Comparing welfare - Ramsey vs Taylor rule

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Comparing welfare - Ramsey vs Taylor rule

Postby zolnier » Fri May 05, 2017 8:49 pm

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
Code: Select all
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
Code: Select all
  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
Code: Select all
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.
zolnier
 
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Joined: Wed Feb 22, 2017 10:22 am

Re: Comparing welfare - Ramsey vs Taylor rule

Postby jpfeifer » Mon May 08, 2017 10:02 am

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
Code: Select all
evaluate_planner_objective.m
------------
Johannes Pfeifer
University of Cologne
https://sites.google.com/site/pfeiferecon/
jpfeifer
 
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Location: Cologne, Germany

Re: Comparing welfare - Ramsey vs Taylor rule

Postby zolnier » Tue May 09, 2017 7:37 pm

Thank you for your reply Prof. Pfeifer.

Then it was as I suspected with the conditional welfare.

If I have understood the code in
Code: Select all
evaluate_planner_objective.m

correctly then it is line 74 that is of interest
Code: Select all
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.)
zolnier
 
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Joined: Wed Feb 22, 2017 10:22 am

Re: Comparing welfare - Ramsey vs Taylor rule

Postby jpfeifer » Wed May 10, 2017 1:50 pm

Yes, that is the line and the solution you suggest also seems correct. I am glad you solved the issue with the welfare ranking.
------------
Johannes Pfeifer
University of Cologne
https://sites.google.com/site/pfeiferecon/
jpfeifer
 
Posts: 6940
Joined: Sun Feb 21, 2010 4:02 pm
Location: Cologne, Germany

Re: Comparing welfare - Ramsey vs Taylor rule

Postby zolnier » Thu May 11, 2017 2:34 pm

Then all is well in the world. Thank you very much for the help professor.
zolnier
 
Posts: 6
Joined: Wed Feb 22, 2017 10:22 am


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