Getting the elasticty from Panel VAR

[researcher101]

This is more if a theoretical question:

Let say I run panel VAR or VAR model. Say I have X and Y variables. I shock X with a positive shock. To get the elasticity I use the following definition:


Elasticity of Y to X = the reaction of Y to a shock to X/ the reaction of X to a shock to X


So I take the mean from the impulse response of Y to a shock in X and divide that by the mean from the impulse response of X to a shock to X. This what I was told the way to get the elasticity in period 1, 2 ,3 and so on.

The questions I have:

1) Do the variable have to be all in logs?

2) I am doing the model with difference of logs, how to transform them to elasticity ?

3) is there any paper support the idea above I can cite?

Thanks a lot!

[TomDoan]

If X and Y are in logs, then standard impulse responses give the elasticity. If they aren't in logs, then standard impulse responses can't really be used because the elasticity depends upon the values of X and Y and not just their dynamics---you would have different elasticities for each value. In general, if elasticities are an interesting concept, that's a very good sign that you should be modeling in logs.

If you run the VAR in log differences, then the elasticities of one variable WRT the other would be obtained by accumulating the responses. A shock still has the same interpretation whether you're shocking dlog X or just log X, but the responses would be responses of dlog Y rather than log Y.

I don't know of any textbook that talks about that in this context (none of the books on multiple time series has "elasticity" in the index other than Hamilton, and that's just the general definition). I guess one would say that it's simply according to the definition of elasticity.

[researcher101]

Thank you for your help!

few questions:
Assume we shock X and we look at the impulse responses of Y
1)
The results with logs are not good at all but with d.log are very good statistically and intuitively. How to overcome this problem? just look at the accumulate impulse responses? those seems odd since the numbers reach about 30-20 at each step. This is extremely elastic.

2) You say if all variables in logs, then the impulse responses can be read as elasticity, I know this is the case for the estimated coefficients but not sure about the impulse responses.
Assume that I get the impulse responses in a table instead of a graph for each step. Assume that the table as following:

steps 95% mean 5%
1 0.9 .8 0.2
2 0.8 .6 0.1
3 0.7 .5 0.1

Then I only look at the mean and report that a 10% increase of X leads to 8% of Y in first year and 6% in second year and so on.

3) In RATS, how do I get the impulse responses in a table? I use @MCGraphIRF but not sure how to get the reported impulse responses in a table instead of a graph.


Thanks a lot for all the help!

[TomDoan]

Thank you for your help!

few questions:
Assume we shock X and we look at the impulse responses of Y
1)
The results with logs are not good at all but with d.log are very good statistically and intuitively. How to overcome this problem? just look at the accumulate impulse responses? those seems odd since the numbers reach about 30-20 at each step. This is extremely elastic.

First, I'm not sure what you mean about results not being good at all, but ... The model in differences is a restricted form of the model in logs. There will rarely be that much of a difference in the implied dynamics unless the model in differences is misspecified (by missing cointegration).

2) You say if all variables in logs, then the impulse responses can be read as elasticity, I know this is the case for the estimated coefficients but not sure about the
impulse responses.
Assume that I get the impulse responses in a table instead of a graph for each step. Assume that the table as following:

steps 95% mean 5%
1 0.9 .8 0.2
2 0.8 .6 0.1
3 0.7 .5 0.1

Then I only look at the mean and report that a 10% increase of X leads to 8% of Y in first year and 6% in second year and so on.

The size of the responses depends upon the size of the shocks. You want to do unit shocks in a log-log model if you want interpret the results directly as elasticities.

3) In RATS, how do I get the impulse responses in a table? I use @MCGraphIRF but not sure how to get the reported impulse responses in a table instead of a graph.

Use @MCPROCESSIRF for that