impulse response functions interpretation

[justin_m]

I have several time series of prices. I compute the returns as the difference in the logarithm of prices, eg: R_t = ln(p_t)-ln(p_{t-1}). I then regress returns on its lags and on monthly dummies and get the absolute value of the residuals, which are interpreted as volatilities.

I do this for many time series and then I create a var will all the time series of the volatilities.

What does a response of 0.15 mean in this case? I assume it means that a one standard deviation shock to X causes a 0.15 percentage point increase. While the dependent variable is in logs, in this case it is just an approximation to R_t = p_t/p_{t-1}-1, which is in percentage point terms. So, in this case, even though the variables are in logs, we do not talk about a 0.15% response but rather about a 0.15 percentage point response, correct?

[dakila]

If you define a new variable (for example, return) then your interpretation is almost correct. But you need to multiply Rt by 100.

[justin_m]

Hi Dakila.

I am not confident I understood what you meant by defining a new variable.

In this case, I have all the variables as log(pt/p_{t-1}) or approximately pt/p_{t-1}-1.

In this case, how would you interpret an impulse response of 0.02, for instance? Are you saying that you would read it as a one unit sd shock leads to a 100 * 0.02 = 2 percentage point increase? I would read it simply as a 0.02 percentage point increase... Would you be so kind as to explain this further, please?

[dakila]

Hi Justin,

I understood that you are trying to explain the return(R_t) not the price (p_t).
You can manually multiply 0.02 by 100.
But more convenient way to do this is to define R_t = (ln(p_t)-ln(p_{t-1}))*100 before the estimation of VAR model .
Interpretation: a one unit sd shock leads to a 100 * 0.02 = 2 percentage point in the return (not the price).
If you are trying to explain the price then this interpretation is totally wrong.

[justin_m]

Hi Justin,

I understood that you are trying to explain the return(R_t) not the price (p_t).
You can manually multiply 0.02 by 100.
But more convenient way to do this is to define R_t = (ln(p_t)-ln(p_{t-1}))*100 before the estimation of VAR model .
Interpretation: a one unit sd shock leads to a 100 * 0.02 = 2 percentage point in the return (not the price).
If you are trying to explain the price then this interpretation is totally wrong.

Thank you Dakila. I get what you mean now. One last question: is it common (or a sign of a problem) to have responses of one variable larger than the shocks to another (not the same) variable?

[dakila]

Yes, it is very common.