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AnSchorfheide_Gaussian.mod
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AnSchorfheide_Gaussian.mod
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%/////////////////////////////////////////////////////////////
%//// Model: An and Schorfheide (2007) ////
%//// Author: Willi Mutschler ////
%//// Email: willi@mutschler.eu ////
%//// Version: August 26, 2016 ////
%/////////////////////////////////////////////////////////////
%----------------------------------------------------------------
% 0. Specify options: User Settings (For other settings and defaults see updateOptions.m
%----------------------------------------------------------------
% Order of approximation
@#define orderApp = 2
% Which distribution: 0:for Gaussian, 1:for Student_t
@#define distrib = 0
opt.HOSThirdOrder = 1; % Use third-order statistics, 0: do not include or 1: include
opt.HOSFourthOrder = 1; % User fourth-order statistics, 0: do not include or 1: include
opt.simdata = 1; % compare theoretical statistics with simulated data, 0: no or 1: yes
opt.MCruns = 1000; % Monte Carlo Runs for comparison
opt.numSim = 10000; % Number of observations of simulated data
opt.burnin = 1000; % Initial burnin periods, will be discarded from simulation
opt.antithetic = 1; % 1: Use antithetic shocks and quadratic resampling to reduce Monte Carlo variation
@#if distrib == 1
opt.distrib = 'Student_t'; %multivariate student-t distribution ('Gaussian' is default)
@#endif
%----------------------------------------------------------------
% 1. Declare variables and parameters
%----------------------------------------------------------------
var c dy p y R g z YGR INFL INT;
varexo e_z e_g e_r;
varobs YGR INFL INT;
parameters tau nu kap cyst psi1 psi2 rhor rhog rhoz rrst pist gamst sig_r sig_g sig_z;
@#if distrib == 1
parameters df_studt; % Please always use df_studt for degrees of freedom
@# endif
%----------------------------------------------------------------
% 2. Calibrate parameter values for simulated series (i.e. true values
%----------------------------------------------------------------
@#if distrib == 1
df_studt = 9;
@# endif
tau = 2.0000;
nu = 0.1000;
kap = 0.3300;
cyst = 0.8500;
psi1 = 1.5000;
psi2 = 0.1250;
rhor = 0.7500;
rhog = 0.9500;
rhoz = 0.9000;
rrst = 1.0000;
pist = 3.2000;
gamst = 0.5500;
sig_r = 0.002;
sig_g = 0.006;
sig_z = 0.003;
%----------------------------------------------------------------
% 3. Declare model equations
%----------------------------------------------------------------
model;
% Auxiliary parameters and variables
#pist2 = exp(pist/400);
#rrst2 = exp(rrst/400);
#bet = 1/rrst2;
#phi = tau*(1-nu)/nu/kap/pist2^2;
#gst = 1/cyst;
#cst = (1-nu)^(1/tau);
#yst = cst*gst;
% Euler equation, eq. (21)
1 = exp(-tau*c(+1)+tau*c+R-z(+1)-p(+1));
% Phillips curve, eq. (22)
(1-nu)/nu/phi/(pist2^2)*(exp(tau*c)-1) = (exp(p)-1)*((1-1/2/nu)*exp(p)+1/2/nu) - bet*(exp(p(+1))-1)*exp(-tau*c(+1)+tau*c+dy(+1)+p(+1));
% Equilibrium condition, eq. (23)
exp(c-y) = exp(-g) - phi*pist2^2*gst/2*(exp(p)-1)^2;
% Taylor Rule, eq. (24)
R = rhor*R(-1) + (1-rhor)*psi1*p + (1-rhor)*psi2*(y-g) + e_r;
% Fiscal rule, eq. (25)
g = rhog*g(-1) + e_g;
% Evolution of technology, eq (26)
z = rhoz*z(-1) + e_z;
% Auxiliary equation for output Growth
dy = y - y(-1);
% Measurement equations, eq. (38)
YGR = gamst+100*(dy+z);
INFL = pist+400*p;
INT = pist+rrst+4*gamst+400*R;
end;
%----------------------------------------------------------------
% 4. Specify variance of shock processes depending on distribution
%----------------------------------------------------------------
shocks;
@#if distrib == 1
% Student-t distribution
var e_r = df_studt/(df_studt-2)*sig_r^2;
var e_g = df_studt/(df_studt-2)*sig_g^2;
var e_z = df_studt/(df_studt-2)*sig_z^2;
@#else
% Gaussian distribution
var e_r = sig_r^2;
var e_g = sig_g^2;
var e_z = sig_z^2;
@#endif
end;
%----------------------------------------------------------------
% 5. Specify steady-state (either steady_state_model or initval)
%----------------------------------------------------------------
steady_state_model;
y = 0;
R = 0;
g = 0;
z = 0;
c = 0;
dy = 0;
p = 0;
YGR = gamst;
INFL = pist;
INT = pist + rrst + 4*gamst;
end;
%----------------------------------------------------------------
% 6. Specify parameters for GMM estimation
% Syntax: parameter, initial value, lower bound, upper bound, unifrom_pdf,,,,,tr
% Note that uniform_pdf has no meaning, we simply abuse Dynare's syntax to enable
% parameter transformations (if selected as an option: opt.transpar = 1, default is opt.transpar = 0)
% tr is parameter transformation type
% 0: no transformation needed
% 1: [a,b] -> [-1,1] -> [-inf,inf] by z/sqrt(1-z^2)
% 2: [0,inf] -> [-inf,inf] by b + ln(z-a);
% with a: lower bound and b: upper bound:
%----------------------------------------------------------------
estimated_params;
%parameter, initial value, lower bound, upper bound, unifrom_pdf,,,,, tr
% tau, 2, 1e-5, 10, uniform_pdf,,,,, 2;
nu, 0.1, 1e-5, 0.99999, uniform_pdf,,,,, 1;
kap, 0.3, 1e-5, 10, uniform_pdf,,,,, 2;
cyst, 0.85, 1e-5, 0.99999, uniform_pdf,,,,, 1;
psi1, 1, 0.1, 10, uniform_pdf,,,,, 2;
% psi2, 0.5, 1e-5, 10, uniform_pdf,,,,, 2;
rhor, 0.5, 1e-5, 0.99999, uniform_pdf,,,,, 1;
rhog, 0.8, 1e-5, 0.99999, uniform_pdf,,,,, 1;
rhoz, 0.66, 1e-5, 0.99999, uniform_pdf,,,,, 1;
% rrst, 0.8, 1e-5, 10, uniform_pdf,,,,, 2;
% pist, 4, 1e-5, 20, uniform_pdf,,,,, 2;
% gamst, 0.4, -5, 5, uniform_pdf,,,,, 0;
% sig_r, 0.003, 1e-8, 5, uniform_pdf,,,,,2;
% sig_g, 0.004, 1e-8, 5, uniform_pdf,,,,,2;
% sig_z, 0.004, 1e-8, 5, uniform_pdf,,,,,2;
end;
%----------------------------------------------------------------
% 7. Computations
%----------------------------------------------------------------
steady; check;
stoch_simul(order=@{orderApp},pruning,noprint,nomoments,irf=0);
DispHOS(opt);