Ramsey Policy vs. Taylor rule

[louisvalentines]

Hello, professors. I have a problem about Ramsey Policy, I run the Ramsey Policy and get this results:

Approximated value of planner objective function
- with initial Lagrange multipliers set to 0: -278.7321
- with initial Lagrange multipliers set to steady state: -278.7449

And I run the baseline model ,and get second order approximation welfare :-278.5189764959624

And my question :is this result right? why the welfare loss in Ramsey is larger than Tayler rule?
ramsey.mod (8.1 KB)
baseline.mod (7.7 KB)

[jpfeifer]

It’s hard to tell.

1. The parameterization is slightly different across files.

2. You are using inconsistent approximation orders. You are comparing Ramsey at order=1 to a Taylor rule at order=2. This problem will hopefully be fixed soon in Dynare 4.7. Once Fixing the regression in behavior in evaluate_planner_objective (Ref: #1680) (!1923) · Merge requests · Dynare / dynare · GitLab has been merged, the attached file will return:

Approximated value of unconditional welfare: -278.76387262

Approximated value of conditional welfare:
- with initial Lagrange multipliers set to 0: -278.75349865
- with initial Lagrange multipliers set to steady state: -278.76365086

ramsey.mod (8.1 KB)

Unconditional welfare with the Taylor rule is -278.5202

[louisvalentines]

Thank you professor for your reply. Can I interpret this as Ramsey policy does not mean that it is always optimal. And choose Ramsey policy as object of comparison sometimes is inappropriate.

[jpfeifer]

No, fixing the inconsistencies, I get

welfare -278.5210

for the Taylor rule and

Approximated value of unconditional welfare: -278.42457509

for Ramsey. Thus, the latter yields higher welfare.
baseline.mod (7.7 KB)
Ramsey.mod (8.1 KB)

[louisvalentines]

Thanks a lot, professor, I get it.

[dypisgood]

Hi Professor,

I am running into the same problem, may I ask if this inconsistency problem is fixed in Dynare version 4.6.4? Thanks in advance!

Best,
Yunpeng

[HelloDynare]

Hi @dypisgood,

You may have a look at:

Dynare 4.7 open beta test phase

Dear users, we are close to releasing Dynare 4.7, which will bring many exciting new features and improvements. Work on the new release has been finished with the exception of some documentation around semi-structural models. At this stage, we would like to invite all users to thoroughly test the beta release candidate available at https://www.dynare.org/beta/ for bugs, compatibility issues, and regression behavior. A list of compatibility breaking features relative to version 4.6 can be found…

Wiki · Dynare / dynare · GitLab

[jpfeifer]

@HelloDynare is right. This was only introduced after 4.6.4.

[kofiemma]

@jpfeifer

welfare -278.5210 (baseline:taylor rule)
unconditional welfare: -278.42457509 (ramsey)

Could these numbers tell us how effective is the Taylor rule policy relative to the optimal policy? Thus, is -278.5210 close or far from -278.4245? Or maybe comparing policies using IRFs is better because at least the units on the y-axis of IRFs have meaning?

Like if Taylor rule IRFs are close to Optimal policy IRFs, then we can say Taylor rule policy is effective (relative to the optimal) given our model and calibrated/estimated parameters?

[jpfeifer]

Usually, you would compute consumption equivalents to have interpretable numbers.

[HelloDynare]

For example, you may have a look at the computation of \Delta^{con} in

Questions on Ramsey welfare in Dynare 4.7

Hello everyone, I would like to ask questions related with welfare calculation under the optimal policy. My computation basically follows this paper: Let me summarize the main steps: Suppose we have a separable utility function: W_t =\displaystyle \mathbb{E}_t\sum^{\infty}_{j=0}\beta^j\left[\frac{{C_{t+j}}^{1-\sigma}}{1-\sigma}-\chi \frac{{N_{t+j}}^{1+\phi}}{1+\phi}\right]. Specifically, in the baseline Competitive Equilibrium (CE) case, we define the conditional welfare: W^b_t = W^{Cb}_…

[kofiemma]

@HelloDynare

Δcon

Thanks! Δ^{con} is consumption equivalence here, right?

[kofiemma]

@jpfeifer

Usually, you would compute consumption equivalents to have interpretable numbers.

Thanks! Something like DSGE_mod/Born_Pfeifer_2018/Welfare/Born_Pfeifer_2018_welfare.mod at master · JohannesPfeifer/DSGE_mod · GitHub. Thus, comparing Taylor rule policy to Ramsey policy under commitment.

What about welfare losses expressed as a percentage of steady-state consumption? Something like
L=(1-par.upsilon)*0.5*(((1+par.varphi)/(1-par.alppha))*variance.y_gap+par.epsilon/par.lambda*variance.pi_h)/100;
This is interpretable?

In the case of Ramsey, maybe just replace y_gap with a welfare-relevant output gap (x).

[jpfeifer]

@kofiemma

welfare losses expressed as a percentage of steady-state consumption

are the typical consumption equivalent people are considering. But the loss function outlined above was analytically derived. It will be different for different models.