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)

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

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.

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?

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).

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