Ramsey optimal policy with uncertainty shocks

Optimal Policy
1

Dear all,
I added Ramsey optimal policy to uncertainty shock model in Dynare 5.0. I would like to compute the conditional steady state welfare.
But I found, the conditional welfare with order=3 is equal to order=2,So I have two questions about Ramsey policy:

  1. Can dynare calculate the welfare under uncertainty shock when order=3?
  2. If dynare could calculate the ramsey welfare, do I need a pretty high approximation order(order=4) in dynare++ to calculate the welfare?
2

I would need to see the file to check what is going on.

3

Thanks for you reply, Prof. Pfeifer.
I send the file to you through message.

4

Have you tried what happens if close the model with a policy rule and compute welfare at order 2 and 3?

5

Thanks for your reply, Prof. Pfeifer.
If the model with baseline Taylor rule, the welfare with order=3 is equal to order=2,
but the equation of calculating welfare is written as you teach:

Y3 = simult_(M_,options_,oo_.dr.ys,oo_.dr,zeros(1,M_.exo_nbr),options_.order); 
Welfare=Y3(utility_pos,2)

And I introduce the welfare formula into your Basu_Bundick_2017, the welfare value order=3 is also equal to order=2.

6

This suggests that it’s not a computational problem in Dynare, but rather something economic. It might indeed be true that uncertainty shocks only matter for conditional welfare at an order higher than 3.