[misso ouhibi]

I understand thanks very much for your explanation.

Then when I use this command: ardl lnY lnX1 lnX2 lnX3 lnX4 lnX5, aic

I get this selection of lags automaticallyARDL(2,1,0,4,0,2) regression.

[misso ouhibi]

After i see your comments i can use SBIC rather then AIC to estimate ARDL model ? because you are mentionned that AIC might choose an optimal lag order which is well below the maximum lag order.

[Sebastian Kripfganz]

The SBIC would typically result in even smaller optimal lag orders than the AIC.

[misso ouhibi]

so it's preferred to use the AIC rather then AIC??

[Sebastian Kripfganz]

It is hard to give a general answer. If you want to carry out a bounds test, then the AIC might be preferable because it reduces the chance for remaining serial error correlation. On the other side, the estimation of additional parameters goes hand in hand with an efficiency loss, i.e. the parameters will be estimated less precisely.

Both the AIC and SBIC address the tradeoff of bias versus efficiency. The SBIC puts more emphasis on efficiency, the AIC on limiting any bias.

[misso ouhibi]

ok, I understand thanks a lot Sebastien for your explanation. I want to ask a question when w estimate the model which option do we ought to use?
1-No intercept, no time trend.
2 Restricted intercept, no time trend.
3 Unrestricted intercept, no time trend.
4 Unrestricted intercept, restricted time trend.
5 Unrestricted intercept, unrestricted time trend.

[misso ouhibi]

hello Sebastien, I want to ask you about the result of ARDL-ECM :

when I estimate the model, I have one variable that has 0 number of lags and the other variable has 5 lags in the table of estimation I didn't find the variable which has 0 lags in the short-run part and the variable which has 5 lags it's presented with just only 4 lags:

Lnx2|
D1. | .0070726 .0368923 0.19 0.848 -.065696 .0798413
LD. | -.013751 .0358621 -0.38 0.702 -.0844877 .0569857
L2D. | -.0668578 .0333552 -2.00 0.046 -.1326497 -.001066
L3D. | -.0887014 .0298535 -2.97 0.003 -.1475864 -.0298165
L4D. | -.0325287 .0250766 -1.30 0.196 -.0819913 .0169339

Please Can You explain to me why?

[Sebastian Kripfganz]

The lag order in the EC model is one less than the lag order in the levels ARDL model. For example, if there are 6 coefficients in levels (i.e. lags 0 to 5), the EC model will contain 1 long-run coefficient and 5 short-run coefficients (lags 0 to 4). If there is only 1 coefficient in levels (lag 0), there will only be a long-run coefficient in the EC model but not short-run coefficients.

A decision about the case regarding the deterministic elements can be guided by a visual inspection of the data. Cases 1 and 2 are consistent with a dependent variable which could possibly be either a stationary variable or a nonstationary variable without any apparent trend. For case 1, you would typically require that all variables have a mean of zero. If the dependent variable appears to follow an upward or downward trend, cases 3 and 4 become relevant. If you have strong reason to believe that the observed trend is likely to be a consequence of a similar trend in one of your independent variables, then case 3 would be most appropriate. Otherwise, case 4 would be the safer option. Case 5 is hardly relevant for most practical situations as it would assume a faster than linear growth under the null hypothesis.

[misso ouhibi]

Hello Sebastien, Thanks a lot for your explanation but after I estimate my model. I want to ask you some questions.

*When I estimate the ARDL-ECM model, I found in one country, all the coefficients are nonsignificant in the long run but in the short run, they are significant any help suggestion, please?
*I want to ask you about the command and the lags that we should put to estimate the model: Firstly, when we estimate the ARDL-ECM model we use all the variables in levels then stata will put the variables in first difference right? means we don't need to put the variable in the first difference again?
*My second question about the lags is, we estimate the model with the number of lags that we get when are we testing the bound test?
*I don't get your point'' The lag order in the EC model is one less than the lag order in the levels ARDL model''? Any help, please

[Sebastian Kripfganz]

• It could well be the case that the variables only have short-term effects but there exists no long-run relationship among them. This is a valid finding.
• Yes, the Stata command automatically transforms the variables into first differences. You do not need to do this yourself.
• You do not necessarily need to re-estimate the model after the bounds test. However, sometimes people use the AIC to obtain the lags for the bounds test and subsequently use the BIC to re-estimate a more parsimonious model afterwards. That is a valid approach.
• Please compare slides 5 and 12 of my 2018 London Stata Conference presentation. On slide 5, you can see the lag orders p and q for the ARDL levels model. On slide 12, you can see that the lag orders become p-1 and q-1 after transforming the model into EC form. The lag order is reduced by one in order to separate out the long-run effects from the short-run effects.

[misso ouhibi]

Thanks a lot sébastian for your answer.
*Firstly, the problem is that the variables have only short-term effects but when i test the bound test i found that there is a long relathionship between this variables.
*Can you explain to me more why we don't necessarily need to re-estimate the model after the bound test?
* the command of the ARDL-ECM model with BIC didn't work, can you tell me how we use BIC in the command of the ARDL-ECM model and for the bound test, because stata didn't accept the command with BIC.
*Ok I will compare the slides to more understand the point thanks a lot for all your help.

[Sebastian Kripfganz]

• If all of your long-run coefficients are statistically insignificant, then it would at least be surprising to find that the bounds test supports the existence of a long-run relationship.
• The EC model, which you estimated for the bounds test, contains all the relevant information. The only thing you could possibly gain from re-estimating the model is an increase in efficiency/precision of the coefficient estimates.
• What does "didn't work" mean? Was there an error message? If so, can you show me the command line you typed and the corresponding error message? You would normally just need to specify the bic option (instead of the aic option).

[misso ouhibi]

• That's why I am so surprised about the results that I get after testing the bound test ( #note: Maybe I do a mistake in the command that I used to run the ARDL-ECM) but I will show you please what I am using the steps with command and I am asking you to correct if there is a problem; another thing, in my model there is a intercept but in the command that I used in my estimation, I didn't take into account the intercept.

The command and steps that i used to estimate the ARDL-ECM:
To test the bound test after testing the unit root i used this command: ardl lnY lnX1 lnX2 lnX3 lnX4 lnX5, maxlags (12) aic maxcombs(5000000) dots ec
estat ectest
After that i estimate the model ARDL-ECM by using this command and i put the same lags that ARDL gives to me in the first step (step of ARDL model) :

ardl lnY lnX1 lnX2 lnX3 lnX4 lnX5, lags (12, 12, .... ) regstore (ecreg) ec
estimate restore ecreg

• Do you think if we put the option it's will change the results from non-significant to significant?
• For bic yes, there is an error message, but when i put for example maxlags (11) bic , ARDL gives me the lags (1,1,0,0,0) i don't know why.
• ardl lnY lnx1 Lnx2 lnx3 lnx4 lnx5, maxlags(11) bic maxcombs(4455516) dots
• Optimal lag selection, % complete:
  ----+---20%---+---40%---+---60%---+---80%---+-100%
  ..................................................
  BIC optimized over 2737152 lag combinations
  ARDL(1,1,0,0,0,0) regression
• Thanks a lot for your help

[Sebastian Kripfganz]

I am not sure I can help you any further based on the information you have given me. There is nothing obvious which could be wrong. An intercept is included by default in the regressions. The BIC tends to selects smaller lag orders, sometimes substantially smaller. The choice of lags (1,1,0,0,0,0) would not necessarily surprise me, especially if there is no evidence of a long-run relationship. Possibly, the significance of the short-run effects in the model chosen by the AIC is a consequence of a high degree of collinearity among the included lags. It might be worth adding a linear time trend with the trend() option unless your variables do not show any trends.

I cannot see an error message from the model with the bic option. What is the error message saying?

[misso ouhibi]

Thanks, Sebastian for your answer. before i have an error message when I used the first one bic after I am trying, now there is no error message but I don't know why bic gives me this number of lags (smaller lags )? and as you know that to test the bound test, you should use the maximum number of lags so the using bic criteria were wrong in this case right?
I didn't get your point (the significance of the short-run effects in the model chosen by the AIC is a consequence of a high degree of collinearity among the included lags. )?? Any more explanation, please.
i want to ask you for something very important when we should test for the stability of the model/autocorrelation and heterodascticity? after ARDL or ARDL-ECM? And when we face a problem of hetero or autocorrelation we should correct the model to estimate the final model and when we do correction, I want to know if the results will be changed or not?