Estmation in deterministic model

Estimation ML/Bayesian estimation
#1

Hi, I wonder whether Dnyare can do the estimation of exogenous shocks (declared in exovar in mod file) in a deterministic model? Is it possible to use MLE for a deterministic model? If so, is there any example code available? Thanks in advance!

For instance, I first declare the shock values in the parameter block and call them in the shock block.

varobs c;
…
exovar z ; // productivity
parameters; z1 z2 z3;
…
shocks;
var z
period 1:3;
values z1 z2 z3;
end;
…

#2

In order to be able to write down a (non-degenerate) likelihood function, the model must feature stochastics. That is not the case in a deterministic model (at least not in the usual sense). You cannot find the “most likely shock”. What sometimes can be done is to invert the model. If there is a one-to-one mapping between observables and shocks, you can infer the exact shock sequence giving rise to the observables (as there is only one such sequence)

#3

Dear Prof.:

Thanks for your reply! I see what you mean. May I bother you with one more question?

Is it possible for ‘lmmcp’ to compute the deterministic model with downward nominal wage rigidity? Coz I want to generate unemployment in my model. In particular, I set:

W_t >= W_t-1 x (1-delta), (each time revise the wage down by delta only)
l_t <= l_bar (l_bar is total labor supply)

I wonder whether including a slackness condition ( W_t - W_t-1 x (1-delta)) x ( l_t - l_bar ) = 0 can help with the computation here.

I get this idea from your code for SIR model, where you mentioned a slackness condition is imposed to present infection number to be negative.

https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Stock_SIR_2020/Stock_SIR_2020.mod

If not working, how about re-setting W_t >= W_bar x (1-delta) (W_bar is constant)?

Thanks very much in advance!

#4

Here is a DNWR example from my own work: BDMP_DNWR.mod (2.7 KB)

1 Like
#5

Hi Prof.:

The sample code is most helpful. Thanks so much!

Regarding your previous suggestion, i.e. infer exact shock from observables in a deterministic model, what comes to my mind is using ‘fminsearch’ with each iteration calling dynare to compute the path. Is there any dynare built-in tool to do so?

I noticed ‘modeqs.mod’ can do variable flipping for steady state and wonder whether any similar function can be applied to transition path?

Thanks so much again!

#6
  1. No, there is not tool to do this in perfect foresight.
  2. You actually don’t need to loop over Dynare, just over the underlying routines. I.e. you miminize over setting oo_.exo_simul and then running perfect_foresight_solver.