2021-11-25 16:16:42 +01:00
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// --+ options: json=compute, stochastic +--
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var y x z v;
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varexo ex ey ez ;
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parameters a_y_1 a_y_2 b_y_1 b_y_2 b_x_1 b_x_2 d_y; // VAR parameters
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parameters beta e_c_m c_z_1 c_z_2; // PAC equation parameters
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a_y_1 = .2;
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a_y_2 = .3;
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b_y_1 = .1;
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b_y_2 = .4;
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b_x_1 = -.1;
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b_x_2 = -.2;
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d_y = .5;
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beta = .9;
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e_c_m = .1;
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c_z_1 = .7;
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c_z_2 = -.3;
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var_model(model_name=toto, structural, eqtags=['eq:x', 'eq:y']);
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pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman);
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pac_target_info(pacman);
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target v;
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auxname_target_nonstationary vns;
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component y;
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growth diff(y(-1));
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auxname pv_y_;
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kind dd;
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component x;
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growth diff(x(-1));
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auxname pv_dx_;
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kind dd;
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end;
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model(use_dll);
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[name='eq:y']
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diff(y) = .01 + a_y_1*diff(y(-1)) + a_y_2*diff(x(-1)) + b_y_1*diff(y(-2)) + b_y_2*diff(x(-2)) + ey ;
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[name='eq:x']
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diff(x) = .05 + b_x_1*diff(y(-2)) + b_x_2*diff(x(-1)) + ex ;
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[name='eq:v']
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v = x + d_y*y ;
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[name='zpac']
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diff(z) = e_c_m*(pac_target_nonstationary(pacman)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman) + ez;
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end;
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shocks;
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var ex = 1.0;
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var ey = 1.0;
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var ez = 1.0;
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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. Please use more sensible values if any...
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initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
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// Simulate the model for 500 periods
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2022-03-25 12:12:32 +01:00
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options_.solve_algo = 9;
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2021-11-25 16:16:42 +01:00
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TrueData = simul_backward_model(initialconditions, 500);
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TrueData.save('example1.data')
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// Print expanded PAC_EXPECTATION term.
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pac.print('pacman', 'eq:pac');
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clear eparams
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eparams.e_c_m = .9;
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eparams.c_z_1 = .5;
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eparams.c_z_2 = .2;
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// Define the dataset used for estimation
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edata = TrueData;
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edata.ez = dseries(NaN(TrueData.nobs, 1), 2000Q1, 'ez');
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pac.estimate.nls('zpac', eparams, edata, 2005Q1:2005Q1+400, 'fmincon');
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e_c_m_nls = M_.params(strmatch('e_c_m', M_.param_names, 'exact'));
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c_z_1_nls = M_.params(strmatch('c_z_1', M_.param_names, 'exact'));
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c_z_2_nls = M_.params(strmatch('c_z_2', M_.param_names, 'exact'));
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save('example1.estimation.mat', 'e_c_m_nls', 'c_z_1_nls', 'c_z_2_nls')
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