[Sebastian Kripfganz]

Assuming that you are interested in the residual autocorrelation, you could do something like the following:

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump
predict res, resid
corrgram res

Please see help corrgram for details.

[Alexander Winberg]

Hello,

Can one in some way measure the first-order autocorrelation coefficient for the ARDL-model?

Thanks for the help!

[Sebastian Kripfganz]

The coefficient of a variable without a log transformation in an ARDL regression with a log-transformed dependent variable is interpreted as in standard linear regression models as a semi-elasticity: how much does the dependent variable change in percent given a one unit change of the independent variable.

Please also see: How to interpret coefficients when with ln transformed dependent variable?

The constant term is usually not interpretable. It captures the means (or the drift in non-stationary models) of all the variables in the model, both from the left- and right-hand side of the regression equation. There is rarely a situation where I would recommend to not include the constant in the model unless you are sure that all the variables are stationary with mean zero (because you may have demeaned the variables first). There is not much that you can lose by including the constant, but your results can easily become rubbish if you exclude it because you would be forcing the regression line to pass through the origin.

[Jonathan Hillgren]

Hi again,

Thanks a lot for your previous replies! We have some more questions about the interpretation of the model from someone who is more experienced with the ardl process. If our independent variable Vol (volatility) is based on/estimated from ln-values, we have decided not to use as an ln-variable so it is not written in the ln-form in our regression, how should we interpret its effect on the regressand if that one is in ln-form, when doing the ardl ec1 regression? The same goes for the dummy variable, which is not in ln-form either.

We are also wondering how to interpret the coefficient of the constant? How does this affect our ln-dependent variable? If it’s significant, should it be included in the model and if not significant, removed? And does the ADJ-term affect all of the independent variables? Best regards Jonathan & Emma

[Sebastian Kripfganz]

Sebastian Kripfganz thanks for all your quick and kind replys and I am really grateful for your responses. Would it in theory be possible for a variable to show a negative long term coefficient but in the short run be positive? best regards Jonathan Hillgren

Yes, this can happen but only if that variable enters the ARDL specification with some lags (not just contemporaneously).

[Jonathan Hillgren]

Sebastian Kripfganz thanks for all your quick and kind replys and I am really grateful for your responses. Would it in theory be possible for a variable to show a negative long term coefficient but in the short run be positive? best regards Jonathan Hillgren

[Sebastian Kripfganz]

Robust standard errors are not currently implemented in ardl but there is a workaround based on the underlying regress estimates:

webuse lutkepohl2
ardl ln_inv ln_inc ln_consump, regstore(ardl)
estimates restore ardl
`e(cmdline)' vce(robust)

The last line re-estimates the ARDL model with the regress command and adds the vce(robust) option.

[Alexander Winberg]

Thank you very much for the answer, I really appreciate it. A further question. My professor suggests that instead of testing for heteroscedasticity one should use robust standard errors. Is there a way to implement these in the ardl command in Stata?

[Sebastian Kripfganz]

The argument of Pesaran et al. (2001) mainly relates to the bounds testing procedure. The respective critical values are obtained under the assumption of no serial correlation. If that assumption is violated, then the critical values for the bounds tests will no longer be valid and inference will be misleading. For testing purposes, their suggestion is thus not to use a too parsimonious lag specification. In other words, the AIC might be preferred over the BIC when choosing the lag order because the AIC tends to prefer models with more lags of the variables and thus reduces the potential for remaining serial correlation.

[Alexander Winberg]

Dear Sebastian,

Pesaran et al (2001) argue that it is really important that the ardl model does not suffer from serial correlation. If it does, in what way will the estimation be wrong? Why is this a key assumption?

Best Alexander

[Marco Giansoldati]

Dear Sebastian,

I am extremely thankful for your kind reply and for providing me with a usesul example.

Your help is extremely appreciated and I do thank you vey much for constant kindness.

Marco

[Sebastian Kripfganz]

We are currently not planning to implement further postestimation commands. With the regstore() option, you can recover the underlying regress estimation results and subsequently use all available postestimation commands for regress, e.g. the Ramsey RESET test:

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

[Marco Giansoldati]

Dear Sebastian,

I read the indications you provided for the ardl postestimation and the slides employed at the Chicago Stata conference.

I was wondering (but correct me if I am wrong) if you also implemented (or are going to implement) a series of diagnostic tests. I am thinking in particular at a Lagrange multiplier of residual serial correlation, a RAMSEY test for functional form misspecification, and White's test for heteroskedasticity.

Many thanks for your kind attention.

Regards

Marco

[Sebastian Kripfganz]

It can happen that the AIC or BIC suggest a model that includes lags of a variable that are all individually statistically insignificant. The t-test for individual significance does not take the covariance of the variables into account while the information criteria do (as does an F-test, for example). The statistically significant long-run coefficient of Vol then indeed highlights that all the lags are jointly significant and it is important to keep them. Intuitively, all three lags have the same sign. When you add all of them up, the sum becomes statistically significant.

For lnPPIne, it is a matter of taste if you want to keep it or not. When you keep it, then you are on the safe side regarding a potential omitted variable bias. You could also use once again the AIC / BIC to compare a model with and without this variable:

ardl lnIMnor lnBNPnor lnPPIne lnNokeur Vol, exog (FinD) aic lags(. . . . .) maxcombs(2500)
estat ic
ardl lnIMnor lnBNPnor lnNokeur Vol, exog (FinD) aic lags(. . . .) maxcombs(2500)
estat ic

The postestimation command estat ic displays the respective values of the information criteria. You would choose the model with the lower value (closer to minus infinity).

[Jonathan Hillgren]

Hi,
When we're running the command "ardl lnIMnor lnBNPnor lnPPIne lnNokeur Vol, exog (FinD) aic lags(. . . . .) maxcombs(2500)" in stata we get an insignificant value for lnPPIne and also for Vol even though the model suggest we should include 2 lags for the volatility. If we keep the variables ans run the command "ardl lnIMnor lnBNPnor lnPPIne lnNokeur Vol, exog (FinD) aic ec1 lags(3 0 0 2 2)" the lnPPIne variable is still insignificant for both long and short run. Should we therefore remove lnPPIne from our model? For the Vol variable it's significant in the long run, but not in short run. What is your suggestion for this variable? Can we keep it even though it's insignificant when we run the first command since it looks significant in the long run?
This is what it looks like:

We would be really thankful for your reply!