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SBModel_CD.m
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SBModel_CD.m
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classdef SBModel_CD < model.DSGEModel
%
properties (SetAccess=protected)
NSTEN % number of endogenous state variables: Vfct.Ndim-1
NSTEX % number of exogenous state variables
NSOL % number of solution vars
NV % number of forecasting variables
NADD % number of additional endogenous variables
Sol_names % NSOLx1 cell array with names of solution variables
% must be in order of functions of Pfct
V_names % NVx1 cell array with names of forecasting variables
% must be in order of functions of Vfct
Sol_baseguess
En_names % NSTENx1 cell array with names of endog state variables
Ex_names % NSTEXx1 cell array with names of exog state variables
Add_names % NADDx1 cell array with names of additional vars
Params % structure array with parameters
Exogenv % structure array with fields mtrans, pts_perm, pts_all
% specifying exog. Markov processes
Vfct % ApproxFunction object for iteration-relevant functions
Pfct % ApproxFunction object for solution jump variables
Tfct % ApproxFunction object for transition of state variable(s) (optional)
end
methods
% constructor
function obj=SBModel_CD(params,endogenv,exogenv,vfct,pfct,tfct)
% call superclass constructor
[email protected](params,endogenv,exogenv,vfct,pfct,tfct);
end
function [nextst,outstr]=calcStateTransition(obj,point,solvec,mode,varargin)
% unpack params
params = obj.Params;
phi = params.phi;
phiK = params.phiK;
nu = params.nu;
alpha = params.alpha;
eta = params.eta ;
deltaK = params.deltaK;
deltaKbar = params.deltaKbar;
if isfield(params,'kappaC')
kappaC = params.kappaC ;
kappaS = params.kappaS ;
else
kappaC=params.kappa;
kappaS=0;
end
epsilon = params.epsilon;
xiC = params.xiC ;
xiS = params.xiS ;
Zbar_disc = params.Zbar_disc;
mu_rhoC = params.mu_rhoC ;
sig_rhoC = params.sig_rhoC ;
mu_rhoS = params.mu_rhoS ;
sig_rhoS = params.sig_rhoS ;
deltaS = params.deltaS;
deltaC = params.deltaC;
chi1C = sig_rhoC^2/mu_rhoC;
chi0C = mu_rhoC/chi1C;
chi1S = sig_rhoS^2/mu_rhoS;
chi0S = mu_rhoS/chi1S ;
if isfield(params,'fullnu')
fullnu=params.fullnu;
else
fullnu=0;
end
piB = params.piB;
% extract state variables
exst=point(1);
K=point(2);
bS=point(3);
bC=point(4);
KSsh=point(5);
Y=obj.Exogenv.pts_perm(exst,1);
Z=obj.Exogenv.pts_perm(exst,2);
Zbar=Zbar_disc*Z;
varrho=obj.Exogenv.pts_perm(exst,3);
if params.use_theta_var
vartheta=obj.Exogenv.pts_perm(exst,4);
else
vartheta=params.theta;
end
if isempty(varargin)
thisvals=obj.evaluateVal(point);
else
thisvals=varargin{1};
end
% extract solution variables
p = exp(solvec(1));
qS = exp(solvec(2));
qC = exp(solvec(3));
BSpol = exp(solvec(4));
BCpol = exp(solvec(5));
KSshpol = exp(solvec(6));
nS = exp(solvec(7)) ;
% small value functions for default cutoffs
vS=phiK/2*(thisvals(8)^2-1);
vC=phiK/2*(thisvals(9)^2-1);
% this period
KS = K*KSsh;
KC = K-KS;
BS = bS*KS;
nH = nS*(Z/Zbar)^(1/(eta-1));
PiS = (1-eta)*Z*nS^eta + p - deltaK + ((p-1)^2)/(2*phi) ;
LS = bS/PiS ;
PiH = (1-eta)*Zbar*nH^eta + p *(1-deltaKbar) ;
xt = PiH./PiS;
lS = varrho.*LS./xt ;
NS = nS*KS*(1-lS) ;
NH = nH*lS*KS ;
DFcutS = ((1-varrho).*LS - (1-lS)*(vS/PiS + deltaS))./(1-lS) ; % REV: new default cutoff
FS = gamcdf(DFcutS,chi0S,chi1S);
FSrho_minusS = mu_rhoS*gamcdf(DFcutS,chi0S+1,chi1S);
FSrho_plusS = mu_rhoS*(1-gamcdf(DFcutS,chi0S+1,chi1S));
nC = nS ;
NC = nC*KC ;
PiC = (1-eta)*Z*nC^eta + p - deltaK + ((p-1)^2)/(2*phi) ;
BC = bC*KC;
LC = bC/PiC;
DFcutC = LC-deltaC - vC/PiC;
FC = gamcdf(DFcutC ,chi0C,chi1C);
FCrho_minusC = mu_rhoC*gamcdf(DFcutC ,chi0C+1,chi1C);
FCrho_plusC = mu_rhoC*(1-gamcdf(DFcutC ,chi0C+1,chi1C));
% investment
IC = ((p-1)/phi + deltaK)*KC ;
i_c = IC/KC ;
IS = ((p-1)/phi + deltaK)*KS*(1-lS) ;
i_s = IS/((1-lS)*KS);
I = (IC + IS) ;
% deadweight losses
DWL_S = xiS*FSrho_minusS* (1-lS)*(PiS-(1-deltaK)*p)*KS ; % REV: no run DWL on HH production
DWL_C = xiC*FCrho_minusC* (PiC-(1-deltaK)*p)*KC ;
% capital transition
Kpol = I + (1-deltaK)*(1-xiC*FCrho_minusC)*KC ...
+ (1-deltaK)*(1-xiS*FSrho_minusS)*KS*(1-lS)...
+ (1-deltaKbar)*KS*lS ;
KSpol = Kpol*KSshpol;
KCpol = Kpol-KSpol;
kS = KSpol/KS;
kC = KCpol/KC;
% consumption
phiI_S = (phi/2)*((i_s - deltaK)^2)*KS*(1-lS) + phiK/2*(kS-1)^2 *KS*(1-lS) ;
phiI_C = (phi/2)*((i_c - deltaK)^2)*KC + phiK/2*(kC-1)^2 *KC ;
Y_S = Z*((1-lS)*KS)^(1-eta)*NS^eta ;
Y_C = Z*(KC^(1-eta))*NC^eta ;
Y_H = Zbar*((lS*KS)^(1-eta))*NH^eta ;
C = Y + Y_S + Y_C + Y_H ....
- IC - phiI_C ...
- IS - phiI_S ....
- DWL_S - DWL_C ;
% liquidity
% Lambda_C = 1;
Lambda_S = ((1-varrho*fullnu)*(1-FS+piB*fullnu*FS))^nu ;
alpha_eff = alpha * Lambda_S;
if epsilon==0
H = (BS.^alpha_eff).*(BC^(1-alpha_eff));
else
H = (alpha_eff*BS^epsilon + (1-alpha_eff)*BC^epsilon)^(1/epsilon) ;
end
% dividends
DS = FSrho_plusS*KS*(1-lS)*PiS - .... REV: only production from non-run capital
(1-FS)*(1-varrho)*BS + (1-FS)*((qS-kappaS)*BSpol -.... REV: only need to pay back deposits not already redeemed
p*KSpol - phiK/2*(kS-1)^2 *KS*(1-lS) );
DC = FCrho_plusC*KC*PiC - (1-FC)*BC + (1-FC)*((qC-kappaC)*BCpol - p*KCpol - phiK/2*(kC-1)^2 *KC );
exnpt = obj.Exogenv.exnpt;
if mode>0
% simulation, mode contains number of next period's state
cind=obj.Exogenv.pts_all(mode,end);
Knext=Kpol;
bSnext=BSpol/KSpol;
bCnext=BCpol/KCpol;
KSshnext=KSpol/Kpol;
else
% solution mode, compute next period's state variables for all
% possible Markov states
cind=obj.Exogenv.pts_all(:,end);
Knext=Kpol*ones(exnpt,1);
bSnext=BSpol/KSpol*ones(exnpt,1);
bCnext=BCpol/KCpol*ones(exnpt,1);
KSshnext=KSpol/Kpol*ones(exnpt,1);
end
nextst=[cind,Knext,bSnext,bCnext,KSshnext];
addvars=struct('Knext',Kpol,...
'BSnext',BSpol,...
'BCnext',BCpol,...
'KSnext',KSpol,...
'kS',kS,...
'kC',kC,...
'H',H,...
'FS',FS,...
'C',C,...
'DS',DS,...
'DC',DC,...
'Z',Z,...
'Y',Y,....
'NH',NH,...
'NC',NC,...
'lS',lS,...
'KS',KS);
outstr=struct;
outstr.addvars=addvars;
outstr.exstvec=[Y;Z;varrho;vartheta];
end
function [fx,V]=calcEquations(obj,exst,nextst,solvec,instr,mode)
% allocate result
fx=zeros(obj.NSOL,1);
% unpack params
params=obj.Params;
alpha = params.alpha;
psi = params.psi ; % weight on liquidity
beta = params.beta ;
eta = params.eta;
Nbar = params.Nbar;
nu = params.nu;
phi = params.phi;
phiK = params.phiK;
deltaK = params.deltaK;
deltaKbar = params.deltaKbar;
Zbar_disc = params.Zbar_disc;
if isfield(params,'kappaC')
kappaC = params.kappaC ;
kappaS = params.kappaS ;
else
kappaC=params.kappa;
kappaS=0;
end
if isfield(params,'fullnu')
fullnu=params.fullnu;
else
fullnu=0;
end
theta = params.theta ;
thetaS = params.thetaS;
gamma = params.gamma ;
gammaH = params.gammaH ;
xiC = params.xiC ;
xiS = params.xiS ;
mu_rhoC = params.mu_rhoC ;
sig_rhoC = params.sig_rhoC ;
mu_rhoS = params.mu_rhoS ;
sig_rhoS = params.sig_rhoS ;
deltaS = params.deltaS;
deltaC = params.deltaC;
piB = params.piB;
if isfield(params,'epsilon')
epsilon=params.epsilon;
else
epsilon=0;
end
chi1C = sig_rhoC^2/mu_rhoC;
chi0C = mu_rhoC/chi1C;
chi1S = sig_rhoS^2/mu_rhoS;
chi0S = mu_rhoS/chi1S;
% extract endogeous variables
p = exp(solvec(1));
qS = exp(solvec(2));
qC = exp(solvec(3));
nS = exp(solvec(7)) ;
lamC = solvec(8);
lamS = solvec(9);
lamCplus=max(0,lamC)^3;
lamCminus=max(0,-lamC)^3;
lamSplus=max(0,lamS)^3;
lamSminus=max(0,-lamS)^3;
% extract some state-dependent values
envec = instr.addvars;
Knext=envec.Knext;
BSnext = envec.BSnext;
BCnext = envec.BCnext;
KSnext = envec.KSnext;
C = envec.C;
H = envec.H;
NH = envec.NH;
NC = envec.NC;
lS = envec.lS;
KS = envec.KS;
KCnext = Knext-KSnext;
kS = envec.kS;
kC = envec.kC;
if params.use_theta_var
theta=instr.exstvec(4);
end
% compute expectation terms
prnext = obj.Exogenv.mtrans(exst,:);
Ynext = obj.Exogenv.pts_perm(:,1) ;
Znext = obj.Exogenv.pts_perm(:,2) ;
%Zbarnext=obj.Exogenv.pts_perm(:,3);
Zbarnext = Zbar_disc*Znext;
varrhonext = obj.Exogenv.pts_perm(:,3);
% projection evaluation
Pol_next = obj.evaluateVal(nextst)';
pnext = Pol_next(:,1);
nSnext = Pol_next(:,7);
nHnext = nSnext.*(Znext./Zbarnext).^(1/(eta-1));
kSnext = Pol_next(:,8);
kCnext = Pol_next(:,9);
vSnext = phiK/2*(kSnext.^2 - 1);
vCnext = phiK/2*(kCnext.^2 - 1);
bSnext = BSnext./KSnext;
PiSnext = (1-eta)*Znext.*(nSnext).^eta + pnext - ....
deltaK + ((pnext-1).^2)./(2*phi) ;
LSnext = bSnext./PiSnext ;
PiHnext = (1-eta)*Zbarnext.*(nHnext).^eta + ....
pnext *(1-deltaKbar) ;
xtnext = PiHnext./PiSnext;
lSnext = varrhonext.*LSnext./xtnext ;
nCnext = nSnext;
NCnext = nCnext .* KCnext;
NSnext = nSnext .* (1-lSnext) .* KSnext;
NHnext = nHnext .* lSnext .* KSnext;
% next period
ICnext = ((pnext-1)/phi + deltaK).*KCnext ;
i_cnext = ICnext/KCnext ;
ISnext = ((pnext-1)/phi + deltaK).*KSnext.*(1-lSnext) ;
i_snext = ISnext./((1-lSnext).*KSnext);
DFcutS = ((1-varrhonext).*LSnext-(1-lSnext).*(vSnext./PiSnext+deltaS))./(1-lSnext) ; % REV: new default threshold
FSnext = gamcdf(DFcutS,chi0S,chi1S);
fSnext = gampdf(DFcutS,chi0S,chi1S);
FSrho_plusSnext = mu_rhoS*(1-gamcdf(DFcutS,chi0S+1,chi1S));
FSrho_minusSnext= mu_rhoS*gamcdf(DFcutS,chi0S+1,chi1S);
bCnext = BCnext./KCnext;
PiCnext = (1-eta)*Znext.*(nCnext).^eta + pnext - ....
deltaK + ((pnext-1).^2)./(2*phi) ;
LCnext = bCnext./PiCnext;
DFcutC = LCnext-deltaC -vCnext./PiCnext;
FCnext = gamcdf(DFcutC,chi0C,chi1C);
FCrho_plusCnext = mu_rhoC*(1-gamcdf(DFcutC,chi0C+1,chi1C));
FCrho_minusCnext = mu_rhoC*gamcdf(DFcutC,chi0C+1,chi1C);
phiISnext = ( (phi/2)*((i_snext - deltaK).^2) + phiK/2*(kSnext-1).^2 ).*KSnext.*(1-lSnext) ;
phiICnext = ( (phi/2)*((i_cnext - deltaK).^2) + phiK/2*(kCnext-1).^2 ).*KCnext ;
DWL_Snext = xiS*FSrho_minusSnext.* (1-lSnext).*(PiSnext-(1-deltaK)*pnext).*KSnext ; % REV: no DWL on HH capital
DWL_Cnext = xiC*FCrho_minusCnext.* (PiCnext-(1-deltaK)*pnext).*KCnext ;
Y_Snext = Znext.*(((1-lSnext).*KSnext).^(1-eta)).*NSnext.^eta ;
Y_Cnext = Znext.*(KCnext.^(1-eta)).*NCnext.^eta ;
Y_Hnext = Zbarnext.*((lSnext.*KSnext).^(1-eta)).*(NHnext.^eta);
C_next = Ynext + Y_Snext + Y_Cnext + Y_Hnext....
- ICnext - phiICnext ...
- ISnext - phiISnext ....
- DWL_Snext - DWL_Cnext ;
% HH SDF
Lambda_Snext = ((1-varrhonext*fullnu).*(1-FSnext+piB*fullnu*FSnext)).^nu ;
alpha_eff = alpha * Lambda_Snext;
U1 = C.^(-gamma) ;
U1next = C_next.^(-gamma) ;
U2next = psi;
SDF = beta * U1next./U1 ;
if epsilon==0
H_next=(BSnext.^alpha_eff) .* BCnext.^(1-alpha_eff);
MRS_S_next = alpha_eff.*(U2next./U1next) .* H_next.^-gammaH .*(BCnext./BSnext).^(1-alpha_eff);
MRS_C_next= (1-alpha_eff).*(U2next./U1next) .* H_next.^-gammaH .*(BCnext./BSnext).^(-alpha_eff);
elseif epsilon==1
H_next=( alpha_eff.*BSnext + (1-alpha_eff).*BCnext );
MRS_S_next = alpha_eff.*(U2next./U1next) .* H_next.^-gammaH ;
MRS_C_next= (1-alpha_eff).*(U2next./U1next) .* H_next.^-gammaH ;
else
H_next=( alpha_eff.*BSnext.^epsilon + (1-alpha_eff).*BCnext.^epsilon ).^(1/epsilon);
MRS_S_next = alpha_eff.*(U2next./U1next) .* H_next.^-gammaH .*(H_next/BSnext).^(1-epsilon);
MRS_C_next= (1-alpha_eff).*(U2next./U1next) .* H_next.^-gammaH .*(H_next./BCnext).^(1-epsilon);
end
if params.use_kappa_fair
FCrCnext=(1-xiC)*FCrho_minusCnext./LCnext;
% FCrCnext=(1-xiC)*FCrho_minusCnext./LCnext;
kappaC = prnext*(SDF.*(FCnext - FCrCnext));
end
% HH FOCs
FSrecov=(1-xiS)*FSrho_minusSnext.*(1-lSnext)./(LSnext.*(1-varrhonext)); % REV: new recovery for S-banks
fx(1) = qS - prnext*(SDF.*( (1-varrhonext).*( 1-FSnext+ FSnext*piB +(1-piB)*FSrecov) + varrhonext + MRS_S_next)); % REV: new HH FOC with runs
fx(2) = qC - prnext*(SDF.*(1 + MRS_C_next));
% shadow banks' FOCs
Lsptnext = (1 - varrhonext)./(1-lSnext).^2; % REV: new L script (app B.3.1)
qSprimebS= -(1-piB)*prnext*(SDF.*( (1-xiS)*FSrho_minusSnext./(LSnext.*bSnext).... % REV: new qSprime (app B.3)
+ Lsptnext.*(fSnext./bSnext).*(xiS*(1-varrhonext).*LSnext+(1-xiS)*(1-lSnext).*(deltaS + vSnext./PiSnext ))));
fx(3) = qS - kappaS + qSprimebS.*bSnext - lamSplus - prnext*(SDF.*( (1-FSnext).*( 1 - varrhonext + lSnext./LSnext.*vSnext./PiSnext) ...
+ FSrho_plusSnext.*lSnext./LSnext )); % REV: new FOC for qS
FStilde_next = FSrho_plusSnext.*(1-lSnext) - ...
(1-FSnext).*((1-varrhonext).*LSnext - (1-lSnext).*vSnext./PiSnext) - FSnext.*(1-lSnext).*deltaS; % REV: new expression for OmegaS
fx(4) = p + phiK*(kS-1) - (qS-kappaS)*bSnext - prnext*(SDF.*PiSnext.*FStilde_next) ;
% commercial banks' FOCs
fx(5) = qC - kappaC - lamCplus - prnext*(SDF.*(1-FCnext));
FCtilde_next = FCrho_plusCnext - (1-FCnext).*(LCnext - vCnext./PiCnext) - FCnext*deltaC;
fx(6) = p + phiK*(kC-1) - (qC-kappaC)*bCnext - prnext*(SDF.*PiCnext.*FCtilde_next) ;
fx(7) = (1-theta)*p - bCnext - lamCminus;
fx(8) = thetaS*p - bSnext - lamSminus;
fx(9) = - Nbar + NC + nS*(1-lS)*KS + NH ;
% if mode==1, also compute marginal value functions
V=[];
if mode==1
Vnext=zeros(obj.Vfct.Nof,1);
VHnext= Pol_next(:,2);
VH = (C^(1-gamma))./(1-gamma) + psi*(H^(1-gammaH))./(1-gammaH) + beta*prnext*VHnext;
DS=envec.DS;
DC=envec.DC;
DSnext=Pol_next(:,3);
DCnext=Pol_next(:,4);
pSnext=Pol_next(:,5);
pCnext=Pol_next(:,6);
pS = prnext*(SDF.*(DSnext+(1-FSnext).*pSnext));
pC = prnext*(SDF.*(DCnext+(1-FCnext).*pCnext));
Vnext(1)= p;
Vnext(2)= VH;
Vnext(3)= DS;
Vnext(4)= DC;
Vnext(5)= pS;
Vnext(6)= pC;
Vnext(7)= nS;
Vnext(8)= kS;
Vnext(9)= kC;
V{1} = Vnext;
V{2} = [];
elseif mode==2
% only during simulation
% counterfactual risk free rate without liquidity services
q = prnext*SDF;
rf = 1/q-1;
% conditional expected returns
DSnext=Pol_next(:,3);
DCnext=Pol_next(:,4);
pSnext=Pol_next(:,5);
pCnext=Pol_next(:,6);
pS = prnext*(SDF.*(DSnext+(1-FSnext).*pSnext));
pC = prnext*(SDF.*(DCnext+(1-FCnext).*pCnext));
exRS=prnext*(DSnext+(1-FSnext).*pSnext)/pS; % note: only compute expected return here,
exRC=prnext*(DCnext+(1-FCnext).*pCnext)/pC; % not expected excess return
exZ =prnext*PiCnext/p;
if params.use_kappa_fair
kappa_fair=kappaC;
else
FCrCnext=(1-xiC)*FCrho_minusCnext./LCnext;
kappa_fair=prnext*(SDF.*(FCnext - FCrCnext));
end
rets=struct('H',H,...
'C',C,...
'MRS_C',prnext*MRS_C_next,...
'MRS_S',prnext*MRS_S_next,...
'rf',rf,...
'exRS',exRS,...
'exRC',exRC,...
'exZ',exZ,...
'kappa_fair',kappa_fair,'theta',theta);
V=rets;
end
end
function [errmat,solmat,retmat]=calcEEError(obj,pointmat)
% function to compute Euler equation error at points in state
% space given by pointmat
errmat=zeros(size(pointmat,1),obj.Pfct.Nof);
solmat=zeros(size(errmat));
retmat=zeros(size(pointmat,1),10);
parfor i=1:size(errmat,1)
point=pointmat(i,:);
soltmp=obj.evaluatePol(point)';
% transition
[nextst,outstr]=obj.calcStateTransition(point,soltmp,0);
% equations
[fx,V]=obj.calcEquations(point(1),nextst,soltmp,outstr,2);
p = exp(soltmp(1));
qS = exp(soltmp(2));
qC = exp(soltmp(2));
normvec=[qS,qC,qS,p,qC,p,p,p,p];
errmat(i,:)=fx'./normvec;
solmat(i,:)=soltmp;
retmat(i,:)=[V.H, V.C, V.MRS_C, V.MRS_S,...
V.rf, V.exRS, V.exRC, V.exZ, V.kappa_fair, V.theta];
end
end
% simulate model
function [simseries,varnames,errmat,nextst]=simulate(obj,NT,NTini,inistvec,simerror,shmat_in,varargin)
if length(inistvec)~=obj.Vfct.SSGrid.Ndim
error('inistvec must be vector of length SSGrid.Ndim');
end
NTtot=NT+NTini;
simseries=zeros(NTtot,1+obj.NSTEX+obj.NSTEN+obj.NSOL+obj.NV+obj.NADD);
if isempty(shmat_in)
rng('default') % set seed
rng(1);
shmat=rand(NTtot,1);
else
shmat=shmat_in;
end
point=inistvec;
if nargin>6
capdestshock=varargin{1};
else
capdestshock=[];
end
pointmat=zeros(NTtot,length(point)) ;
for t=1:NTtot
try
pointmat(t,:)=point;
catch
disp(point);
end
exst=point(1);
% next period's exog. state
transprob=cumsum(obj.Exogenv.mtrans(exst,:));
exnext=find(transprob-shmat(t)>=0,1,'first');
% transition to next period
solvec=obj.evaluatePol(point)';
valvec=obj.evaluateVal(point)';
[nextst,outstr]=obj.calcStateTransition(point,solvec,exnext);
if ~isempty(capdestshock) && t==1
nextst(2)=nextst(2)*capdestshock;
nextst(3:4)=nextst(3:4)/capdestshock;
end
addvec=model.DSGEModel.structToVec(outstr.addvars)';
% write different categories of variables in one row
simseries(t,:)=[point(1),outstr.exstvec',point(2:end),solvec,valvec,addvec];
point=nextst;
end
simseries=simseries(NTini+1:end,:);
varnames=[{'exst'}, obj.Ex_names, obj.En_names, ....
obj.Sol_names, obj.V_names, obj.Add_names];
errmat=[];
if simerror
[errmat,~,retmat]=obj.calcEEError(pointmat);
errmat=errmat(NTini+1:end,:);
retmat=retmat(NTini+1:end,:);
simseries=[simseries,retmat];
varnames=[varnames,{'H','C','MRS_C','MRS_S','rf','exRS',....
'exRC','exZ','kappa_fair','theta'}];
end
end
function mobj=polIter(mobj,MAXIT,revisitFailed,printmode,avg_tol)
gridSt=mobj.Vfct.SSGrid.Pointmat; % use points from BaseGrid here
NPT=mobj.Vfct.SSGrid.Npt;
exnpt=size(mobj.Exogenv.pts_perm,1);
% initialize
resmat=mobj.evaluatePol(gridSt)';
resmat_prev=resmat;
% split up matrix of points for better output
gr_points = cell(exnpt,1);
gr_index = cell(exnpt,2);
for i=1:exnpt
grinlog=(gridSt(:,1)==i);
grind=find(grinlog);
gr_points{i}=gridSt(grinlog,:);
gr_index{i,1}=grinlog;
gr_index{i,2}=grind;
end
% value function
VF=mobj.evaluateVal(gridSt)';
VFnext=zeros(size(VF));
% control flags
iter=0;
disp(' ');
disp('Starting main loop ...');
disp(' ');
while 1
% counter
iter=iter+1;
% ===========================================
% loop over state space
% ===========================================
% matrix for failed points
failedPoints=[];
% outer loop: all exogenous states
for ei=1:exnpt
tmp_grid=gr_points{ei};
tmp_indlog=gr_index{ei,1};
tmp_index=gr_index{ei,2};
tmp_resmat=resmat(tmp_indlog,:);
tmp_resmat_prev=resmat_prev(tmp_indlog,:);
disp(['State ',num2str(ei)]);
[tmp_resmat_new,tmp_VF,~,tmp_failed]=mobj.solvePointList(tmp_grid,tmp_resmat,tmp_resmat_prev,printmode,[]);
if revisitFailed
failedPoints=[failedPoints; tmp_index(tmp_failed)];
end
resmat_prev(tmp_indlog,:)=tmp_resmat;
resmat(tmp_indlog,:)=tmp_resmat_new;
VFnext(tmp_indlog,:)=tmp_VF;
%TFnext(tmp_indlog,:)=tmp_TF;
end
if ~isempty(failedPoints)
disp( '~~~~~~~~~~~~~~~~~~~');
disp(['Revisiting failed points: ',num2str(length(failedPoints)),' add. points ...']);
% try to solve at failed points
[new_resmat,new_VF,~,n_succ]=mobj.solvePointListFailed(gridSt,failedPoints,resmat,1,printmode,[]);
resmat(failedPoints,:)=new_resmat;
VFnext(failedPoints,:)=new_VF;
%TFnext(failedPoints,:)=new_TF;
disp(['Revisiting solved ',num2str(n_succ),' points.']);
end
% approximate functions for next guess
mobj=mobj.updateVfct(VFnext);
% convergence criterion (based on points in BaseGrid)
val_range=2;
VF_val = VF(:,val_range);
VFnext_val=VFnext(:,val_range);
[dist,wh]=max(abs(VF_val(:)-VFnext_val(:)));
[mean_dist,col]=max(abs(mean(VF_val-VFnext_val)));
[wh_1,wh_2]=ind2sub(size(VFnext_val),wh);
disp(['-- Iteration: ',num2str(iter),', max distance: ',num2str(dist),' in ',char(mobj.V_names(val_range(1)-1+wh_2)), ...
' at point ',num2str(wh_1),': ',num2str(mobj.Vfct.SSGrid.Pointmat(wh_1,:))]);
disp(['-- Iteration: ',num2str(iter),', mean distance: ',num2str(mean_dist),' in ',char(mobj.V_names(val_range(1)-1+col))]);
disp(' ');
if dist<avg_tol
disp('Converged.');
break;
elseif iter>=MAXIT
disp('Max.iter. exceeded.');
break;
end
% update guess
VF=VFnext;
end
% resulting policy functions
mobj=mobj.updatePfct(resmat);
end
function [simseries, varnames] = computeSimulationMoments(obj, simseries, varnames, varargin)
% make HashMap with mapping of names to indices
indexmap=java.util.HashMap;
for i=1:length(varnames)
indexmap.put(varnames{i},i);
end
% list of indices
loglist=model.HelperCollection.makeListFromNames(indexmap,{'qS','qC'});
multlist=model.HelperCollection.makeListFromNames(indexmap,{'lamC','lamS'});
% conversion of log-values
simseries(:,loglist)=exp(simseries(:,loglist));
% conversion of multipliers
simseries(:,multlist)=max(simseries(:,multlist),0).^(1/3);
if nargin>3
firstrow=varargin{1};
simseries=[firstrow; simseries];
end
params=obj.Params;
% ---------------------------------------------------------------------
% state vars
% ---------------------------------------------------------------------
Y = simseries(:,indexmap.get('Y'));
Z = simseries(:,indexmap.get('Z'));
Zbar = params.Zbar_disc*Z;
varrho= simseries(:,indexmap.get('varrho'));
% ---------------------------------------------------------------------
% prices and interest rates
% ---------------------------------------------------------------------
p = simseries(:,indexmap.get('p'));
qS = simseries(:,indexmap.get('qS'));
qC = simseries(:,indexmap.get('qC'));
rateS = 1./qS-1;
rateC = 1./qC-1;
EretZ=(Z(2:end)+p(2:end))./p(1:end-1);
EEretZ_S=EretZ - rateS(1:end-1) -1;
EEretZ_C=EretZ - rateC(1:end-1) -1;
ratespr = 1./qS-1./qC;
MRS_C = simseries(:,indexmap.get('MRS_C'));
MRS_S = simseries(:,indexmap.get('MRS_S'));
MRSspr = MRS_C - MRS_S;
liqbenC = MRS_C - params.kappaC;
% ---------------------------------------------------------------------
% C bank and S bank
% ---------------------------------------------------------------------
K = simseries(:,indexmap.get('K'));
KSsh = simseries(:,indexmap.get('KSsh'));
lS = simseries(:,indexmap.get('lS'));
KS=K.*KSsh ;
KC=K-KS;
BS = simseries(:,indexmap.get('bS')).*KS;
BC = simseries(:,indexmap.get('bC')).*KC;
BSsh = BS./(BS+BC);
deltaK=params.deltaK;
deltaKbar=params.deltaKbar;
Slev = BS./(KS.*p);
Slevbk = BS./KS;
Clev = BC./(KC.*p);
Clevbk = BC./KC;
nS = simseries(:,indexmap.get('nS'));
eta = params.eta;
phi = params.phi;
nC = nS;
nH = nS .*(Zbar./Z).^(1/(1-eta));
PiS = (1-eta)*Z.*nS.^eta + p - deltaK + ((p-1).^2)/(2*phi);
PiC = (1-eta)*Z.*nC.^eta + p - deltaK + ((p-1).^2)/(2*phi);
PiH = (1-eta)*Zbar.*nH.^eta + p*(1 - deltaKbar);
LS = BS./(KS.*PiS);
LC = BC./(KC.*PiC);
AC = BC;
AS = BS;
chi1C=params.sig_rhoC^2/params.mu_rhoC;
chi0C=params.mu_rhoC/chi1C;
chi1S=params.sig_rhoS^2/params.mu_rhoS;
chi0S=params.mu_rhoS/chi1S;
% fire sales
xt= PiH./PiS;
ell= lS;
% S bank
kS = simseries(:,indexmap.get('kS'));
vS = params.phiK/2*(kS.^2-1);
DFcutS = ((1-varrho).*LS-(1-ell).*(vS./PiS+params.deltaS))./(1-ell); % REV
FS = gamcdf(DFcutS, chi0S, chi1S);
rhoplus_S = params.mu_rhoS*(1-gamcdf(DFcutS, chi0S+1, chi1S))./(1-FS);
FSrhominus_S = params.mu_rhoS*gamcdf(DFcutS, chi0S+1, chi1S);
DWL_S = params.xiS*FSrhominus_S.*PiS.*(1-ell).*KS; % REV
lamS_binds= (simseries(:,indexmap.get('lamS'))>0);
rhominus_S=FSrhominus_S./FS;
rhominus_S(FS==0)=0;
recS = (1-params.xiS)*rhominus_S./(LS.*(1-varrho)); % REV
ERS = simseries(:,indexmap.get('exRS'));
pS = simseries(:,indexmap.get('pS'));
KSnext = KS .* kS;
BSnext = simseries(:,indexmap.get('BSnext'));
EERS = ERS - 1./qS;
totvalS = pS + qS.*BSnext;
waccS1 = (ERS-1).*pS./totvalS + rateS.*qS.*BSnext./totvalS;
waccS2 = (ERS-1).*(p.*KSnext-qS.*BSnext)./(p.*KSnext) + rateS.*(qS.*BSnext)./(p.*KSnext);
costperKS = p - qS.*BSnext./KS + params.phiK*(kS-1);
% C bank
kC = simseries(:,indexmap.get('kC'));
vC = params.phiK/2*(kC.^2-1);
FC = gamcdf(LC-params.deltaC-vC./PiC, chi0C, chi1C);
rhoplus_C = params.mu_rhoC*(1-gamcdf(LC-params.deltaC-vC./PiC, chi0C+1, chi1C))./(1-FC);
FCrhominus_C = params.mu_rhoC*gamcdf(LC-params.deltaC-vC./PiC, chi0C+1, chi1C);
DWL_C = params.xiC*FCrhominus_C.*PiC.*KC;
lamC = simseries(:,indexmap.get('lamC'));
rhominus_C=FCrhominus_C./FC;
rhominus_C(FC==0)=0;
recC = (1-params.xiC)*rhominus_C./LC;
ERC = simseries(:,indexmap.get('exRC'));
pC = simseries(:,indexmap.get('pC'));
EERC = ERC - 1./qC;
KCnext = KC .* kC;
BCnext = simseries(:,indexmap.get('BCnext'));
totvalC = pC + (qC-params.kappaC).*BCnext;
rateC_eff = 1./(qC-params.kappaC) -1;
waccC1 = (ERC-1).*pC./totvalC + rateC_eff.*(qC-params.kappaC).*BCnext./totvalC;
waccC2 = (ERC-1).*(p.*KCnext-qC.*BCnext)./(p.*KCnext) + rateC_eff.*(qC.*BCnext)./(p.*KCnext);
costperKC = p - (qC-params.kappaC).*BCnext./KC + params.phiK*(kC-1);
capgrdiff = kC - kS;
waccdiff1 = waccC1 - waccS1;
waccdiff2 = waccC2 - waccS2;
if ~isfield( params,'fullnu')
params.fullnu= 1;
end
LambdaS= ((1-varrho*params.fullnu).*(1-FS+FS*params.piB*params.fullnu)).^params.nu;
assetsC= p.*KC;
assetsS= p.*KS;
NS = nS.*KS.*(1-lS) ;
NC = nC.*KC ;
NH = nH.*lS.*KS ;
% Production
YH = Zbar.*((lS.*KS).^(1-eta)).*(NH.^eta) ;
YS = Z.*(((1-lS).*KS).^(1-eta)).*(NS.^eta) ;
YC = Z.*(KC.^(1-eta)).*(NC.^eta) ;
YB = YS + YC;
gYB = YB(2:end)./YB(1:end-1)-1;
ishare = (p-1)/params.phi + deltaK;
IC = ishare.*KC ;
IS = ishare.*(1-lS).*KS ;
I= IS + IC;
irate = I./K;
GDP = YH + YS + YC + Y ;
FinShare = (YC + YS)./GDP;
krate = (1-KSsh).*kC + KSsh.*kS;
pkrate = log(p(2:end).*K(2:end))-log(p(1:end-1).*K(1:end-1));
iyrate = I./(YS+YC);
C=simseries(:,indexmap.get('C'));
cyrate = C./GDP;
logC = log(C);
% Run-induced losses in ouput and excess depreciation
DWL_run = (Z-Zbar).*((lS.*KS).^(1-eta)).*(NH.^eta) + (deltaKbar-deltaK)*lS.*KS;
% ---------------------------------------------------------------------
% HH and welfare
% ---------------------------------------------------------------------
Safe_sh = (BS+BC)./(p.*K);
DWL = (DWL_S + DWL_C + DWL_run)./GDP;
% add to simseries
simseries=[simseries(:,2:end),rateS,EERS,waccS1,waccS2,costperKS,Slev,Slevbk,LS,FS,rhoplus_S,DWL_S,recS,assetsS,LambdaS,ratespr,MRSspr,liqbenC,...
rateC,EERC,waccC1,waccC2,costperKC,Clev,Clevbk,LC,FC,rhoplus_C,DWL_C,recC,assetsC,lamC,lamS_binds,capgrdiff,...
I,irate,krate,iyrate,cyrate,logC,Safe_sh,xt,lS,YH, YS, YC, YB, DWL, FinShare, BSsh, GDP, waccdiff1, waccdiff2];
simseries=[simseries(2:end,:),EretZ,EEretZ_S,EEretZ_C, NS(2:end), NC(2:end,:),NH(2:end,:)....
AS(2:end), AC(2:end,:), KC(2:end,:),pkrate ,gYB]; % dynamic variables
varnames_add={'rateS','EERS','waccS1','waccS2','costperKS','Slev','Slevbk','LS','FS','rhoplus_S','DWL_S','recS','assetsS','LambdaS','ratespr','MRSspr','liqbenC',...
'rateC','EERC','waccC1','waccC2','costperKC','Clev','Clevbk','LC','FC','rhoplus_C','DWL_C','recC','assetsC','lamC','lamS_binds','capgrdiff',...
'I','irate','krate','iyrate','cyrate','logC',...
'Safe_sh','xt','lS','YH','YS','YC','YB','DWL','FinShare','BSsh','GDP','waccdiff1','waccdiff2',...
'EretZ','EEretZ_S','EEretZ_C','NS','NC','NH','AS','AC','KC','pkrate','gYB'};
varnames=[varnames(2:end), varnames_add];
end
end %of object methods
%==============================================================================
methods (Static)
% static class-specific methods
function [fx,stvals]=compStSt(x,params,printmode)
% unpack parameters
theta = params.theta;
if isfield(params,'kappaC')
kappaC = params.kappaC ;
kappaS = params.kappaS ;
else
kappaC=params.kappa;
kappaS=0;
end
nu = params.nu;
xiS = params.xiS;
xiC = params.xiC;
beta = params.beta;
psi = params.psi;
phi = params.phi;
gamma = params.gamma;
gammaH = params.gammaH;
alpha = params.alpha;
piB = params.piB;
if isfield(params,'epsilon')
epsilon=params.epsilon;
else
epsilon=0;
end
deltaS = params.deltaS ;
deltaC = params.deltaC ;
deltaK = params.deltaK;
deltaKbar = params.deltaKbar;
eta = params.eta;
Nbar = params.Nbar;
Y = params.muY;
Z = params.muZ;
Zbar = params.muZbar ;
varrhoS = params.varrhoS_ss ;
mu_rhoC = params.mu_rhoC;
mu_rhoS = params.mu_rhoS;
sig_rhoC = params.sig_rhoC;
sig_rhoS = params.sig_rhoS;
chi1C = sig_rhoC^2/mu_rhoC;
chi0C = mu_rhoC/chi1C;
chi1S = sig_rhoS^2/mu_rhoS;
chi0S = mu_rhoS/chi1S;
% unpack variables
if sum(~isreal(x))>0
disp(x);
end
p = exp(x(1));
bS = exp(x(2));
C = exp(x(3));
AC = exp(x(4));
AS = exp(x(5));
nS = exp(x(6));
K = exp(x(7));
muS = x(8);
muC = x(9);
if params.calib_eps
epsilon=2/(1+exp(-x(10)))-1;
end
phizero=false;
if phi==0
phi=1;
phizero=true;
end
bC = (1-theta)*p;
BS = AS;
BC = AC;
KS = BS/bS;
KC = BC/bC;
nH = nS*(Z/Zbar)^(1/(eta-1));
PiS = (1-eta)*Z*nS^eta + p - deltaK + ((p-1)^2)/(2*phi) ;
LS = bS/PiS ;
PiH = (1-eta)*Zbar*nH^eta + p *(1-deltaKbar) ;
xt = PiH./PiS;
lS = varrhoS.*LS./xt ;
NH = nH*lS*KS ;