Problems of Welfare Analysis

Optimal Policy
1

Dear all，

I built a DSGE model to compare the effects of several monetary policies.
The welfare loss function is in the form of Woodford (2003) and Galí and Monacelli（2005）.
image
I bulit a m.file in matlab：
“- (1- alpha)/2 beta ( epsilon/lambda * oo_.var(3,3) + (1+ phi)*oo_.var(2,2) )”
I have two questions as following.
（1）Numerical value of oo_.var are a little different according to different times of MH algorithm.
How much times should MH algorithm be? 10000 times？or 250 times？
（2）I’m not familiar with welfare analysis，so ask a basic question. In some articles，they also did different types of shocks on welfare losses，for example ， technology shocks ，monetary policy shocks, etc（I’m not sure whether other shocks are not taken into account, only taking one kind shocks ?）. I want to ask them how they did it. oo_.var has only one aggregate volatility？
Thank you in advance for answering my questions.

2

Hi,

  1. This is related to the convergence of the MH algorithm. If you observe changes in the welfare loss (computed with the parameters at the posterior expectation) when you increase the number of iterations, it probably means that the MH did not converge to the posterior distribution. Actually, you should assess convergence before doing anything with the MH draws. We have multiple approaches for doing that, search the forum or the reference manual.

  2. I suppose they turn off some of the shocks (putting variances to zero). In principle you could use the variance decomposition to do that.

Best,
Stéphane.

3

Stéphane，thank you for your answering.

4

Regarding 2. @stepan-a is right. See https://github.com/JohannesPfeifer/DSGE_mod/blob/master/Gali_2015/Gali_2015_chapter_4.mod