Optimal simple rule

Dear Michel,

I have repeatedly used the optimal simple rule (osr) routine in linearized NNS models with a loss function over inflation and output.

Dealing with non-linear models now raises some questions, and I am not sure whether I have properly understood the manual on these issues.

I am looking for the optimal simple policy under a standard utility function, where

W (wealth) is the discounted sum of period utility, and

U = U© – d*U(N)

is period utility as the sum of consumption utility U© and the weighted (d) disutility of labour U(N).

As I understood

x a; pie b;

minimizes the LOSS function L = ax^2 + bpie^2.


  1. Maximizing WELFARE should be written as MINIMIZING the inverse of the welfare measure (or the deviation from flexprice or steady state welfare)?

  2. Does osr focus on welfare as the discounted sum of period utility, or does it look at period utility and discounts it itself? Put differently, should I use W or U in the optim_weights expression?

  3. Supposed that I use U instead of W, the weights in optim_weights may be expressed as either
    U 1; (i.e. using period utility)
    U© 1; U(N) –d; (i.e. stating the two components of period utility separately)
    Is there any reason to prefer one version over the other?

Thanks a lot!


Dear Lukas

OSR will only work with quadratic objective. If you want another objective function, you need to write another version of osr_obj.m