Welfare cost of business cycle stochastic simulation

I am doing research on the welfare cost of business cycle using two-agent DSGE model.

I compare lifetime welfare of fluctuating economy(where aggregate shock prevails) and the lifetime welfare of non-fluctuating economy(consuming steady state level consumption forever). Since I am using unconditonal welfare cost measure, I specify V = U + beta*V(+1) in the mod file, simulate economy for 100,000 periods(with order=2), and take simulated mean(oo_.mean) as a lifetime welfare for fluctuating economy. For the steady state level of consumption, I solved it manually by hands and calculate welfare analytically. Lastly I compare the two welfare estimates(Since I specified log consumption utility function, there exists closed form solution for welfare cost.).

Question is that

  1. Conceptually, am I doing right for calcuating welfare cost of business cycle using second order approximation?
  2. I specified shock as A = (1-rhoA)*As + rhoA*A(-1) + sA*eA for TFP shock and found out that welfare cost and simulated means are significantly different when I use above shock process and A = (1-rhoA)*As + rhoA*A(-1) - sA*eA. This is somewhat counter-intuitive since if eA are drawn from symmetric normal distribution + or - sign in front of eA should not cause large difference.( I checked this phenomenon by changing seeds of simulation and cound observe same pattern for all cases.) . I wonder if there exist right way to specify shock process, simulation period, approximation order in calculating welfare cost( should I use A = (1-rhoA)*As + rhoA*A(-1) + sA*eA only for stochastic simulation?).

Always thanks for kind-reply.

  1. Yes, using a second order approximation is correct.
  2. That is correct, the sign should not change the results. My guess is that your simulation is still too short and has not converged yet. Is there a reason you do not use theoretical moments?

Are you suggesting that using theoretical moment for V(lifetime utility) by setting periods=0 rather than simulated moment(oo_.mean) with periods =100,000(and keep order=2 for both cases)?

Yes, exactly.


I will check the result of my analysis in both ways(using theoretical moment and lengthening the periods to more than 100,000).

Always thanks for your fast and kind reply!