Identification issue in 3-eq NK model

Estimation
1

Hi all,

I have a model that is not identified. For example, the following one:

image
image1115×412 25.1 KB

It’s not hard to see that (also the code gives me this result) (\phi, \theta) are not identified.
three_eq_nk3.mod (4.0 KB)

I tried to ran the code as attached and it refused to continue., showing the following:

'POSTERIOR KERNEL OPTIMIZATION PROBLEM!
(minus) the Hessian matrix at the "mode" is not positive definite!

And when i remove \phi from the estimated_params block, it works just fine.
My question is, even if the model is not identified, as long as my prior is informative, shouldn’t Bayesian estimation give me something (as if it is identified)?

Any insights?
Thank you!

2

Please try mode_compute=5, prior_trunc=0 as additional options. Your mode-finding failed. When I now run your file, the problem is the upper bound for rhoR, which prevents an interior solution.

1 Like
3

Thank you, professor, now I relax the bound for rhoR and it goes! It is surprising that it would ever hit the bound when the posterior is far away from that.

Another follow-up question would be: why does the solution from stoch_simul look like that?

POLICY AND TRANSITION FUNCTIONS
                                   y              pi               r             s_D             s_S             s_r
s_D(-1)                     0.769261        1.211527        1.913448        0.900000               0               0
s_S(-1)                    -4.234464        1.587924        1.852578               0        0.900000               0
s_r(-1)                    -0.385491       -0.109563        0.187469               0               0        0.400000
e_D                         0.085473        0.134614        0.212605        0.100000               0               0
e_S                        -0.470496        0.176436        0.205842               0        0.100000               0
e_R                        -0.096373       -0.027391        0.046867               0               0        0.100000

I understand Dynare is using perturbation methods to solve the LRE. When I look at the report of policy and transition functions, it only has all the coefficients of s_D(-1), s_S(-1), s_r(-1), and three shocks. However, if I understand it correctly, it should also have y(-1), r(-1), pi(-1) on the RHS of the equation in the solution. Where are they?

4

Why should that be the case? The lags of these variables do not appear in the model and are therefore irrelevant. r(-1) would for example only appear for \rho\neq 0

5

I see your point. I was being dogmatic. Again, thanks for your clarification!