Policy function approximations away from the deterministic SS

Stochastic simulations
1

I’m interested in computing an approximation to the policy function away from the deterministic steady state.

Dynare++ provides a way to do that using the –steps option discussed in Section 4.2 of the dynare++ manual. Since the regular version of dynare relies on dynare++ binaries, I was wondering whether it is possible to invoke that option in regular dynare somehow (I’m trying to avoid porting my regular dynare .mod file, which relies on a number features incompatible with ++…)?

If the answer is ‘no’ (as I fear), one alternative I’m considering (based on this thread) is to have dynare++ compute the fixed point of the decision rule corresponding to non-zero sigma, and then specify it in dynare’s steady_state_model block, with option nocheck selected. While in general I would not expect this to yield correct results (in line with the suggestion in the linked thread), the one case it could, in principle, work correctly is when it’s manually ‘fed’ a fixed point corresponding to non-zero sigma?

Thoughts / suggestions would be appreciated. Thanks in advance,
Pawel

ps. If I have a spare sec, I may compare the two (i.e. the dynare ‘hack’ and directly invoking dynare++) using a simple RBC model, in which case I will also post back the outcome.

2
  1. As you correctly guessed, that is not possible with Dynare.
  2. The risky steady state option may give you something similar.
  3. What exactly are you trying to do?
3

Thanks Johannes!

  1. Thanks for confirming.
  2. This is super helpful - I wasn’t aware that this had already been implemented (I think I understand what Michel did a bit better than Ondra’s multi-step procedure; either would be fine at this stage). Just to double check, to get this going do I need anything other than:

options_.risky_steadystate = 1;

  • And also, would you know whether there are there any restrictions - e.g. does this work at third order?
  1. Thanks for asking. I’m trying to port a continuous time model (by Adrian and Duarte) to discrete time. The original model has interesting properties related to risk (a negative relationship between the conditional mean and conditional volatility of GDP growth) which don’t survive the translation. I’m trying to figure out why (I’ve jacked up volatility to the max, with simulations borderline (un)stable already). Clearly, I could have messed something up in the process, but, that aside, one hypothesis is that a local approximation around the deterministic steady is the culprit. I could test that by using projection methods, but thought I’d first explore ‘lower cost’ possibilities first… The risky steady state option seemed like one worth looking into. Very open to alternative suggestions, of course :wink:

Thanks in advance!
Pawel

4
  1. I don’t think you need to do more.
  2. That command is still preliminary, so I don’t have much experience. @MichelJuillard should know more.
  3. I don’t know that paper. But usually, a regular third order perturbation should be sufficient to see effects of time-varying risk. The approximation at a different point typically helps you to get this at first order already. I would go back to the paper and check what you may need conceptually.
5

Many thanks - appreciated, and agreed 100% on 3.!

I’ll definitely look into this further (also because I’m also mildly curious how the results of the two available methods differ from each other). If I have anything of interest to report, I’ll post back here.

Thanks for the help and support,
Pawel