I am trying to find out the optimal policy parameters for macroprudential policy in my model:
taue = 0.9*taue(-1) + 0.1*(alpha_le*(leverage_e/leverage_e(-1) - 1) + alpha_qky*((qe*ke/ye)/(qe(-1)*ke(-1)/ye(-1)) -1) + alpha_ve*(ve/ve(-1) - 1) + alpha_cg*(cg - 1));
0.9 is the persistence parameter. What I am trying to find out is the optimal value of alpha_le, alpha_qky, alpha_ve, and alpha_cg that optimizes the welfare.
This is how I calculate the welfare (omega_e):
util_e = log(ce) - (he^(1+psi))/(1+psi); omega_e = util_e + beta*omega_e(+1);
To calculate welfare, I usually run stoch_simul in 2nd order.
Attach is my code. It is written in non-linear model.
My question is: how do I get the optimal macroprudential policy parameters above, subject to maximizing welfare, where my code is written in non-linear form?
It appears to me that, we can get the optimal policy parameters using osr command, but it can only be done if the model is linear. Is that correct?
Should I translate my model into a linear form (which I do not prefer as it will be time-consuming to translate the model into the linear form by hand)?
Thank you in advance.
Fed_paper_26Apr_mp_opt.mod (11.7 KB)