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/*
* Copyright © 2004-2023 Dynare Team
*
* This file is part of Dynare.
*
* Dynare is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Dynare is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Dynare. If not, see <https://www.gnu.org/licenses/>.
*/
var m ${m}$ (long_name='money growth')
P ${P}$ (long_name='Price level')
c ${c}$ (long_name='consumption')
e ${e}$ (long_name='capital stock')
W ${W}$ (long_name='Wage rate')
R ${R}$ (long_name='interest rate')
k ${k}$ (long_name='capital stock')
d ${d}$ (long_name='dividends')
n ${n}$ (long_name='labor')
l ${l}$ (long_name='loans')
gy_obs ${\Delta \ln GDP}$ (long_name='detrended capital stock')
gp_obs ${\Delta \ln P}$ (long_name='detrended capital stock')
y ${y}$ (long_name='detrended output')
dA ${\Delta A}$ (long_name='TFP growth')
;
varexo e_a ${\epsilon_A}$ (long_name='TFP shock')
e_m ${\epsilon_M}$ (long_name='Money growth shock')
;
parameters alp ${\alpha}$ (long_name='capital share')
bet ${\beta}$ (long_name='discount factor')
gam ${\gamma}$ (long_name='long-run TFP growth')
logmst ${\log(m^*)}$ (long_name='long-run money growth')
rho ${\rho}$ (long_name='autocorrelation money growth')
phi ${\phi}$ (long_name='labor weight in consumption')
del ${\delta}$ (long_name='depreciation rate')
;
% roughly picked values to allow simulating the model before estimation
alp = 0.33;
bet = 0.99;
gam = 0.003;
logmst = log(1.011);
rho = 0.7;
phi = 0.787;
del = 0.02;
model;
[name='NC before eq. (1), TFP growth equation']
dA = exp(gam+e_a);
[name='NC eq. (2), money growth rate']
log(m) = (1-rho)*logmst + rho*log(m(-1))+e_m;
[name='NC eq. (A1), Euler equation']
-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
[name='NC below eq. (A1), firm borrowing constraint']
W = l/n;
[name='NC eq. (A2), intratemporal labour market condition']
-(phi/(1-phi))*(c*P/(1-n))+l/n = 0;
[name='NC below eq. (A2), credit market clearing']
R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
[name='NC eq. (A3), credit market optimality']
1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
[name='NC eq. (18), aggregate resource constraint']
c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
[name='NC eq. (19), money market condition']
P*c = m;
[name='NC eq. (20), credit market equilibrium condition']
m-1+d = l;
[name='Definition TFP shock']
e = exp(e_a);
[name='Implied by NC eq. (18), production function']
y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
[name='Observation equation GDP growth']
gy_obs = dA*y/y(-1);
[name='Observation equation price level']
gp_obs = (P/P(-1))*m(-1)/dA;
end;
shocks;
var e_a; stderr 0.014;
var e_m; stderr 0.005;
end;
steady_state_model;
dA = exp(gam);
gst = 1/dA;
m = exp(logmst);
khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/m )^(-1);
nust = phi*m^2/( (1-alp)*(1-phi)*bet*gst^alp*khst^alp );
n = xist/(nust+xist);
P = xist + nust;
k = khst*n;
l = phi*m*n/( (1-phi)*(1-n) );
c = m/P;
d = l - m + 1;
y = k^alp*n^(1-alp)*gst^alp;
R = m/bet;
W = l/n;
ist = y-c;
q = 1 - d;
e = 1;
gp_obs = m/dA;
gy_obs = dA;
end;
steady;
check;
% Table 1 of Schorfheide (2000)
estimated_params;
alp, beta_pdf, 0.356, 0.02;
bet, beta_pdf, 0.993, 0.002;
gam, normal_pdf, 0.0085, 0.003;
logmst, normal_pdf, 0.0002, 0.007;
rho, beta_pdf, 0.129, 0.223;
phi, beta_pdf, 0.65, 0.05;
del, beta_pdf, 0.01, 0.005;
stderr e_a, inv_gamma_pdf, 0.035449, inf;
stderr e_m, inv_gamma_pdf, 0.008862, inf;
end;
varobs gp_obs gy_obs;
estimation(order=1, datafile=fs2000_data, loglinear,logdata, mode_compute=4, mh_replic=20000,
nodiagnostic, mh_nblocks=4, mh_jscale=0.8, posterior_sampler_options = ('save_tmp_file', 1),nograph);
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