# Welfare after discretionary_policy

Dear Dynare team,

I am interested in obtaining welfare associated with discretionary monetary policy. The model I am using has an efficient steady-state. My understanding is that using the Dennis (2007) LQ approach is therefore in principal valid, avoiding spurious welfare ranking (Kim and Kim, 2003).

So I was planning to use discretionary_policy on a linearized verison of the model, where the planner objective is something like pi^2 + lambda*x^2, where pi is inflation, x is the output gap and lambda is a weight.

Now, I want to find welfare associated to discretionary policy with that particular quadratic planner objective. Including welfare recursively in the model is not possible, however, because discretionary_policy requires a purely linear model.

Is there a way how I can back out welfare after solving the model? I was thinking of simulating the model using periods = large number, backing out the levels of consumption and labor using their steady state (which I know) and then computing household utility each period. But I am not quite sure how to get from there to welfare.

Are you interested in conditional or unconditional welfare? You could approximate the utility function quadratically and then plug in for the required mean and (co)-variances from the theoretical moments provided by the `discretionary_policy` command

Thank you for your quick reply. At this stage, I am largely indifferent between the two welfare concepts and could work with what is feasible. So if I understand you correctly, I should do something similar to Welfare cost of business cycles?

In terms of theoretical moments: If I am not mistaken they are going to be zero for all log-linearized variables in any case, providing me no information. So should I instead use the periods = large number simulation to approximate the theoretical moments?

Only the first moments will be 0. The variances will not be 0. If your objective is purely quadratic, only these variances will matter and you can use theoretical moments.

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Thank you. You are right of course - I did not think this through carefully. And just to be 100% sure: This corresponds to unconditional welfare, correct?

There is no general answer here as it depends on the objective function. But usually, as you are relying on unconditional second moments you will get a measure that is related to unconditional welfare.

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