The RATS Software Forum

Dear Tom,

I have problems in interpreting the scale of impulse response functions.
I estimated a 3 variable VAR. The variables are the nominal spot exchange rate, the industrial production index and the cpi.
The spot exchange rate is in homecurrency/USD, the industrial production index is scaled such that the base year is 100 and so is the cpi.
The VAR is estimated in log levels and the IRFs are orthogonalized via Cholesky decomposition.
The code is:
The resulting IRFs to a one standard deviation shock in the log exchange rate are for example:

Responses to Shock in Log Spot
Entry LNSPOT LNCPI LNIP
1 0.0207177 0.00047419 0.00022617
2 0.0166352 0.00049447 0.00013977
3 0.0153595 0.00083263 0.00010607
4 0.0144799 0.00065299 0.00027672
5 0.0113365 0.00072607 0.00086013
6 0.0119417 0.00076993 0.00112513
7 0.0127854 0.00079535 0.00115847
8 0.0121028 0.00086965 0.00082416
9 0.0123179 0.00090341 0.00058561
10 0.0117931 0.00091782 0.00049253

How would I interpret these numbers?
Take for example entry 7 in column LNIP, which is 0.00115847. As far as I understand that table right it would mean that a one standard deviation shock in the log spot rate leads to an increase of the log-industrial production index by 0.00115847.
So when I want to interpret that number it would mean the actual industrial production index (not the log of it) would increase by exp( 0.00115847) = 1.0012, which would be an increase of around 1 percent 7 months after the initial shock in the log spot rate. Is that correct?

How would I concert the IRFs into percentage changes?

Thank you in advance

Best Jules

First off, if you look at the IMPULSES.RPF example (and most of our other examples, and most of the replication examples), you'll see that they don't take logs, but 100*logs:

*
* Scaling the log series by 100 gives the responses a more natural scale.
*
set logcangdp  = 100.0*log(canexpgdpchs)
set logcandefl = 100.0*log(canexpgdpds)
set logcanm1   = 100.0*log(canm1s)
set logusagdp  = 100.0*log(usaexpgdpch)
set logexrate  = 100.0*log(canusxsr)

The fact that CPI and IP are scaled to 100 in any particular base year is irrelevant once you take logs.

At your scale, 0.00115847 would mean .115847% in the typical interpretation (with log changes as percentage changes). Note that if you multiply up by 100, then you just read that off as percentages. The response of the growth rate in period 7 is the difference between 7 and 6.

Why is the fact that cpi and IP are scaled to 100 irrelevant wegen I take logs?
In general what is the advantage of taking logs?

Best jules

Jules89 wrote: Why is the fact that cpi and IP are scaled to 100 irrelevant wegen I take logs?

log(cx)=log(c)+log(x)

so any scalar c just washes into the intercept.

Jules89 wrote: In general what is the advantage of taking logs?

This is discussed in the User's Guide, bottom of the page.

Dear Tom,

often I read papers, which estimate VARs and do impulse response analysis. Sometimes the variables in the VAR are demeaned and standardized. This is often the case when the same VAR is estimated for several countries. I guess to make everything comparable...
I don't really get why this is necessary.
If I do the 100*log transformation to all variables except for example for variables like unemployment or interest rates, which are already in percentage points or are non trending, then the "Impulse" function will by default do a cholesky shock. Then the values of the impulse responses can be interepreted as percentages and the shocks are one standard deviation shocks, right?

What is then the advantage of demeaning and standardizing the variables? When I standardize the variables and use the impulse function, what is then the scale of the shock?

Thank you

Best Jules

You should probably ask the people who did that. Rescaling doesn't change the shape (of either the responses or the error bands), so if that's all that's of interest (whether a response is (significant and) positive or negative), the scaling would have no real effect (for good or bad). However, the "units" themselves are almost impossible to interpret.

Hi Tom,

again I have a question regarding the scale of the IRF.
Assume I have a linear VAR with all variables, which are usually put into logs, in logs (eg. Industrial Production, CPI, Stock Market indices, etc) and all variables which are in percentage points untransformed (unemployment, interest rates). Then the IRFs calculated wit "impulse" read off as percentages (after I multiplied by 100).

1) Is this also true for the untransformed variables like interest rates and unemployment?

2) When all variables are demeaned and standardized by their standard deviation (after log transformation) then the scale of the IRF is no longer interpreted as percentage points right?

3)What if I standardize only one of the variables. For example, I want to compare the impact of shocks coming from several stock market indices on the same macroeconomic variables. Then I standardize the stock market indices and leave everything else in logs. Then the scale of a standardized stock market index shock on for example 100*log(cpi) should still read of as percentage points, right?

4) Does it make sense to standardize the different stock market indeces and then I estimate several VARs to compare the scale of the IRFs?

Thank you in advance

Jules

Jules89 wrote: Assume I have a linear VAR with all variables, which are usually put into logs, in logs (eg. Industrial Production, CPI, Stock Market indices, etc) and all variables which are in percentage points untransformed (unemployment, interest rates). Then the IRFs calculated wit "impulse" read off as percentages (after I multiplied by 100).

1) Is this also true for the untransformed variables like interest rates and unemployment?

The responses are in the measurement unit used for the interest rates or unemployment.

Jules89 wrote: 2) When all variables are demeaned and standardized by their standard deviation (after log transformation) then the scale of the IRF is no longer interpreted as percentage points right?

Correct. They're now in standard deviations. Which require extra information in order to interpret. Which is why you shouldn't do it.

Jules89 wrote: 3)What if I standardize only one of the variables. For example, I want to compare the impact of shocks coming from several stock market indices on the same macroeconomic variables. Then I standardize the stock market indices and leave everything else in logs. Then the scale of a standardized stock market index shock on for example 100*log(cpi) should still read of as percentage points, right?

Correct. Standardizing or otherwise scaling variable x has no effect on the responses to variable y, just to its own responses.

Jules89 wrote: 4) Does it make sense to standardize the different stock market indeces and then I estimate several VARs to compare the scale of the IRFs?

No. See the previous answer.