[Eddie Hill]

Thanks again Sebastian, much appreciated

[Eddie Hill]

Thanks Sebastian, I’m still slightly unsure as to how best to interpret the coefficient values of first differences of the natural logarithm of a variable. I have set out a couple of examples:

1) If you have a coefficient value of e.g. 0.54321 for the first difference of the natural logarithm of e.g. indepvar1 would it imply that a 1% increase in the period-on-period change in indepvar1 (as defined by the variable being first differenced) would lead to a 0.54321% increase in the value of the dependent variable at time t, holding all else constant. In other words, the coefficient represents the % change in the dependent variable, given a 1% change in the change of the independent variable. This would be my interpretation for the 6 out of 7 variables that I have in first differences of natural logarithms.

2) I do however, have one variable that wasn’t transformed into natural logarithms due to it generating negative values, but it was first differenced. I’m wondering how the interpretation would differ for this variable when the dependent variable is first differences of the natural log but this particular indepvar2 is just first differenced.

My current understanding is that a coefficient value on this indepvar2 of e.g. 1.23456 would be interpreted as meaning that a 1 unit increase in the first differenced indepvar2 would lead to a 1.23456 unit increase in the dependent variable. However, I think I may be getting confused because first differences represent a change, and so when referring to a “1 unit increase / decrease” would I actually be referring to a 1 % change or should it still be as a unit? To add to the complication, the indepvar2 in this case actually represents an interest rate variable, so even in levels it’s actually representing a percentage level.

Any insight or assistance either from yourself or other forum members would be greatly appreciated.

Eddie

[Sebastian Kripfganz]

1) If we interpret first differences of variables in logs as growth rates, then a coefficient of 0.54 would mean that a 1%-point increase in the growth rate of the independent variable leads to a 0.54%-point increase in the growth rate of the dependent variable, everything else equal. (Note, a 1%-point increase in the growth rate effectively corresponds to a 1% increase in the level of that variable, as long as we just look at the current period.)

2) A 1 unit increase in the per-period change of the independent variable leads to a 0.54%-point increase in the growth rate of the dependent variable, everything else equal. (Note, a 1 unit increase in the change of a variable effectively also means a 1 unit increase in the level of that variable, as long as we just look at the current period.) If this variable is already measured in %, then the interpretation becomes similar to the one in 1).

[Eddie Hill]

Hi Sebastian, that makes sense - thank you for the interpretation.

Eddie

[Eddie Hill]

Dear all,

Could anyone assist in advising how best to test for causality between variables following an ARDL specification in STATA ("ardl" command). I understand that Granger-Causality and the "vargranger" is typically applied to VAR specifications, however I have an ARDL specification with mixed I(0) and I(1) series, no cointegration and different optimal lag lengths.

Many thanks,
Eddie

[Sebastian Kripfganz]

You can just implement this manually by running a regression of Y on its own lags as well as lags of X, and then testing for insignificance of the lags of X.

[Eddie Hill]

Hi Sebastian, I've now been able to replicate the suggestion and it's produced the desired results. Thanks again,
Eddie

[NIP NIP]

Hello! Guys, could you share your experience on how robust is ARDL method against multicollinearity?

[ahmed mohamed ak]

I saw your article in the section related to the conditional error correction model, where you indicated that the derivation of this model is based on d(y). If the dependent variable is I(0), how do we derive the CECM ?

[Kong Chantha]

Dear sir/madam,
in case, ARDL (EC representative) if DV is I(0) and IV is I(1), can we run ARDL in EC form for co-integration? If can't, what can we go on?
Thank

[Sebastian Kripfganz]

You can estimate an ARDL model with an I(0) dependent variable. However, a cointegrating relationship can only exist between I(1) variables. Thus, if your dependent variable is I(0), a long-run relationship cannot be interpreted as a cointegrating relationship.

[Kong Chantha]

You can estimate an ARDL model with an I(0) dependent variable. However, a cointegrating relationship can only exist between I(1) variables. Thus, if your dependent variable is I(0), a long-run relationship cannot be interpreted as a cointegrating relationship.

We can estitmate an ARDL in level form or in ECM form or both?

[ahmed mohamed ak]

thank you very much professor

[Sebastian Kripfganz]

We can estitmate an ARDL in level form or in ECM form or both?

You can estimate the ARDL model in level form or EC form even if the dependent variable is I(0). You just cannot interpret the long-run relationship (if it exists) as a cointegrating relationship.

Note: If you have pre-tested that the dependent variable is I(0), then strictly speaking the ARDL bounds test no longer makes sense. Under the null hypothesis of the bounds test, the dependent variable is I(1). Under the alternative hypothesis, it can be I(0). Because the ARDL model is so flexible, there is generally no need for pre-testing the integration order.

[ahmed mohamed ak]

You can estimate the ARDL model in level form or EC form even if the dependent variable is I(0). You just cannot interpret the long-run relationship (if it exists) as a cointegrating relationship.

Note: If you have pre-tested that the dependent variable is I(0), then strictly speaking the ARDL bounds test no longer makes sense. Under the null hypothesis of the bounds test, the dependent variable is I(1). Under the alternative hypothesis, it can be I(0). Because the ARDL model is so flexible, there is generally no need for pre-testing the integration order.

We know that CECM is based on DY (the diff which we usually use to convert non-stationary variables to stationary variables). If the dependent variable is I(0), how do we derive the error correction model? Is it with y or dy (because in this case we don't need dy because y is already constant)