433 lines
22 KiB
Modula-2
433 lines
22 KiB
Modula-2
% this is the Smets and Wouters (2007) model for which Komunjer and Ng (2011)
|
|
% derived the minimal state space system. In Dynare, however, we use more
|
|
% powerful minreal function
|
|
/*
|
|
* This file provides replication files for
|
|
* Smets, Frank and Wouters, Rafael (2007): "Shocks and Frictions in US Business Cycles: A Bayesian
|
|
* DSGE Approach", American Economic Review, 97(3), 586-606, that are compatible with Dynare 4.5 onwards
|
|
*
|
|
* To replicate the full results, you have to get back to the original replication files available at
|
|
* https://www.aeaweb.org/articles.php?doi=10.1257/aer.97.3.586 and include the respective estimation commands and mode-files.
|
|
*
|
|
* Notes:
|
|
* - The consumption Euler equation in the paper, equation (2), premultiplies the risk premium process \varepsilon_t^b,
|
|
* denoted by b in this code, by the coefficient c_3. In the code this prefactor is omitted by setting the
|
|
* coefficient to 1. As a consequence, b in this code actually is b:=c_3*\varepsilon_t^b. As a consequence, in
|
|
* the arbitrage equation for the value of capital in the paper, equation (4), the term 1*\varepsilon_t^b
|
|
* is replaced by 1/c_3*b, which is equal to \varepsilon_t^b given the above redefinition. This rescaling also explains why the
|
|
* standard deviation of the risk premium shock in the AR(1)-process for b has a different standard deviation than reported
|
|
* in the paper. However, the results are unaffected by this scaling factor (except for the fact that the posterior distribution
|
|
* reported in the paper cannot be directly translated to the present mod-file due to parameter correlation in the posterior.
|
|
* - As pointed out in Del Negro/Schorfheide (2012): "Notes on New-Keynesian Models"
|
|
* in the code implementation of equation (8) for both the flex price and the sticky price/wage economy,
|
|
* there is a (1/(1+cbetabar*cgamma)) missing in the i_2 in front of q_t (denoted qs in the code).
|
|
* Equation (8) in the paper reads:
|
|
* (1-(1-delta)/gamma)*(1+beta*gamma^(1-sigma))*gamma^2*varphi
|
|
* which translates to the code snippet:
|
|
* (1-(1-ctou)/cgamma)*(1+cbetabar*cgamma)*cgamma^2*csadjcost
|
|
* But the code implements
|
|
* (1-(1-ctou)/cgamma)*cgamma^2*csadjcost
|
|
* which corresponds to an equation reading
|
|
* (1-(1-delta)/gamma)*gamma^2*varphi
|
|
* - Chib/Ramamurthy (2010): "Tailored randomized block MCMC methods with application to DSGE models", Journal of Econometrics, 155, pp. 19-38
|
|
* have pointed out that the mode reported in the original Smets/Wouters (2007) paper is not actually the mode. \bar \pi (constepinf) is estimated lower
|
|
* while \bar \l (constelab) is higher.
|
|
* - Note that at the prior mean, [cmap,crhopinf] and [cmaw,crhow] are pairwise collinear. Thus, running identification at the prior
|
|
* mean will return a warning. But this is only a local issue. These parameters are only indistinguishable at the prior mean, but not
|
|
* at different points.
|
|
* - In the prior Table 1A in the paper, the
|
|
* - habit parameter $\lambda$ is erroneously labeled h
|
|
* - the fixed cost parameter $\phi_p$ is labeled $\Phi$
|
|
* - Table 1B claims that $\rho_{ga}$ follows a beta prior with B(0.5,0.2^2), but the code shows that it actually
|
|
* follows a normal distribution with N(0.5,0.25^2)
|
|
*
|
|
* This file was originally written by Frank Smets and Rafeal Wouters and has been updated by
|
|
* Johannes Pfeifer.
|
|
*
|
|
* Please note that the following copyright notice only applies to this Dynare
|
|
* implementation of the model
|
|
*/
|
|
|
|
/*
|
|
* Copyright © 2007-2013 Frank Smets and Raf Wouters
|
|
* Copyright © 2013-15 Johannes Pfeifer
|
|
* Copyright © 2020 Dynare Team
|
|
*
|
|
* This 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.
|
|
*
|
|
* This file 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 can receive a copy of the GNU General Public License
|
|
* at <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
var labobs ${lHOURS}$ (long_name='log hours worked')
|
|
robs ${FEDFUNDS}$ (long_name='Federal funds rate')
|
|
pinfobs ${dlP}$ (long_name='Inflation')
|
|
dy ${dlGDP}$ (long_name='Output growth rate')
|
|
dc ${dlCONS}$ (long_name='Consumption growth rate')
|
|
dinve ${dlINV}$ (long_name='Investment growth rate')
|
|
dw ${dlWAG}$ (long_name='Wage growth rate')
|
|
ewma ${\eta^{w,aux}}$ (long_name='Auxiliary wage markup moving average variable')
|
|
epinfma ${\eta^{p,aux}}$ (long_name='Auxiliary price markup moving average variable')
|
|
zcapf ${z^{flex}}$ (long_name='Capital utilization rate flex price economy')
|
|
rkf ${r^{k,flex}}$ (long_name='rental rate of capital flex price economy')
|
|
kf ${k^{s,flex}}$ (long_name='Capital services flex price economy')
|
|
pkf ${q^{flex}}$ (long_name='real value of existing capital stock flex price economy')
|
|
cf ${c^{flex}}$ (long_name='Consumption flex price economy')
|
|
invef ${i^{flex}}$ (long_name='Investment flex price economy')
|
|
yf ${y^{flex}}$ (long_name='Output flex price economy')
|
|
labf ${l^{flex}}$ (long_name='hours worked flex price economy')
|
|
wf ${w^{flex}}$ (long_name='real wage flex price economy')
|
|
rrf ${r^{flex}}$ (long_name='real interest rate flex price economy')
|
|
mc ${\mu_p}$ (long_name='gross price markup')
|
|
zcap ${z}$ (long_name='Capital utilization rate')
|
|
rk ${r^{k}}$ (long_name='rental rate of capital')
|
|
k ${k^{s}}$ (long_name='Capital services')
|
|
pk ${q}$ (long_name='real value of existing capital stock')
|
|
c ${c}$ (long_name='Consumption')
|
|
inve ${i}$ (long_name='Investment')
|
|
y ${y}$ (long_name='Output')
|
|
lab ${l}$ (long_name='hours worked')
|
|
pinf ${\pi}$ (long_name='Inflation')
|
|
w ${w}$ (long_name='real wage')
|
|
r ${r}$ (long_name='nominal interest rate')
|
|
a ${\varepsilon_a}$ (long_name='productivity process')
|
|
b ${c_2*\varepsilon_t^b}$ (long_name='Scaled risk premium shock')
|
|
g ${\varepsilon^g}$ (long_name='Exogenous spending')
|
|
qs ${\varepsilon^i}$ (long_name='Investment-specific technology')
|
|
ms ${\varepsilon^r}$ (long_name='Monetary policy shock process')
|
|
spinf ${\varepsilon^p}$ (long_name='Price markup shock process')
|
|
sw ${\varepsilon^w}$ (long_name='Wage markup shock process')
|
|
kpf ${k^{flex}}$ (long_name='Capital stock flex price economy')
|
|
kp ${k}$ (long_name='Capital stock')
|
|
;
|
|
|
|
varexo ea ${\eta^a}$ (long_name='productivity shock')
|
|
eb ${\eta^b}$ (long_name='Investment-specific technology shock')
|
|
eg ${\eta^g}$ (long_name='Spending shock')
|
|
eqs ${\eta^i}$ (long_name='Investment-specific technology shock')
|
|
em ${\eta^m}$ (long_name='Monetary policy shock')
|
|
epinf ${\eta^{p}}$ (long_name='Price markup shock')
|
|
ew ${\eta^{w}}$ (long_name='Wage markup shock')
|
|
;
|
|
|
|
parameters curvw ${\varepsilon_w}$ (long_name='Curvature Kimball aggregator wages')
|
|
cgy ${\rho_{ga}}$ (long_name='Feedback technology on exogenous spending')
|
|
curvp ${\varepsilon_p}$ (long_name='Curvature Kimball aggregator prices')
|
|
constelab ${\bar l}$ (long_name='steady state hours')
|
|
constepinf ${\bar \pi}$ (long_name='steady state inflation rate')
|
|
constebeta ${100(\beta^{-1}-1)}$ (long_name='time preference rate in percent')
|
|
cmaw ${\mu_w}$ (long_name='coefficient on MA term wage markup')
|
|
cmap ${\mu_p}$ (long_name='coefficient on MA term price markup')
|
|
calfa ${\alpha}$ (long_name='capital share')
|
|
czcap ${\psi}$ (long_name='capacity utilization cost')
|
|
csadjcost ${\varphi}$ (long_name='investment adjustment cost')
|
|
ctou ${\delta}$ (long_name='depreciation rate')
|
|
csigma ${\sigma_c}$ (long_name='risk aversion')
|
|
chabb ${\lambda}$ (long_name='external habit degree')
|
|
ccs ${d_4}$ (long_name='Unused parameter')
|
|
cinvs ${d_3}$ (long_name='Unused parameter')
|
|
cfc ${\phi_p}$ (long_name='fixed cost share')
|
|
cindw ${\iota_w}$ (long_name='Indexation to past wages')
|
|
cprobw ${\xi_w}$ (long_name='Calvo parameter wages')
|
|
cindp ${\iota_p}$ (long_name='Indexation to past prices')
|
|
cprobp ${\xi_p}$ (long_name='Calvo parameter prices')
|
|
csigl ${\sigma_l}$ (long_name='Frisch elasticity')
|
|
clandaw ${\phi_w}$ (long_name='Gross markup wages')
|
|
crdpi ${r_{\Delta \pi}}$ (long_name='Unused parameter')
|
|
crpi ${r_{\pi}}$ (long_name='Taylor rule inflation feedback')
|
|
crdy ${r_{\Delta y}}$ (long_name='Taylor rule output growth feedback')
|
|
cry ${r_{y}}$ (long_name='Taylor rule output level feedback')
|
|
crr ${\rho}$ (long_name='interest rate persistence')
|
|
crhoa ${\rho_a}$ (long_name='persistence productivity shock')
|
|
crhoas ${d_2}$ (long_name='Unused parameter')
|
|
crhob ${\rho_b}$ (long_name='persistence risk premium shock')
|
|
crhog ${\rho_g}$ (long_name='persistence spending shock')
|
|
crhols ${d_1}$ (long_name='Unused parameter')
|
|
crhoqs ${\rho_i}$ (long_name='persistence risk premium shock')
|
|
crhoms ${\rho_r}$ (long_name='persistence monetary policy shock')
|
|
crhopinf ${\rho_p}$ (long_name='persistence price markup shock')
|
|
crhow ${\rho_w}$ (long_name='persistence wage markup shock')
|
|
ctrend ${\bar \gamma}$ (long_name='net growth rate in percent')
|
|
cg ${\frac{\bar g}{\bar y}}$ (long_name='steady state exogenous spending share')
|
|
;
|
|
|
|
// fixed parameters
|
|
ctou=.025;
|
|
clandaw=1.5;
|
|
cg=0.18;
|
|
curvp=10;
|
|
curvw=10;
|
|
|
|
// estimated parameters initialisation
|
|
calfa=.24;
|
|
cbeta=.9995;
|
|
csigma=1.5;
|
|
cfc=1.5;
|
|
cgy=0.51;
|
|
|
|
csadjcost= 6.0144;
|
|
chabb= 0.6361;
|
|
cprobw= 0.8087;
|
|
csigl= 1.9423;
|
|
cprobp= 0.6;
|
|
cindw= 0.3243;
|
|
cindp= 0.47;
|
|
czcap= 0.2696;
|
|
crpi= 1.488;
|
|
crr= 0.8762;
|
|
cry= 0.0593;
|
|
crdy= 0.2347;
|
|
|
|
crhoa= 0.9977;
|
|
crhob= 0.5799;
|
|
crhog= 0.9957;
|
|
crhols= 0.9928;
|
|
crhoqs= 0.7165;
|
|
crhoas=1;
|
|
crhoms=0;
|
|
crhopinf=0;
|
|
crhow=0;
|
|
cmap = 0;
|
|
cmaw = 0;
|
|
|
|
constelab=0;
|
|
|
|
%% Added by JP to provide full calibration of model before estimation
|
|
constepinf=0.7;
|
|
constebeta=0.7420;
|
|
ctrend=0.3982;
|
|
|
|
model(linear);
|
|
//deal with parameter dependencies; taken from usmodel_stst.mod
|
|
#cpie=1+constepinf/100; %gross inflation rate
|
|
#cgamma=1+ctrend/100 ; %gross growth rate
|
|
#cbeta=1/(1+constebeta/100); %discount factor
|
|
|
|
#clandap=cfc; %fixed cost share/gross price markup
|
|
#cbetabar=cbeta*cgamma^(-csigma); %growth-adjusted discount factor in Euler equation
|
|
#cr=cpie/(cbeta*cgamma^(-csigma)); %steady state net real interest rate
|
|
#crk=(cbeta^(-1))*(cgamma^csigma) - (1-ctou); %R^k_{*}: steady state rental rate
|
|
#cw = (calfa^calfa*(1-calfa)^(1-calfa)/(clandap*crk^calfa))^(1/(1-calfa)); %steady state real wage
|
|
//cw = (calfa^calfa*(1-calfa)^(1-calfa)/(clandap*((cbeta^(-1))*(cgamma^csigma) - (1-ctou))^calfa))^(1/(1-calfa));
|
|
#cikbar=(1-(1-ctou)/cgamma); %k_1 in equation LOM capital, equation (8)
|
|
#cik=(1-(1-ctou)/cgamma)*cgamma; %i_k: investment-capital ratio
|
|
#clk=((1-calfa)/calfa)*(crk/cw); %labor to capital ratio
|
|
#cky=cfc*(clk)^(calfa-1); %k_y: steady state output ratio
|
|
#ciy=cik*cky; %consumption-investment ratio
|
|
#ccy=1-cg-cik*cky; %consumption-output ratio
|
|
#crkky=crk*cky; %z_y=R_{*}^k*k_y
|
|
#cwhlc=(1/clandaw)*(1-calfa)/calfa*crk*cky/ccy; %W^{h}_{*}*L_{*}/C_{*} used in c_2 in equation (2)
|
|
#cwly=1-crk*cky; %unused parameter
|
|
|
|
#conster=(cr-1)*100; %steady state federal funds rate ($\bar r$)
|
|
|
|
// flexible economy
|
|
|
|
[name='FOC labor with mpl expressed as function of rk and w, flex price economy']
|
|
0*(1-calfa)*a + 1*a = calfa*rkf+(1-calfa)*(wf) ;
|
|
[name='FOC capacity utilization, flex price economy']
|
|
zcapf = (1/(czcap/(1-czcap)))* rkf ;
|
|
[name='Firm FOC capital, flex price economy']
|
|
rkf = (wf)+labf-kf ;
|
|
[name='Definition capital services, flex price economy']
|
|
kf = kpf(-1)+zcapf ;
|
|
[name='Investment Euler Equation, flex price economy']
|
|
invef = (1/(1+cbetabar*cgamma))* ( invef(-1) + cbetabar*cgamma*invef(1)+(1/(cgamma^2*csadjcost))*pkf ) +qs ;
|
|
[name='Arbitrage equation value of capital, flex price economy']
|
|
pkf = -rrf-0*b+(1/((1-chabb/cgamma)/(csigma*(1+chabb/cgamma))))*b +(crk/(crk+(1-ctou)))*rkf(1) + ((1-ctou)/(crk+(1-ctou)))*pkf(1) ;
|
|
[name='Consumption Euler Equation, flex price economy']
|
|
cf = (chabb/cgamma)/(1+chabb/cgamma)*cf(-1) + (1/(1+chabb/cgamma))*cf(+1) +((csigma-1)*cwhlc/(csigma*(1+chabb/cgamma)))*(labf-labf(+1)) - (1-chabb/cgamma)/(csigma*(1+chabb/cgamma))*(rrf+0*b) + b ;
|
|
[name='Aggregate Resource Constraint, flex price economy']
|
|
yf = ccy*cf+ciy*invef+g + crkky*zcapf ;
|
|
[name='Aggregate Production Function, flex price economy']
|
|
yf = cfc*( calfa*kf+(1-calfa)*labf +a );
|
|
[name='Wage equation, flex price economy']
|
|
wf = csigl*labf +(1/(1-chabb/cgamma))*cf - (chabb/cgamma)/(1-chabb/cgamma)*cf(-1) ;
|
|
[name='Law of motion for capital, flex price economy (see header notes)']
|
|
kpf = (1-cikbar)*kpf(-1)+(cikbar)*invef + (cikbar)*(cgamma^2*csadjcost)*qs ;
|
|
|
|
// sticky price - wage economy
|
|
[name='FOC labor with mpl expressed as function of rk and w, SW Equation (9)']
|
|
mc = calfa*rk+(1-calfa)*(w) - 1*a - 0*(1-calfa)*a ;
|
|
[name='FOC capacity utilization, SW Equation (7)']
|
|
zcap = (1/(czcap/(1-czcap)))* rk ;
|
|
[name='Firm FOC capital, SW Equation (11)']
|
|
rk = w+lab-k ;
|
|
[name='Definition capital services, SW Equation (6)']
|
|
k = kp(-1)+zcap ;
|
|
[name='Investment Euler Equation, SW Equation (3)']
|
|
inve = (1/(1+cbetabar*cgamma))* (inve(-1) + cbetabar*cgamma*inve(1)+(1/(cgamma^2*csadjcost))*pk ) +qs ;
|
|
[name='Arbitrage equation value of capital, SW Equation (4)']
|
|
pk = -r+pinf(1)-0*b
|
|
+ (1/((1-chabb/cgamma)/(csigma*(1+chabb/cgamma))))*b
|
|
+ (crk/(crk+(1-ctou)))*rk(1)
|
|
+ ((1-ctou)/(crk+(1-ctou)))*pk(1) ;
|
|
[name='Consumption Euler Equation, SW Equation (2)']
|
|
c = (chabb/cgamma)/(1+chabb/cgamma)*c(-1)
|
|
+ (1/(1+chabb/cgamma))*c(+1)
|
|
+((csigma-1)*cwhlc/(csigma*(1+chabb/cgamma)))*(lab-lab(+1))
|
|
- (1-chabb/cgamma)/(csigma*(1+chabb/cgamma))*(r-pinf(+1) + 0*b) +b ;
|
|
[name='Aggregate Resource Constraint, SW Equation (1)']
|
|
y = ccy*c+ciy*inve+g + 1*crkky*zcap ;
|
|
[name='Aggregate Production Function, SW Equation (5)']
|
|
y = cfc*( calfa*k+(1-calfa)*lab +a );
|
|
[name='New Keynesian Phillips Curve, SW Equation (10)']
|
|
pinf = (1/(1+cbetabar*cgamma*cindp)) * ( cbetabar*cgamma*pinf(1) +cindp*pinf(-1)
|
|
+((1-cprobp)*(1-cbetabar*cgamma*cprobp)/cprobp)/((cfc-1)*curvp+1)*(mc) ) + spinf ;
|
|
[name='Wage Phillips Curve, SW Equation (13), with (12) plugged for mu_w']
|
|
w = (1/(1+cbetabar*cgamma))*w(-1)
|
|
+(cbetabar*cgamma/(1+cbetabar*cgamma))*w(1)
|
|
+(cindw/(1+cbetabar*cgamma))*pinf(-1)
|
|
-(1+cbetabar*cgamma*cindw)/(1+cbetabar*cgamma)*pinf
|
|
+(cbetabar*cgamma)/(1+cbetabar*cgamma)*pinf(1)
|
|
+(1-cprobw)*(1-cbetabar*cgamma*cprobw)/((1+cbetabar*cgamma)*cprobw)*(1/((clandaw-1)*curvw+1))*
|
|
(csigl*lab + (1/(1-chabb/cgamma))*c - ((chabb/cgamma)/(1-chabb/cgamma))*c(-1) -w)
|
|
+ 1*sw ;
|
|
[name='Taylor rule, SW Equation (14)']
|
|
r = crpi*(1-crr)*pinf
|
|
+cry*(1-crr)*(y-yf)
|
|
+crdy*(y-yf-y(-1)+yf(-1))
|
|
+crr*r(-1)
|
|
+ms ;
|
|
[name='Law of motion for productivity']
|
|
a = crhoa*a(-1) + ea;
|
|
[name='Law of motion for risk premium']
|
|
b = crhob*b(-1) + eb;
|
|
[name='Law of motion for spending process']
|
|
g = crhog*(g(-1)) + eg + cgy*ea;
|
|
[name='Law of motion for investment specific technology shock process']
|
|
qs = crhoqs*qs(-1) + eqs;
|
|
[name='Law of motion for monetary policy shock process']
|
|
ms = crhoms*ms(-1) + em;
|
|
[name='Law of motion for price markup shock process']
|
|
spinf = crhopinf*spinf(-1) + epinfma - cmap*epinfma(-1);
|
|
epinfma=epinf;
|
|
[name='Law of motion for wage markup shock process']
|
|
sw = crhow*sw(-1) + ewma - cmaw*ewma(-1) ;
|
|
ewma=ew;
|
|
[name='Law of motion for capital, SW Equation (8) (see header notes)']
|
|
kp = (1-cikbar)*kp(-1)+cikbar*inve + cikbar*cgamma^2*csadjcost*qs ;
|
|
|
|
// measurement equations
|
|
[name='Observation equation output']
|
|
dy=y-y(-1)+ctrend;
|
|
[name='Observation equation consumption']
|
|
dc=c-c(-1)+ctrend;
|
|
[name='Observation equation investment']
|
|
dinve=inve-inve(-1)+ctrend;
|
|
[name='Observation equation real wage']
|
|
dw=w-w(-1)+ctrend;
|
|
[name='Observation equation inflation']
|
|
pinfobs = 1*(pinf) + constepinf;
|
|
[name='Observation equation interest rate']
|
|
robs = 1*(r) + conster;
|
|
[name='Observation equation hours worked']
|
|
labobs = lab + constelab;
|
|
|
|
end;
|
|
|
|
steady_state_model;
|
|
dy=ctrend;
|
|
dc=ctrend;
|
|
dinve=ctrend;
|
|
dw=ctrend;
|
|
pinfobs = constepinf;
|
|
robs = (((1+constepinf/100)/((1/(1+constebeta/100))*(1+ctrend/100)^(-csigma)))-1)*100;
|
|
labobs = constelab;
|
|
end;
|
|
|
|
shocks;
|
|
var ea;
|
|
stderr 0.4618;
|
|
var eb;
|
|
stderr 1.8513;
|
|
var eg;
|
|
stderr 0.6090;
|
|
var eqs;
|
|
stderr 0.6017;
|
|
var em;
|
|
stderr 0.2397;
|
|
var epinf;
|
|
stderr 0.1455;
|
|
var ew;
|
|
stderr 0.2089;
|
|
end;
|
|
|
|
|
|
estimated_params;
|
|
// PARAM NAME, INITVAL, LB, UB, PRIOR_SHAPE, PRIOR_P1, PRIOR_P2, PRIOR_P3, PRIOR_P4, JSCALE
|
|
// PRIOR_SHAPE: BETA_PDF, GAMMA_PDF, NORMAL_PDF, INV_GAMMA_PDF
|
|
stderr ea,0.4618,0.01,3,INV_GAMMA_PDF,0.1,2;
|
|
stderr eb,0.1818513,0.025,5,INV_GAMMA_PDF,0.1,2;
|
|
stderr eg,0.6090,0.01,3,INV_GAMMA_PDF,0.1,2;
|
|
stderr eqs,0.46017,0.01,3,INV_GAMMA_PDF,0.1,2;
|
|
stderr em,0.2397,0.01,3,INV_GAMMA_PDF,0.1,2;
|
|
stderr epinf,0.1455,0.01,3,INV_GAMMA_PDF,0.1,2;
|
|
stderr ew,0.2089,0.01,3,INV_GAMMA_PDF,0.1,2;
|
|
crhoa,.9676 ,.01,.9999,BETA_PDF,0.5,0.20;
|
|
crhob,.2703,.01,.9999,BETA_PDF,0.5,0.20;
|
|
crhog,.9930,.01,.9999,BETA_PDF,0.5,0.20;
|
|
crhoqs,.5724,.01,.9999,BETA_PDF,0.5,0.20;
|
|
crhoms,.3,.01,.9999,BETA_PDF,0.5,0.20;
|
|
crhopinf,.8692,.01,.9999,BETA_PDF,0.5,0.20;
|
|
crhow,.9546,.001,.9999,BETA_PDF,0.5,0.20;
|
|
cmap,.7652,0.01,.9999,BETA_PDF,0.5,0.2;
|
|
cmaw,.8936,0.01,.9999,BETA_PDF,0.5,0.2;
|
|
csadjcost,6.3325,2,15,NORMAL_PDF,4,1.5;
|
|
csigma,1.2312,0.25,3,NORMAL_PDF,1.50,0.375;
|
|
chabb,0.7205,0.001,0.99,BETA_PDF,0.7,0.1;
|
|
cprobw,0.7937,0.3,0.95,BETA_PDF,0.5,0.1;
|
|
csigl,2.8401,0.25,10,NORMAL_PDF,2,0.75;
|
|
cprobp,0.7813,0.5,0.95,BETA_PDF,0.5,0.10;
|
|
cindw,0.4425,0.01,0.99,BETA_PDF,0.5,0.15;
|
|
cindp,0.3291,0.01,0.99,BETA_PDF,0.5,0.15;
|
|
czcap,0.2648,0.01,1,BETA_PDF,0.5,0.15;
|
|
cfc,1.4672,1.0,3,NORMAL_PDF,1.25,0.125;
|
|
crpi,1.7985,1.0,3,NORMAL_PDF,1.5,0.25;
|
|
crr,0.8258,0.5,0.975,BETA_PDF,0.75,0.10;
|
|
cry,0.0893,0.001,0.5,NORMAL_PDF,0.125,0.05;
|
|
crdy,0.2239,0.001,0.5,NORMAL_PDF,0.125,0.05;
|
|
constepinf,0.7,0.1,2.0,GAMMA_PDF,0.625,0.1;//20;
|
|
constebeta,0.7420,0.01,2.0,GAMMA_PDF,0.25,0.1;//0.20;
|
|
constelab,1.2918,-10.0,10.0,NORMAL_PDF,0.0,2.0;
|
|
ctrend,0.3982,0.1,0.8,NORMAL_PDF,0.4,0.10;
|
|
cgy,0.05,0.01,2.0,NORMAL_PDF,0.5,0.25;
|
|
calfa,0.24,0.01,1.0,NORMAL_PDF,0.3,0.05;
|
|
end;
|
|
|
|
stoch_simul(order=1,irf=0,periods=0);
|
|
options_.qz_criterium = 1;
|
|
|
|
indx = [M_.nstatic+(1:M_.nspred)]';
|
|
indy = 1:M_.endo_nbr';
|
|
|
|
SS.A = oo_.dr.ghx(indx,:);
|
|
SS.B = oo_.dr.ghu(indx,:);
|
|
SS.C = oo_.dr.ghx(indy,:);
|
|
SS.D = oo_.dr.ghu(indy,:);
|
|
|
|
[CheckCO,minnx,minSS] = identification.get_minimal_state_representation(SS,0);
|
|
|
|
Sigmax_full = lyapunov_symm(SS.A, SS.B*M_.Sigma_e*SS.B', options_.lyapunov_fixed_point_tol, options_.qz_criterium, options_.lyapunov_complex_threshold, 1, options_.debug);
|
|
Sigmay_full = SS.C*Sigmax_full*SS.C' + SS.D*M_.Sigma_e*SS.D';
|
|
|
|
Sigmax_min = lyapunov_symm(minSS.A, minSS.B*M_.Sigma_e*minSS.B', options_.lyapunov_fixed_point_tol, options_.qz_criterium, options_.lyapunov_complex_threshold, 1, options_.debug);
|
|
Sigmay_min = minSS.C*Sigmax_min*minSS.C' + minSS.D*M_.Sigma_e*minSS.D';
|
|
|
|
([Sigmay_full(:) - Sigmay_min(:)]');
|
|
sqrt(([diag(Sigmay_full), diag(Sigmay_min)]'));
|
|
dx = norm( Sigmay_full - Sigmay_min, Inf);
|
|
if dx > 3e-8
|
|
error(sprintf('something wrong with minimal state space computations, as numerical error is %d',dx))
|
|
else
|
|
fprintf('numerical error for moments computed from minimal state system is %d\n',dx)
|
|
end
|