Not so gleeful after all upon return. Anyways, whilst utilising the modified “dynare_estimation_1.m” code version

```
if ~options_.mh_posterior_mode_estimation && options_.cova_compute
[cholmat,negeigennvalues]=cholcov(hh,0);
if negeigennvalues~=0 && ~isnan(negeigennvalues)
[V,D] = eig(hh);
D=abs(D);
temp=diag(D);
temp(temp<1e-8)=1e-8;
D=diag(temp);
hh=1e-4*eye(size(hh));
[hh,negeigenvalues1]=cholcov(hh,0);
end
```

en lieu of the classic one

```
if ~options_.mh_posterior_mode_estimation && options_.cova_compute
try
chol(hh);
catch
disp(' ')
disp('POSTERIOR KERNEL OPTIMIZATION PROBLEM!')
disp(' (minus) the hessian matrix at the "mode" is not positive definite!')
disp('=> posterior variance of the estimated parameters are not positive.')
disp('You should try to change the initial values of the parameters using')
disp('the estimated_params_init block, or use another optimization routine.')
warning('The results below are most likely wrong!');
end
end
```

I have come across the following hindrance when exploiting mode_compute=4.

[code]Configuring Dynare …

[mex] Generalized QZ.

[mex] Sylvester equation solution.

[mex] Kronecker products.

[mex] Sparse kronecker products.

[mex] Local state space iteration (second order).

[mex] Bytecode evaluation.

[mex] k-order perturbation solver.

[mex] k-order solution simulation.

[mex] Quasi Monte-Carlo sequence (Sobol).

[mex] Markov Switching SBVAR.

Starting Dynare (version 4.3.3).

Starting preprocessing of the model file …

Substitution of endo lags >= 2: added 3 auxiliary variables and equations.

Found 20 equation(s).

Evaluating expressions…done

Computing static model derivatives:

- order 1

Computing dynamic model derivatives:
- order 1
- order 2

Processing outputs …done

Preprocessing completed.

Starting MATLAB/Octave computing.

You did not declare endogenous variables after the estimation/calib_smoother command.

Prior distribution for parameter rho_g has two modes!

Warning: File ‘usvs1/prior’ not found.

In CheckPath at 41

In set_prior at 264

In dynare_estimation_init at 123

In dynare_estimation_1 at 59

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

Loading 67 observations from simdata.m

## Initial value of the log posterior (or likelihood): -16917479858827.47

f at the beginning of new iteration, 16917479858827.4726562500

Predicted improvement: 725111275279083473207296.000000000

lambda = 1; f = 354799973695706816.0000000

lambda = 0.33333; f = 39437255816629904.0000000

lambda = 0.11111; f = 4396954658578081.5000000

lambda = 0.037037; f = 503588139409747.3125000

lambda = 0.012346; f = 70991951559073.2187500

lambda = 0.0041152; f = 22925739150193.5273438

lambda = 0.0013717; f = 17585059111086.7675781

lambda = 0.00045725; f = 16991653627368.1953125

lambda = 0.00015242; f = 16925720821237.9707031

lambda = 5.0805e-05; f = 16918395332725.2246094

lambda = 1.6935e-05; f = 16917581515835.4941406

lambda = 5.645e-06; f = 16917491133829.4179688

lambda = 1.8817e-06; f = 16917481105415.2265625

lambda = 6.2723e-07; f = 16917479995823.9375000

lambda = 2.0908e-07; f = 16917479873822.2539062

lambda = 6.9692e-08; f = 16917479860426.5898438

lambda = 2.3231e-08; f = 16917479858984.1835938

lambda = 7.7435e-09; f = 16917479858839.1464844

lambda = 2.5812e-09; f = 16917479858827.7714844

lambda =

-6.2723e-07

## lambda = -6.2723e-07; f = 16917536766842.5214844

lambda = -2.0908e-07; f = 16917486180643.0429688

lambda = -6.9692e-08; f = 16917480560822.5234375

lambda = -2.3231e-08; f = 16917479936685.8984375

lambda = -7.7435e-09; f = 16917479867432.6699219

lambda = -2.5812e-09; f = 16917479859769.2148438

Norm of dx 1.2043e+10

Improvement on iteration 1 = 0.000000000

improvement < crit termination

smallest step still improving too slow, reversed gradient

Objective function at mode: 16917479858827.472656

MODE CHECK

Fval obtained by the minimization routine: 16917479858827.472656

RESULTS FROM POSTERIOR MAXIMIZATION

parameters

prior mean mode s.d. t-stat prior pstdev

eta 2.450 2.4500 10.0000 0.2450 norm 0.7500

sigma_c 1.620 1.6200 10.0000 0.1620 norm 0.3750

h 0.690 0.6900 10.0000 0.0690 beta 0.1000

omicron 5.860 5.8600 10.0000 0.5860 norm 2.0000

omega 3.230 3.2300 10.0000 0.3230 norm 0.1000

rho_rn 0.880 0.8800 10.0000 0.0880 norm 0.1000

phi_pi 1.480 1.4800 10.0000 0.1480 norm 0.1000

phi_y 0.080 0.0800 10.0000 0.0080 norm 0.0500

tau 0.660 0.6600 10.0000 0.0660 beta 0.1000

xi 0.870 0.8700 10.0000 0.0870 beta 0.1000

rho_kappa 0.490 0.4900 10.0000 0.0490 beta 0.1000

rho_z 0.750 0.7500 10.0000 0.0750 beta 0.1000

rho_s 0.866 0.8660 10.0000 0.0866 beta 0.1000

rho_a 0.822 0.8220 10.0000 0.0822 beta 0.1000

rho_vphi 0.700 0.7000 10.0000 0.0700 beta 0.1000

rho_g 0.980 0.9800 10.0000 0.0980 beta 0.1000

standard deviation of shocks

prior mean mode s.d. t-stat prior pstdev

e_kappa 0.250 0.2500 10.0000 0.0250 invg Inf

e_z 0.250 0.2500 10.0000 0.0250 invg Inf

e_a 0.250 0.2500 10.0000 0.0250 invg Inf

e_s 0.250 0.2500 10.0000 0.0250 invg Inf

e_vphi 0.250 0.2500 10.0000 0.0250 invg Inf

e_g 0.250 0.2500 10.0000 0.0250 invg Inf

Log data density [Laplace approximation] is -16917479858756.599609.

Warning: File ‘usvs1/metropolis’ not found.

In CheckPath at 41

In metropolis_hastings_initialization at 62

In random_walk_metropolis_hastings at 69

In dynare_estimation_1 at 931

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Multiple chains mode.

MH: Searching for initial values…

MH: I couldn’t get a valid initial value in 100 trials.

MH: You should Reduce mh_init_scale…

MH: Parameter mh_init_scale is equal to 0.400000.

MH: Enter a new value… 0.01

MH: I couldn’t get a valid initial value in 100 trials.

MH: You should Reduce mh_init_scale…

MH: Parameter mh_init_scale is equal to 0.010000.

MH: Enter a new value… 0.009

MH: Initial values found!

MH: Number of mh files : 1 per block.

MH: Total number of generated files : 3.

MH: Total number of iterations : 1000.

MH: average acceptation rate per chain :

0 0 0

MH: Total number of Mh draws: 1000.

MH: Total number of generated Mh files: 1.

MH: I’ll use mh-files 1 to 1.

MH: In mh-file number 1 i’ll start at line 500.

MH: Finally I keep 500 draws.

MH: I’m computing the posterior mean and covariance… Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 6.048776e-20.

In compute_mh_covariance_matrix at 74

In marginal_density at 50

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 6.048776e-20.

In marginal_density at 56

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

Done!

MH: I’m computing the posterior log marginale density (modified harmonic mean)…

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 6.048776e-20.

In marginal_density at 67

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: The support of the weighting density function is not large enough…

MH: I increase the variance of this distribution.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.766881e-18.

In marginal_density at 102

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.628578e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 7.020776e-19.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 3.854419e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.434634e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 3.001022e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.185226e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 2.664325e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.092922e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 2.740423e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.211734e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 8.509851e-19.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 5.124496e-19.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 1.230393e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 4.619124e-19.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 2.226457e-18.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: Let me try again.

Warning: Matrix is close to singular or badly scaled. Results may be

inaccurate. RCOND = 9.653391e-19.

In marginal_density at 108

In dynare_estimation_1 at 948

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

MH: There’s probably a problem with the modified harmonic mean estimator.

ESTIMATION RESULTS

Log data density is -Inf.

parameters

prior mean post. mean conf. interval prior pstdev

eta 2.450 2.5128 2.4941 2.5234 norm 0.7500

sigma_c 1.620 1.5726 1.5293 1.6490 norm 0.3750

h 0.690 0.7136 0.6796 0.7588 beta 0.1000

omicron 5.860 5.8657 5.8194 5.8977 norm 2.0000

omega 3.230 3.1770 3.1271 3.2162 norm 0.1000

rho_rn 0.880 0.8338 0.8009 0.8599 norm 0.1000

phi_pi 1.480 1.3702 1.2954 1.4627 norm 0.1000

phi_y 0.080 0.0732 0.0564 0.0975 norm 0.0500

tau 0.660 0.7306 0.6805 0.8035 beta 0.1000

xi 0.870 0.8748 0.8302 0.9003 beta 0.1000

rho_kappa 0.490 0.4879 0.4520 0.5515 beta 0.1000

rho_z 0.750 0.8181 0.7703 0.8459 beta 0.1000

rho_s 0.866 0.8520 0.8303 0.8792 beta 0.1000

rho_a 0.822 0.8696 0.8229 0.9085 beta 0.1000

rho_vphi 0.700 0.6995 0.5958 0.7931 beta 0.1000

rho_g 0.980 0.9080 0.7955 0.9659 beta 0.1000

standard deviation of shocks

prior mean post. mean conf. interval prior pstdev

e_kappa 0.250 0.2046 0.1689 0.2707 invg Inf

e_z 0.250 0.2836 0.1910 0.3328 invg Inf

e_a 0.250 0.3017 0.2543 0.3651 invg Inf

e_s 0.250 0.4057 0.3421 0.4611 invg Inf

e_vphi 0.250 0.2365 0.1649 0.3108 invg Inf

e_g 0.250 0.3230 0.2239 0.4111 invg Inf

Warning: BETAINV did not converge for a = 0.9408, b = 0.0192, p = 0.999.

In betainv at 61

In draw_prior_density at 47

In PlotPosteriorDistributions at 80

In dynare_estimation_1 at 951

In dynare_estimation at 70

In usvs1 at 322

In dynare at 120

Total computing time : 0h00m52s[/code]

It need be recollected that the model’s structural shocks have diminished to six: equalling the amount of observed variables, thus annihilating the erstwhile raised issue of stochastic singularity. Why do you believe to be there yet an issue with the modified harmonic mean estimator? Withal, mode_compute=6 doesn’t even work. As mentioned in a previous post of mine, ulterior model re-specification would but integrally belittle the underlying research question; I would just wish to estimate these parameters in one way or another: how is one to surmount this all? Thank you.