128 lines
3.7 KiB
Modula-2
128 lines
3.7 KiB
Modula-2
// --+ options: json=compute, stochastic +--
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var x1 x2 x1bar x2bar z y gg;
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varexo ex1 ex2 ex1bar ex2bar ez ey g;
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parameters
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rho_1 rho_2
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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 beta ;
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rho_1 = .9;
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rho_2 = -.2;
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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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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, growth=0.5*gg(-1)+beta+ex1, model_name=pacman);
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model;
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[name='eq:gg']
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gg = g;
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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: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: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) = e_c_m*(x1(-1)-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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// 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 5000 periods
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TrueData = simul_backward_model(initialconditions, 5000);
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// NLS estimation
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// Define a structure describing the parameters to be estimated (with initial conditions).
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clear eparams
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eparams.e_c_m = .5;
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eparams.c_z_1 = .2;
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eparams.c_z_2 =-.1;
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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, 2005Q1:2000Q1+200, 'lsqnonlin');
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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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resid_nls = oo_.pac.pacman.residual;
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fprintf('Estimate of e_c_m: %f \n', e_c_m_nls)
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fprintf('Estimate of c_z_1: %f \n', c_z_1_nls)
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fprintf('Estimate of c_z_2: %f \n', c_z_2_nls)
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skipline(2)
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// Iterative OLS estimation using estimates from NLS
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// Define a structure describing the parameters to be estimated (with initial conditions).
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clear eparams
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eparams.e_c_m = e_c_m_nls;
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eparams.c_z_1 = c_z_1_nls;
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eparams.c_z_2 = c_z_2_nls;
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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.iterative_ols('zpac', eparams, edata, 2005Q1:2000Q1+200);
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// Test printing of PAC expectations
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pac.print('pacman','zpac');
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// Print equations where the variable appears in
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search('x1bar')
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search('x2bar', 'withparamvalues')
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e_c_m_iterative_ols = M_.params(strmatch('e_c_m', M_.param_names, 'exact'));
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c_z_1_iterative_ols = M_.params(strmatch('c_z_1', M_.param_names, 'exact'));
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c_z_2_iterative_ols = M_.params(strmatch('c_z_2', M_.param_names, 'exact'));
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resid_iterative_ols = oo_.pac.pacman.residual;
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fprintf('Estimate of e_c_m: %f \n', e_c_m_iterative_ols)
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fprintf('Estimate of c_z_1: %f \n', c_z_1_iterative_ols)
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fprintf('Estimate of c_z_2: %f \n', c_z_2_iterative_ols)
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difference = abs(resid_nls-resid_iterative_ols);
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if any(difference.data > 1e-4)
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error('Iterative OLS and NLS do not provide consistent results.')
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end
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