var k i z s y mu v v_k dmudk dvdk v_k_lag dmudk_lag dvdk_lag v_mu dmudmu_lag v_v dmudv_lag dvdv_lag v_y dmudy v_y_lag dmudy_lag dvdy_lag v_s dmuds;
varexo e_g_err e_g e_z e_eps e_s; 
parameters m, beta, alpha,  delta, z_0, rho_z, sigma_z, sigma_e, sigma_s, g_0, rho_g, sigma_g, nu;
beta = 0.990000000000;
alpha = 0.300000000000;
delta = 0.100000000000;
z_0 = 1.000000000000;
rho_z = 0.800000000000;
sigma_z = 0.100000000000;
sigma_e = 0.040000000000;
sigma_s = 0.020000000000;
g_0 = 1.020000000000;
rho_g = 0.800000000000;
sigma_g = 0.020000000000;
nu = 0.000000000000;
m = 1.000000000000;
model;
-y+beta*m*(v_k(+1) + v_y(+1)*((g_0+rho_g*mu)*(z(+1)/z)*y^alpha*(exp(k)/exp(k(-1)))^alpha*alpha/exp(k))) = 0;
v_k = 1-delta +beta*m*(v_mu(+1)*dmudk + v_v(+1)*dvdk + v_k_lag(+1) + v_y(+1)*((z(+1)/z)*y^alpha*(exp(k)/exp(k(-1)))^alpha*rho_g*dmudk + (g_0+rho_g*mu)*(z(+1)/z)*y^alpha*(-(exp(k)/exp(k(-1)))^alpha*alpha/exp(k(-1)))) + v_s(+1)*dmudk);
v_k_lag = beta*m*(v_mu(+1)*dmudk_lag + v_v(+1)*dvdk_lag + v_y(+1)*(y^alpha*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha*rho_g*dmudk_lag) + v_s(+1)*dmudk_lag);
v_mu = beta*m*(v_mu(+1)*dmudmu_lag + v_y(+1)*(y^alpha*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha*rho_g*dmudmu_lag)+v_s(+1)*dmudmu_lag);
v_v = beta*m*(v_mu(+1)*dmudv_lag + v_v(+1)*dvdv_lag +v_y(+1)*(y^alpha*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha*rho_g*dmudv_lag) + v_s(+1)*dmudv_lag);
v_y = 1 - exp(k) +beta*m*(v_mu(+1)*dmudy + v_y(+1)*(y^alpha*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha*rho_g*dmudy + (g_0+rho_g*mu)*alpha*y^(alpha-1)*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha) + v_y_lag(+1) + v_s(+1)*dmudy);
v_y_lag = beta*m*(v_mu(+1)*dmudy_lag + v_v(+1)*dvdy_lag + v_y(+1)*(y^alpha*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha*rho_g*dmudy_lag) + v_s(+1)*dmudy_lag);
v_s = beta*m*(v_mu(+1)*dmuds + v_y(+1)*(y^alpha*(z(+1)/z)*(exp(k)/exp(k(-1)))^alpha*rho_g*dmuds) + v_s(+1)*dmuds);
dvdk = 2*y(-1)^(-2*alpha*(-1+nu))*z^2*z(-1)^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*alpha*(-1+nu)*(rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))^2*sigma_e^2/((sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)))^2*exp(k(-1)));
dmudk = -(rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))*alpha*z*z(-1)*(2*y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*nu*y*sigma_e^2*exp(v(-1))*(z/z(-1))^(2*nu)-y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*y*sigma_e^2*sigma_s^2*(z/z(-1))^(2*nu)-y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*y*sigma_e^2*exp(v(-1))*(z/z(-1))^(2*nu)+sigma_g^2*sigma_s^2*y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y+y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y*sigma_g^2*exp(v(-1))-2*nu*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*mu(-1)*sigma_s^2*sigma_e^2-2*nu*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*s*exp(v(-1))*sigma_e^2+2*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*mu(-1)*sigma_s^2*sigma_e^2+2*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*s*exp(v(-1))*sigma_e^2+y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y*rho_g^2*exp(v(-1))*sigma_s^2-2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*nu*z*g_0*sigma_e^2*sigma_s^2*z(-1)*(z/z(-1))^(2*nu)+2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*g_0*sigma_e^2*exp(v(-1))*z(-1)*(z/z(-1))^(2*nu)+2*y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*nu*y*sigma_e^2*sigma_s^2*(z/z(-1))^(2*nu)-2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*nu*z*g_0*sigma_e^2*exp(v(-1))*z(-1)*(z/z(-1))^(2*nu)+2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*g_0*sigma_e^2*sigma_s^2*z(-1)*(z/z(-1))^(2*nu))/(exp(k(-1))*(sigma_e^2*sigma_s^2*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+sigma_e^2*exp(v(-1))*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*exp(v(-1)))^2);
dvdk_lag = -2*y(-1)^(-2*alpha*(-1+nu))*z^2*z(-1)^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*alpha*(-1+nu)*(rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))^2*sigma_e^2/((sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)))^2*exp(k(-2)));
dmudk_lag = (rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))*alpha*z*z(-1)*(sigma_g^2*sigma_s^2*y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y+y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y*sigma_g^2*exp(v(-1))+2*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*mu(-1)*sigma_s^2*sigma_e^2+2*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*s*exp(v(-1))*sigma_e^2+y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y*rho_g^2*exp(v(-1))*sigma_s^2-2*nu*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*mu(-1)*sigma_s^2*sigma_e^2-2*nu*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*s*exp(v(-1))*sigma_e^2-y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*y*sigma_e^2*sigma_s^2*(z/z(-1))^(2*nu)-y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*y*sigma_e^2*exp(v(-1))*(z/z(-1))^(2*nu)+2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*g_0*sigma_e^2*sigma_s^2*z(-1)*(z/z(-1))^(2*nu)+2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*g_0*sigma_e^2*exp(v(-1))*z(-1)*(z/z(-1))^(2*nu)+2*y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*nu*y*sigma_e^2*sigma_s^2*(z/z(-1))^(2*nu)+2*y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*nu*y*sigma_e^2*exp(v(-1))*(z/z(-1))^(2*nu)-2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*nu*z*g_0*sigma_e^2*sigma_s^2*z(-1)*(z/z(-1))^(2*nu)-2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*nu*z*g_0*sigma_e^2*exp(v(-1))*z(-1)*(z/z(-1))^(2*nu))/(exp(k(-2))*(sigma_e^2*sigma_s^2*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+sigma_e^2*exp(v(-1))*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*exp(v(-1)))^2);
dmudy = y(-1)^(-alpha*(-1+2*nu))*z*z(-1)*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-alpha*(-1+2*nu))*(rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))/(sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)));
dmudy_lag = (rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))*alpha*z*z(-1)*(-2*y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*nu*y*sigma_e^2*sigma_s^2*(z/z(-1))^(2*nu)-2*y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*nu*y*sigma_e^2*exp(v(-1))*(z/z(-1))^(2*nu)+2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*nu*z*g_0*sigma_e^2*sigma_s^2*z(-1)*(z/z(-1))^(2*nu)-2*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*mu(-1)*sigma_s^2*sigma_e^2-2*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*s*exp(v(-1))*sigma_e^2-y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y*rho_g^2*exp(v(-1))*sigma_s^2+2*nu*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*mu(-1)*sigma_s^2*sigma_e^2+2*nu*y(-1)^(2*alpha*(nu+1))*z(-1)*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*rho_g*s*exp(v(-1))*sigma_e^2-sigma_g^2*sigma_s^2*y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y-y(-1)^(3*alpha)*(exp(k(-1))/exp(k(-2)))^(3*alpha)*z^2*y*sigma_g^2*exp(v(-1))+2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*nu*z*g_0*sigma_e^2*exp(v(-1))*z(-1)*(z/z(-1))^(2*nu)+y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*y*sigma_e^2*sigma_s^2*(z/z(-1))^(2*nu)+y(-1)^(alpha*(2*nu+1))*z(-1)^2*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+1))*y*sigma_e^2*exp(v(-1))*(z/z(-1))^(2*nu)-2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*g_0*sigma_e^2*sigma_s^2*z(-1)*(z/z(-1))^(2*nu)-2*y(-1)^(2*alpha*(nu+1))*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+1))*z*g_0*sigma_e^2*exp(v(-1))*z(-1)*(z/z(-1))^(2*nu))/(y(-1)*(sigma_e^2*sigma_s^2*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+sigma_e^2*exp(v(-1))*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*exp(v(-1)))^2);
dvdy_lag = 2*y(-1)^(2*alpha-2*alpha*nu-1)*z^2*z(-1)^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*alpha*(-1+nu)*(rho_g^2*exp(v(-1))*sigma_s^2+sigma_g^2*sigma_s^2+sigma_g^2*exp(v(-1)))^2*sigma_e^2/(sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)))^2;
dmuds = rho_g*exp(v(-1))*z(-1)^2*sigma_e^2/(sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)));
dmudmu_lag = rho_g*sigma_s^2*z(-1)^2*sigma_e^2/(sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)));
dvdv_lag = rho_g^2*z(-1)^4*sigma_e^4*sigma_s^4/(sigma_e^2*sigma_s^2*z(-1)^2+sigma_e^2*exp(v(-1))*z(-1)^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*sigma_s^2+y(-1)^(-2*alpha*(-1+nu))*z^2*(z/z(-1))^(-2*nu)*(exp(k(-1))/exp(k(-2)))^(-2*alpha*(-1+nu))*sigma_g^2*exp(v(-1)))^2;
dmudv_lag = (2*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*s*sigma_g^2*sigma_e^2*z(-1)^2*z^2*exp(v(-1))-2*sigma_s^2*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*mu(-1)*sigma_e^2*z(-1)^2*z^2*sigma_g^2+2*sigma_s^2*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*s*sigma_g^2*sigma_e^2*z(-1)^2*z^2-y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*mu(-1)*z^4*exp(v(-1))*sigma_s^4*rho_g^4-rho_g^3*sigma_s^4*exp(v(-1))*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*z^4*g_0+rho_g^3*sigma_s^4*exp(v(-1))*y(-1)^(alpha*(2*nu+3))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+3))*z(-1)*z^3*y-rho_g^2*sigma_s^4*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*mu(-1)*z^4*sigma_g^2-rho_g^2*sigma_s^4*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*mu(-1)*sigma_e^2*z(-1)^2*z^2+rho_g^2*sigma_s^2*exp(v(-1))*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*s*sigma_g^2*z^4-2*rho_g^2*sigma_s^2*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*mu(-1)*z^4*exp(v(-1))*sigma_g^2+rho_g^2*sigma_s^2*exp(v(-1))*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*sigma_e^2*z(-1)^2*s*z^2-2*rho_g^2*sigma_s^2*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*mu(-1)*sigma_e^2*z(-1)^2*z^2*exp(v(-1))+rho_g*sigma_s^4*y(-1)^(alpha*(2*nu+3))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+3))*z(-1)*z^3*y*sigma_g^2-rho_g*sigma_s^4*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*sigma_e^2*z(-1)^2*z^2*g_0+rho_g*sigma_s^4*y(-1)^(alpha*(4*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(4*nu+1))*sigma_e^2*z(-1)^3*z*y-rho_g*sigma_s^4*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*z^4*g_0*sigma_g^2+rho_g*sigma_s^2*y(-1)^(alpha*(2*nu+3))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(2*nu+3))*z(-1)*z^3*y*exp(v(-1))*sigma_g^2-rho_g*sigma_s^2*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*sigma_e^2*z(-1)^2*z^2*g_0*exp(v(-1))+rho_g*sigma_s^2*y(-1)^(alpha*(4*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(4*nu+1))*sigma_e^2*z(-1)^3*z*y*exp(v(-1))-rho_g*sigma_s^2*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*z^4*g_0*exp(v(-1))*sigma_g^2-y(-1)^(6*alpha*nu)*(z/z(-1))^(6*nu)*(exp(k(-1))/exp(k(-2)))^(6*alpha*nu)*sigma_e^4*z(-1)^4*mu(-1)*exp(v(-1))+y(-1)^(6*alpha*nu)*(z/z(-1))^(6*nu)*(exp(k(-1))/exp(k(-2)))^(6*alpha*nu)*sigma_e^4*z(-1)^4*s*exp(v(-1))-y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*mu(-1)*z^4*sigma_g^4*exp(v(-1))+y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*s*sigma_g^4*z^4*exp(v(-1))-sigma_s^2*y(-1)^(6*alpha*nu)*(z/z(-1))^(6*nu)*(exp(k(-1))/exp(k(-2)))^(6*alpha*nu)*sigma_e^4*z(-1)^4*mu(-1)+sigma_s^2*y(-1)^(6*alpha*nu)*(z/z(-1))^(6*nu)*(exp(k(-1))/exp(k(-2)))^(6*alpha*nu)*sigma_e^4*z(-1)^4*s+sigma_s^2*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*s*sigma_g^4*z^4-sigma_s^2*y(-1)^(2*alpha*(nu+2))*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(nu+2))*mu(-1)*z^4*sigma_g^4-2*y(-1)^(2*alpha*(2*nu+1))*(z/z(-1))^(4*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*(2*nu+1))*mu(-1)*sigma_e^2*z(-1)^2*z^2*sigma_g^2*exp(v(-1)))*sigma_e^2*z(-1)^2*sigma_s^2*rho_g/(sigma_e^2*sigma_s^2*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+sigma_e^2*exp(v(-1))*y(-1)^(2*alpha*nu)*z(-1)^2*(z/z(-1))^(2*nu)*(exp(k(-1))/exp(k(-2)))^(2*alpha*nu)+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*rho_g^2*exp(v(-1))*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*sigma_s^2+y(-1)^(2*alpha)*z^2*(exp(k(-1))/exp(k(-2)))^(2*alpha)*sigma_g^2*exp(v(-1)))^3;
y*exp(k) = (1-delta)*exp(k(-1)) + exp(i);
exp(v) = 1/(1/(rho_g^2/(1/exp(v(-1))+1/sigma_s^2)+sigma_g^2)+(y(-1)^(alpha*(1-nu))*(z/z(-1))^(1-nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(1-nu)))^2/sigma_e^2);
mu = (rho_g*(mu(-1)/exp(v(-1))+s/sigma_s^2)/((rho_g^2/(1/exp(v(-1))+1/sigma_s^2)+sigma_g^2)*(1/exp(v(-1))+1/sigma_s^2))+(y(-1)^(alpha*(1-nu))*(z/z(-1))^(1-nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(1-nu)))^2*(y*z(-1)/(y(-1)^alpha*z*(exp(k(-1))/exp(k(-2)))^alpha)-g_0)/sigma_e^2)/(1/(rho_g^2/(1/exp(v(-1))+1/sigma_s^2)+sigma_g^2)+(y(-1)^(alpha*(1-nu))*(z/z(-1))^(1-nu)*(exp(k(-1))/exp(k(-2)))^(alpha*(1-nu)))^2/sigma_e^2);
y = (g_0 + rho_g*(mu(-1)+sqrt(exp(v(-1)))*e_g_err) + sigma_g*e_g)*y(-1)^alpha*(z/z(-1))*(exp(k(-1))/exp(k(-2)))^alpha + sigma_e*e_eps*y(-1)^(alpha*nu)*(z/z(-1))^nu*(exp(k(-1))/exp(k(-2)))^(alpha*nu);
s = mu(-1)+sqrt(exp(v(-1)))*e_g_err+sigma_s*e_s;
z = (1-rho_z)*z_0+rho_z*z(-1)+sigma_z*e_z;
end;
initval;
k = -3.48685459403546580000;
i = -5.53717692750551470000;
z = 1.00000000000000000000;
s = 0.00000000000000000000;
y = 1.02869341470660110000;
mu = 0.00000000000000000000;
v = -7.83700925667097080000;
v_k = -26.16229665739608400000;
dmudk = -2.51029553843983690000;
dvdk = -0.00194350115614084160;
v_k_lag = 13.29295518673595400000;
dmudk_lag = 2.51029553843983690000;
dvdk_lag = 0.00194350115614084160;
v_mu = 1.59676728481873800000;
dmudmu_lag = 0.30154000631904715000;
v_v = 0.00000000000000847134;
dmudv_lag = 0.00000000000000145227;
dvdv_lag = 0.09092637541089099200;
v_y = 2.69688251989579970000;
dmudy = 0.24888339965631406000;
v_y_lag = -0.39537924850195910000;
dmudy_lag = -0.07466501989689422500;
dvdy_lag = -0.00005780656112828870;
v_s = 1.57620158510455120000;
dmuds = 0.29765629622507722000;
end;
vcov = [1.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000; 0.000000000000 1.000000000000 0.000000000000 0.000000000000 0.000000000000; 0.000000000000 0.000000000000 1.000000000000 0.000000000000 0.000000000000; 0.000000000000 0.000000000000 0.000000000000 1.000000000000 0.000000000000; 0.000000000000 0.000000000000 0.000000000000 0.000000000000 1.000000000000];

order = 2;