 # The rank condition: when simple AR decides

Dear Professor Pfeifer,
I have a very simple model, with four processes

Blockquote
%%% process
tau_c = rho_c * tau_c(-1) + (1-rho_c) * tau_c_bar + rho_cb *(b(-1) - b_bar) + z_c; %%% 17
tau_w = rho_w * tau_w(-1) + (1-rho_w) * tau_w_bar + rho_wb *(b(-1) - b_bar) + z_w; %%% 18
tau_k = rho_k * tau_k(-1) + (1-rho_k) * tau_k_bar + rho_kb *(b(-1) - b_bar) + z_k; %%% 19
g = rho_g * g(-1) + (1-rho_g) * g_bar - rho_gb *(b(-1) - b_bar)+ rho_gy *(y(-1) - y_bar)+ rho_go *(o(-1) - o_bar) + z_g; %%% 20

the program works well when rho_cb, rho_wb, rho_kb, rho_gb are qual to (for example) x1, x2, etc, but when they have a higher value (or different combinations), I face BK condition error.
I am just asking this question that how these simple processes can change the rank condition? and if this shows an error in my program? and is there any solution?

Looking forward to hearing from you,

Kind regards,
Leo

It’s not a simple AR due to the feedback from endogenous variables. Essentially, you have a VAR and the largest eigenvalue changes.

Thank you so much. So how I can deal with this problem? I have changed the model a little bit and now for any value of rho_gb (even 0.001), I have the BK condition error.
I appreciate your time.

Kind regards,
Leo

You need to play around with the coefficients to see how you can achieve a stable fiscal rule. For example, it the feedback on g is too strong, you may be able to decrease it for the tax rates first.