Verified Commit 54f80e88 authored by Stéphane Adjemian's avatar Stéphane Adjemian
Browse files

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.
parent 547b7aef
......@@ -42,9 +42,9 @@ if nargin < 2
end
if strcmp(auxiliary_model_type, 'var')
AR = feval([M_.fname '.var_ar'], auxiliary_model_name, M_.params);
[AR, ~] = feval(sprintf('%s.varmatrices', M_.fname), auxiliary_model_name, M_.params, M_.var.(auxiliary_model_name).structural);
elseif strcmp(auxiliary_model_type, 'trend_component')
[AR, A0, A0star] = feval([M_.fname '.trend_component_ar_a0'], auxiliary_model_name, M_.params);
[AR, A0, A0star] = feval(sprintf('%s.trend_component_ar_a0', M_.fname), auxiliary_model_name, M_.params);
else
error('Unknown type of auxiliary model.')
end
......
Subproject commit c9c36c037aa6d6c67f8fbb2236b03729a22e5878
Subproject commit 6b9d94405c44fe2533a2d8bc377173a2a70f3a54
......@@ -461,6 +461,8 @@ ECB_MODFILES = \
var-expectations/8/substitution.mod \
var-expectations/9/example1.mod \
var-expectations/10/example1.mod \
var-expectations/11/example1.mod \
var-expectations/12/example1.mod \
trend-component-and-var-models/vm1.mod \
trend-component-and-var-models/vm2.mod \
trend-component-and-var-models/vm3.mod \
......@@ -494,6 +496,8 @@ ECB_MODFILES = \
pac/var-5/substitution.mod \
pac/var-6/example1.mod \
pac/var-6/substitution.mod \
pac/var-7/example1.mod \
pac/var-7/substitution.mod \
pac/trend-component-1/example1.mod \
pac/trend-component-2/example1.mod \
pac/trend-component-3/example1.mod \
......@@ -842,6 +846,8 @@ pac/var-5/substitution.m.trs: pac/var-5/example1.m.trs
pac/var-5/substitution.o.trs: pac/var-5/example1.o.trs
pac/var-6/substitution.m.trs: pac/var-6/example1.m.trs
pac/var-6/substitution.o.trs: pac/var-6/example1.o.trs
pac/var-7/substitution.m.trs: pac/var-7/example1.m.trs
pac/var-7/substitution.o.trs: pac/var-7/example1.o.trs
pac/trend-component-14/substitution.m.trs: pac/trend-component-14/example1.m.trs
pac/trend-component-14/substitution.o.trs: pac/trend-component-14/example1.o.trs
......
function run_all_tests()
% Copyright (C) 2018 Dynare Team
% Copyright © 2018-2021 Dynare Team
%
% This file is part of Dynare.
%
......@@ -23,6 +23,9 @@ r = [r; run_this_test('var-1')];
r = [r; run_this_test('var-2')];
r = [r; run_this_test('var-3')];
r = [r; run_this_test('var-4')];
r = [r; run_this_test('var-5')];
r = [r; run_this_test('var-6')];
r = [r; run_this_test('var-7')];
r = [r; run_this_test('trend-component-1')];
r = [r; run_this_test('trend-component-2')];
......@@ -31,6 +34,8 @@ r = [r; run_this_test('trend-component-4')];
r = [r; run_this_test('trend-component-5')];
r = [r; run_this_test('trend-component-6')];
r = [r; run_this_test('trend-component-7')];
r = [r; run_this_test('trend-component-8-mc-iterative-ols')];
r = [r; run_this_test('trend-component-8-mc-nls')];
r = [r; run_this_test('trend-component-9')];
r = [r; run_this_test('trend-component-10')];
r = [r; run_this_test('trend-component-11')];
......@@ -40,7 +45,25 @@ r = [r; run_this_test('trend-component-13b')];
r = [r; run_this_test('trend-component-14')];
r = [r; run_this_test('trend-component-15')];
r = [r; run_this_test('trend-component-16')];
r = [r; run_this_test('trend-component-17')];
r = [r; run_this_test('trend-component-18')];
r = [r; run_this_test('trend-component-19')];
r = [r; run_this_test('trend-component-19-growth-lin-comb')];
r = [r; run_this_test('trend-component-20-1')];
r = [r; run_this_test('trend-component-20-2')];
r = [r; run_this_test('trend-component-20-3')];
r = [r; run_this_test('trend-component-20-4')];
r = [r; run_this_test('trend-component-21')];
r = [r; run_this_test('trend-component-22')];
r = [r; run_this_test('trend-component-23')];
r = [r; run_this_test('trend-component-24')];
r = [r; run_this_test('trend-component-25')];
r = [r; run_this_test('trend-component-26')];
r = [r; run_this_test('trend-component-27')];
r = [r; run_this_test('trend-component-28')];
r = [r; run_this_test('trend-component-29')];
r = [r; run_this_test('trend-component-30')];
r = [r; run_this_test('trend-component-31')];
print_results(r);
......
#!/bin/sh
rm -rf example1
rm -rf +example1
rm -f example1*.mat
rm -f example1.log
rm -rf substitution
rm -rf +substitution
rm -f substitution*.mat
rm -f substitution.log
// --+ options: json=compute, stochastic +--
var y x z u;
varexo ex ey ez eu;
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
parameters g beta e_c_m c_z_1 c_z_2; // PAC equation parameters
a_y_0 = .4;
a_y_1 = .2;
a_y_2 = .3;
b_y_1 = .1;
b_y_2 = .4;
b_x_0 = -.1;
b_x_1 = -.1;
b_x_2 = -.2;
beta = .9;
e_c_m = .1;
c_z_1 = .7;
c_z_2 = -.3;
g = .1;
var_model(model_name=toto, structural, eqtags=['eq:x', 'eq:y']);
pac_model(auxiliary_model_name=toto, discount=beta, model_name=pacman, growth=diff(u(-1)));
model;
[name='eq:u']
diff(u) = g + eu;
[name='eq:y']
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 ;
[name='eq:x']
diff(x) = b_x_0*y + b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2) + ex ;
[name='eq:pac']
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;
end;
shocks;
var ex = 1.0;
var ey = 1.0;
var ez = 1.0;
var eu = 0.1;
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. Please use more sensible values if any...
initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
// Simulate the model for 20 periods
set_dynare_seed('default');
TrueData = simul_backward_model(initialconditions, 20);
// Print expanded PAC_EXPECTATION term.
pac.print('pacman', 'eq:pac');
verbatim;
set_dynare_seed('default');
y = zeros(M_.endo_nbr,1);
y(1:M_.orig_endo_nbr) = rand(M_.orig_endo_nbr, 1);
x = randn(M_.exo_nbr,1);
y = example1.set_auxiliary_variables(y, x, M_.params);
y = [y(find(M_.lead_lag_incidence(1,:))); y];
[residual, g1] = example1.dynamic(y, x', M_.params, oo_.steady_state, 1);
save('example1.mat', 'residual', 'g1', 'TrueData');
end;
// --+ options: transform_unary_ops, json=compute, stochastic +--
var y x z u;
varexo ex ey ez eu;
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
parameters e_c_m c_z_1 c_z_2; // PAC equation parameters
a_y_0 = .4;
a_y_1 = .2;
a_y_2 = .3;
b_y_1 = .1;
b_y_2 = .4;
b_x_0 = -.1;
b_x_1 = -.1;
b_x_2 = -.2;
beta = .9;
e_c_m = .1;
c_z_1 = .7;
c_z_2 = -.3;
g = .1;
@#include "example1/model/pac-expectations/eq0-pacman-parameters.inc"
model;
[name='eq:u']
diff(u) = g + eu;
[name='eq:y']
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 ;
[name='eq:x']
diff(x) = b_x_0*y + b_x_1*y(-2) + b_x_2*diff(x(-1)) + g*(1-b_x_2) + ex ;
[name='eq:pac']
diff(z) = e_c_m*(x(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) +
@#include "example1/model/pac-expectations/eq0-pacman-growth-neutrality-correction.inc"
+
@#include "example1/model/pac-expectations/eq0-pacman-expression.inc"
+ ez;
end;
shocks;
var ex = 1.0;
var ey = 1.0;
var ez = 1.0;
var eu = 0.1;
end;
// Set initial conditions to zero. Please use more sensible values if any...
initialconditions = dseries(zeros(10, M_.endo_nbr+M_.exo_nbr), 2000Q1, vertcat(M_.endo_names,M_.exo_names));
// Simulate the model for 20 periods
set_dynare_seed('default');
TrueData = simul_backward_model(initialconditions, 20);
verbatim;
set_dynare_seed('default');
y = zeros(M_.endo_nbr,1);
y(1:M_.orig_endo_nbr) = rand(M_.orig_endo_nbr, 1);
x = randn(M_.exo_nbr,1);
y = substitution.set_auxiliary_variables(y, x, M_.params);
y = [y(find(M_.lead_lag_incidence(1,:))); y];
example1 = load('example1.mat');
[residual, g1] = substitution.dynamic(y, x', M_.params, oo_.steady_state, 1);
if max(abs(example1.TrueData.data(:)-TrueData.data(:)))>1e-9
error('Simulations do not match.')
end
if ~isequal(length(residual), length(example1.residual)) || max(abs(example1.residual-residual))>1e-8
warning('Residuals do not match!')
end
if ~isequal(length(g1(:)), length(example1.g1(:))) || max(abs(example1.g1(:)-g1(:)))>1e-8
warning('Jacobian matrices do not match!')
end
delete('example1.mat');
end;
// --+ options: stochastic,json=compute +--
var foo z x y;
varexo e_x e_y e_z;
parameters a b c d e f beta ;
a = .9;
b = -.2;
c = .3;
f = .8;
d = .5;
e = .4;
beta = 1/(1+.02);
// Define a VAR model from a subset of equations in the model block.
var_model(structural, model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
// Define a VAR_EXPECTATION_MODEL
var_expectation_model(model_name = varexp, expression = diff(log(x)), auxiliary_model_name = toto, horizon = 1, discount = beta) ;
model;
[ name = 'X' ]
diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + (1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
[ name = 'Z' ]
diff(z) = f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
[ name = 'Y' ]
log(y) = diff(log(x)) + d*log(y(-2)) + e*diff(z(-1)) + e_y;
foo = var_expectation(varexp);
end;
[ar, a0] = example1.varmatrices('toto', M_.params);
assert(isequal(diag(a0), ones(3,1)), 'Diagonal of a0 is wrong.')
assert(a0(1,3)==-b, 'Element (1,3) in A0 is wrong.')
assert(a0(1,2)==0, 'Element (1,2) in A0 is wrong.')
assert(a0(2,1)==-1, 'Element (2,1) in A0 is wrong.')
assert(a0(2,3)==0, 'Element (2,3) in A0 is wrong.')
assert(a0(3,1)==f, 'Element (3,1) in A0 is wrong.')
assert(a0(3,2)==0, 'Element (3,1) in A0 is wrong.')
assert(isequal(ar(:,:,1), [a 0 0; 0 0 e; 0 0 f]), 'First autoregressive matrix is wrong');
assert(isequal(ar(:,:,2), [1-a 0 c; 0 d 0; 0 0 c]), 'Second autoregressive matrix is wrong');
// --+ options: stochastic,json=compute +--
var foo z x y;
varexo e_x e_y e_z;
parameters a b c d e f beta ;
a = .9;
b = -.2;
c = .3;
f = .8;
d = .5;
e = .4;
beta = 1/(1+.02);
// Define a VAR model from a subset of equations in the model block.
var_model(structural, model_name = toto, eqtags = [ 'X' 'Y' 'Z' ]);
// Define a VAR_EXPECTATION_MODEL
var_expectation_model(model_name = varexp, expression = diff(log(x)), auxiliary_model_name = toto, horizon = 1, discount = beta) ;
model;
[ name = 'X' ]
diff(log(x)) = b*diff(z) + a*diff(log(x(-1))) + (1-a)*diff(log(x(-2))) + c*diff(z(-2)) + e_x;
[ name = 'Z' ]
diff(z) = f*(diff(z(-1))-diff(log(x)))+c*diff(z(-2)) + e_z;
[ name = 'Y' ]
log(y) = diff(log(x)) + d*log(y(-2)) + e*diff(z(-1)) + e_y;
foo = var_expectation(varexp);
end;
// Initialize the VAR expectation model, will build the companion matrix of the VAR.
var_expectation.initialize('varexp')
// Update VAR_EXPECTATION reduced form parameters
var_expectation.update('varexp');
// Print expanded VAR_EXPECTATION expression in a file (to be included in substitution.mod).
var_expectation.print('varexp');
shocks;
var e_x = .01;
var e_y = .01;
var e_z = .01;
end;
verbatim;
initialconditions =zeros(3,4);
initialconditions(3,1) = .1; % foo(-1)
initialconditions(:,2) = .2; % y(-1)
initialconditions(3,3) = .3; % z(-1)
initialconditions(2,3) = .4; % z(-2)
initialconditions(3,4) = .5; % x(-1)
initialconditions(2,4) = .6; % x(-2)
initialconditions(1,4) = .7; % x(-3)
initialconditions = ...
dseries(initialconditions, dates('2000Q1'), {'foo', 'y','z', 'x'});
set_dynare_seed('default');
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;
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