Add structural VAR as an auxiliary model for VAR based expectations and PAC expectations.
Ref. #1785 Just add option `structural` to the `var_model` command.var-model-with-constant
parent
547b7aef45
commit
54f80e88d2
GPG Key ID:
295C1FE89E17EB3C
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@ -42,9 +42,9 @@ if nargin < 2
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end
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if strcmp(auxiliary_model_type, 'var')
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AR = feval([M_.fname '.var_ar'], auxiliary_model_name, M_.params);
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[AR, ~] = feval(sprintf('%s.varmatrices', M_.fname), auxiliary_model_name, M_.params, M_.var.(auxiliary_model_name).structural);
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elseif strcmp(auxiliary_model_type, 'trend_component')
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[AR, A0, A0star] = feval([M_.fname '.trend_component_ar_a0'], auxiliary_model_name, M_.params);
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[AR, A0, A0star] = feval(sprintf('%s.trend_component_ar_a0', M_.fname), auxiliary_model_name, M_.params);
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else
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error('Unknown type of auxiliary model.')
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end
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@ -1 +1 @@
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Subproject commit c9c36c037aa6d6c67f8fbb2236b03729a22e5878
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Subproject commit 6b9d94405c44fe2533a2d8bc377173a2a70f3a54
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@ -461,6 +461,8 @@ ECB_MODFILES = \
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var-expectations/8/substitution.mod \
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var-expectations/9/example1.mod \
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var-expectations/10/example1.mod \
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var-expectations/11/example1.mod \
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var-expectations/12/example1.mod \
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trend-component-and-var-models/vm1.mod \
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trend-component-and-var-models/vm2.mod \
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trend-component-and-var-models/vm3.mod \
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@ -494,6 +496,8 @@ ECB_MODFILES = \
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pac/var-5/substitution.mod \
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pac/var-6/example1.mod \
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pac/var-6/substitution.mod \
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pac/var-7/example1.mod \
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pac/var-7/substitution.mod \
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pac/trend-component-1/example1.mod \
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pac/trend-component-2/example1.mod \
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pac/trend-component-3/example1.mod \
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@ -842,6 +846,8 @@ pac/var-5/substitution.m.trs: pac/var-5/example1.m.trs
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pac/var-5/substitution.o.trs: pac/var-5/example1.o.trs
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pac/var-6/substitution.m.trs: pac/var-6/example1.m.trs
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pac/var-6/substitution.o.trs: pac/var-6/example1.o.trs
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pac/var-7/substitution.m.trs: pac/var-7/example1.m.trs
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pac/var-7/substitution.o.trs: pac/var-7/example1.o.trs
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pac/trend-component-14/substitution.m.trs: pac/trend-component-14/example1.m.trs
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pac/trend-component-14/substitution.o.trs: pac/trend-component-14/example1.o.trs
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@ -1,6 +1,6 @@
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function run_all_tests()
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% Copyright (C) 2018 Dynare Team
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% Copyright © 2018-2021 Dynare Team
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%
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% This file is part of Dynare.
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%
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@ -23,6 +23,9 @@ r = [r; run_this_test('var-1')];
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r = [r; run_this_test('var-2')];
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r = [r; run_this_test('var-3')];
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r = [r; run_this_test('var-4')];
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r = [r; run_this_test('var-5')];
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r = [r; run_this_test('var-6')];
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r = [r; run_this_test('var-7')];
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r = [r; run_this_test('trend-component-1')];
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r = [r; run_this_test('trend-component-2')];
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@ -31,6 +34,8 @@ r = [r; run_this_test('trend-component-4')];
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r = [r; run_this_test('trend-component-5')];
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r = [r; run_this_test('trend-component-6')];
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r = [r; run_this_test('trend-component-7')];
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r = [r; run_this_test('trend-component-8-mc-iterative-ols')];
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r = [r; run_this_test('trend-component-8-mc-nls')];
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r = [r; run_this_test('trend-component-9')];
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r = [r; run_this_test('trend-component-10')];
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r = [r; run_this_test('trend-component-11')];
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@ -40,7 +45,25 @@ r = [r; run_this_test('trend-component-13b')];
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r = [r; run_this_test('trend-component-14')];
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r = [r; run_this_test('trend-component-15')];
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r = [r; run_this_test('trend-component-16')];
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r = [r; run_this_test('trend-component-17')];
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r = [r; run_this_test('trend-component-18')];
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r = [r; run_this_test('trend-component-19')];
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r = [r; run_this_test('trend-component-19-growth-lin-comb')];
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r = [r; run_this_test('trend-component-20-1')];
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r = [r; run_this_test('trend-component-20-2')];
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r = [r; run_this_test('trend-component-20-3')];
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r = [r; run_this_test('trend-component-20-4')];
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r = [r; run_this_test('trend-component-21')];
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r = [r; run_this_test('trend-component-22')];
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r = [r; run_this_test('trend-component-23')];
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r = [r; run_this_test('trend-component-24')];
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r = [r; run_this_test('trend-component-25')];
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r = [r; run_this_test('trend-component-26')];
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r = [r; run_this_test('trend-component-27')];
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r = [r; run_this_test('trend-component-28')];
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r = [r; run_this_test('trend-component-29')];
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r = [r; run_this_test('trend-component-30')];
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r = [r; run_this_test('trend-component-31')];
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print_results(r);
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@ -0,0 +1,10 @@
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#!/bin/sh
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rm -rf example1
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rm -rf +example1
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rm -f example1*.mat
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rm -f example1.log
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rm -rf substitution
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rm -rf +substitution
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rm -f substitution*.mat
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rm -f substitution.log
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@ -0,0 +1,79 @@
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// --+ options: json=compute, stochastic +--
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var y x z u;
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varexo ex ey ez eu;
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parameters a_y_0 a_y_1 a_y_2 b_y_1 b_y_2 b_x_0 b_x_1 b_x_2 ; // VAR parameters
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parameters g beta e_c_m c_z_1 c_z_2; // PAC equation parameters
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a_y_0 = .4;
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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_0 = -.1;
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b_x_1 = -.1;
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b_x_2 = -.2;
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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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g = .1;
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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, growth=diff(u(-1)));
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model;
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[name='eq:u']
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diff(u) = g + eu;
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[name='eq:y']
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y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + a_y_0*diff(x) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
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[name='eq:x']
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diff(x) = b_x_0*y + b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2) + ex ;
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[name='eq:pac']
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diff(z) = e_c_m*(x(-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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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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var eu = 0.1;
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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 20 periods
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set_dynare_seed('default');
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TrueData = simul_backward_model(initialconditions, 20);
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// Print expanded PAC_EXPECTATION term.
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pac.print('pacman', 'eq:pac');
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verbatim;
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set_dynare_seed('default');
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y = zeros(M_.endo_nbr,1);
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y(1:M_.orig_endo_nbr) = rand(M_.orig_endo_nbr, 1);
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x = randn(M_.exo_nbr,1);
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y = example1.set_auxiliary_variables(y, x, M_.params);
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y = [y(find(M_.lead_lag_incidence(1,:))); y];
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[residual, g1] = example1.dynamic(y, x', M_.params, oo_.steady_state, 1);
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save('example1.mat', 'residual', 'g1', 'TrueData');
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end;
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@ -0,0 +1,88 @@
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// --+ options: transform_unary_ops, json=compute, stochastic +--
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var y x z u;
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varexo ex ey ez eu;
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parameters a_y_0 a_y_1 a_y_2 b_y_1 b_y_2 b_x_0 b_x_1 b_x_2 g; // VAR parameters
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parameters e_c_m c_z_1 c_z_2; // PAC equation parameters
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a_y_0 = .4;
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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_0 = -.1;
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b_x_1 = -.1;
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b_x_2 = -.2;
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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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g = .1;
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@#include "example1/model/pac-expectations/eq0-pacman-parameters.inc"
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model;
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[name='eq:u']
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diff(u) = g + eu;
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[name='eq:y']
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y = a_y_1*y(-1) + a_y_2*diff(x(-1)) + a_y_0*diff(x) + b_y_1*y(-2) + b_y_2*diff(x(-2)) + ey ;
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[name='eq:x']
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diff(x) = b_x_0*y + b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2) + ex ;
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[name='eq:pac']
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diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) +
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@#include "example1/model/pac-expectations/eq0-pacman-growth-neutrality-correction.inc"
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+
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@#include "example1/model/pac-expectations/eq0-pacman-expression.inc"
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+ 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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var eu = 0.1;
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end;
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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 20 periods
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set_dynare_seed('default');
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TrueData = simul_backward_model(initialconditions, 20);
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verbatim;
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set_dynare_seed('default');
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y = zeros(M_.endo_nbr,1);
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y(1:M_.orig_endo_nbr) = rand(M_.orig_endo_nbr, 1);
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x = randn(M_.exo_nbr,1);
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y = substitution.set_auxiliary_variables(y, x, M_.params);
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y = [y(find(M_.lead_lag_incidence(1,:))); y];
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example1 = load('example1.mat');
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[residual, g1] = substitution.dynamic(y, x', M_.params, oo_.steady_state, 1);
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if max(abs(example1.TrueData.data(:)-TrueData.data(:)))>1e-9
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error('Simulations do not match.')
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end
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if ~isequal(length(residual), length(example1.residual)) || max(abs(example1.residual-residual))>1e-8
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warning('Residuals do not match!')
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end
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if ~isequal(length(g1(:)), length(example1.g1(:))) || max(abs(example1.g1(:)-g1(:)))>1e-8
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warning('Jacobian matrices do not match!')
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end
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delete('example1.mat');
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end;
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// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(structural, model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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// Define a VAR_EXPECTATION_MODEL
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var_expectation_model(model_name = varexp, expression = diff(log(x)), auxiliary_model_name = toto, horizon = 1, discount = beta) ;
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model;
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[ name = 'X' ]
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diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + (1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
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[ name = 'Z' ]
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diff(z) = f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
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[ name = 'Y' ]
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log(y) = diff(log(x)) + d*log(y(-2)) + e*diff(z(-1)) + e_y;
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foo = var_expectation(varexp);
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end;
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[ar, a0] = example1.varmatrices('toto', M_.params);
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assert(isequal(diag(a0), ones(3,1)), 'Diagonal of a0 is wrong.')
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assert(a0(1,3)==-b, 'Element (1,3) in A0 is wrong.')
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assert(a0(1,2)==0, 'Element (1,2) in A0 is wrong.')
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assert(a0(2,1)==-1, 'Element (2,1) in A0 is wrong.')
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assert(a0(2,3)==0, 'Element (2,3) in A0 is wrong.')
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assert(a0(3,1)==f, 'Element (3,1) in A0 is wrong.')
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assert(a0(3,2)==0, 'Element (3,1) in A0 is wrong.')
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assert(isequal(ar(:,:,1), [a 0 0; 0 0 e; 0 0 f]), 'First autoregressive matrix is wrong');
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assert(isequal(ar(:,:,2), [1-a 0 c; 0 d 0; 0 0 c]), 'Second autoregressive matrix is wrong');
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// --+ options: stochastic,json=compute +--
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var foo z x y;
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varexo e_x e_y e_z;
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parameters a b c d e f beta ;
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a = .9;
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b = -.2;
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c = .3;
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f = .8;
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d = .5;
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e = .4;
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beta = 1/(1+.02);
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// Define a VAR model from a subset of equations in the model block.
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var_model(structural, model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
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// Define a VAR_EXPECTATION_MODEL
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var_expectation_model(model_name = varexp, expression = diff(log(x)), auxiliary_model_name = toto, horizon = 1, discount = beta) ;
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model;
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[ name = 'X' ]
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diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + (1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
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[ name = 'Z' ]
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diff(z) = f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
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[ name = 'Y' ]
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log(y) = diff(log(x)) + d*log(y(-2)) + e*diff(z(-1)) + e_y;
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foo = var_expectation(varexp);
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end;
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// Initialize the VAR expectation model, will build the companion matrix of the VAR.
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var_expectation.initialize('varexp')
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// Update VAR_EXPECTATION reduced form parameters
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var_expectation.update('varexp');
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// Print expanded VAR_EXPECTATION expression in a file (to be included in substitution.mod).
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var_expectation.print('varexp');
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shocks;
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var e_x = .01;
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var e_y = .01;
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var e_z = .01;
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end;
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verbatim;
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initialconditions =zeros(3,4);
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initialconditions(3,1) = .1; % foo(-1)
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initialconditions(:,2) = .2; % y(-1)
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initialconditions(3,3) = .3; % z(-1)
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initialconditions(2,3) = .4; % z(-2)
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initialconditions(3,4) = .5; % x(-1)
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initialconditions(2,4) = .6; % x(-2)
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initialconditions(1,4) = .7; % x(-3)
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initialconditions = ...
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dseries(initialconditions, dates('2000Q1'), {'foo', 'y','z', 'x'});
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set_dynare_seed('default');
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ts = simul_backward_model(initialconditions, 15);
|
||||
foo = ts.foo.data;
|
||||
% Evaluate the (VAR) expectation term
|
||||
ts{'toto'} = example1.var_expectations.varexp.evaluate(ts);
|
||||
% Check that the evaluation is correct.
|
||||
range = dates('2000Q4'):dates('2004Q2');
|
||||
if max(abs(ts(range).foo.data-ts(range).toto.data))>1e-5
|
||||
error('Expectation term evaluations do not match!')
|
||||
end
|
||||
end;
|
||||
Loading…
Reference in New Issue