EViews.com

The EViews 9 User's Guide for ARDL testing, equation (27.1), shows an auto-regressive equation, with both y and x terms in levels. In turning this into an estimate of cointegrated and long-run relationships, (27.3) then transforms (27.1) into an ECM form -- with both x and y in first difference lagged forms, with an embedded cointegrating equation in lagged *levels*. All standard so far.

But this is not at all the way that EViews 9 carries out its test of long-run and cointegrating relationships. Entering an ARDL relationship in levels does produce an equation similar to (27.1). So far, so good. In estimating a ECM form via View/Coefficient Diagnostics/Cointegration and Long Run Form, however, one finds that the dependent variable is still in levels, rather than the first-difference form shown in (27.3) Note that this is even though the Bounds Test is carried out via an equation like (27.5), a form similar to (27.3) but "unconstrained" in its error-correction portion.

Can I get an ECM form similar to (27.3)? (That is, instead of estimating a VECM model directly, with the much more restrictive conditions that would imply.) Of course I can just re-estimate (27.1) but with the dependent variable in first-difference form -- this does give a result identical to the bounds test; i.e., the equation shown as (27.5). But then the cointegrated long-run form estimate on this ARDL form looks very different from the desired (27.3) -- with second-difference terms. (Yikes!)

Is the documentation is misleading, or have I just interpreted it badly? I hope I have been clear enough in my questions. If not please respond, and I will try to clarify.

When you click on View->Cointegration and Long Run form, the dependent variable shown is the original dependent variable, and not the one used during the cointegration estimation. The cointegration estimation is in differences.

Thank you for this reply, but I still don't understand. I see that the RHS variables are in differences, as you say, while the cointegrating equation itself is in levels -- as normal for an ECM. And I see that the LHS variable is in levels, as you say -- so not standard ECM form.

Why does the documentation for EViews 9 show a transformation to ECM with a first-difference LHS term? So where is this "cointegration estimation ... in differences?" Is it possible to retrieve that form? The current documentation nowhere references the "ARDL Cointegrating And Long Run Form" as actually shown, with its LHS in levels. It seems to me that this documentation is misleading and incomplete. Am I missing something very basic?

The LHS is not in levels. It is in differences.

OK, thank you for clarifying that. But let me suggest that I may not be alone in reading the EViews output literally. In my variable LRTURN, it reads:

"ARDL Cointegrating And Long Run Form
Dependent Variable: LRTURN."

According to what you're saying, shouldn't it read D(LRTURN)? Note that for the Bounds Test, which should be a quite similar form, it does read:

"ARDL Bounds Test ....
Test Equation:
Dependent Variable: D(LRTURN)."