In R, I have two variables, x and y, and a basic VAR model with just one lag, i.e. (as I understand it) the model basically is:
x(t) = a*x(t-1) + b*y(t-1) + c + error1
y(t) = d*x(t-1) + e*y(t-1) + f + error2
with a,b,c,d,e,f some constants.
How do you interpret the irf output (impulse response coefficients)?
What magnitude is the impulse and what are the irf plot y-axis units?
Specifically I was puzzled by the observation that when I scaled my two time series by multiplying both by 100, the irf plot y-axis values and impulse response coefficients were also multiplied by 100.
I would have thought that they remain the same (e.g. "one unit shock in x(t) leads to units response in y(t+1)", and that the coefficient between the two does not depend on the units we use for both of the variables).
Can you help with the irf result interpretation and why the scaling leads to such a result?
Best Answer
When you conduct VAR all variables should be on the same scale or same variable transformation basis (or as close as possible). It makes perfect sense that when you multiply your original variables by a 100, the IRF graph also reflects responses that are 100 times greater than in the original. The revised graph proportionally has not changed the response (visually the graphs will look identical). You are just using a different scale (i.e. 1 instead of 1% or something similar).
An IRF indicates what is the impact of an upward unanticipated one-unit change in the "impulse" variable on the "response" variable over the next several periods (typically 10).
IRFs do not have coefficients. The original regressions as you specified them have the coefficients. The IRFs has three main outputs: the expected level of the shock in a given period surrounded by a 95% Confidence Interval (a low estimate and a high estimate). And, all those also generate the IRF graphs.