To take an example, I’ll use the code of Herbst and Schorfheide:

GAM0(eq_1,y_t) = 1;

GAM0(eq_1,R_t) = 1/tau;

GAM0(eq_1,g_t) = -(1-rho_g);

GAM0(eq_1,z_t) = -rho_z/tau;

GAM0(eq_1, Ey_t1) = -1;

GAM0(eq_1, Epi_t1) = -1/tau;

GAM0(eq_2,y_t) = -kappa;

GAM0(eq_2,pi_t) = 1;

GAM0(eq_2,g_t) = kappa;

GAM0(eq_2, Epi_t1) = -bet;

GAM0(eq_3,y_t) = -(1-rho_R)*psi2;

GAM0(eq_3,pi_t) = -(1-rho_R)*psi1;

GAM0(eq_3,R_t) = 1;

GAM0(eq_3,g_t) = (1-rho_R)*psi2;

GAM1(eq_3,R_t) = rho_R;

PSI(eq_3,R_sh) = 1;

GAM0(eq_4,y1_t) = 1;

GAM1(eq_4,y_t) = 1;

GAM0(eq_5,g_t) = 1;

GAM1(eq_5, g_t) = rho_g;

PSI(eq_5, g_sh) = 1;

GAM0(eq_6,z_t) = 1;

GAM1(eq_6, z_t) = rho_z;

PSI(eq_6, z_sh) = 1;

GAM0(eq_7, y_t) = 1;

GAM1(eq_7, Ey_t1) = 1;

PPI(eq_7, ey_sh) = 1;

GAM0(eq_8, pi_t) = 1;

GAM1(eq_8, Epi_t1) = 1;

PPI(eq_8, epi_sh) = 1;

If I wanted to include a variable that stands for the expectation at time t of output at time t, I would create an auxiliary variable for lagged output, call it x_1t, and use the expectation of that, which would require the following additional code:

GAM0(eq_9, x_1t) = 1;

GAM1(eq_9, Ex_1t) = 1;

PPI(eq_9, ex_1tsh) = 1;

GAM0(eq_10,x_1t)=1;

GAM1(e1_10,x_t) = 1;

I do not know how to reverse this, however, and simulate the expectation at time-t of output at time t+2