Welfare after discretionary_policy


#1

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.

Would appreciate your help, thanks in advance!


#2

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


#3

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?


#4

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.


#5

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?


#6

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.