Two m files and two mod files

[HelloDynare]

@jpfeifer

It is not clear that the Ramsey steady state is unique, i.e. you may approximate around a wrong point. Using RamSOE.mod (5.2 KB) yielded
-163.345 for Ramsey.

Dynare finds the result more quickly than a two-instrument version of RamseySOE, so we didn’t notice the uniqueness. However, in the two-instrument version, we indeed realized it, very sensitive to our initval guess. So here is my question:

Optimal policy parameters in a non-linear model

The cmaes optimizer seems to work pretty well in practice, but it takes quite long to run. You would need something along the lines of %set CMAES options H0=0.2*ones(size(x_start,1),1) cmaesOptions = options_.cmaes; cmaesOptions.LBounds = [-1000;-1000]; cmaesOptions.UBounds = [1000;1000]; [x_opt_hat, fhat, COUNTEVAL, STOPFLAG, OUT, BESTEVER] = cmaes('welfare_objective',x_start,H0,cmaesOptions,x_opt_name); x_opt_hat=BESTEVER.x;

Will CMAES be helpful in Ramsey problem?
(I plan to substitute CMAES for fminsearch function)

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Besides, your reply gives me the impression that the upper bound of the welfare of OSR-SOE, by deliberately choosing Taylor parameters, can dominate the lower bound of the welfare of Ramsey-SOE, by arbitrarily guessing initial values. Is it true?

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I’m in no hurry

[jpfeifer]

1. It’s not that Welfare is wrongly simulated. The problem is that when using Ramsey in Dynare, you cannot enter a recursive definition of welfare in the mod-file as it will create a singularity. That’s why there is a separate function to evaluate the planner objective. For that reason, simult_ will not be helpful unless you use it to integrate out future shocks using simulations. My hunch is that this will be infeasible.
2. CMAES will not help. It’s not about your optimizer in the steady state file converging to something only locally optimal. It’s about Dynare’s routines internally converging to a local optimum. As of right now, there is no way to change this other than trying different initial conditions. But even with a global optimizer, that would be someone should do to make sure results are not driven by initial conditions.
3. Yes, Taylor can dominate the lower bound of Ramsey results. One of the theoretical reasons can be that we do not check second order conditions. So you may end up approximating around a local minimum instead of a maximum. But there are no general results available for this. If you have multiplicity, quite often anything goes.