VECM & Generalised impulse response function interpretation

[huidan_xue]

Hello,

I esimated a VEC model with index variables (such as fertilizer price index, butter export price index, cpi for food, ect) because all the variables are I(1) and have cointegrating relations (all the variables are converted to their index form). I use genralised IRFs and tried to find out how different factors( like fertilizer price) affects the butter export price. However, I am quite confused to explain the scales of y axis of the GIRFs. Should it shows how a positive one-standard-deviation shock (let's say it 0.009) to the first difference of fertilizer price index (growth of fertilizer price index) affects the first difference of butter export price index (or to say growth of butter export price index)?

For example, the GIRFs y axis of butter export price is 0.01 at 1st month, then stablized at the level of 0.02 after 5 months. Should I interpret this: 0.9 percentage point increases in the growth of fertilizer price index causes a 1 percentage point increases in the growth of butter export price for the 1 month and the impacts stablized after 5 months with increases in the growth of butter export price index at 0.02 percentage point?

The GIRFs for VECM usually are not dying out to 0 but stablised at a constant level, I am very confused about this issue as well, is this due to the long-run equilibrium / Cointegration among the variables. I am trying to find a right way to interpret the VECM's IRFs but failed to find the right one.

Thank you very much!

Huidan

[TomDoan]

First of all, you didn't say it, but are you doing everything in logs? It sounds like you should. (Converting to indexes merely changes the scale). The standard transformation for a price index is 100*log(..). 100*log(..) makes the responses read off directly as percentages, that is, 1.5 is 1.5%.

In a VECM, the target variables are done in their undifferenced form. That's why they don't converge to zero. The responses of a stationary series will converge to zero, but those of a non-stationary variable usually won't.

[huidan_xue]

First of all, you didn't say it, but are you doing everything in logs? It sounds like you should. (Converting to indexes merely changes the scale). The standard transformation for a price index is 100*log(..). 100*log(..) makes the responses read off directly as percentages, that is, 1.5 is 1.5%.

Thank you for your reply!

No, I didn't convert the variable into logs form, they are in their index level, like 103.5, 115.2, 102.9,..., So I guess the read off would mean growth in level instead of growth rate? Maybe I should redo the index to read off as percentages.

So, if all variables are in log-form case, should I say the butter export price increases by 1.5% after 1 positive one-standard-deviation shock to fertilizer price? This one-standard-deviation shock should be one-standard-deviation of residuals for fertilizer price equation, right?

[/quote]In a VECM, the target variables are done in their undifferenced form. That's why they don't converge to zero. The responses of a stationary series will converge to zero, but those of a non-stationary variable usually won't.[/quote]

Thank you for explaining this to me! Helps a lot!

[TomDoan]

First of all, you didn't say it, but are you doing everything in logs? It sounds like you should. (Converting to indexes merely changes the scale). The standard transformation for a price index is 100*log(..). 100*log(..) makes the responses read off directly as percentages, that is, 1.5 is 1.5%.

Thank you for your reply!

No, I didn't convert the variable into logs form, they are in their index level, like 103.5, 115.2, 102.9,..., So I guess the read off would mean growth in level instead of growth rate? Maybe I should redo the index to read off as percentages.

No. You should do them in log form (most conveniently 100*log(...)). An unlogged price index doesn't provide any useful interpretation. Think about this: when was the last time you heard someone say that the CPI went up by 1? Not 1%, just 1. I'm going to guess never since it has no meaning without also knowing the level. +1 at a value of 30 is completely different than +1 at a value of 300.

So, if all variables are in log-form case, should I say the butter export price increases by 1.5% after 1 positive one-standard-deviation shock to fertilizer price? This one-standard-deviation shock should be one-standard-deviation of residuals for fertilizer price equation, right?

If you do the 100*log(..) transformation, then a response of +1.5 means a positive 1.5% change in response to the shock.

In a VECM, the target variables are done in their undifferenced form. That's why they don't converge to zero. The responses of a stationary series will converge to zero, but those of a non-stationary variable usually won't.

Thank you for explaining this to me! Helps a lot!