# Optimal monetary policy

Dear all,

I have a question about the optimal monetary rule. I know that Dynare compute Ramsey policy and optimal simple rule. I want to reproduce results in this paper ( search and matching frictions and optimal monetary policy, Thomas (2008)). The author talk about a LQ approach that requires obtaining a second-order approximation of the representative households’ welfare criterion:
1/ is that possible to use Ramsey policy with this kind of welfare? is that possible to do this with a non-linearized model? I can’t find example for dynare’s codes with LQ approach.

Thank you!

Clara.

If you use Dynare’s Ramsey command with order=1, Dynare will do a first order approximation to the Lagrangian of the Ramsey planner and a quadratic approximation to the planner objective. That should correspond to the LQ approach in the Thomas paper. However, I could not identify whether Thomas does Ramsey from the timeless perspective or what Woodford calls t_0 optimal policy, i.e. where the initial Lagrange multiplier is 0.

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Dear Mr Pfeifer,

I found this in another paper ( The analysis in Thomas (2008), for example, is also from the timeless perspective, as are dynamics results from all Ramsey monetary models
descending from Lucas and Stokey (1983) and CCK of which we are aware). How would this affect your suggestion in the above message? Can I do the ramsey method that corresond to LQ from a non-loglinearized model?

Thank you!

Clara

Sorry, but what exactly is your new question?

Dear Mr Pfeifer,

1. Do I need to have a log-linearized model to compute Ramesy policy (command with order 1)?
2)Thomas (2008) does Ramsey from the timeless perspective, If I use Dynare’s Ramsey command with order=1, That should correspond to the LQ approach in his paper?

Thank you !

Clara

1. No, you do not need a log-linearized model. The order=1 will take care of that
2. Yes, that should be the case

Dear Mr Pfeifer,

I try to use Dynare’s Ramsey command with order=1, I get the following error massage. The model runs and gives me the steady state if I do not add the ramsey command.
Is there any problem with my model?

Error using print_info (line 42)
Blanchard Kahn conditions are not satisfied: no stable equilibrium
Error in stoch_simul (line 98)
print_info(info, options_.noprint, options_);
Error in ramsey_policy (line 25)
info = stoch_simul(var_list);
Error in clara_ramsey_test (line 633)
ramsey_policy(var_list_);
Error in dynare (line 180)
evalin(‘base’,fname) ;
Error in exucte_clara_ramsey (line 125)
dynare clara_ramsey_test

Thank you!

Clara

The problem is that there can be multiple steady states with Ramsey. By choosing the nominal interest rate, the planner is also determining the steady state inflation rate. It might be that the solver currently ends up at a steady state where indeterminacy arises. You should try to provide a conditional steady state file and then vary the initial value of the instrument to try finding other potential steady states. See the lasts posts in the thread [Ramsey Policy)

Dear Mr Pfeifer,

1. In last post you asked me to use a conditional steady state file,Q1: what does this mean? is it having the steady_state_model block in the same mod.file, fix r=1 in initval and try to use the find_m file?

2. I run the example on dynare about ramsey:

var pai, c, n, r, a;
varexo u;
parameters beta, rho, epsilon, omega, phi, gamma;

beta=0.99;
gamma=3;
omega=17;
epsilon=8;
phi=1;
rho=0.95;

model;
a = rhoa(-1)+u;
1/c = beta
r/(c(+1)pai(+1));
pai
(pai-1)/c = betapai(+1)(pai(+1)-1)/c(+1)+epsilonphin^(gamma+1)/omega -exp(a)n(epsilon-1)/(omega*c);
exp(a)n = c+(omega/2)(pai-1)^2;
end;

initval;
r=1;
end;

a = 0;
pai = betar;
c = find_c(0.96,pai,beta,epsilon,phi,gamma,omega);
n = c+(omega/2)
(pai-1)^2;
end;

Q2: Why variables in the model block come without exp(.)?

1. I want to calculate the welfare cost (loss) of going from 0 to 4 percent infation in term of consumption ( steady state and the mean). I used the ramsey command and my model run but I don’t know if results make sens. My question:

Q3: where can I found results about the welfare loss?
Have I to comapre:
Approximated value of planner objective function
- with initial Lagrange multipliers set to 0: 739.539
- with initial Lagrange multipliers set to steady state: 766.4222

under inflation =0% and =4% and the diffrence between the two is my welafre loss?

Thank you a lot

Clara
excute_clara_ramsey_nash.m (2.59 KB)
Clara_ramsey_nash.mod (5.34 KB)

1. Yes, it means taking the value for r specified in initval as given and then analytically compute the steady state based on this value for r. You can to this within a steady_state_model-block or in a separate steady_state-file

2. Because this model was solved in levels, not in log-levels. Therefore, no exp()-substitution was done

3. Yes, usually you would compare the planner objective with initial Lagrange multipliers set to steady state under the different policies (assuming the present discounted value of the planner objective is your welfare measure)