# Finding impulse response function based on Dynare output

1. How can I find the form of the impulse response function that created the impulse response graphs based on my .mod file?

2. Am I right in thinking that the impulse response function uses the figures in the Policy and Transition Functions table as inputs?

Thanks so much. The folks on this forum have been fantastic.
ireland_9May2101.mod (10.5 KB)

1. What do you mean with “the form”? The numbers of the IRFs are stored in the results structure oo_.irfs that is in the workspace after running the code.
2. Yes, the IRFs come from the computed model solution. The respective matrices are stored in oo_.dr. For more information see the manual dynare.org/documentation-and-support/manual/manual.pdf/view pages 30-31.

If I had to write down the equation that describes the impulse responses, how could I do that? Presumably, the figures in oo_.irfs are plugged into the impulse response function to create the graphs of the function.

No, the figures in oo_.irfs are actually the already computed IRFs. You are looking for the state space representation. If you look into the manual on page 30 you see for the first order approximation the formula

where ys is the steady state. Subtracting ys from both sides you get

where y_t-ys is the deviation from steady at t=1 and yh_t-1 is the deviation from steady state at t-1. For impulse responses, at t=0 everything is in steady state, so y_0-ys=yh_-1=u=0. Then you shock the system at t=1 by shocking an element of u, afterwards, for all t>1 u is again the zero vector. By recursively computing the above formula, you get the deviations from steady state following the shock for all times. Nothing else than the values of this equation is stored in oo_.irfs.
The formula also is valid for the endogenous variables’ IRFs as it contains the policy funtion (the decision rule to choose the endogenous variables as a function of the shocks and states).
So all you need to report are the matrices A and B. You can find in the manual how they are stored in Dynare.

I’ve read a lot about this oo_.irfs file, but can’t seem to find it anywhere. The manual doesn’t appear to give any clues. What does it look like? How do I retrieve it?

Actually, this is not a file, but a structure, i.e. a variable, that you can find in the Matlab-workspace (the memory if you will) after you ran your Dynare code.

Hello jpfeifer,

maybe you could also give me a hand here, since I am new to the whole topic.
When I run the attached simple RBC model I get the following policy functions:

POLICY AND TRANSITION FUNCTIONS
c k z
Constant 2.754310 37.987290 1.000000
k(-1) 0.044827 0.965275 0
z(-1) 1.355140 2.311810 0.990000
e 1.368828 2.335162 1.000000

so I go by the assumption that z(t) = z_steady +[z(t-1) - z_steady]0.99 + 1e.
How is the impulse response function calculated? Is it calculated with the above formula?
If we consider z_steady = z(0) = 1 and the schock e=0.007 like it is in the model then we get:
z(1) = 1 + 0.007 = 1.007
z(2) = 1 + 0.007*0.99 = 1.0069
etc.

but the values in oo_.irfs.z_e are:
0.0837
0.0828
0.0820

How are these values calculated?
Test_Model.mod (642 Bytes)

Dynare uses a one-standard deviation shock, which is sqrt(0.007)=0.0837. After that, the IRF decays at rate 0.9.

Hello,

I have a question. In Dynare, the matrix A has as rows all the endogenous variables and as columns the state variables.

What happend when the number of state variables (m) is smaller than the number of endogenous variables (n) ?

How can we do the operation Ay^h_t if the matrix size are not agree (A is (nxm) and y^h_t is (nx1))? How the remaining part of the matrix A is fill up?