Optimal Monetary Policy with nonlinear loss function

[Beav]

Thank you so much, I will be doing that for sure.

I have a couple more query. I am sorry to ask you so many things, but you have been very helpful!


1) I was also thinking of trying to apply the extended path method to the model, to have an approximate result of what would happen if expectations were to be taken into account.

Even without the ZLB, I run into an error message when I try to simulate an exogenous cost-push shock, as follows

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%define natural rate shock
shocks;
% var r_nat;
% periods 1:6;
% values -1;
var u_cp; stderr 0.01;
end;

extended_path(periods=100,order=2);

In particular, the error is

Reference to non-existent field 'IntegrationAlgorithm'.
Error in setup_integration_nodes (line 4)
switch EpOptions.IntegrationAlgorithm
Error in extended_path_initialization (line 119)
[nodes,weights,nnodes] = setup_integration_nodes(DynareOptions.ep,pfm);
Error in extended_path (line 39)
[initialconditions, innovations, pfm, ep, verbosity, DynareOptions, DynareResults] = ...
Error in Model (line 183)
extended_path([], 100, [], options_, M_, oo_);
Error in dynare (line 223)
evalin('base',fname) ;

Is there any way in which you could provide me a reference where I could see how the extended path method is to be implemented in Dynare, e.g. some explanatory mod files? If they included the ZLB, then it would be even more awesome.

2) Do you think it would be possible to simulate the model stochastically with a cost-push shock via

Code: Select all

stoch_simul(periods=300, order=2)

, even though the model presents a nonlinear target function, in particular

Code: Select all

x_t=-k*(exp^(a*pi)-1)/a

? Clearly, without ZLB. I have done it and the model gets solved and changes for different parametrization of a, but I wanted to understand whether the results make sense.


Thanks you so much!

[jpfeifer]

1. We are still working on this part of the code. You should use the unstable version. Example files are at https://github.com/DynareTeam/dynare/tree/master/tests/ep
2. As long as your nonlinear function is differentiable, that should work. Even if it is not differentiable, you can still go for a penalty function approach. See the last post at http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=7882&p=23180#p23180

[Beav]

Thank you so much!

I have been trying to apply a penalty function approach lately, so as to implement the ZLB without the need of the max function in a stochastic context, but dynare seems to have some difficulty in finding the steady state. I have tried to lower the value of the variance of the shock, but I had no luck there.

Thank you so much again for all your help!