Estimation with mode_compute only and model comparison

Estimation ML/Bayesian estimation
1

Dear all, I would kindly ask two conceptual questions about estimation.

i) I use the estimation command with mode_compute option to compute the mode with uniform priors for all parameters (large intervals). Then I use the mode results to simulate the model. From my perspective, this appears to be straight up equivalent to maximum likelihood estimation, right ?

ii) Let’s say I have 3 models M = 1, 2, 3 estimated by ML and with the respective likelihood p^M(y_T / \theta_M ), where \theta_M is the estimated parameter vector obtained. I would like to choose only one model to work with. From the Bayesian point of view, we could choose based on marginal likelihood. But from the “ML” process above, since I do not have any complex priors, choosing the one with highest likelihood p^M(y_T / \theta_M ) is enough?

Thanks in advance !

2
  1. Yes, that is equivalent to ML.
  2. No, frequentist comparisons based on the likelihood are only valid for nested models (likelihood ratio tests). For non-nested models you have to use Bayesian model comparison using the marginal data density. Also note that implicit prior truncation due to e.g. Blanchard-Kahn violations may affect comparisons even for “simple” priors.
3

Thanks for your response, professor.

I noticed that, accordingly to the manual, the output

oo_.MarginalDensity.LaplaceApproximation

Is produced after the estimation command, even with mh_replic = 0. It is enough to compare this statistic between the models?

4

See

5

Perfect, so we do not need metropolis for the laplace approximation algorithm. I’ll work with that.

As always, many thanks for your availability Professor !