ARDL bound test

[EValpha2015]

Dear Eviews team,
Implementation ARDL long run analysis and PSS bound test in Eviews 9 seems to be very useful. Unfortunately, this procedure in Eviews is incomplete and in several cases may be misleading. In Pesaran, Shin, and Smith (2001), five different cases are considered with appropriate critical values:
1. No constant, no trend
2. Restricted constant, no trend
3. Unrestricted constant, no trend
4. Unrestricted constant, restricted trend
5. Unrestricted constant, unrestricted trend
Eviews 9 allows only cases 1, 3, and 5. However, if the restrictions in cases 2 and 4 are ignored, a constant term in the first-difference equation can generate a linear trend in the levels equation, and an unrestricted trend in the first-difference equation can generate a quadratic trend in the levels-equation. I think it will be not difficult to add cases 2 and 4 to current version of Eviews. It makes this procedure more useful for applied researchers. Moreover, this has been already realized in Stata ado package (http://www.kripfganz.de/stata).
All these procedures can be easily done manually, but without such an addition ARDL bound test in Eviews is not complete. Additionally, it should be useful to add an option that permits exclusion of right-hand variables with zero lags if necessary.

[EViews Gareth]

I'm not sure how those cases would fit in with the Trend specification combo box on the estimation itself. The Bounds Test results are tied to the initial estimation option.

[EValpha2015]

Dear Gareth,

I will try to consider the simplest ARDL model with two variables (y and x) and two lags. The most general unrestricted model transformed into error correction form to perform PSS bounds test is as follows:

Dy(t)=a(0)+a(1)t+a(2)y(t-1)+a(4)x(t-1)+a(5)Dy(t-1)+a(6)Dx(t)+a(7)Dx(t-1)+u(t).

In the first case (no constant, no trend), a(0)+a(1)t is absent and our H0: a(2)=a(4)=0 using F-test. Cointegrated vector is ecm=y(t)-([(4)/|a(1)|]*x(t)). All is OK in Eviews here.

In the second case (restricted constant, no trend) a(1)t is absent and our H0: a(2)=a(4)=0 and a(0)=0. We should use critical values (asymptotic) from Table CI(ii) from PSS (2001). Cointegrated vector here should be ecm=y(t)-([(a(4)/|a(1)|]*x(t)+[a(0)/|a(1)|]). This case in fact is not presented in Eviews. Now Eviews actually uses bounds test for the case with unrestricted constant (critical values from Table CI(iii) in PSS (2001), but cointegrated vector is presented as for restricted case.

In the third case (unrestricted constant, no trend) all is OK in Eviews except representation of cointegrated vector. It should be as follows y(t)-([a(4)/|a(1)|]*x(t)) – no constant in long-run relation, only in short-run part of the model.

In the fourth case (unrestricted constant, restricted trend) our H0: a(2)=a(4)=0 and a(1)=0. Here one should use the critical values from Table CI(iv) from PSS (2001). So cointegrated vector in this case should be ecm=y(t)-([a(4)/|a(1)|]*x(t)+[a(1)/|a(1)|]). No constant in long-run equation, only in the short part of the model.

The fifth case (unrestricted constant, restricted trend) is usually unrealistic, but it actually realized in Eviews for trend option (critical values from Table CI(v) from PSS (2001)). However, a long-run equation is incorrect in Eviews. When constant and trend are unrestricted, they should be included only in a short run part of the model.

Actually, all this things can be easily done manually to use PSS bounds test, only optimal lag selection needs some automation. Moreover, Pesaran’s Microfit 5 (I have look at the demo) does not realize this procedure as authors presented it in PSS (2001).

Nevertheless, PSS bounds test is extremely popular (frankly, I don’t know why ) and Eviews can be a leader in implementation of this procedure. Especially, if all cases will be taken into account and more so if critical values for small sample will be available (may be bootstrap or at least those from Narayan, P. K. (2005) "The saving and investment nexus for China: evidence from cointegration, tests", Applied Economics, 37:17, 1979-1990). Exclusion of right-hand variables with zero lags is also discussed by the authors and this is useful when it is not clear that regressors are weakly exogenous.

I think all these things are not difficult to implement, if you consider this is useful. Hope my comment will be useful at least for those who use bounds test in their research.

Thanks for a great possibility to evaluate demo copy of Eviews 9!

Best regards,
EValpha2015

[EViews Gareth]

I'm still not sure I follow how you would tie it in to the estimation options. Are you saying that we should display two sets of critical values for the bounds test in certain cases?

[EValpha2015]

Dear Gareth,

You can add in “Trend specification” 2 additional options. So “Trend specification” menu will have the following options:
1. None
2. Restricted constant (level)
3. Unrestricted constant (level)
4. Restricted liner trend
5. Unrestricted liner trend
This “design” is somewhat similar to the Johansen cointegration test menu in Eviews.

The required changes are:

1. None: no changes

2. Restricted constant (level): ARDL in levels will be the same as in Eviews now. “Cointegration and Long run form”: constant should be excluded from “Cointegration Form” and included in “cointeq” and “Long Run Coefficients”. ARDL in the error correction form after the bounds test will be the same as now. H0: lagged levels and constant are equal to zero (joint F-test). Critical values are from the Table CI(ii).

3. Unrestricted constant (level): ARDL in levels will be the same as in Eviews now. “Cointegration and Long run form”: constant should be in included in “Cointegration Form” and excluded from “cointeq” and “Long Run Coefficients”. ARDL in the error correction form after the bounds test will be the same as now. H0: lagged levels are equal to zero (joint F-test). Critical values – all is OK now (Table CI(iii)).

4. Restricted liner trend: ARDL in levels will be the same as in Eviews now. “Cointegration and Long run form”: constant should be included in “Cointegration Form” and excluded from “cointeq” and “Long Run Coefficients” (only trend should be included into a long-run equation). H0: lagged levels and trend are equal to zero (joint F-test). Critical values are from the Table CI(iv).

5. Unrestricted liner trend: ARDL in levels will be the same as in Eviews now. “Cointegration and Long run form”: constant and trend should be in included in “Cointegration Form” and excluded from “cointeq” and “Long Run Coefficients” (no deterministic terms in a long-run equation). H0: lagged levels are equal to zero (joint F-test). Critical values are from the Table CI(v).

As you can see, (i) critical values are different for each case; (ii) two additional cases (2 and 4) should be added to menu “Trend specification” (of cause, if it is possible in current version of Eviews), and (iii) for cases (3) and (5), several amendments are required.

[EViews Gareth]

Got it. Thanks for the detailed follow up. We'll give it a whirl.

[ecofin]

hi,
these new opions will be added in the next patch.

[ecofin]

there is no Unrest linear trend in the menu, it should be have 5 options:
1. None
2. Rest constant (level)
3. Unrest constant (level)
4. Rest liner trend
5. Unrest liner trend

nice day for all. ecofin

[EViews Gareth]

We decided not to include that option, for now

[ecofin]

thank you for your reply.

[ecofin]

hi,
i have replicate the example used by David E. Giles ( gas & crude) http://davegiles.blogspot.com/2015/01/a ... ews-9.html.
the problem the result in coint and long run form with the new menu trend specification (Restrict linear trend) have not the same result with the classic menu, i used an another way restrict const in menu and generate trend ( genr t=@trend+1) the result in the long run coef (cons and t) the result did not change.
I had to return to the previous patch 08-05-2015 to make the example in exact result.
is that the result is different because the Unrest linear trend not included in the menu?
can you make 2 menu for trend specification
simple menu with: none, cont (level), linear trend.
and menu like this now.
it's better to have two menu
nice day for all.

[ecofin]

hi,
1-i have used two software EViews 9 and microfit 5 to estimate ARDL with constant and linear trend, but the constant should be in Long Run Coefficients and in coineq, just the constant excluded for cointegration form (like microfit 5);
2-in dependent variable should be D(Y) no Y (in coin and long rum form out put);
3-the bound test not same with microfit 5.
I'm not exactly sure where I have to choose

[startz]

One issue is that it appears you are having EViews use 58 observations while MicroFit uses 56.

[ecofin]

i can use the order of ARDL in microfit 5, for example 2 lags 58 obs for the both (EViews & microfit) the same result Mr startz.
...

[igor]

Dear ecofin,

All is OK in Eviews with ARDL bounds test.
You can see that in your case the ECM terms in Micrifit and Eviews are different.
Why it is so? I recommend you to refer to original Pesaran' paper on ARDL bounds testing and then to run you regressions and tests manually.
Then you can compare the results from your manial estimations, Microfit and Eviews. It is also important to specify deterministic terms of your models in accodance with 5 cases (now in Eviews - 4) and use the appropriate critical values (hint: when trend (or constant) is restricted in cointegration vector, then trend (or constant) should be included in the appropriate F-test).
Additionaly, I suppose that Pesarans' Microfit does not follow exactly Pesanans' paper, while Eviews do exactly the same as the paper suggests (just one exclusion now - exotic case 5 is not included in Eviews).

Best regards,
Igor