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Hello,

I am trying to calculate how welfare changes over time in a simple 3 equation new keynesian model, and I am trying to obtain an impulse-response plot for this. Is it appropriate to linearise the utility function around the steady state an then put it in a recursive form as below;

V = (1-beta)*U + beta*V(+1);

where U is the linearised utility function.

Please suggest how else I can approach this if the above is incorrect.

Thank you very much.

Anup

Yes, you can do this, but the usual disclaimer on approximation orders for welfare apply. I also don't understand where the

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 (1-beta)

comes from. Usually the recursive form is

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V = U + beta*V(+1);

Thank you very much Prof. Pfeifer. The (1-beta) is from the infinite sum of beta^t multiplying the utility function. I will ignore it if it seems incorrect. Also, could you please tell me where I could find more on what you meant by "usual disclaimer on approximation orders for welfare apply"? Is it something to do with the fact that the approximation will not be very accurate given that there are second order effects on welfare of inflation and output gap?

Thank you very much once again for the help.

Anup

I still don't get where the 1-beta comes from, because

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beta^0=1

.
Regarding the "usual disclaimer", you should look at Woodford (2002): "Inflation Stabilization and Welfare"

Thank you Prof. Pfeifer!