1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
/*
* This file replicates the estimation of the cash in advance model (termed M1
* in the paper) described in Frank Schorfheide (2000): "Loss function-based
* evaluation of DSGE models", Journal of Applied Econometrics, 15(6), 645-670.
*
* The data are taken from the replication package at
* http://dx.doi.org/10.15456/jae.2022314.0708799949
*
* The prior distribution follows the one originally specified in Schorfheide's
* paper. Note that the elicited beta prior for rho in the paper
* implies an asymptote and corresponding prior mode at 0. It is generally
* recommended to avoid this extreme type of prior.
*
* Because the data are already logged and we use the loglinear option to conduct
* a full log-linearization, we need to use the logdata option.
*
* The equations are taken from J. Nason and T. Cogley (1994): "Testing the
* implications of long-run neutrality for monetary business cycle models",
* Journal of Applied Econometrics, 9, S37-S70, NC in the following.
* Note that there is an initial minus sign missing in equation (A1), p. S63.
*
* This implementation was originally written by Michel Juillard. Please note that the
* following copyright notice only applies to this Dynare implementation of the
* model.
*/
/*
* 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=2, mh_jscale=0.8, mode_check);
%uncomment the following lines to generate LaTeX-code of the model equations
%write_latex_original_model(write_equation_tags);
%collect_latex_files;
|
