Welfare in Ramsey lower than under simple rule

Optimal Policy
1

Good afternoon,

I have a related conceptual problem when comparing optimal policy and optimal simple rules. In both cases, I use dynare but I do not use OSR or the Ramsey procedure in dynare. Instead:

  1. For simple rules, I put the nonlinear model and the expression for representative household welfare into the model file and then evaluate the entire model to second order for different policy rule parameters. To get welfare:
[~, info, M_temp, oo_temp] = resol(0, M_temp, options_, oo_temp);
WELF    = oo_temp.mean(WELF_pos);

I then apply the formula for compensating consumption variation to get the CCV welfare gain relative to a “loose policy” baseline. I pick the best parameter combination.
3. For optimal policy, I use the same model file, including welfare, but of course excluding the monetary policy rule. I add the nonlinear Ramsey equations derived in matlab using the symbolic toolbox (the model is medium-sized). The deterministic steady states of the two models are the same. I evaluate welfare in the same way as under 1, using second-order approximation. I get one number for Ramsey.

Problem: Welfare under Ramsey optimal policy is slightly lower than under the best simple rules. Is this common? Is there a literature on this?

2

No, that is not common and, theoretically, should not happen. Occasionally it happens if the tolerance of the steady state solver is too high. In that case, virtually identical numbers may be represented differently.