Contemporaneous reaction of interest rate to variable w/ one lag

Dear all,

As I have not found anything about this in the Dynare manual or in the forum, I would like to ask you the following question:
if I run an estimated, log-linearized model in Dynare, can I see somewhere in the Dynare generated output the contemporaneous response of the interest rate to variable X, where variable X enters the Taylor rule with one lag and not in period t?

Many thanks for your help!


I am not sure I understand the question. If X is an endogenous variable, a “response” to this variable is not a well-defined object.

Thank you very much! Let me try to clarify:

Consider the estimated version (for instance, mode calibration) of Smets and Wouters (2007):

The Taylor rule is r_t = f(pi_t, ygap_t, plus lagged variables). Thus only inflation and output enter the policy function at time t with coefficients phi_pi and phi_ygap (abstracting from interest rate smoothing).

Other variables (e.g., consumption, investment) do not explicitly enter the rule. Yet, since they co-move with, e.g., output, I’m wondering whether one can obtain the DGP-implied implicit reaction to these variables?

To make an analogy: in a SVAR model (without contemporaneous zero-restriction), the interest rate equation contains slopes for the time t response of the interest rate to all other variables.

I’m wondering: is it possible, to obtain such implicit “slopes” to all the endogenous variables, given the calibration of SW07 using something like an SVAR (or SVARMA) representation of the model delivering the “true” A0 SVAR matrix?

Thank you very much in advance!

That is tricky, because the DSGE model has a VAR representation in the state variables and the variables you are interested in are not states. But you can try to represent the DSGE model as a (infinite order) VAR in the observables and then proceed like in a VAR.
DSGE_mod/Sims_2012/Sims_2012_RBC.mod at master · JohannesPfeifer/DSGE_mod · GitHub would be a starting point.