Discretionary_policy and first order conditions give different results

Hello everyone,

I have set up a simple New Keynesian model (mod file attached) where the policy maker’s loss contains interest rate volatility (weight = \lambda_{R}). I have solved the model by

  • using discretionary_policy
    and
  • combining the first order conditions and running stoch_simul
    For low values of \lambda_{R} the results are identical, as one would expect. However, as soon as this weight begins to rise (e.g., to 0.5) I obtain indeterminacy when solving stoch_simul but not when using discretionary_policy.
    Moreover, I’ve tested it using Klein’s solab.m and it also results in indeterminacy.
    Given that we have an analytical expression for policy under this simple model the two solution methods should yield identical results. Is this a bug in discretionary_policy?

Thank you.
NK_omp_R_volatility_forum.mod (1.0 KB)

Can you please elaborate on the setup so that I can check the analytical part.

Sorry about that. A short pdf setting up the model and resulting equilibrium equations is attached (do let me know if anything is unclear).
Thank you.
OMP with R in loss function.pdf (149.7 KB)

Thanks. That clarifies it. My hunch is that the solution technique by Dennis (2007) by construction rules out non-fundamental solutiond, while stoch_simul will check whether such solutions may exist.

Thank you for that. I struggled to understand the reason for the discrepancy.