Help about ramsey policy

[JeanPaul]

Hello all,

I've been running a ramsey policy program where the planner objective is a quadratic loss function of the central bank. The aim is to collect the pairs of variances of inflation and output for each value of the policy's preference parameter (lambda) in order to draw the taylor efficience curve.
The program run, but what seems weird is that whenever I change the value of the policy preference in the planner objective function (lambda lies from 0:0.5:1) I still get the same values for the inflation and output variances and the same reaction function (optimal policy).
Secondly, when I tried to run the model with lambda=10.00, the program run and give the same results. which possible value the parameter lambda does lie according to my planner objective function?

What can I do to get variances and the policy function which change to each value of lambda.
I'm using dynare 4.1.
thanks for your help !

Here is my code :

close all
%----------------------------------------------------------------
% 1. Defining variables
%----------------------------------------------------------------

var x inflation R;

varexo eps_x eps_infl eps_R;

parameters beta lambda delta alpha phi kappa rho_infl rho_x;
% sigma_eps_x sigma_eps_infl sigma_eps_R;

%----------------------------------------------------------------
% 2. Calibration
%----------------------------------------------------------------

beta = 0.99;
delta = 0.492;
alpha = 0.60;
phi = 0.019;
kappa = 0.021;
rho_infl = 1.519;
rho_x = 0.633;
%sigma_eps_x = sqrt(0.21);
%sigma_eps_infl = sqrt(1.16);
%sigma_eps_R = sqrt(0.24);
lambda = 0.50;


%----------------------------------------------------------------
% 3. Model
%----------------------------------------------------------------

model (linear);
x = (1-delta)*x(-1)+ (1-delta)*x(+1)-phi*(R-inflation(+1))+eps_x;
inflation = (1-alpha)*inflation(-1)+ alpha*inflation(+1)+kappa*x+eps_infl;
R = rho_infl*inflation+rho_x*x+eps_R;
end;

%----------------------------------------------------------------
% 4. Defining chocs
%----------------------------------------------------------------

shocks;

var eps_x; stderr 0.366;
var eps_infl; stderr 0.384;
var eps_R; stderr 5.814;
end;

planner_objective (1-lambda)*inflation^2 + lambda*x^2;

ramsey_policy(planner_discount=0.99);

[AssiaEzzeroug]

Hi

you didn't comment out the interest rate rule. I tried to run the ramsey with different values for lambda (0.5, 0.7)and then get different results. The variances and decision rule are reported in output (respectively in "theoritical moments" and "policy and transition functions sections)

Best

[JeanPaul]

Hi,

tks for your help. but how can I do to comment out the interest rate rule? Do I have to remove it from the model equations or set it with backward variables of inflation and output, plus all shocks.
Also, the discount factor in OSR is it 0.99 or 0.95. If it is 0.95 what can I do if I want to perform OSR with beta=0.99.
All the best,

[MichelJuillard]

1) When using ramsey_policy, you should not write the equation setting interest rate in the model block. It is the optimization procedure that determines its form. It is the only case where a model block should have less equations than endogenous variables.
2) Currently OSR minimizes the weighted sum of variances. This objective function is consistent with a discount factor tending towards 1.0

Best

Michel