Comparing welfare - Ramsey vs Taylor rule

[zolnier]

Hello,

I have a quick question about the possibility to compare welfare that we get from a second order approximation with the planner objective value from a Ramsey policy.

In the case of a Taylor rule I have specified the welfare recursively as

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Welf = Util + \beta*Welf(+1)

From the output of Dynare I have understood that you could then either look at the stochastic steady state computed as

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  W_pos=strmatch('y',M_.endo_names,'exact');
oo_.dr.ys(W_pos)+0.5*oo_.dr.ghs2(oo_.dr.inv_order_var(W_pos))     

which is the Constant in the Policy and Transition Functions, or the theoretical mean found in

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oo_.mean

as the welfare mesures. My question is then, which one of these is comparable to the planner objective value that is reported when the initial Lagrange multipliers are set to steady state? As far as I've understood it is the first way of doing it, but that yields the odd result that welfare is superior in a world governed by a simple Taylor rule compared to the Ramsey policy which is why I ask this question.

Thank you in advance.

[jpfeifer]

The first one would be conditional welfare, i.e. the welfare being in steady state. The mean welfare in contrast would be unconditional welfare.
The output from Ramsey would be conditional welfare. However, an important difference is that Ramsey takes the shocks in period 0 as known. Therefore, the uncertainty correction only applies from period 1 onwards, while in your manual computation it would start at time 0. Put differently, the uncertainty correction only gets weight beta instead of 1.
You may want to look into

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evaluate_planner_objective.m

[zolnier]

Thank you for your reply Prof. Pfeifer.

Then it was as I suspected with the conditional welfare.

If I have understood the code in

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evaluate_planner_objective.m

correctly then it is line 74 that is of interest

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Wss = beta*Wuu*M.Sigma_e(:)/(1-beta);

and the solution would be to either remove the \beta from this line or to add \beta to my manual computation for a proper comparison to be made.

(The odd welfare ranking was an unrelated problem that has been solved.)

[jpfeifer]

Yes, that is the line and the solution you suggest also seems correct. I am glad you solved the issue with the welfare ranking.

[zolnier]

Then all is well in the world. Thank you very much for the help professor.