Posterior kernel optimization problem!

Dear all,

I am trying to run a Bayesian DSGE model but receiving the following error:

(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.
Warning: The results below are most likely wrong!

In dynare_estimation_1 at 458
In dynare_estimation at 70
In linear_model at 428
In dynare at 120 [/quote]

The command window stopped here:

[quote]Error using chol
Matrix must be positive definite.
Error in metropolis_hastings_initialization (line 68)
d = chol(vv);

The /identification;/ in dynare output as:

The rank of H (model) is deficient!
psi is not identified in the model!
[dJ/d(psi)=0 for all tau elements in the model solution!]
The rank of J (moments) is deficient!
psi is not identified by J moments!
[dJ/d(psi)=0 for all J moments!]
[rhot,et] are PAIRWISE collinear (with tol = 1.e-10) !
ei is collinear w.r.t. all other params!
phipi is collinear w.r.t. all other params!
phiy is collinear w.r.t. all other params!
rhoi is collinear w.r.t. all other params![/quote]

I think I can understand that psi, the inverse elasticity of labor supply, is difficult to identify in the model, especially with limited number of observable. The priors of rhot, ei, phipi, phiy, rhoi, are similar to SW(2007):

[quote] prior mean mode s.d. t-stat prior pstdev
h 0.700 0.7382 0.0063 116.5629 gamm 0.1000
psi 0.500 0.5000 0.2500 2.0000 norm 0.2500
phipi 1.500 1.4385 0.0351 40.9271 norm 0.2500
phiy 0.125 0.1279 0.0502 2.5495 norm 0.0500
rhoa 0.850 0.9944 0.0004 2445.2232 beta 0.2000
rhog 0.850 0.9857 0.0007 1364.3778 beta 0.2000
rhot 0.850 1.0000 0.0000 0.0000 beta 0.2000
rhosg 0.500 0.5000 0.2426 2.0607 beta 0.2000
rhobg 0.500 0.5000 0.2123 2.3552 beta 0.2000
rhoi 0.750 0.9388 0.0047 197.9226 beta 0.1000
standard deviation of shocks
prior mean mode s.d. t-stat prior pstdev
ea 0.400 0.5441 0.0059 91.9176 invg 2.0000
eg 0.400 0.4231 0.0299 14.1266 invg 2.0000
ei 0.400 0.4143 0.0000 0.0000 invg 2.0000
esg 0.400 0.4000 0.0000 0.0000 invg 2.0000
ebg 0.400 0.4000 0.0000 0.0000 invg 2.0000
et 0.400 0.4359 0.0730 5.9671 invg 2.0000[/quote]

Can anyone in this forum please give me some clue to fix the posterior kernel optimization problem?

Thanks a lot for your time.
pb.mod (8.78 KB)
dataUS.xls (33 KB)

When identification says a parameter is not identifiable it does not mean that it is hard to identify but that it is proven to be impossible to estimate it. If you think it should be possible to estimate it, there is still an error in the equations you entered.

If you fixed the identification issue and the problem still pops up, search the forum for other suggestions (e.g. different mode_compute). There are dozens of posts on this.