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Commit deec7ca5 authored by Stéphane Adjemian's avatar Stéphane Adjemian
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Added new example.

This example allows to test that:

1. the routines are working as expected if the VAR equations are
preceeded by other equations.

2. the simulation algorithm is working if the PAC equation is
augmented by an endogenous variables (exogenous wrt the auxiliary
model model).
parent fc925895
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#!/bin/sh
rm -rf example
rm -f example*.json
rm -f example*.m
rm -f example*.mat
rm -f example.log
\ No newline at end of file
// --+ options: json=compute, stochastic +--
var x1 x2 x1bar x2bar z y;
varexo ex1 ex2 ex1bar ex2bar ez ey;
parameters
rho_1 rho_2
a_x1_0 a_x1_1 a_x1_2 a_x1_x2_1 a_x1_x2_2
a_x2_0 a_x2_1 a_x2_2 a_x2_x1_1 a_x2_x1_2
e_c_m c_z_1 c_z_2 gamma beta ;
rho_1 = .9;
rho_2 = -.2;
a_x1_0 = -.9;
a_x1_1 = .4;
a_x1_2 = .3;
a_x1_x2_1 = .1;
a_x1_x2_2 = .2;
a_x2_0 = -.9;
a_x2_1 = .2;
a_x2_2 = -.1;
a_x2_x1_1 = -.1;
a_x2_x1_2 = .2;
beta = .2;
e_c_m = .5;
c_z_1 = .2;
c_z_2 = -.1;
gamma = .7;
var_model(model_name=toto, eqtags=['eq:x1', 'eq:x2', 'eq:x1bar', 'eq:x2bar']);
pac_model(var_model_name=toto, discount=beta, model_name=pacman, undiff('eq:x1', 1), undiff('eq:x2', 1));
model;
[name='eq:y']
y = rho_1*y(-1) + rho_2*y(-2) + ey;
[name='eq:x1', data_type='nonstationary']
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;
[name='eq:x2', data_type='nonstationary']
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;
[name='eq:x1bar', data_type='nonstationary']
x1bar = x1bar(-1) + ex1bar;
[name='eq:x2bar', data_type='nonstationary']
x2bar = x2bar(-1) + ex2bar;
[name='eq:pac']
diff(z) = gamma*(e_c_m*(x1(-1)-z(-1)) + c_z_1*diff(z(-1)) + c_z_2*diff(z(-2)) + pac_expectation(pacman)) + (1-gamma)*y + ez;
end;
shocks;
var ex1 = 1.0;
var ex2 = 1.0;
var ex1bar = 1.0;
var ex2bar = 1.0;
var ez = 1.0;
var ey = 0.1;
end;
// Build the companion matrix of the VAR model (toto).
get_companion_matrix('toto', 'pacman');
// Update the parameters of the PAC expectation model (h0 and h1 vectors).
pac.update.equation('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 500 periods
TrueData = simul_backward_model(initialconditions, 500);
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