[Sebastian Kripfganz]

The speed-of-adjustment coefficient (ADJ) is expected to fall into the range [-1, 0]. In your case, it is not statistically significantly different from -1. The interpretation would be that any deviation from the long-run relationship is fully corrected instantaneously.

[Jonathan Hillgren]

what is the difference between the two different methods here with ec1 and ec? With the help command we get ec = estimate with depvar in first differences and display output in error-correction form and ec1 = like option ec, but parameterizes long-runcoefficients as of time t-1. How would this affect our results? Regards Jonathan Hillgren


ardl lnIMsve lnBNPSve lnPPIse lnSekeur lnVol, exog (FinD) aic ec1 lags(3 0 0 0 2), ardl lnIMsve lnBNPSve lnPPIse lnSekeur lnVol, exog (FinD) aic ec lags(3 0 0 0 2)

[Sebastian Kripfganz]

The long-run coefficients are the same in both specifications. Only the short-run coefficients of the contemporaneous changes of the exogenous regressors differ. In addition to the help file remarks section on "Long-run coefficients expressed in time t or t-1", this difference can also be seen on slide 9 of my presentation at the Stata Conference 2016 in Chicago.

[Jonathan Hillgren]

Thanks for your answer! Which one would you recommend when we are using log variables?

[Sebastian Kripfganz]

Whether your variables are in logs or not does not matter for this question. It is more a matter of taste and most people seem to prefer the ec1 option.

[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!

[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).

[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]

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 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

[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

[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]

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]

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.

[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