[Sebastian Kripfganz]

Anil Raj
When you use the maxlag() option, the underlying estimation sample (i.e. the number of observations) changes. The test results are then not directly comparable any more. Moreover, it is always possible that a test rejects the null hypothesis when it is true (type-I error) or does not reject it when it is not true (type-II error).

[Anil Raj]

As you replied to the query of Mr.Sebastian Li as "An underlying assumption of the ARDL model is that there exists at most one cointegrating relationship that involves the dependent variable. (There might be additional cointegrating relationships among the independent variables themselves.)". ....

1)Say I have one dependent variable and 3 independent variable. I can test the cointegration by running a regression involving one dependent variable and another independent variable and then test for stationarity of the error terms? If the dependent variable and independent variable are non-stationary and the errors are stationary we can conclude that cointegration exists. Is it right? Or as above should we run the regression for one dependent variable and all other independent variable and then test for error term's stationarity? Does conintegration happens only for a pair of variables?
2) Is there any other method in built in ardl model to test cointegration?

Here my doubt is how we know that there is atleast one cointegrating relationship?

Thanks in advance.

[Sebastian Kripfganz]

Cointegration does not necessarily occur pairwise but can, and often does, involve several variables.

With the ardl command, if your variables are I(1), you can test for cointegration with the bounds test that is implemented in the postestimation command estat ectest. The existence of a level relationship is equivalent to cointegration if all the variables are I(1); see slide 2 of my my presentation at last year's London Stata Conference.

The estat ectest postestimation command is part of the new version of the ARDL command that is discussed in the following Statalist topic:
ARDL: updated Stata command for the estimation of autoregressive distributed lag and error correction models

[Anil Raj]

I have used the vecrank command in stat to check for cointegration. And the results are

vecrank bnchmrk	repo cof lgnpa, trend(constant) max
	Johansen tests for cointegration
Trend: constant	Number	of obs	=	34
Sample: 3 - 36	Lags	=	2
5%
maximum	trace critical
rank parms	LL eigenvalue statistic value
0 20	76.161843 . 57.4386 47.21
1 27	89.835272 0.55261 30.0917 29.68
2 32	97.807025 0.37433 14.1482* 15.41
3 35	104.19286 0.31315 1.3765 3.76
4 36	104.88112 0.03968
5%
maximum	max critical
rank parms	LL eigenvalue statistic value
0 20	76.161843 . 27.3469 27.07
1 27	89.835272 0.55261 15.9435 20.97
2 32	97.807025 0.37433 12.7717 14.07
3 35	104.19286 0.31315 1.3765 3.76
4 36	104.88112 0.03968

Does this means that the model has 2 cointegrating relationship or 1 cointegrating relationship, which value should I select from first table or second table?
If I have more than one cointegrating relationship as mentioned in table 1, can I use ARDL model to fit the data?

[Sebastian Kripfganz]

In your case, the trace statistic and the maximum-eigenvalue statistic yield conflicting results. It is up to you to make a judgement which of the two statistics to use. If you conclude that there are two cointegrating relationships, this test is still not informative enough about the applicability of the ARDL model. The latter requires that there is at most 1 cointegrating relationship involving the dependent variable. This does not preclude the case of 2 or more overall cointegrating relationships if all of these other relationships are among the independent variables only. You might have to make an assumption that these additional cointegrating relationships indeed do not involve the dependent variable of the ARDL model.

[Anil Raj]

@Dr.SebastianThanks a lot for the clarification. One more doubt please. When I run ardl regression without ec (ardl1.jpg) and with ec(ardl2), what is the difference in coefficients of ardl1 and short run coefficients of ardl2? How do we interpret it ? I have gone through your presentation and in page 16 you have said that the short-run accounts for short run fluctuations not due to deviations from long run equilibrium.

In my model the bouds test indicate that there is no levels relationship, so it means that I should ignore the short run coefficients listed in ardl2 ? ie with ec and interpret the ardl1 (with out ec) coefficents ?

Stata screen shots attached.

Kindly help.

[Sebastian Kripfganz]

The short-run coefficients in the EC representation are linear functions of the underlying ARDL coefficients. The ARDL coefficients (without option ec) are less easily interpretable. See my comment #340 about the interpretation of the short-run coefficients.

If there is no level relationship, then you can ignore the long-run effects (not the short-run effects). You would still interpret the short-run effects from the EC representation.

[Anil Raj]

Hello Everyone,
Can we interpret the p-values of adj term, LR and SR as normal? In my case the adj coeff is -0.072 with a p value of 0.215 and in LR indepvar1 coeff is 1.77 with p value 0.020 and indepvar2 is -1.18 with p value 0.125. I have read in one of the topic that if p value is not significant there is no long term relation. I feel a bit confused here. In this case if there is no long term relationship as per the bounds test results should we interpret the LR with significant p value or should we avoid it LR and interpret only SR results?
Please help.

[Sebastian Kripfganz]

The p-value of the speed-of-adjustment term in the regression output does not have a meaningful interpretation. Instead, the p-value of the bounds t-test reported by estat ectest should be considered.

The p-values of the LR and SR coefficients have the usual interpretation. Note that the LR coefficients become meaningless if you cannot reject the null hypothesis that the adjustment coefficient equals zero, i.e. you should not attempt to interpret the LR coefficients if the bounds test does not provide evidence for the existence of a LR relationship. The SR coefficients can still be interpreted.

[Anil Raj]

Thank you so much for the quick reply. So does it mean that the speed of adjustment is irrelevant if there is no LR ? Then we should interpret SR results only ?

[Sebastian Kripfganz]

It means that both the speed-of-adjustment and the LR coefficients are "irrelevant" when there is no LR relationship, in the sense that the speed-of-adjustment coefficient is not statistically significantly different from zero. This conclusion can in itself be "relevant".

[Anil Raj]

Thank you so much Dr.Sebastian.

[Anil Raj]

Sir, please tell me the difference between D1, LD, L2D, L3D etc in SR output. Does it means first difference(D1), one value Lagged (LD), 2 lags (L2D) ? Also how to interpret depvar's LD (its own first lag?) Why the output is showing the ec test result as "D.depwar" ? Has it estimated with first difference?Thank you.

[Sebastian Kripfganz]

Please see Slide 12 of my presentation at the 2018 London Stata Conference about the formulation of the model in EC form. The dependent variable in the EC representation is the first difference of depvar. Regarding the time series operators, please consult the following Stata help file:

help tsvarlist

[Sean Harris]

Hi, Can anyone help me?
im experiencing heteroskedasticity within my ARDL and im not sure how to get round this

Thanks