147 lines
3.4 KiB
Modula-2
147 lines
3.4 KiB
Modula-2
// --+ options: json=compute, stochastic +--
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/* This file tests the matlab/backward/shock_decomposition_backward.m routine,
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used for shock decomposition of nonlinear backward models */
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var x1 x2 x3 x1bar x2bar z y x u v s;
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varexo ex1
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ex2
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ex1bar (used='estimationonly')
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ex2bar (used='estimationonly')
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ez
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ey
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ex
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eu
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ev
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es;
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parameters
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rho_1 rho_2 rho_3 rho_4
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a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
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a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
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e_c_m c_z_1 c_z_2 c_z_dx2 c_z_u c_z_dv c_z_s cx cy beta
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lambda
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px3;
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rho_1 = .9;
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rho_2 = -.2;
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rho_3 = .4;
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rho_4 = -.3;
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a_x1_0 = -.9;
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a_x1_1 = .4;
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a_x1_2 = .3;
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a_x1_x2_1 = .1;
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a_x1_x2_2 = .2;
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a_x2_0 = -.9;
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a_x2_1 = .2;
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a_x2_2 = -.1;
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a_x2_x1_1 = -.1;
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a_x2_x1_2 = .2;
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beta = .2;
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e_c_m = .5;
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c_z_1 = .2;
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c_z_2 = -.1;
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c_z_dx2 = .3;
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c_z_u = .3;
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c_z_dv = .4;
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c_z_s = -.2;
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cx = 1.0;
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cy = 1.0;
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lambda = 0.5; // Share of optimizing agents.
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px3 = -.1;
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trend_component_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar'], targets=['eq:x1bar', 'eq:x2bar']);
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pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
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model;
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[name='eq:s']
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s = .3*s(-1) - .1*s(-2) + es;
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[name='eq:diff(v)']
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diff(v) = .5*diff(v(-1)) + ev;
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[name='eq:u']
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u = .5*u(-1) - .2*u(-2) + eu;
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[name='eq:y']
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y = rho_1*y(-1) + rho_2*y(-2) + ey;
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[name='eq:x']
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x = rho_3*x(-1) + rho_4*x(-2) + ex;
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[name='eq:x1']
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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;
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[name='eq:x2']
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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;
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[name='eq:x3']
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x3 = px3*x + y ;
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[name='eq:x1bar']
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x1bar = x1bar(-1) + ex1bar;
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[name='eq:x2bar']
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x2bar = x2bar(-1) + ex2bar;
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[name='zpac']
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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;
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end;
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shocks;
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var ex1 = 1.0;
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var ex2 = 1.0;
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var ex1bar = 1.0;
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var ex2bar = 1.0;
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var ez = 1.0;
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var ey = 0.1;
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var ex = 0.1;
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var eu = 0.05;
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var ev = 0.05;
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var es = 0.07;
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end;
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shock_groups;
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g1 = ex, ey, ez;
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g2 = eu, ev;
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end;
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// Initialize the PAC model (build the Companion VAR representation for the auxiliary model).
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pac.initialize('pacman');
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// Update the parameters of the PAC expectation model (h0 and h1 vectors).
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pac.update.expectation('pacman');
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// Set initial conditions to zero for non logged variables, and one for logged variables
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init = zeros(10, M_.endo_nbr+M_.exo_nbr);
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initialconditions = dseries(init, 2000Q1, vertcat(M_.endo_names,M_.exo_names));
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// Simulate the model for 500 periods
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TrueData = simul_backward_model(initialconditions, 500);
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decomposition = shock_decomposition_backward(TrueData, initialconditions, { 'g1', 'g2', 'es' }, { 'z', 'y', 'u'});
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% Verify that y is only influenced by g1 (which contains ey)
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y_idx = find(strcmp(M_.endo_names, 'y'));
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if ~(all(all(decomposition(y_idx, 2:3, :) == 0)) && all(all(decomposition(y_idx, 1, :) ~= 0)))
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error('Wrong decomposition for y')
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end
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% Verify that u is only influenced by g2 (which contains eu)
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u_idx = find(strcmp(M_.endo_names, 'u'));
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if ~(all(all(decomposition(u_idx, [1 3], :) == 0)) && all(all(decomposition(u_idx, 2, :) ~= 0)))
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error('Wrong decomposition for u')
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end
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