# Third order simulation equity premium

Hi all,

I am working with an NK model and trying to simulate a time-varying risk premium using 3rd order simulation. However, the problem is that, when there is a technology shock, the 3rd-order simulated ERP is negative, but the average ERP calculated using 2nd-order simulation is positive. I wonder whether this is due to issues with my definition of ERP or to the interpretation of the simulation results.

For 3rd-order simulation, I define:

``````ERP=[(v_eq(1)+d_p(1))/v_eq] - r_b;
``````

and run:
stoch_simul(k_order_solver,order = 3,irf=30,periods=500,noprint) erp;

For 2nd-order simulation, I run:

``````stoch_simul(k_order_solver,order = 2,irf=0,periods=5000,noprint) v_eq d_p r_b;
E_r_b=mean(exp(r_blog)-1)*100
R=(exp(v_eqlog(2:end))+exp(d_log(2:end)))./exp(v_eqlog(1:end-1));
E_r_k=(mean(R)-1)*100
E_r_k-E_r_b
``````

The results have different signs regarding a positive TFP shock, with the 3rd-order being negative (which should have generated a positive ERP).

Please comment if anyone has any ideas! Thank you.

RANK_1CapitalCost.mod (3.6 KB)

Please see the mod file. The result using 2nd order is 0.0234, and the result using 3rd order is like (I have rescaled by ERP*10000, but the issue is regarding the sign):

What exactly are you comparing? Simulation at `order=2` vs IRFs at `order=3`?