[Zuhura Anne]

I have tried the cusum6 and from the output, I do not have parameter stability. How can I address the issue of parameter stability?
In addition, if some variables are I(2) which model would you advise one to use?

Thank you very much Sebastian for the timely responses.

[Sebastian Kripfganz]

The bounds test clearly requires that all variables are I(0) or I(1). If you have structural breaks, you might want to directly model them. Otherwise, your model is likely to be misspecified. Depending on the nature of the breaks, you could for example include dummy variables for a specific time period with the exog() option of ardl. For the the bounds test to be still valid in the presence of such dummy variables, the time period that is captured by them should be limited. For example, you could specify a dummy variable that takes on the value 1 for a small number of periods if these periods are structurally different such that they cause a temporary break in the time series. The bounds test is not suitable in the presence of permanent structural breaks.

[Anne Wanyonyi]

Sebastian, I have gone back and looked at my data again.
All my variables are I(0) or I(1) when I test for unit root using ADF. When I apply the unit root tests with breaks not all are I(1) or I(0). Does this invalidate the use of ARDL?

Lastly, how do I incorporate the time trend in the ARDL?

[Sebastian Kripfganz]

Anne Wanyonyi: Don't panic! If there is only weak evidence for non-normality of the errors, you could still use the bounds test and maybe add a comment in your work that the results need to be interpreted with caution. If there is strong evidence for non-normality, you might have to go back to the drawing board and think about your model specification. If you have not yet included a time trend, this could be worth trying.

[Sebastian Kripfganz]

Zuhura Anne: You could try Kit Baum's cusum6 package:

ssc describe cusum6

I have never used it and thus cannot give any further advice on it. Please consult its help file to find out how to use it.

[Anne Wanyonyi]

Thank you Sebastian.

I am now in panic mode.
I have 40 observations. I had already carried out the bounds test procedure and it points to existence of cointegration. So that means, there is a high chance the conclusion I made from the bounds test is incorrect?
All my variables are in log form.

[Zuhura Anne]

Thank you Sebastian for the response. Unfortunately, I am using stata 14 and I do not have access to stata 15. Which test can I use in this case? What was being used initially before the recent release of stata 15?

With stata 14, I get the error message

subcommand estat sbcusum is unrecognized

[Sebastian Kripfganz]

Which syntax can I use in order to carry out parameter stability tests as a postestimation for ARDL?

Or how do I test for a structural break with unknown date?

Stata 15 has the new postestimation command sbcusum. It works after regress but does not work directly after ardl, but you can recover the underlying regress estimation results:

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump, regstore(ardl)
estimates restore ardl
estat sbcusum

Hello,
Is it okay to continue with estimation when there is non-normality or my results will be biased?

Or how can I correct for non-normality?

For the estimation of the coefficients, non-normality of the errors usually is not much of a problem. You cannot use the t-distribution or F-distribution for finite-sample hypothesis tests in this case. If your sample size is large enough, hypothesis tests (for short-run coefficients) that have standard asymptotics can still be used. In contrast, the Pesaran et al. (2001) bounds test procedure for the existence of a long-run level relationship, implemented in estat btest after ardl, has non-standard asymptotics. Its critical values rely on the assumption of i.i.d. normally distributed errors.

There is no general approach to deal with non-normality. Sometimes, a log-transformation of some or all of your variables can help, in particular if you expect these variables to fluctuate around a balanced growth path.

[Anne Wanyonyi]

Hello,
Is it okay to continue with estimation when there is non-normality or my results will be biased?

Or how can I correct for non-normality?

[Zuhura Anne]

Which syntax can I use in order to carry out parameter stability tests as a postestimation for ARDL?

Or how do I test for a structural break with unknown date?

[Mahana Noorma]

Dear Sebastian,

Thank you very much for your quick reply and for your pieces of advice.

Kind regards

[Sebastian Kripfganz]

Your description of the procedure is very accurate. In principle, there is no need to adjust the lag structure when you remove the error correction term from the model (assuming that the result of the bounds test is correct). In practice, however, it can happen that for a given sample the AIC or BIC indicate a different lag order for the ARDL model in first differences (equ:fin2). It is an interesting question and spontaneously I do not have a clear opinion on whether I would reestimate the model with a different lag order.

In any case, to be comparable, you should reduce the maximum lag order that you are using in the model selection by one when you compute the AIC / BIC for the first-differenced ARDL model compared to the ARDL model in levels. Say, maxlag(4) for the ARDL model in levels would correspond to maxlag(3) for the ARDL model in first differences.

[Mahana Noorma]

Dear Sebastian,
Dear all,

I have a theoretical question regarding the bounds testing approach developed by Pesaran et al. (2001). It is related to the determination of the optimal lag length when the bounds test indicates that there is no long-run relationship between the variables.

According to Giles’s blog (2013: http://davegiles.blogspot.ch/2013/06...nds-tests.html), we start the bounds testing procedure with the following equation
Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + Σδ_kΔx_2t-k + θ₀y_t-1 + θ₁x_1t-1 + θ₂ x_2t-1 + e_t (Unconstrained ECM)
Source: http://davegiles.blogspot.ch/2013/06...nds-tests.html

The appropriate lag structure of this equation is determined by means of one information criteria such as AIC or BIC. If this model is stable and that there is no serial autocorrelation of the errors, the bounds test can be performed. If the latter indicates that there is a long-run relationship between the variables, the final equation would be:

Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + Σδ_kΔx_2t-k + φz_t-1 + e_t (equ : fin1)
where z_t is the error correction term.

On the other hand, if the bounds test indicates that there is no long-run relationship between the variables, the final equation would be:
Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + Σδ_kΔx_2t-k + e_t (equ : fin2)

My question is the following: if the bounds tests indicates that there is no long-run relationship between the variables, would the optimal lag structure be the same as the one determined at the beginning of the bounds testing procedure or is it necessary to determine it once again directly from the equation (fin2)?

I kindly thank you for your help and your commitment.

Best regards

[Sebastian Kripfganz]

Why "regress" output and "ardl" output are not exactly the same?
I used the ardl specification, for instance, (2,0,2) and I ran normal least square regression with the excatly the same lags for the dependent and independent variables, but the results are not exactly the same.

Above question crossposted here: Question regarding ARDL adon.

The ardl command silently estimates many models with different lag combinations and picks the one with the smallest value of the AIC. To ensure comparability of the models, all of them are estimated based on the sample. This sample is determined by the largest lag order which is 4 by default.

The regress command estimates the model as specified, in your case with a maximum of 2 lags. It thus uses 2 more observations. Because the samples do not coincide, the estimation results consequently differ from ardl.

You can obtain identical results by restricting the sample in the following way (based on the help file example):

. webuse lutkepohl2
. ardl ln_inv ln_inc ln_consump
. regress L(0/1).ln_inv ln_inc L(0/2).ln_consump if e(sample)

[NIP NIP]

Why "regress" output and "ardl" output are not exactly the same?
I used the ardl specification, for instance, (2,0,2) and I ran normal least square regression with the excatly the same lags for the dependent and independent variables, but the results are not exactly the same.