Second order moments to obtain welfare

[leycxgy]

Dear Johannes,

I am currently trying to use estimated Smets Wouters (2003) model to compare welfare under interest rate rule and constant money growth rule. According to Michel Juillard (2006) "welfare-based monetary policy rules in an estimated DSGE model of the US economy" and Stephane Adjemian (2007) "Optimal Monetary Policy in an Estimated DSGE for the Euro Area'', they can use the estimated parameters to compute to model and solve the welfare by using second order moments from non-linearized model.
However, you said we can't do it in this way. Could you give me some suggestions about this problem, please? Thank you very much!


Best wishes,
Michael

[StephaneAdjemian]

Dear Michael,

Could you give a link to what Johannes said about this issue?

Best,
Stéphane.

[jpfeifer]

The approach you outline is not 100 percent consistent due to using different orders for estimation and evaluation, but can be used if one accepts this caveat. The actual problem lies in the Smets/Wouters (2003/2007) model. It features markup shocks. These markup shocks imply that the nonlinear Keynesian Phillips curve does not have a recursive representation due to the time-varying exponents. This implies you cannot solve the nonlinear model at second order (unless you truncate the arising infinite sum).