# Impulse responses

Dear Johannes, I have a model with two unit root shocks. First one is technology shocks (A) and second one is labor supply shock (B). so, hours has trend B, productivity (also wages) has trend A. The rest of the variables has trend A and B (I stationarized the model based on that) . I see that the impulses responses for the variables are the same for both shocks. I think that the IRs should be the different but I could not figure out the problem. Could you please look at my codes and tell me why I get the same IRs? Please see attached file. Best,
I also have this in model solution:
model1.mod (2.3 KB)

Dear Johannes, could you please also look at my codes?

Hi, first of all, questions on the forum where I need to run codes and think about model-specific output take longer to answer, because they are non-standard.

Now to your model: the IRFs from the detrended model must be the same. If you look at your model equations, both shocks always only appear as a sum in exactly the same place and are therefore indistinguishable. Differences might appear in the non-detrended IRFs where you do not add both trends back to the detrended variables.

I think thats why I obtained correlation of simulated variables as 1:

CORRELATION OF SIMULATED VARIABLES

VARIABLE y h y_h w c
y 1.0000 -1.0000 1.0000 1.0000 1.0000
h -1.0000 1.0000 -1.0000 -1.0000 -1.0000
y_h 1.0000 -1.0000 1.0000 1.0000 1.0000
w 1.0000 -1.0000 1.0000 1.0000 1.0000
c 1.0000 -1.0000 1.0000 1.0000 1.0000

Actually, my concern is not IRs. I need the simulated data from the model. The model runs perfectly but I am not still sure that I stationarized the model correctly especially for hours, wages and C_Y:

h^(1/psi) = c^(-1)w;
w= alpha
(y/h);
c_y = c/y;

Do you think I stationarized correctly these equations in above? h is has a trend B. w has a trend A (like productivity) , c has a trend AB, y has a trend AB so c_y does not have any trend. This is how I stationarized them.

Best

This looks sensible at first sight, but I cannot check your whole model for you.