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// --+ options: json=compute, stochastic +--
/* This file tests the matlab/backward/shock_decomposition_backward.m routine,
used for shock decomposition of nonlinear backward models */
var x1 x2 x3 x1bar x2bar z y x u v s;
varexo ex1
ex2
ex1bar (used='estimationonly')
ex2bar (used='estimationonly')
ez
ey
ex
eu
ev
es;
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 c_z_dx2 c_z_u c_z_dv c_z_s cx cy beta
lambda
px3;
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;
c_z_dx2 = .3;
c_z_u = .3;
c_z_dv = .4;
c_z_s = -.2;
cx = 1.0;
cy = 1.0;
lambda = 0.5; // Share of optimizing agents.
px3 = -.1;
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:s']
s = .3*s(-1) - .1*s(-2) + es;
[name='eq:diff(v)']
diff(v) = .5*diff(v(-1)) + ev;
[name='eq:u']
u = .5*u(-1) - .2*u(-2) + eu;
[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:x3']
x3 = px3*x + y ;
[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) + c_z_s*s + c_z_dv*diff(v) ) + (1-lambda)*( cy*y + cx*x) + c_z_u*u + c_z_dx2*diff(x2) + 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;
var eu = 0.05;
var ev = 0.05;
var es = 0.07;
end;
shock_groups;
g1 = ex, ey, ez;
g2 = eu, ev;
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 for non logged variables, and one for logged variables
init = zeros(10, M_.endo_nbr+M_.exo_nbr);
initialconditions = dseries(init, 2000Q1, vertcat(M_.endo_names,M_.exo_names));
// Simulate the model for 500 periods
TrueData = simul_backward_model(initialconditions, 500);
decomposition = shock_decomposition_backward(TrueData, initialconditions, { 'g1', 'g2', 'es' }, { 'z', 'y', 'u'});
% Verify that y is only influenced by g1 (which contains ey)
y_idx = find(strcmp(M_.endo_names, 'y'));
if ~(all(all(decomposition(y_idx, 2:3, :) == 0)) && all(all(decomposition(y_idx, 1, :) ~= 0)))
error('Wrong decomposition for y')
end
% Verify that u is only influenced by g2 (which contains eu)
u_idx = find(strcmp(M_.endo_names, 'u'));
if ~(all(all(decomposition(u_idx, [1 3], :) == 0)) && all(all(decomposition(u_idx, 2, :) ~= 0)))
error('Wrong decomposition for u')
end
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