds procedure is also provided for the related cointegration test proposed by Banerjee
et al. (1998) which is based on earlier contributions by Banerjee et al. (1986) and Kremers et al.
(1992). Their test is based on the t-statistic associated with the coefficient of the lagged dependent
variable in an unrestricted conditional ECM. The asymptotic distribution of this statistic is obtained
for cases in which all regressors are purely I(1), which is the primary context considered by these
authors, as well as when the regressors are purely I(0) or mutually cointegrated. The relevant
critical value bounds for this t-statistic are also detailed.

In other words, when the ARDL bounds test is inconclusive (falls between the bounds) you must know the integrating rank of your variables matrix. That is, you must know how many (if any, or all) of your variables are I(1). Once you know that, you can derive an ECM equation, like the one in equation (11) of PSS, and run a number of appropriate tests. For instance, you can run the test of Banerjee, Dolado and Mestre (BDM), which assumes that all variables are I(1). Alternatively, you can run the test of Kremers et al.

Hopefully this helps.

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ARDL/ECM Bounds test question (EVIEWS11)

ARDL/ECM Bounds test question (EVIEWS11)

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