Dear Dynare users,
I have some questions regarding optimal policy computation in Dynare:
- Is it possible to compute optimal policy under commitment in a timeless perspective in Dynare? If yes, how? If I’m right the ramsey_policy command gives us optimal policy which is time inconsistent.
- I tried to compute optimal policy using the command ramsey_policy. The model I use is linear - variables are expressed as percentage deviations from ss. The objective function I use is: y^2 + lambda*pi^2 with discount factor equal 1.
The procedure works well, but in the end I get the following results:
Approximated value of planner objective function
- with initial Lagrange multipliers set to 0: NaN
- with initial Lagrange multipliers set to steady state: NaN
What does it mean? Is there any problem?
- Is there any way to compare the welfare losses achieved under optimal policy (ramsey_policy command with objective function y^2 + lambdapi^2 and discount factor equal 1) and under optimal simple rule (osr command with objective function var(y)+ lambdavar(pi))?
In the following paper (see page 18, Table1)
authors simply read the variances and insert them into loss function, say var(y)+ lambda*var(pi), and compare the results? Is it correct?
Thank you in advance for all your answers.
could you please clarify what kind of welfare analysis can I generally perform with a log-linearized model? Since the model is linear I cannot do second order approximation, but can I calculate optimal Ramsey policy then?
In general, this is only possible if you are working with a model that has a non-distorted steady state, i.e. where due to (close to) optimality the second order terms evaluate to 0. Please take a look at e.g. Woodford 2002 - Inflation Stabilization and Welfare.
Dear Mr Pfeifer,
I’m also interested in computing optimal policy using the command ramsey_policy in Dynare.
Let me give a concrete example. Suppose we use a well-known DSGE model developed by Adolfson et al. 2007: Bayesian estimation of an open economy DSGE model with incomplete pass-through.
The features of this model are the following:
- model is log-linearized - variables are expressed as percentage deviations from SS, that is x_hat for a generic variable x
- in SS x_hat =0 (by definition)
My objective function is linear-quadratic of the following form: L = lambda*y_hat^2 + pi_hat^2.
My question is: can I use the command ramsey_policy in the context of this model (i.e. Adolfson et al. 2007)?
My understanding is that this is not possible. The optimal policy depends on some cross-derivatives that would be absent due to the model already being linear. As far as I remember, their model has a distorted steady state so that the naive linear quadratic approach you are trying will result in wrong results.
a related question - is it also not possible to use osr in such a model?
That is possible, but not Ramsey.