[Babacar Mbengue]

Hi Sebastian Kripfganz

Sorry, my fault. Indeed, your t-statistic is larger than the critical value. But the reason is once again that the speed-of-adjustment coefficient exceeds zero. The t-test is designed for a one-sided hypothesis test based on the assumption that the speed-of-adjustment coefficient falls into the range [-1, 0]. Under the null hypothesis, it is zero. Under the alternative hypothesis, it is negative. It does not make sense to apply the bounds test to the t-statistic if the latter has a positive sign. The model is simply misspecified and/or poorly estimated.

For the misspecification, which model should I correct the ardl or ec conditionnal? Sometimes I have a well specification for ardl but not for ec conditionnal. I remark also in the btest stata do not give the t-statistic, what's appen in that case?

[Sebastian Kripfganz]

@Pandi Sarr:
Without seeing the output, my guess is that the actual lag order for lnT in the ARDL level representation is equal to 1 (not 0). For the second-specification, the option ec1 would add one lag for the variable lnT to be able to express the long-run relationship in terms of the t-1 variables (even though the maximum number of lags is set to zero). However, there would then indeed be a restriction imposed on the coefficient of this extra lag, which manifests itself in the observation that the short-run coefficient should equal the negative of the product of the corresponding long-run coefficient and the speed-of-adjustment coefficient, i.e. \(\omega = \alpha \theta\) on slide 9 of my Stata Conference presentation. All the other coefficients remain the same as if the model would be estimated without that extra lag. Compare with the results obtained with the ec option instead.

So if I use ARDL and change the dependent variable and run it 4 times for each variable that I have, it wouldn't yield results with sufficient evidence against a long run relationship? (given that the ardl bounds test fails to reject the null?)

You should not do that. An underlying assumption of the single-equation ARDL / EC model is that there exists at most one cointegrating relationship that involves a given dependent variable. That means, the dependent variable in one model should not appear as a regressor in another. There would be an inherent endogeneity problem. The solution would again be to estimate a VAR / VEC model.

[Sebastian Kripfganz]

Babacar Mbengue:
First and foremost, you need to reduce the number of lags in your model either with the option lags() or the option maxlags(). Given the small number of observations and the relatively large number of regressors, you cannot have a model with 4 lags of each of the regressors. This just results in too many parameters relative to the sample size. The EC model is just a reformulation of the ARDL model. If you correct one, the other is automatically corrected as well.

The bounds test critical values for the t-statistic are only tabulated for the cases with unrestricted deterministic components, i.e. without the ardl option restricted. But actually, the restriction does not matter for the t-statistic. For case 2 you could just use the critical values for the t-statistic from case 3, and similarly for case 4 you can use the critical values from case 5.

[Pandi Sarr]

Sebastian Kripfganz
I see ok Thanks I will try that

There are some blogs that suggest doing that though?
Would it make sense if I estimated each variant of the model in basic OLS and then did the wald test for each model? Since the VAR only allows a set number of lags and the lags cannot be zero?
and when I try to put the differenced variables in the exogenous variable list and do granger causality I get the following output, but this doesnt make sense does it?

var D.lnY, lags(1/2) exog(dum D.lnA DL.lnA D.lnB DL.lnB D.lnC DL.lnC D.lnD DL.lnD L.lnY L.lnA L.lnB L.lnC L.lnD) small dfk

   Granger causality Wald tests
  +------------------------------------------------------------------------+
  |          Equation           Excluded |     F      df    df_r  Prob > F |
  |--------------------------------------+---------------------------------|
  |                 _                ALL |  5.2104    16      27   0.0032  |
  +------------------------------------------------------------------------+

Thanks again,

[Sebastian Kripfganz]

Could be that I am wrong. If you follow what is said in these blogs, you are probably on the safe side. I lack experience on Granger causality tests in Stata and thus I am afraid that I cannot be of any help in that respect. Sorry!

[Babacar Mbengue]

Sebastian Kripfganz

First and foremost, you need to reduce the number of lags in your model either with the option lags() or the option maxlags(). Given the small number of observations and the relatively large number of regressors, you cannot have a model with 4 lags of each of the regressors. This just results in too many parameters relative to the sample size. The EC model is just a reformulation of the ARDL model. If you correct one, the other is automatically corrected as well.

The bounds test critical values for the t-statistic are only tabulated for the cases with unrestricted deterministic components, i.e. without the ardl option restricted. But actually, the restriction does not matter for the t-statistic. For case 2 you could just use the critical values for the t-statistic from case 3, and similarly for case 4 you can use the critical values from case 5.

I will try to reduce the lags in my variables. Can we use the "vecstable" command in stata after the ECM model? I tried it but the software signaled me a error.

[Sebastian Kripfganz]

Can we use the "vecstable" command in stata after the ECM model? I tried it but the software signaled me a error.

No, you cannot. What you have in mind is essentially the bounds test for the t-statistic. A positive t-statistic implies that the model is explosive.

[Babacar Mbengue]

Sebastian Kripfganz

No, you cannot. What you have in mind is essentially the bounds test for the t-statistic. A positive t-statistic implies that the model is explosive.

I do new regressions and I have this result for the moment. It's not perfect but I think I am close to the right model. I need your advices to perfect my model.

[Sebastian Kripfganz]

The new results already look much better given that the speed-of-adjustment coefficient now falls into the [-1, 0] range. In any case, you should not expect to get very reliable results from your model given your small sample size. That will remain a limiting factor in any case, and there will be no "perfect" or "right" model.

How did you choose the number of lags for your model, lags(2 2 2 3 0 1 0)? Overall, you still tend to have too many coefficients to be estimated relative to your sample size. I would probably restrict the maximum lag order to maxlags(1) or maxlags(2) and let the AIC or BIC choose the "optimal" lag order given that restriction. It is true that in principle we would like to be less conservative with the choice of the lag orders to make sure that there is no remaining serial correlation in the error term because the latter invalidates the bounds test. However, given your sample size you have to take this risk.

In addition, you might want to consider removing some regressors from the model which will also help to free up some degrees of freedom. In particular, ldef_fbcf_priv is highly statistically insignificant in your most recent results.

[Babacar Mbengue]

Sebastian Kripfganz

The new results already look much better given that the speed-of-adjustment coefficient now falls into the [-1, 0] range. In any case, you should not expect to get very reliable results from your model given your small sample size. That will remain a limiting factor in any case, and there will be no "perfect" or "right" model.

How did you choose the number of lags for your model, lags(2 2 2 3 0 1 0)? Overall, you still tend to have too many coefficients to be estimated relative to your sample size. I would probably restrict the maximum lag order to maxlags(1) or maxlags(2) and let the AIC or BIC choose the "optimal" lag order given that restriction. It is true that in principle we would like to be less conservative with the choice of the lag orders to make sure that there is no remaining serial correlation in the error term because the latter invalidates the bounds test. However, given your sample size you have to take this risk.

In addition, you might want to consider removing some regressors from the model which will also help to free up some degrees of freedom. In particular, ldef_fbcf_priv is highly statistically insignificant in your most recent results.

I think I finally get a more acceptable model with ardl( 2 3 2 2 0 1 0). To obtain this form I compute many time the ardl command with a maxlag(1), maxlag(2) maxlag(3) and I regard the evolution of lags for every variables. I remark somethimes some lags never change. It's that's lags are robust. Subqunetly, I vary the other lags by myself with the lag() in goal to satisfy all tests. While changing the lags, I observe the variation of the bound test to see if the F-statisitic or the t-statistic go up or they go down. After that, I constat that existe a bound of lags which make converge the model . I get this result below

I want now to run the cusum test, but when I use this command after the ardl'one below I got a error

estimates store ardl_res
estimates restore regress_res  
cusum regress_res

[Sebastian Kripfganz]

What you are doing sounds very much as if you are changing the model until you get your a priori desired results from the bounds test. That is not a very scientific approach. I still recommend to choose the lag orders with the aic or bic (in combination with maxlags()) which is automatically done by the ardl command if you do not use the lags() option.

Regarding the CUSUM test, Stata's official cusum command is not what you are looking for. Instead, you probably want to have a look at the user-written cusum6 command that is available from SSC:

ssc describe cusum6

(I cannot give any further comment about cusum6 because I have never used it.)

[Babacar Mbengue]

Sebastian Kripfganz
I know that it's not very scientific, but if I take those criteria I will have some problems of specification or Heterokesdasticity. In fact, the computer tries to fit the model that the maximun of information of the dependant variable but I don't have enough observations so I must ajust the model to validate the tests of diagnostic. The ardl and ec have both passed those tests. Moreover, the model I get is not so far from the recommanded one given by computer, I had a problem of Heterokedasticity so I must reduce the lags of a variable that I decide to diminue the lag of a variable which have not a significant coefficient.
For the cusum command I have seen your recommand in your previous comment, but to run this command I must write the regression form and I don't know how extract the regression

[Babacar Mbengue]

Sebastian Kripfganz

I think about your last post and I beleave you are right. Like you said I must use the bic or aic criterias to select the best model. Therefore, I redo my estimation with the command below
[CODE]. ardl lfbcf_priv ltxx lfbcf_pub lide ldebt_ext ldef_fbcf_priv lcb , ///
trendvar(timevar) maxlag(2 3 2 2 1 1 1) maxcombs(1500000) regstore(regress_res) //
/CODE]

I select the values in the lags max by refering to the economic theory for exemple I suppose that a growth rate recorded over 3 years ago can not affect the investment behaviour that's why I put a lag max of 3 at the second column. A other supposition I have done is that according to the accelerator theory we can have adjustment cost in the private investment that why I put a maxlag of 2 in the first column. At the beginning, I don't know that I have the possibility to choose for each variable a specific lagmax. Finally the models (ardl & ECM) I obtain pass all diagnostic tests and are better than the others even for the bound test. Here below you can find my result

Hope, this time, my modelisation is more scientific.

Now I am tring to find a why to do the cusum test after a ardl command. It's seem it impossible to that for the moment (see cusum6 reference). I am waiting for your opinion.

[Sebastian Kripfganz]

Your approach to combine the AIC/BIC with economic arguments sounds good. Regarding cusum6, I am afraid that I cannot be of any further help because I am not familiar with that command and it is not directly related to the ardl command. Good luck with your work!

[Babacar Mbengue]

Sebastian Kripfganz
Thanks for your help, I will not have a such progression in my work without your relevant advices. If I find a way to do the cusum6 test I will contact you. One again, thanks to you