// --+ options: json=compute, stochastic +--

var x1 x2 x1bar x2bar z ;

varexo ex1 ex2 ex1bar ex2bar ez ;

parameters a_x1_0 a_x1_0_ a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
	   a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
	   e_c_m c_z_1 c_z_2 gamma beta ;

a_x1_0 =  -.9;
a_x1_0_ =  -.8;
a_x1_1 =  .4;
a_x1_2 =  .3;
a_x1_x2_1 = .1;
a_x1_x2_2 = .2;


a_x2_0 =  -.9;
a_x2_1 =   .2;
a_x2_2 =  -.1;
a_x2_x1_1 = -.1;
a_x2_x1_2 = .2;

beta  =  .2;
e_c_m =  .5;
c_z_1 =  .2;
c_z_2 = -.1;

gamma =  .9;

trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], targets=['eq:x1bar', 'eq:x2bar']);

pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);

model;

[name='eq:x1']
diff(x1) = a_x1_0*(x1(-1)-x1bar(-1))+a_x1_0_*(x2(-1)-x2bar(-1)) + a_x1_1*diff(x1(-1)) + a_x1_2*diff(x1(-2)) + + a_x1_x2_1*diff(x2(-1)) + a_x1_x2_2*diff(x2(-2)) + ex1;     

[name='eq:x2']
diff(x2) = a_x2_0*(x2(-1)-x2bar(-1)) + a_x2_1*diff(x1(-1)) + a_x2_2*diff(x1(-2)) + + a_x2_x1_1*diff(x2(-1)) + a_x2_x1_2*diff(x2(-2)) + ex2;     

[name='eq:x1bar']
x1bar = x1bar(-1) + ex1bar;

[name='eq:x2bar']
x2bar = x2bar(-1) + ex2bar;

[name='eq:pac']
diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1))  + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*ez;

end;

shocks;
    var ex1 = 1.0;
    var ex2 = 1.0;
    var ex1bar = 1.0;
    var ex2bar = 1.0;
    var ez = 1.0;
end;

// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
pac.initialize('pacman');

// Update the parameters of the PAC expectation model (h0 and h1 vectors).
pac.update.expectation('pacman');

// Set initial conditions to zero. Please use more sensible values if any...
initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));

// Simulate the model for 500 periods
TrueData = simul_backward_model(initialconditions, 5000);