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// --+ options: json=compute, stochastic +--
var x1 x2 x1bar x2bar z y x;
varexo ex1
ex2
ex1bar
ex2bar
ez
ey (status='observed') // This shock is observed...
ex (status='observed') // ... this one also. Other shocks will be considered as non observed.
;
parameters
rho_1 rho_2 rho_3 rho_4
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 beta
lambda;
rho_1 = .9;
rho_2 = -.2;
rho_3 = .4;
rho_4 = -.3;
a_x1_0 = -.9;
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;
lambda = 0.5; // Share of optimizing agents.
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:y']
y = rho_1*y(-1) + rho_2*y(-2) + ey;
[name='eq:x']
x = rho_3*x(-1) + rho_4*x(-2) + ex;
[name='eq:x1']
diff(x1) = a_x1_0*(x1(-1)-x1bar(-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='zpac']
diff(z) = lambda*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-lambda)*( y + x) + ez;
end;
shocks;
var ex1 = 1.0;
var ex2 = 1.0;
var ex1bar = 1.0;
var ex2bar = 1.0;
var ez = 1.0;
var ey = 0.1;
var ex = 0.1;
end;
verbatim;
if ~isequal(M_.observed_exo_names, {'ey'; 'ex'})
error()
end
end;
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