Stochastic simulation following estimation command

Stochastic simulations
1

Hi all,
I have a question about how stoch simul works if I put this command after doing Bayesian estimation. Ideally I would like stochastic simulation to use all the estimated parameters and perform the simulation to print theoretical moments and correlations. But I suspect, it does not do it. It basically takes the parameter values declared at the start of the mod file and ignores all the estimated parameters to do the stoch simul. Am I right?

I am attaching the mod file for your perusal.

PB
adj_cost4_est.mod (3.2 KB)

2

Hi,

No after the estimation command the parameter values are updated according to the inference. If you do not run a MCMC, the estimated parameters are updated to the posterior mode estimate. If you run a MCMC (mh_replic>0) the estimated parameters are updated to the posterior mean. If you find an example where this is not the case, it may be a bug on our side.

best,
Stéphane.

3

@pb2415 Note that this default behavior of setting the parameters to the estimated ones is also documented in the manual.

4

Hi Stephane,
Thank you for your email response to my query.
I attach a code and the datafile where stochastic simulation follows the Bayesian estimation and I see a major difference in variance decomposition results.

There is one more strange thing happening in this code which I can’t resolve. I have brought a variable iR which is fixed at irbar always. However, in variance decomposition, its variance is explained by two shocks. Since iR is a constant, its variance is zero by default. How come its variance is explained some shocks? This is very puzzling to me. I am using dynare 4.5.4…

PBboj_project_June21_Oct28_est.mod (11.5 KB)
. BoJ_Data_ready11v9inv2gov2IDclosed.xlsx (39.5 KB)

5

This seems to be numerical imprecision. You can see that iR is constant:

THEORETICAL MOMENTS
VARIABLE MEAN STD. DEV. VARIANCE
iR 0.0000 0.0000 0.0000

A general remark: your estimation results are wrong as you are not handling parameter dependence correctly. You can see that if you change

biglamda  = 1.02;     // balanced growth rate (new)

Then your steady state file will not work. See e.g.

6

Thank you for this comment. I am aware of this issue. However, I don’t quite see why parameter dependence is an issue here. In fact the model has a steady state at biglamda=1.02. No obvious problem is detected in model diagnostics.

The problem only occurs at the estimation level. I am setting the prior in such a way that biglamda is plausible. This is based on Japanese data and biglanda=1.02 may be too high. Thus I don’t see what is really the issue here.

STEADY-STATE RESULTS:

m 0.951557
iL 0.0509091
k 20.635
h 1.75179
y 4.22659
c 2.31622
i 0.910368
d 1.04818
mR 0.994868
mT 0.760232
mRprop 0.566844
mm 1.03037
S 15.1376
pii 0.02
Q 1
realW 1.15811
Adj 0
Adjprime 0
P_Pw 1.33333
A 1
div 0.10784
Debt 9.82259
ytd 1.05091
Rytd 1.0303
hpr 1.05091
rhpr 1.0303
rk 0.030303
bg 0.648886
G 1
T 0.991378
lamda 0.4
Zx 1
ip 0.001
ytm2 0.0296556
Sr 22
tp 0.0198026
nytm 0.0496556
mR_d 0.949142
log_y 1.44139
log_c 0.839936
log_i -0.0939066
log_G 0
log_mR -0.0051453
log_mT -0.274131
log_d 0.0470518
log_h 0.560637
log_Q 0
log_S 2.71718
log_k 3.02699
mbgrate 1.02
y_obs 0
i_obs 0
G_obs 0
c_obs 0
mR_obs 0
mT_obs 0
d_obs 0
h_obs 0
k_obs 0
Q_obs 0
S_obs 0
MODEL_DIAGNOSTICS: No obvious problems with this mod-file were detected.

I will be grateful if you please elaborate a bit on this.

7

You define as independent parameters

bettastar = betta/biglamda;    // new
Omega   = (((1-bettastar*(1-deltak))/(alpha*bettastar*Abar*biglamda^-alpha ))* (eps_Y/(eps_Y-1) ) ) ^ (1/(alpha-1));

which both depend on biglamda. For the first run with biglamda=1.02, everything works fine. But in estimation, the prior mean is biglamda=1.01. As the two composite parameters above are not updated to reflect the new value for biglamda, you get an error message.

8

Many many thanks. You are absolutely right! I am now keeping biglamda outside the estimation loop. It is a growth rate. I am setting this beforehand.

9

No, you should move the two composite objects into the model block as model-local variables, because you will have the same issue with eps_Y.

10

You are brilliant! I see your point. Thank you.

11

@pb2415 Note that a bug has been found in Dynare 4.5 that can explain your variance decomposition findings: https://git.dynare.org/Dynare/dynare/merge_requests/1627

12

Thanks for this. I don’t know how to merge this. I am using dynare 4.5.2.

I think I will bypass the MCMC by setting mh_replic to zero and only use mode compute and then put stochastic simulation right below it. I believe that I will then get VD based on stochastic simulation using the posterior mode estimates. This should be bug free. Am I right?

Best.

PB

13

Yes, that should work. But I hope we can get a fixed version 4.5.7 out this or next week.