Second order approximation and Shock sizes

Stochastic simulations
1

Dear, professor jpfeifer,

I simulate my model at first order, everything goes right and I get the corresponding IRFs.

The problem is the second order approximation for welfare analysis.

I find the means of variables are extremely huge if I use the shock sizes calibrated from literature.

If I reduce all the shock sizes by dividing by 100, the means of variables are similar with the first order.

Can I just reduce the shock sizes and use them in first order for IRFs and second order for welfare analysis? However, the shock sizes will differ with relevant literature.

I update the files and hope you can run it and give me some suggestions on why these happen; How to set the shock size and obtain welfare results at second order.

Thank you so much!

finalcode202509.mod (23.9 KB)

finalcode202509calib.m (5.6 KB)

finalcode202509_steady.m (4.6 KB)

2

Dear professor jpfeifer, I still can not handle this problem. Hope you can give me some suggetions when you have time. Thank you so much.

3

Your model looks overly volatile to me. If I use

stoch_simul(order=1,irf=0,replic=1000,irf_shocks=(e_Df2,e_Xh, e_M)) Ci Hi;

I get

THEORETICAL MOMENTS
VARIABLE           MEAN    STD. DEV.     VARIANCE
Ci               0.4747       0.4422       0.1955
Hi               0.1873       0.4094       0.1676

which is a fourty percent standard deviation of consumption! That is huge and explains the welfare results. You need to understand why the model produces behavior like that.

4

Yes, you are right, professor.

I check all the variables and find 5-6 variables have huge standard deviations.

I will rethink and modify the model and parametrization parts.

Always thank you for your times and substantial helps.

Thank you so much!