Ramsey vs osr

Optimal Policy
1

Hi all,

I have the following problem/question.

Suppose that the central bank wants to minimize the volatility of inflation and consumption, i.e. the Loss Function is the sum of inflation and output variances.

I first run the Ramsey policy (see model_Ramsey.mod) where

planner_objective PI^2+C^2;
ramsey_policy(planner_discount=0.99);

and found that the Loss Function is 15.5275 (this is NOT the “Approximated value of planner objective function” reported by Dynare)

Then I run the same model with osr (actually I did a grid search for the coefficient in the Taylor rule, see model_osr.mod) and found that the Loss Function is 1.6949.

So the loss function under the Ramsey policy is bigger than the loss function obtained with an optimal Taylor rule, which is not what I expected to find (I used the same discount factor, 0.99).

Is there an explanation for this result?

Many thanks for your help

Best

Fabio
model_osr.mod (1.54 KB)
model_Ramsey.mod (1.19 KB)

2

I have an additional question. Why the Ramsey code does not work if I use

planner_objective PI^2+0.1*C^2;

?

What can I do in this case?

Thanks again

3

Are you discounting in both cases? Maybe in Ramsey you are computing a discounted sum of variances, in osr just the current one.

4

Dear experts,

I have donwloaded the codes but it gives the following errors, ı dont understand why.I would be thankful if you give an answer.Sincereley,

??? Undefined function or method ‘steadys’ for input arguments of type ‘double’.

Error in ==> model_osr at 118
[ZU,HU,RU,PIU,CU] = steadys(pitarget,beta,phi,tau,theta,psi);

Error in ==> dynare at 120
evalin(‘base’,fname) ;

5

I forgot to upload the file that computes the steady state
steadys.m (966 Bytes)

6

Dear Matteo,
I am discounting using the same discount factor, and I am computing the sum of the unconditional variances (as reported by Dynare)
Thanks