[Adam Ng]

Sebastian Kripfganz , apologies , it should be bounds test. Also when I tried running the ARDL model with two variables y(dependent) and x1, there is a significant LR relationship but when I ran it with three variables y, x1 and x2, there is insignificant LR relationship for both x1 and x2. What would be the intuition behind this?
Thanks!

[Sebastian Kripfganz]

It could just be an omitted variable bias in the smaller model that lets your coefficients become larger and thus statistically significant. Alternatively, in the larger model, the estimates are less precise due to more coefficients to be estimated, which increases the standard errors and thus the chance to obtain insignificant results.

[Robbert Henk]

Hello,

I have (again) another question about the ARDL model. if there is no cointegration, can you still use the error correction model (the short run model) ? In more general terms, in case of no cointegration, can you use all the functionalities of the model?

[Sebastian Kripfganz]

If there is no cointegration / no long-run relationship, you can still use the error correction model for the short-run dynamics but it would be more efficient to just estimate the model directly in first differences.

[Robbert Henk]

Hi Sebastian,

thank you for your answer. Could you perhaps also explain why it is more efficient?

thanks for all your help

[Sebastian Kripfganz]

It is the same argument as with irrelevant regressors in a simple linear regression models. If you exclude the irrelevant regressors (here: the long-run terms), you have fewer coefficients to estimate such that you can estimate the remaining coefficients more precisely / efficiently.

[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!

[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.

[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]

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.

[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]

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]

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]

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)).

[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!!!