Ramsey policy with flexible prices

Stochastic simulations
1

Hi Professor Pfeifer et al.,

I am trying to solve SGU monetary economy with flexible prices using a first order perturbation (Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. “Optimal fiscal and monetary policy under imperfect competition,” Journal of Macroeconomics, Elsevier, vol. 26(2), pages 183-209, June.). To do so, I use two different approaches which should be equivalent: 1) command ramsey_policy with the FONCs of the households 2) command stoch_simul with the FONCs of the planner. I attach the .mod file (stoch_simul is launched from the .m file calculating the steady state).

In each case, the model is not solved as the matrix of the static problem appears to be singular. The diagnostic points out to a colinear relationship between the FONCs with respect to debt and the FONC with respect to inflation. I suspect that price flexibility induces indeterminacy of the inflation path. However, I would have tought that with only risk-free debt, the inflation path becomes determinate. Any help about what can cause this issue would therefore be much appreciated.

PS: I wanted to upload the .mod files but it says that new users are not allowed to do so. Could you let me know how to overcome this?

Kind regards,
Charles de Beauffort

2
  1. There is no mod-file attached.
  2. In most of the 2004-2007 SGU optimal policy papers there is a fundamental indeterminacy that prevents Dynare from solving the model with its Ramsey command. The issue is that there is some form of (implicit) lump sum taxes available available and Ricardian equivalence holds. That mean, bonds and the lump-sum taxes are perfect substitutes and one cannot determine these values separately. That is why these SGU-papers fix the debt to GDP ratio to 60% and then compute the steady state conditional on that assumption.
3

Dear Prof. Pfeifer,

Thank you for your reply. I was aware from the indeterminacy problem which is recurrent in optimal fiscal policy literature. That is why I solve for the steady state in a separate .m file with a given value for hours worked ‘h’ (so I fix one of the variables but it could also be debt). Dynare find steady state results but the problem comes from the eigenvalues of the matrix which are close to zero. Why do I have this kind of collinearity even when I fix the steady state value of debt?

The files can be found here (since I cannot upload them on the forum):
https://we.tl/77SaD4YT25