3 equations New keynesian model

General DSGE Modeling
1

Dear all,
I am trying to estimate the simple New keynesian model of three equations. First of all I have some super simple theoretical questions that I think it would be good if I clarify. Secondly, I have some problems with my code, I think it is something related to steady states, but I am not sure.

My super simple theoretical questions are:

-1st: If I make the bayesian estimation of the model that I attached( the new keynesian model with 3 equations (IS, P.C, Monetary rule)), these equations are linealized, their variables are in deviations w.r.t steady state. What I get is the posterior distributions of all the parameters associated to these three equations, in this case, people say that this is solving a DGSE model, or people say that this is solving a BSVAR model? I guess this is a silly confusion, but what I imagine is that with these parameters I can construct a SVAR representation (maybe following canonical form of sims (2001)?). If my guess is wrong and this is not the same than solving a BSVAR, then which is the difference between solving this 3eq model and solving a model with H.H foc’s, firm’s focs, and all the associated equations of market clearing conditions, perturbations… as you do in the baseline NK model example of Dynare folder?

-2nd: If variables are in deviations w.r.t steafy state, should not be the case that all the steady states (of R, pi, output gap…) are 0?

Code problems:
-I have this problem:
You did not declare endogenous variables after the estimation/calib_smoother command.
But I do not see what I need to change.

  • The second problem is:
    POSTERIOR KERNEL OPTIMIZATION PROBLEM!
    (minus) the hessian matrix at the “mode” is not positive definite!
    => posterior variance of the estimated parameters are not positive.
    You should try to change the initial values of the parameters using
    the estimated_params_init block, or use another optimization routine.

Is this because of my initial values (steady state assumptions)?

Regards, Joan.
Data1.m (7.3 KB)
pruebacompleta.mod (984 Bytes)

2
  1. The solution to a DSGE model has the form of a VARMA process. It is not certain that a finite order VAR representation in the observables exists. For that reason, a SVAR is not (necessarily) equivalent
  2. Yes, all steady states in this case should be 0 (which they are in your model)
  3. You are having an identification issue:

==== Identification analysis ====

Testing prior mean

WARNING !!!
The rank of H (model) is deficient!

[rho_R,SE_er_R] are PAIRWISE collinear (with tol = 1.e-10) !

WARNING !!!
The rank of J (moments) is deficient!

[rho_R,SE_er_R] are PAIRWISE collinear (with tol = 1.e-10) !

and psi_pi runs into the upper bound of your prior. For the latter you may want to use an informative prior. Also, use mode_check to investigate the issue.