Question for jpeifer: Optimal Policy under Committement

[Ana]

Dear jpeifer,

I have got conflicting answers throughout this board on the first question and the second is related. I would very much appreciate your clarification:

1. Some documentation says that Ramsey Optimal Policy can be done in a linearized model entered into Dynare (with y^2 + pi^2 as the objective function instead of u(c,l): http://www.dynare.org/DynareWiki/OptimalPolicy and viewtopic.php?f=1&t=3948

But you have said before that the model should be non-linear - this is because the problems calls for a second-order Taylor approximation instead of first. Here one can enter u(c,l) and non-linear constraints and Dynare will take the 2-order TA.

- So, can you clarify if the objective function: y^2 + pi^2 in a linear Dynare model can also be used to give Ramsey optimal policy predictions (as compared to the objective function u(c,l) in a non-linear model)? This seems to be claimed in the documentation linked to.

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2. The following code, entered into Dynare ++ (open economy New Keynesian model with two sectors demanding labour) does not work. This is another attempt to compute Ramsey policy. Is it a problem with the syntax or a more structural issue? Is there an example .mod Dynare++ file for an open economy that you can provide.

Thank you!
Ana

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var Y NY C Q CH N NR prf;

varexo eps_prf ;

parameters alpha alphaR phi rho beta ;

alpha = 0.4 ;
alphaR = 0.4 ;
phi = 3 ;
who = 0.8 ;
beta = 0.99 ;

planner_objective Ln(C) + N^(1-phi)/(1-phi);

planner_discount beta;

model;
C = Q ;
N = NR + NY ;
NR = (1-alphaR)*prf*Q^(1/*1-alpha)) ;
NY = Y ;
Y = CH ;
CH = (1-alpha)*C*Q^(1/*1-alpha)) ;
prf = rho*prf(-1) + eps_prf ;
end;

initval;
prf = 0 ;
NR = 0 ;
Q = 1;
C = 1;
CH = (1-alpha) ;
Y = (1-alpha) ;
NY = (1-alpha) ;
N = (1-alpha) ;

order = 2;
vcov = [
0.01
];

[jpfeifer]

1. There can be cases where a naive linear quadratic problem gives correct results. As shown in Woodford (2002), this is the case if the steady state is undistorted. The example you linked to is one of these cases. But in general, you should not do this.
2. What is the problem? Please provide an error message.