Dear Johannes,

Sorry, Johannes, this question is long…Hope you could have a look at your convenience.

I set up and estimate an indeterminate model with specified trend with permanent Tech, preference, sunspot and measurement error to output and investment, totally 5 shocks.

using growth rates of y c I h , totally 4 data. 5 shocks >4 observable variables to rule out stochastic singular.

I use mode_compute=6 several times to find the mode, until the log posterior does not change(but hessian matrix is still negative definite at mode if I run mode_compute=9 or 4 here). Then I run MCMC 4 MILLION draws and drop the first half as the burn-in.

I also use endogenous_prior command.

Results show:

[quote]parameters

prior mean post. mean 90% HPD interval prior pstdev

miu 1.400 1.4489 1.4479 1.4499 beta 0.0200

rhoz 0.500 0.9975 0.9958 0.9992 beta 0.2000

rhod 0.500 0.0033 0.0004 0.0061 beta 0.2000

standard deviation of shocks

prior mean post. mean 90% HPD interval prior pstdev

sunspot 0.001 0.0042 0.0039 0.0045 invg Inf

e_z 0.001 0.0632 0.0225 0.1114 invg Inf

e_d 0.001 0.0068 0.0064 0.0071 invg Inf

i_Me 0.004 0.0079 0.0079 0.0079 unif 0.0023

y_Me 0.002 0.0034 0.0034 0.0034 unif 0.0010[/quote]

rhoz is persistence of preference shock, while rhod is persistence of permanent technology shock. Measurement errors hit upper bound otherwise the variance decomposition would be too large.

**Please find attached posterior plots.**

This result has **very good model dynamics **compared to growth rates data(including std, autocorrelation coefficient , correlation with output growth rates) . However, the 90% HPD interval for e_z preference shock is **TOO WIDE** so that the posterior plot is almost a flat line, and std of e_z is very large compared with other shocks. I have never seen such problem before, do you have any advice on why this happens?

Many thanks in advance.

Huan

growthtrendredeem_PriorsAndPosteriors1.pdf (61.5 KB)