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CModel.m
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CModel.m
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classdef CModel < 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=CModel(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 ;
Nbar = params.Nbar;
% extract state variables
exst=point(1);
K=point(2);
bC=point(3);
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));
qC = exp(solvec(2));
BCpol = exp(solvec(3));
% small value functions for default cutoffs
vC=phiK/2*(thisvals(5)^2-1);
% this period
KC = K;
NC = Nbar;
nC = NC/KC;
%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));
%
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 ;
% deadweight losses
DWL_C = xiC*FCrho_minusC* (PiC-(1-deltaK)*p)*KC ;
% capital transition
Kpol = IC + (1-deltaK)*(1-xiC*FCrho_minusC)*KC;
KCpol = Kpol;
kC = KCpol/KC;
% consumption
phiI_C = (phi/2)*((i_c - deltaK)^2)*KC + phiK/2*(kC-1)^2 *KC ;
Y_C = Z*(KC^(1-eta))*NC^eta ;
C = Y + Y_C + ....
- IC - phiI_C ...
- DWL_C ;
% liquidity
% 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
H = BC;
% dividends
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;
bCnext=BCpol/KCpol;
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);
bCnext=BCpol/KCpol*ones(exnpt,1);
end
nextst=[cind,Knext,bCnext];
addvars=struct('Knext',Kpol,...
'BCnext',BCpol,...
'kC',kC,...
'H',H,...
'C',C,...
'DC',DC,...
'Z',Z,...
'Y',Y,....
'NC',NC);
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
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));
qC = exp(solvec(2));
lamC = solvec(4);
lamCplus=max(0,lamC)^3;
lamCminus=max(0,-lamC)^3;
% extract some state-dependent values
envec = instr.addvars;
Knext=envec.Knext;
BCnext = envec.BCnext;
C = envec.C;
H = envec.H;
NC = envec.NC;
KCnext = Knext;
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);
kCnext = Pol_next(:,5);
vCnext = phiK/2*(kCnext.^2 - 1);
NCnext = Nbar*ones(size(Znext));
nCnext = NCnext ./ KCnext;
% next period
ICnext = ((pnext-1)/phi + deltaK).*KCnext ;
i_cnext = ICnext/KCnext ;
% 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);
phiICnext = ( (phi/2)*((i_cnext - deltaK).^2) + phiK/2*(kCnext-1).^2 ).*KCnext ;
DWL_Cnext = xiC*FCrho_minusCnext.* (PiCnext-(1-deltaK)*pnext).*KCnext ;
Y_Cnext = Znext.*(KCnext.^(1-eta)).*NCnext.^eta ;
C_next = Ynext + Y_Cnext ....
- ICnext - phiICnext ...
- DWL_Cnext ;
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);
% 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
H_next = BCnext;
MRS_C_next= (U2next./U1next) .* H_next.^-gammaH;
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(1) = qC - prnext*(SDF.*(1 + MRS_C_next));
% shadow banks' FOCs
% Lsptnext = (1- lSnext./LSnext.*( deltaS*(1-xtnext) - xtnext.*vSnext./PiSnext) )./....
% ((1-lSnext.*(1-xtnext)).^2);
% 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(2) = qC - kappaC - lamCplus - prnext*(SDF.*(1-FCnext));
FCtilde_next = FCrho_plusCnext - (1-FCnext).*(LCnext - vCnext./PiCnext) - FCnext*deltaC;
fx(3) = p + phiK*(kC-1) - (qC-kappaC)*bCnext - prnext*(SDF.*PiCnext.*FCtilde_next) ;
fx(4) = (1-theta)*p - bCnext - lamCminus;
%fx(5) = thetaS*p - bSnext - lamSminus;
% 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;
DC=envec.DC;
DCnext=Pol_next(:,3);
pCnext=Pol_next(:,4);
pC = prnext*(SDF.*(DCnext+(1-FCnext).*pCnext));
Vnext(1)= p;
Vnext(2)= VH;
Vnext(3)= DC;
Vnext(4)= pC;
Vnext(5)= 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
DCnext=Pol_next(:,3);
pCnext=Pol_next(:,4);
pC = prnext*(SDF.*(DCnext+(1-FCnext).*pCnext));
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,...
'rf',rf,...
'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),8);
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));
qC = exp(soltmp(2));
normvec=[qC,p,qC,p];
errmat(i,:)=fx'./normvec;
solmat(i,:)=soltmp;
retmat(i,:)=[V.H, V.C, V.MRS_C,...
V.rf, V.exRC, V.exZ, V.kappa_fair, V.theta];
end
end
% simulate model
function [simseries,varnames,errmat]=simulate(obj,NT,NTini,inistvec,simerror,shmat_in)
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;
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);
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','rf',....
'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)';
% VF=mobj.evaluateVal(gridSt);
VFnext=zeros(size(VF));
% TF=zeros(size(VF,1),mobj.Tfct.Nof);
% TFnext=TF;
% 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
%VFnext=0.75*VFnext+0.25*VF;
mobj=mobj.updateVfct(VFnext);
%mobj=mobj.updateTfct(TFnext);
% 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)));
% [distT,whT]=max(abs(TF(:)-TFnext(:)));
[wh_1,wh_2]=ind2sub(size(VFnext_val),wh);
% [whT_1,whT_2]=ind2sub(size(TFnext),whT);
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(['-- Iteration: ',num2str(iter),', max T distance: ',num2str(distT),' in col ',num2str(whT_2), ...
% ' at point ',num2str(whT_1),': ',num2str(mobj.Vfct.SSGrid.Pointmat(whT_1,:))]);
disp(' ');
% if dist<0.001 && mean_dist<0.0001 && distT<0.001
if mean_dist<avg_tol
disp('Converged.');
break;
elseif iter>=MAXIT
disp('Max.iter. exceeded.');
break;
end
% update guess
VF=VFnext;
%TF=TFnext;
end
% resulting policy functions
mobj=mobj.updatePfct(resmat);
end
function [simseries, varnames] = computeSimulationMoments(obj, simseries, varnames)
% 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,{'qC'});
multlist=model.HelperCollection.makeListFromNames(indexmap,{'lamC'});
% conversion of log-values
simseries(:,loglist)=exp(simseries(:,loglist));
% conversion of multipliers
simseries(:,multlist)=max(simseries(:,multlist),0).^(1/3);
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'));
qC = simseries(:,indexmap.get('qC'));
rateC = 1./qC-1;
EretZ=(Z(2:end)+p(2:end))./p(1:end-1);
EEretZ_C=EretZ - rateC(1:end-1) -1;
MRS_C = simseries(:,indexmap.get('MRS_C'));
liqbenC = MRS_C - params.kappaC;
% ---------------------------------------------------------------------
% C bank and S bank
% ---------------------------------------------------------------------
K = simseries(:,indexmap.get('K'));
KC=K;
BC = simseries(:,indexmap.get('bC')).*KC;
deltaK=params.deltaK;
deltaKbar=params.deltaKbar;
Clev = BC./(KC.*p);
Clevbk = BC./KC;
nC = params.Nbar./KC;
eta=params.eta;
phi=params.phi;
PiC = (1-eta)*Z.*nC.^eta + p - deltaK + ((p-1).^2)/(2*phi);
LC = BC./(KC.*PiC);
AC = BC;
chi1C=params.sig_rhoC^2/params.mu_rhoC;
chi0C=params.mu_rhoC/chi1C;
% 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);
assetsC= p.*KC;
NC = nC.*KC ;
% Production
YC = Z.*(KC.^(1-eta)).*(NC.^eta) ;
ishare = (p-1)/params.phi + deltaK;
IC = ishare.*KC ;
I= IC;
irate = I./K;
GDP = YC + Y ;
FinShare = (YC)./GDP;
krate = kC;
pkrate = log(p(2:end).*K(2:end))-log(p(1:end-1).*K(1:end-1));
iyrate = I./(YC);
C=simseries(:,indexmap.get('C'));
cyrate = C./GDP;
logC = log(C);
% ---------------------------------------------------------------------
% HH and welfare
% ---------------------------------------------------------------------
Safe_sh = (BC)./(p.*K);
DWL = DWL_C;
% add to simseries
simseries=[simseries(:,2:end),liqbenC,...
rateC,EERC,waccC1,waccC2,costperKC,Clev,Clevbk,LC,FC,rhoplus_C,DWL_C,recC,assetsC,lamC,...
I,irate,krate,iyrate,cyrate,logC,Safe_sh,YC, DWL, FinShare, GDP];
simseries=[simseries(2:end,:),EretZ,EEretZ_C, NC(2:end,:),....
AC(2:end,:), KC(2:end,:),pkrate ]; % dynamic variables
varnames_add={'liqbenC',...
'rateC','EERC','waccC1','waccC2','costperKC','Clev','Clevbk','LC','FC','rhoplus_C','DWL_C','recC','assetsC','lamC',...
'I','irate','krate','iyrate','cyrate','logC',...
'Safe_sh','YC','DWL','FinShare','GDP',...
'EretZ','EEretZ_C','NC','AC','KC','pkrate'};
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));
C = exp(x(2));
AC = exp(x(3));
% K = exp(x(4));
phizero=false;
if phi==0
phi=1;
phizero=true;
end
bC = (1-theta)*p;
BC = AC;
KC = BC/bC;
K = KC;
NC = Nbar;
nC = NC/KC ;
PiC = Z*(1-eta)*nC^eta + p-deltaK + (1/(2*phi))*(p-1)^2;
LC = bC/PiC;
w = eta*Z*nC^(eta-1);
% compute probs, rhos
DFcutC = LC-deltaC ;
FC = gamcdf(DFcutC, chi0C,chi1C);
FCrho_plusC = mu_rhoC*(1-gamcdf(DFcutC, chi0C+1,chi1C));
FCrho_minusC =mu_rhoC*gamcdf(DFcutC, chi0C+1,chi1C);
FC_spt = FCrho_plusC - (1-FC)*LC - FC*deltaC ;
% U1, U2, and H
U1 = C.^(-gamma) ;
U2 = psi;
Hint=BC;
H = 1/(1-gammaH)* (Hint^(1-gammaH));
MRS_C= (U2./U1) .* Hint.^-gammaH;
% C-bank
qC = beta*(1+MRS_C);
FCrC = (1-xiC)*FCrho_minusC/LC;
rC = FCrC/FC;
% use fair kappa?
if params.use_kappa_fair
kappaC=beta*FC*(1-rC);
end
% solve for remaining quantities
% also needs changin PiS and PiC respectively
DC = FCrho_plusC*KC*PiC-(1-FC)*BC+(1-FC)*KC*((qC-kappaC)*bC-p);
pC = (beta/(1-beta*(1-FC)))*DC;
G = BC*(FC*(1-rC)-kappaC);
M = beta ;
lambC = M*( MRS_C + FC ) - kappaC ;
W = -Y - w + G + C + pC + qC*AC;
VH = (1/(1-M))*( (C^(1-gamma))./(1-gamma) + psi*H ) ;
% consumption
IC = ((p-1)/phi + deltaK)*KC ;
i_c = IC/KC ;
I = IC;
phiI_C = (phi/2)*((i_c - deltaK)^2)*KC ;
DWL_C = xiC*FCrho_minusC* (PiC-(1-deltaK)*p)*KC ;
Y_C = Z*(KC^(1-eta))*NC^eta ;
DWL_C_total = xiC*FCrho_minusC* PiC *KC ;
% equations
if phizero
fx(1)=p-1;
else
fx(1) = p - (qC-kappaC)*bC - beta*(PiC*FC_spt);
end
fx(2) = C - (Y + Y_C ....
- IC - phiI_C ...
- DWL_C);
fx(3) = I - K + (1-deltaK)*(1-xiC*FCrho_minusC)*KC;
% fx(4) = nC - (eta*Z/w)^(1/(1-eta));
svals=[];
% write output (and assign return structure)
if printmode>=1
rtC = rC*FC ;
DepShare = (BC)/(Y+Y_C );
DepC = (BC)/(C);
% welfare consumption scale relative to benchVH
scaleVH = ( C * H^(psi/(1-psi)) ) / ((1-M)*(1-gamma)*params.benchVH)^(1/((1-gamma)*(1-psi)));
% not correct
GDP=Y+Y_C;
if printmode>1
disp('------- States -------');
disp(['K :',num2str(K)]);
disp(['bC :',num2str(bC)]);
disp('------- Capital -------');
disp(['GDP :',num2str(GDP)]);
disp(['FinDepGDP/GDP :',num2str((Y_C)/GDP)]);
disp(['p*K/GDP :',num2str(p*K/GDP)]);
disp(['I/K :',num2str(I/K)]);
disp('------- Labor -------');
disp(['Nall :',num2str(NC)]);
disp('------- Recovery -------');
disp(['rC :',num2str(rC)]);
disp('------- Leverage -------');
disp(['LC :',num2str(LC)]);
disp('------- Default Risk -------');
disp(['FC :',num2str(FC)]);
disp(['MRS_C :',num2str(MRS_C)]);
disp(['MRS_C - kappa :',num2str(MRS_C-params.kappaC)]);
disp(['SD(rhoC) :',num2str(PiC*params.sig_rhoC)]);
disp('------- Prices -------');
disp(['p :',num2str(p)]);
disp(['rateC :',num2str(100*(1/qC-1)) ' %']);
disp(['qC :',num2str(qC)]);
disp('------- HH -------');
disp(['C / Y :',num2str(C/GDP)]);
disp(['C :',num2str(C)]);
disp(['AC :',num2str(BC)]);
disp(['Welfare :',num2str(VH)]);
% disp(['ScaleVH :',num2str(scaleVH)]);
disp('------- Gov -------');
disp(['G :',num2str(G)]);
end
svals=struct;
names={'K','KC','BC','bC','p','pC','qC','C','H','I',... 15
'G','Y','W','DC','M','rC','lambC','LC','DWL_total',...30
'U1','U2','MRS_C','FC','FCrho_plusC',...45
'FCrho_minusC','welfare','C_EV',...
'AC','w','PiC'}; %% 51
vars=[K,KC,BC,bC,p,pC,qC,C,H,I,... 15
G,GDP,W,DC,M,rC,lambC,LC,DWL_C_total,...30
U1,U2,MRS_C,FC,FCrho_plusC,...45
FCrho_minusC,VH,scaleVH,...
AC,w,PiC];
for i=1:length(names)
svals.(names{i})=vars(i);
end
Sol=struct( 'p',p,...
'qC',qC,...
'BCnext',BC,...
'lamC',lambC^(1/3));
V=struct('p',p,...
'VH',VH,...
'DC',DC,...
'pC',pC,...
'kC',1);
Add =struct('Knext',K,...
'BCnext',BC,...
'kC',1,...
'H',H,...
'C',C,...
'DC',DC,...
'Z',Z,...
'Y',Y,....
'NC',NC);
State=struct('K',K,...
'bC',bC);
Sparam=struct('') ;
% 'PhiB',PhiB,...
% 'Mbar',MB,...
% 'Zbar',ZA,...
% 'dbar',dI,...
% 'qbar',q);
%
statsout=struct([]) ; %'ndebt',nomdebt,...
% 'norig',PhiB*bB,...
% 'rB',rB,...