Problems trying to compute Ramsey Policy

Optimal Policy
1

Hello everyone,

I am trying to compute Ramsey policy but I have to problems with this. First, the planner objective has habits on consumption so I need to run…

planner_objective((log(cons - hcons*cons(-1)) - lpsi*((lab^(1+vartheta))/(1+vartheta))));
ramsey_policy(planner_discount=0.99,order=1);

and I get the error:

ERROR: Leads and lags on variables are forbidden in ‘planner_objective’
Is there a way of introducing lags in the planner objective? If not, how can I get an equivalent function?

Second, does anyone know whether it is possible to compute ramsey policy in Dynare for a model that uses external funtions? When I change the objetive equation to avoid the lags problem and use this command

planner_objective((log(cons - hcons*cons) - lpsi*((lab^(1+vartheta))/(1+vartheta))));
ramsey_policy(planner_discount=0.99,order=1);

I get this new error:

ERROR: third order derivatives of external functions are not implemented

Thank you for your help!
M

2

Regarding the second error, I would need to see the file. Regarding the first issue: you can circumvent the problem by defining a lagged variable in the model:

cons_lag=cons(-1)
and then writing the objective as

planner_objective((log(cons - hcons*cons_lag) - lpsi*((lab^(1+vartheta))/(1+vartheta))));
3

Hello jpfeifer,

I attach here the mod-file.

MMwelfare2.mod (33.9 KB)

paramfileopenMPRUBOTH.mat (8.8 KB)

Thank you very much

4

This is a limitation of Dynare, see https://git.dynare.org/Dynare/dynare/issues/300
You are calling external functions and for this optimal policy problem, the third derivatives would be required.

5

Ok. So the only way would be then to compute the third derivatives by hand and then indicate to dynare in some way which they are, right? or is there an alternative?

6

As far as I can see, there is no reason to use external functions. You can use Dynare’s builtin function for the Gaussian PDF and CDF, e.g.:

Fwbar = log(normcdf(omega,-(1/2)*(sig^2),sig));
Fwbarw = log(normpdf(omega,-(1/2)*(sig^2),sig));