[Sebastian Kripfganz]

For the bounds test, it is advisable to use the AIC, yes.

If your variables are very persistent over time, then their lags can be highly collinear. As a consequence, the estimator might have difficulties differentiating between the different short-run effects. Having many lags with large coefficients but opposite signs - such that the sum of the effects is still close to zero - could then fit the data possibly similarly well as a model without significant lags.

The error terms of the ARDL and ARDL-EC models are identical. Thus, it does not matter which model you choose to test for autocorrelation or heteroskedasticity. If you want to test for stability of all coefficients jointly, then again it does not matter because the coefficients of the ARDL-EC model are just reparameterizations of those in the ARDL model. Stability of the coefficients in one model, implies stability in the other.

If you select the optimal model with the AIC, chances are high that there is no serial correlation problem. If the model chosen by the BIC suffers from serial correlation, it could be advisable again to use the AIC instead. Dealing with heteroskedasticity can be more difficult; and I am afraid I do not have a general advice regarding this matter.

[Cornelius Mwangangi]

Making up a follow up on Newey-West Standard Errors.
I used this command as you advised and these are the results. The command,
quietly ardl dHDI dFDI INF dTRADE dGEXP, lags(3 3 3 0 2) aic regstore(ardlreg)
quietly estimates restore ardlreg
local cmdline `"`e(cmdline)'"'
gettoken cmd cmdline : cmdline
newey `cmdline' lag(3)

[Cornelius Mwangangi]

Also, i made use of the following code
ardl dHDI dFDI INF dTRADE dGEXP, lags(3,3,3,0,2) ec regstore(ardlreg)
estimates restore ardlreg
local cmdline `"`e(cmdline)'"'
gettoken cmd cmdline : cmdline
newey `cmdline' lag(3)

My question is how do i identify the long run and short run results based from the two pictures?

[Sebastian Kripfganz]

To get the long-run results from the second estimation for dFDI, type

nlcom _b[dFDI] / (1 - _b[L.dHDI])

and similarly for the variables INF dTRADE dGEXP.

[Cornelius Mwangangi]

Thank you very much for your assistance.

[Sebastian Kripfganz]

An update is available to our ardl package. The latest version 1.0.5 can be installed either from SSC,

ssc install ardl, replace

or from my personal website,

net install ardl, from(http://www.kripfganz.de/stata/) replace

Besides some minor improvements, the most useful change is probably that you no longer need to use the regstore() option to access most of the standard postestimation commands. A large number of postestimation commands for the regress command can now be used directly after the ardl command. Please see the help files for details:

help ardl
help ardl postestimation

For the 'bounds test' postestimation command estat ectest, a new decision table has been added, which provides a quick indication of whether there is evidence for or against a long-run relationship. The elements of the Stata output to be displayed for estat ectest can now be tailored with the additional options nocritval, norule, nodecision; see again the postestimation help file.

Furthermore, we have written a documentation for the command:

• Kripfganz, S., and D. C. Schneider (2022). ardl: Estimating autoregressive distributed lag and equilibrium correction models.

The manuscript discusses the econometric background in, hopefully, simple enough words to provide an accessible introduction to the topic. As an illustration, we replicate the original Pesaran, Shin, and Smith (2001, Journal of Applied Econometrics) empirical results.

[misso ouhibi]

Hello sébastien, I hope that you are doing well,
I want to ask you an important question please I need your answer,

When we estimate the ARDL model then we give us the number of lags for each variable, then when we estimate the ECM model, this model didn't take the variables with the same lags which are fixed by ARDL model
For example, ARDL (5,3,4,4,2)
Then when we estimate the short run, why we didn't get the results with the same lags ??

[Sebastian Kripfganz]

I am not sure I understand your question. Due to the first differencing, the number of lags for the short-run terms in the EC model is one less than the number of lags for the ARDL model. Please see our documentation - which I referenced in my previous post - for further information.

[Monir Ahmed]

Many articles like Pata and Isik (2021) “Determinants of the load capacity factor in China: A novel dynamic ARDL approach for ecological footprint accounting” reports the bound-test results like the following:

F-stats (overall)	9.731*
t-test (for dependent)	-6.858*
F-stats (independent)	5.048**

F and t stats are readily available at ARDL package after ectest. I know that the additional F-stats for independent test are proposed by Sam et al and McNown et al. I want to know that the ARDL STATA’s F and t tests are sufficient to conclude our result? Or, we need to do additional F-Stats for independent variables after regress option?

[Sebastian Kripfganz]

If the F-test and t-test both reject the null hypothesis of no long-run relationship, you still might want to test for individual (or joint) significance of the long-run coefficients. Since they are asymptotically normally distributed, you can just directly use the t-statistics from the "LR" section of the ardl regression output.

[Sebastian Kripfganz]

A new update for the ardl command is available both on SSC and my personal website.

adoupdate ardl, update

This latest version 1.0.6. comes with significant speed improvements when the command is called with option ec for large models. It also fixes a bug that lead to an error message in some cases if option exog() was specified with time-series operators or an underscore in the variable name.

[Eddie Hill]

Hi there,

Thank you for all the useful information already provided in this post. I have some ARDL questions and would really appreciate it if you could provide some answers:

1) I have a model comprising of 7 macroeconomic variables. Having tested for unit roots, it became apparent that one of the independent variables is I(0) and the other 6 variables (including the dependent variable) are I(1). I ran the “ardl” command on the variables in log-level transformation and not first differences.
2) I then used the “varsoc” command to determine the optimal lags for each variable.
3) I then reproduced the “ardl” command but now including the lags for each variable.
4) I then extended the model to include “ec” and “btest”.
5) My results suggested no evidence of cointegration and I therefore believe it is now appropriate to stick with the ARDL model specification and not pursue the ECM.

My question is: if I was to stick with the ARDL specification, should I specify the ARDL model with my stationary variables I.e. in first differences (and the one I(0) variable in levels)? If so, do I need to determine the optimal lags again after re-specifying the command now with first differences variables as I’m assuming the optimal lags will change if the model is respecified with first differences variables as opposed to variables in levels.

many thanks.

[Sebastian Kripfganz]

There is no need to use the varsoc command for ARDL lag specification. The ardl command has its own automatic lag selection implemented. The varsoc command is designed for lag selection in a VAR model.

The ec option just reparameterizes the model coefficients; it does not change the model itself. If estat ectest - note that estat btest is depreciated and should not be used anymore - suggests no evidence of a long-run relationship, then it would ne appropriate to estimate an ARDL model in first differences. You don't necessarily need to determine the optimal lags again (although you could). Notice that the lag order in first differences is 1 less than the lag order in levels.

[Eddie Hill]

Thank you for the response Sebastian,

That’s makes sense. I had one other question, given that log-transformations can help to reduce variability and assist in stabilisation, would it also be appropriate to transform the series into natural-logs and then take first differences of the log-transformed series to re-estimate the ARDL specification?

many thanks

[Sebastian Kripfganz]

Taking first differences of log-transformed variables is perfectly fine; this would approximately yield growth rates.