[NIP NIP]

Hello all!

In the ARDL methology, there is 5 cases.
Could you please help me with some guidelines about when a case should selected over the others?

I'm trying to estimate a ARDL model as follows:

Y = Intercept + b1*Trend + b2*X1 + b3*X2

I selected case II (restricted intercepts; no trends) and then I added the "Trend" variable as a fixed regressor. Is this ok? Will bounds test and long run estimators be ok?

Thanks & Regards!

[mehmed han]

Hello Sebastian;

Some people says you can use panel ARDL in stata by command by installing xtmg ve xtpmg and using pmg, ccemg, amg estimations.
What is your idea about that?
Thank you for your interest

[Sebastian Kripfganz]

In addition to my previous post, the following Statalist discussion might be of interest regarding panel ARDL:
xtdcce2 - estimate CS-ARDL & CS-DL

[mehmed han]

Hello Sebastian;
Thank you for your help.
İf I can't do panel ARDL in Stata, how can I do it then?
Can I make it vith Eviews?

[Sebastian Kripfganz]

The ardl command is for use with time-series data only. It does not support the estimation of panel ARDL models.

The following Statalist topics might be helpful:

• ARDL panel model in Stata
• Optimal lag length for ARDL in panel

In addition, you might want to search for mean-group (MG) and pooled mean-group (PMG) estimators. In Stata:

search mg
search pmg

[mehmed han]

Hello Sebastian Kripfganz anl all;

I am new in panel ARDL. When I try to do panel ARDL, I got this message: "sample may not include multiple panels". So, I cannot do panel ARDL.
How can I solve this problem?
Thank you

[zt lin]

I have sent you a private message here on Statalist.

Hi, Sebastian,

I met the same problem when installing ardl package.

What should I do?

Much appreciated!!!

[Sebastian Kripfganz]

This depends on your research question, in particular whether you are interested in analyzing a relationship between prices or between returns. From an econometric perspective, both work (assuming that your log prices are at most I(1)).

[Robbert Henk]

Hello Sebastian,

Perhaps one last question, what considerations would you take into account in order to decide whether the log (ln(X) or log return a.k.a. log differences (ln(xt/xt-1) is more appropriate?

Thank you for all the help so far. Really helpful for my master thesis.

[Sebastian Kripfganz]

A high R² is quite common in time series models when the variables are I(1) and significantly trending over time. In a dynamic model (such as the ARDL model), this is not per se a problem. The R² is just not very meaningful in this case. (The familiar spurious regression problem relates to static models.)

Notice that \(\ln (x_t / x_{t-1}) = \ln (x_t) - \ln (x_{t-1})\), i.e. you are essentially estimating a model directly in first differences. (You are thus effectively removing the long-run level relationship from the model.) All variables being stationary does not mean that you cannot obtain the equilibrium-correction relationship. It just cannot be interpreted as a cointegrating relationship but merely as a long-run relationship between your stationary variables. Whether such an interpretation is economically meaningful for log returns is a different story.

[Robbert Henk]

Hi again,

Should I worry about an inflated adjusted R2 regarding the ardl model? Adjusted R2 is around 99.95%.
Results:

After specifying the EC option adjusted R2 looks normal again.

Variables were transformed to the natural logs. (ln(x))

----
I did the same analysis again but this time, I transformed the variables to log returns i.e. ln(x/xt-1) where t = time and t-1 is the previous observation.
Then, the adjusted R2 is not inflated. However, I cannot use the EC option anymore since the variables are all stationary due to the log return transformation.

My questions:
1. Is the inflated R2 even bad/ should I be concerned? (note: DV = the price of an asset. IV contains variables that are in some cases prices as well).
2. Or, is it more appropriate to use log returns since DV and some IVs are price series? (But choosing for this option means that I cannot estimate the error correction model --> so I made everything stationary)

I

[Sebastian Kripfganz]

1. Any two tests, even if they were asymptotically equivalent, may yield different conclusions in finite samples.
2. The Engle-Granger (EG) cointegration test and the Pesaran-Shin-Smith (PSS) test for the existence of a long-run relationship are not even asymptotically equivalent. The EG test (first step of their two-step procedure) is a test for cointegration between some variables, taking it as given that all variables are I(1). The representation theorem states that cointegration between any two (or more) variables exists if and only if there exists an error-correction model for either variable (or all of them). However, the EG test does not require that any specific variable follows an error-correction process. In contrast, the PSS requires that there is an error-correction mechanism for only one specific variable (the dependent variable in the ARDL/EC model). At the same time, it also allows for I(0) variables in the long-run relationship. In short, the underlying assumptions / hypotheses differ to some extent.
3. Your contrasting findings might thus be due to classical type-1 / type-2 errors in hypothesis testing. It could also be an incorrect classification of regressors as I(1) in the EG procedure. (Note that there might be a pretesting problem.) It could be a power problem of the EG test in finite samples because of the neglected dynamics. But it could also be that the assumption of a single error-correction relationship in the PSS approach is incorrect. And there are possibly other arguments, too, that I do not immediately recall out of the top of my head.

The following presentation slides might be helpful as well:

• Nielsen, H. B. (2007). Non-Stationary Time Series, Cointegration, and Spurious Regression. Lecture Notes (Econometrics 2), University of Copenhagen, Department of Economics.
• Kripfganz, S., and D. Schneider (2016). ardl: Stata module to estimate autoregressive distributed lag models. Presented July 29, 2016, at the Stata Conference, Chicago.

[Adam Ng]

Dear Sebastian,
When we perform the cointegration test (according to the Engle-Granger method), we found no cointegration between the variables which I believe that it implies there's no LR relationship.
However, when we went ahead with the ARDL model and the bounds test, we found that there is a significant LR relationship. What would be the intuition behind these two contrasting findings?
Thanks!

[Sebastian Kripfganz]

You have estimated an ARDL(1, 1, 0) model. The last variable has zero lags in the level representation. This corresponds to zero short-run coefficients in the ec representation. Please see the help file remarks section "Long-run coefficients expressed in time t or t-1" for details about the relationship between the different model parameterizations.

[Jessica Chong]

Hi Sebastian Kripfganz ,
Assume that we have 3 variables y, x1 and x2,
When I run the ARDL model to find the LR and SR coefficients, I could only see coefficient for x1 in the SR section while I could see coefficient for x1 and x2 in the LR section.
Why would one of the variables be omitted for SR?
For example, in the attachment, x1 and x2 should be un and infl respectively, however only one of them appear in the SR section
Many thanks!