Log likelihood of initial point is reasonable in first-order but not in second-order

Estimation ML/Bayesian estimation
1

Hi Johannes,

I was switching my first-order estimation to second-order, and by setting mode_compute=0 and mode_file = xxx_mode I believe I’m using the same initial point. While in the first-order estimation, the (minus) loglikelihood was evaluated as a finite value (some value around 500), the second-order one yields a huge minus loglikelihood (with several thousand particle filters, I believe), which essentially means the first-order guess is a complete failure. I was wondering how to fix that issue, and whether there’s anything I’m missing? I already set all the pruning options to be 1.
Thanks a lot!

2

I would need to see the files. Can it be due to the measurement error specification?

3

I specify the same measurement error though.
Let me provide the mode file, the dynare mod and the data here. Thanks!

base_est.mod (13.7 KB)
base_est_mode.mat (675 Bytes)
data.csv (16.3 KB)

4

Using

temp=load('base_est_mode');
M_ = set_all_parameters(temp.xparam1,estim_params_,M_);

stoch_simul(order=1) inflation FFR realWageGrowth realGDPGrowth HoursPerCapita inverseInvestmentPriceGrowth;
stoch_simul(order=2) inflation FFR realWageGrowth realGDPGrowth HoursPerCapita inverseInvestmentPriceGrowth;

shows that at first order

THEORETICAL MOMENTS
VARIABLE                             MEAN  STD. DEV.   VARIANCE
inflation                          0.0101     0.7447     0.5546
FFR                                0.0166     3.6130    13.0539
realWageGrowth                    -5.4621    12.8128   164.1683
realGDPGrowth                     -5.4621    26.2434   688.7182
HoursPerCapita                    -1.7059    24.3213   591.5246
inverseInvestmentPriceGrowth      -0.0046     2.9547     8.7304

and at second order

APPROXIMATED THEORETICAL MOMENTS
VARIABLE                             MEAN  STD. DEV.   VARIANCE
inflation                        -39.3546     0.7447     0.5546
FFR                              -77.3680     3.6130    13.0539
realWageGrowth                  -117.3884    12.8128   164.1683
realGDPGrowth                    544.9635    26.2434   688.7182
HoursPerCapita                   405.8434    24.3213   591.5246
inverseInvestmentPriceGrowth      -0.0046     2.9547     8.7304

Both seems pretty far off from the actual data used. But given the high volatility in the model, the nonlinearities kicking in at order=2 are huge, explaining the difference.

5

I see, yes, indeed the volatility should be one magnitude lower than what I have here. Then there’s another issue coming up: I cannot really set those initial points of shocks close to 0 as Dynare somehow exports some error, even though I’m using inv_gamma distributions.

6

Ah, nvm, I think I found a critical issue in the mod file I provided. Stupid me.
Thanks a lot for your help! It actually helped me debugging the mod file.

7

You used a prior as in Smets/Wouters, but there the data was multiplied by 100. That is not easily feasible with higher order approximations.

8

No, that data multiplication was intended. My mistake was taking an exponential of the shock variances which I shouldn’t. Therefore the variance indeed explode, and I didn’t catch that error because I was checking the behavior of the first-order solutions – you know, those shock variances don’t matter in that case.
Many thanks for your help!