The RATS Software Forum

Hi

I have run an ECM with CATS and exported the CATS model and run the following code:

impulse(model=catsmodel,results=catsirfs,cv=%identity(2),steps=24,print)

This is the output from the first 5 impulse responses:

Entry DBRENT DKRW BRENT KRW
1 1.0000000 0.0000000 1.0000000 0.0000000
2 0.3541989 -1.4003036 1.3541989 -1.4003036
3 0.0850391 -0.1909792 1.4392380 -1.5912828
4 -0.0056548 0.6184702 1.4335833 -0.9728127
5 -0.0643851 0.4254872 1.3691981 -0.5473255


If I understand correctly the one standard deviation shock from Brent results in zero response in KRW in period 1.

I am interested in converting the response into percentages

My questions:

1) If I want to convert to percentage do I simply do the following:1/0 for period 1. 1.3541989/1.4003036 for period 2, 1.4392380/-1.5912828 for period 3 etc.
2) What is the one stanadrad deviation for BRent in terms of percent of Brent price? I see it has been normalized at 1, but I need to explain that one standard deviation meansd 5,10 or 15%? Let's say it is 10%, and I wanted to see what 20% shock would be - I would simply double the response in KRW?

Thanks so much!

Is BRENT in levels or logs? If it's in logs then an impact of 1 can be interpreted as a 1% shock (through it would be more common to use a .01 impact for that, just to get normal looking scales out of everything else). Like VAR's, VECM's are linear so you can freely scale either the shocks or the responses to suit the interpretation.

The initial data is all in levels not in logs.


Would I divide each KRW impulse by the initial BRent shock or the corresponding Brent impulse respose (e.g., KRW 3rd period with Brent 3rd period) or the original Brent shock.

Assuming that BRENT is the oil price, it seems odd to not have that in logs.

However, if they're both in levels and you're trying to estimate a "scale-up" factor, then yes, the ratio of one response to the other will be independent of the scale of the initial shock.

Thanks Tom - I reestimated in logs.

So - to be clear - if I want the Brent shock to be 20%, I would multiply all the KRW by 20 as the initial shock is 1% from brent?

Thanks for your help?

Entry DBRENT DKRW BRENT KRW
1 1.0000000 0.0000000 1.0000000 0.0000000
2 0.3541989 -1.4003036 1.3541989 -1.4003036
3 0.0850391 -0.1909792 1.4392380 -1.5912828
4 -0.0056548 0.6184702 1.4335833 -0.9728127
5 -0.0643851 0.4254872 1.3691981 -0.5473255
6 -0.0881294 0.3777656 1.2810687 -0.1695599
7 -0.0881548 0.4560702 1.1929139 0.2865103
8 -0.0849528 0.4242420 1.1079611 0.7107523
9 -0.0808363 0.3717828 1.0271248 1.0825352
10 -0.0747095 0.3479800 0.9524153 1.4305152
11 -0.0684087 0.3223089 0.8840066 1.7528240
12 -0.0627031 0.2919144 0.8213034 2.0447385
13 -0.0573261 0.2661482 0.7639774 2.3108867
14 -0.0522956 0.2435666 0.7116817 2.5544533
15 -0.0477108 0.2220616 0.6639710 2.7765149
16 -0.0435274 0.2023637 0.6204435 2.9788787
17 -0.0396966 0.1846193 0.5807469 3.1634979
18 -0.0362005 0.1683872 0.5445465 3.3318852
19 -0.0330137 0.1535334 0.5115328 3.4854186
20 -0.0301064 0.1400103 0.4814264 3.6254289
21 -0.0274544 0.1276842 0.4539720 3.7531132
22 -0.0250362 0.1164359 0.4289358 3.8695490
23 -0.0228310 0.1061785 0.4061048 3.9757275
24 -0.0208199 0.0968265 0.3852849 4.0725540

A shock of 20 to BRENT in levels means $20, not 20%. That's why you usually do those in logs.

Hi Tom.

What if all my variables are returns defined as log(p_t/p_{t-1})?

I have all the shocks in standard deviation terms. If the impulse response is 0.01, could I then say that a one unit standard deviation shock leads to an increase of 0.01 percentage points? My confusion is that log(p_t/p_{t-1}) is just an approximation to p_t/p_{t-1}-1, which is in percentage point terms..hence, even though the variable is in logs, I think it would be more intuitive to interpret it as a percentage point increase rather than a % increase.

It's usually easier to convert to 100.0*log(p/p{1}) (or 100.0*(p/p{1}-1) if you're doing that type of return). As you have that written a .01 response would be 1%, not .01%. With the 100 multiplier, you can just read off the percentage directly.