Log differenced data and dummy variable regression

[KElizabeth925]

Hello all-

I am trying to estimate the following ARDL equation: y= a + y(t-i) +o(t-i) +u, where y=quarterly log differenced US GDP and o is quarterly log differenced oil prices (data are all quarterly and lag length=5):
-->I am having an issue with my specification in Eviews for the functional form of "o" : my model is such that oil prices only matter if the log-differenced value is >0. In order to estimate the equation, I have first created a series that is log-differenced oil prices (log_difference_oil). I then created a series for dummy variables, where dummy=1 if log_difference_oil>1.

-->to run the regression accurately, do I specify "log_difference_oil*dummy" as the explanatory variable of oil prices? And then, to account for the lagged data, shall I code it as "log_difference_oil(-1)*dummy(-1)" ..."log_difference_oil(-2)*dummy(-2)?

Is there another way to code the regression such that I do not need to create a new series that reflects the log-differenced oil prices, but rather the code will reflect the fact I want only positive log-differences from the log-oil price series proper?

Just want to make sure that this coding is accurately reflecting what I am trying to accomplish econometrically.
Help very much appreciated--thanks!

[EViews Gareth]

It isn't clear what you're trying to do here.

Do you only want to include observations for which log-difference > 0?

Or do you want to estimate different coefficients depending on whether log-difference is > 0 or not?

[KElizabeth925]

Thanks for your reply. I would like to do both:

Firstly, I would only like to include those observations for which the log-difference is >0.
For example, if in 1953Q:2 the log-difference is 0.14, I would like that observation to be included in the regression.
If, instead, the log-difference is -0.14, I do not want it included in the regression.

After I have that regression sorted, I would then like to estimate a second, "opposite," regression, for which I would only like to include those observations for which the log-difference is negative. At that point I imagine (and hope) the coefficients would be different.

Hope this clarifies...if not please let me know.
Thanks again.

[EViews Gareth]

Specify your equation without dummies. Enter the estimation sample as:

Code: Select all

@all if dlog(o)>0

where "o" is the name of your oil price series.

Then do the same thing again, but this time put <0.

[KElizabeth925]

Brilliant-thanks very much.

I would like to now include three oil price variables: dlog(oil) as it is; dlog(oil) >0; and dlog(oil)<0
Essentially, I am now looking to see the magnitude of each coefficient w/in the same regression.

How best to specify this equations--I assume @all will not work in this case?

[EViews Gareth]

Just include those three terms:

Code: Select all

dlog(oil) dlog(oil)>0 dlog(oil)<0

Be careful not to put spaces next to the < and >.


From an econometrics point of view, you're probably close to perfect multicolinearity.

[KElizabeth925]

Right-I'm going to run several variations of this model (next will be to put it into a VAR) but am aware of the possibility of multicolinearity with that particular one-thanks for the heads up though.

Your comments are much simpler to follow and make more sense than trying to create a dummy variable series-thank you!!

[KElizabeth925]

EViews Gareth:

I ran into an issue using the specification/code that you had posted here, regarding the oil price increases/decreases:
I ran two separate VARs, both with log-differenced GDP and real oil prices as the endogenous variables. In addition, for each regression, I included lagged values if the following exogenous variables:
Regression 1: dlog(oil)>0 (so only positive oil growth counts), and
Regression 2: dlog(oil)<0 (so only negative oil growth counts)

-->I got coefficients of the exact same magnitude, but of opposite sign, for each regression. I know this is not economically feasible, so wondering what could be going on with Eviews...
-->In addition, I ran the exact same code using a different oil price series w/in the VAR framework, and did NOT run into this problem (ie. got different coefficient estimates altogether, different magnitude, different signs, as I'd expect).
Help!

[jason_ll]

Hello all-

I am trying to estimate the following ARDL equation: y= a + y(t-i) +o(t-i) +u, where y=quarterly log differenced US GDP and o is quarterly log differenced oil prices (data are all quarterly and lag length=5):
-->I am having an issue with my specification in Eviews for the functional form of "o" : my model is such that oil prices only matter if the log-differenced value is >0. In order to estimate the equation, I have first created a series that is log-differenced oil prices (log_difference_oil). I then created a series for dummy variables, where dummy=1 if log_difference_oil>1.

-->to run the regression accurately, do I specify "log_difference_oil*dummy" as the explanatory variable of oil prices? And then, to account for the lagged data, shall I code it as "log_difference_oil(-1)*dummy(-1)" ..."log_difference_oil(-2)*dummy(-2)?

Is there another way to code the regression such that I do not need to create a new series that reflects the log-differenced oil prices, but rather the code will reflect the fact I want only positive log-differences from the log-oil price series proper?

Just want to make sure that this coding is accurately reflecting what I am trying to accomplish econometrically.
Help very much appreciated--thanks!

What you really want to do here is run two separate equations:
1. One where the log_difference_oil is always positive
2. One where it's always negative

So you run the exact same regression (equation), but you run it twice, and it's a different sample each time.

The first time, you set the sample as:

Code: Select all

@all if log_difference_oil<0

and the second time you set it as

Code: Select all

@all if log_differemce_oil>0

If your hypothesis is correct (that oil price only matters if the price is growing), then the first equation will have a non-statistically significant coefficient, while the second one will.

-->to run the regression accurately, do I specify "log_difference_oil*dummy" as the explanatory variable of oil prices? And then, to account for the lagged data, shall I code it as "log_difference_oil(-1)*dummy(-1)" ..."log_difference_oil(-2)*dummy(-2)?

So yes, this should work. It should also give you the same result as the setup I proposed above.

The reason you were getting the same coefficients (but different sign) is because adding a term like

Code: Select all

dlog(o)>0

to the equation will simply add a dummy variable equal to 1 if dlog(o)>0, and 0 otherwise. It won't let you measure how the change in oil prices affects GDP.

[KElizabeth925]

-->Regarding the @all command: I want to run two VARs, where I've got differenced GDP[d(lgdp)] and differenced oil prices[d(loil)] (as they are) as endogenous variables. As additional exogenous variables, I need to include 1) log_difference_oil>0, and then a second VAR where 2)log_difference_oil<0.
-->the @all specification you gave me only allows me to include only positive, or only negative, log differences for oil. How do I code a VAR to allow me to use both d(loil) (including both positive and negative growth) and differenced_oil prices (including only positive growth[and then including only negative growth]) in the same sample?


Thank you!

[KElizabeth925]

Can someone confirm that this command: dlog(o)>0 is indeed =1 and so a dummy variable for the said specification, rather than a variable which measures the actual positive log-difference effect on GDP? Have gotten conflicting responses. Thanks

[EViews Gareth]

Yes, it is a dummy variable.

Type:

Code: Select all

show dlog(o)>0

in the EViews command window to view it.

[KElizabeth925]

Okay, so in order to account for the magnitude of the effect of positive log-differenced oil on log-differenced GDP, would I then just input:

dlog(o(-1))*dlog(o(-1))>0 dlog(o(-2))*dlog(o(-2))>0

And so on for each lag, into the "exogenous variables" box under the VAR specification tab?

[startz]

You probably need some parentheses in the expression.

[KElizabeth925]

Eviews allowed me to run the VAR w/out extra parentheses, though gave results I was not expecting and not sure they are accurate...just checking that my specification mentioned before is correct in measuring the magnitude of positive log-differences.


dlog(o(-1))*dlog(o(-1))>0 dlog(o(-2))*dlog(o(-2))>0

If so then that's fine