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OLGIntermediaryModel.asv
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OLGIntermediaryModel.asv
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classdef OLGIntermediaryModel < 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
NCOND % number of conditional expectations of period-ahead 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
Cond_names %NCONDx1 cell array with names of conditional variables
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)
Ffct
Basegrid % base grid
nodes % for Gaussian integration
weights % for Gaussian integration
Addit % Additional Variables
end
methods
% constructor
function obj=OLGIntermediaryModel(params,endogenv,exogenv,vfct,pfct,tfct,ffct,basegrid,nodes,weights,addvar)
% call superclass constructor
[email protected](params,endogenv,exogenv,vfct,pfct,tfct,ffct);
obj.Basegrid=basegrid;
obj.NCOND=length(endogenv.condnames);
obj.Cond_names=reshape(endogenv.condnames,1,obj.NCOND);
obj.nodes=nodes;
obj.weights=weights;
% Add this to get the extra variables, needed to compute the
% PTI constraints.
obj.Addit = addvar;
end
function [nextst,outstr]=calcStateTransition(obj,point,solvec,mode,varargin)
params=obj.Params;
exogenv=obj.Exogenv;
if ~isempty(varargin)
if length(varargin)>1
params=varargin{2};
exogenv=varargin{3};
end
end
% unpack relevant params
theta=params.theta;
nu=params.nu;
tau=params.tau;
Hbar=params.Hbar;
deltaH=params.deltaH;
phi=params.phi;
gamma=params.gamma;
chi=params.chi;
piM=params.piM;
G=params.mu_G;
M2=params.M2;
dRoW=params.dRoW;
rental = params.rental;
tax = params.tax;
if isfield(params,'MITshockloss')
MITshockloss = params.MITshockloss;
else
MITshockloss =0;
end
if rental
kappaY = params.kappaY;
end
% compute next period's states
if isempty(varargin)
State_next=obj.evaluateTrans(point);
else
if mode>1
% simulation mode with different Tfct
thistfct=varargin{1};
State_next=thistfct.evaluateAt(point);
else
% solution mode
State_next=varargin{1};
end
end
% extract state variables
exst=point(1);
whatM=point(2);
eI=point(3);
Y=exogenv.pts_perm(exst,1);
sig_epsY=exogenv.pts_perm(exst,2);
sig_epsM=exogenv.pts_perm(exst,3);
% extract solution variables
R=exp(solvec(1));
P=exp(solvec(2));
q=exp(solvec(3));
pY=exp(solvec(4));
pM=exp(solvec(5));
dM=exp(solvec(6));
dY=exp(solvec(7));
cM=exp(solvec(8));
cY=exp(solvec(9));
if rental
hY=solvec(10);
else
hY=exp(solvec(10));
end
Itilde=exp(solvec(13));
RebMort=solvec(17);
% Market clearing
DI = dY + dM;
hM = Hbar - hY;
if rental
sY = (Hbar)/(1+(cM/cY));
sM = Hbar - sY;
rhoM = theta*cM/((1-theta)*sM);
rhoY = rhoM;
else
sM = hM;
sY = hY;
rhoM = theta*cM/((1-theta)*sM);
rhoY = theta*cY/((1-theta)*sY);
end
% Wealth distribution
Yhat = Y - lumptax;
I = (1-Itilde)/chi;
xI = tau*eI - I;
WMO = whatM + q+xI + pM;
Phi = phi^(1/gamma)/(1+phi^(1/gamma));
% Values for the old agents
WO = piM * WMO;
BO = Phi * WO;
cO = WO - BO;
% Change: the taxation and the demand for assets affects the
% wealth of the agents.
whatY = (1-deltaH)*P + BO + RebMort + (M2-dRoW)/G + Yhat - whatM - eI - MITshockloss;
WY = whatY + pY;
WM = WMO - WO;
fullendogvars=[whatM,eI];
% Budget Constraints
QYHH = cY + rhoY*sY + (P-rhoY)*hY + dY/R + pY - WY;
QMHH = cM + rhoM*sM + (P-rhoM)*hM + q + pM + dM/R - WM;
SM = (P-rhoM)*hM + q + pM + dM/R - QMHH; % implied savings
SY = (P-rhoY)*hY + pY + dY/R - QYHH; % implied savings
% tax adjustment for mortgage rate
QY = QYHH/(1+tax);
QM = QMHH/(1+tax);
% Find the Rebate:
%point_state = [exst,mobj.whatM,eI];
Rebate_list=obj.evaluateForec(point)';
Rebate_today = Rebate_list(exst);
Y_star_today = Y + BO + RebMort + Rebate_today;
% [~,index]=ismember(obj.Basegrid.Pointmat,point,'rows');
% state_index = find(index==1);
% Rebate_today = obj.Ffct.Vals(state_index,exst);
% Y_star_today = Y + BO + Rebate_today;
if mode>0
% simulation, mode contains number of next period's state
exst=mode;
nst=exogenv.exnpt;
cind=exogenv.pts_all(exst,end);
whatMnext=State_next(exst,1);
eInext=State_next(nst+exst,1);
nextst=[cind,whatMnext,eInext];
else
% solution mode, compute next period's state variables for all
% possible Markov states
cind=exogenv.pts_all(:,end);
nst=exogenv.exnpt;
whatMnext=State_next(1:nst,1);
eInext=State_next(nst+(1:nst),1);
% matrix of next period states
nextst=[cind,whatMnext,eInext];
end
addvars=struct('WY',WY,...
'WM',WM,...
'DI',DI,...
'hM',hM,...
'sM',sM,...
'rhoM',rhoM,...
'sY',sY,...
'rhoY',rhoY,...
'QYHH',QYHH,...
'QMHH',QMHH,...
'QY',QY,...
'QM',QM,...
'I',I,...
'xI',xI,...
'SM', SM, ...
'SY', SY, ...
'cO',cO,...
'BO',BO,...
'Y',Y,...
'lumptax',lumptax,...
'end_yieldM',obj.Addit.end_yieldM,...
'end_yieldY',obj.Addit.end_yieldY,...
'Rebate_today',Rebate_today,...
'Y_star_today',Y_star_today);
outstr=struct;
outstr.addvars=addvars;
outstr.exstvec=[Y;sig_epsY;sig_epsM];
%outstr.Jvec=[F_eps,F_eps_cond,jacout];
outstr.fullendogvars=fullendogvars;
end
function [fx,J,V]=calcEquations(obj,exst,nextst,solvec,instr,mode,checkTrans,varargin)
params=obj.Params;
% unpack params
beta=params.beta;
betaO=params.betaO;
gamma=params.gamma;
theta=params.theta;
psiY=params.psiY;
psiM=params.psiM;
chi=params.chi;
tau=params.tau;
nu=params.nu;
lambdaY=params.lambdaY;
lambdaM=params.lambdaM;
xi=params.xi;
xiDWL=params.xiDWL;
piM=params.piM;
piY=params.piY;
ebarY=params.ebarY;
ebarM=params.ebarM;
deltaH=params.deltaH;
Hbar=params.Hbar;
G=params.mu_G;
phi=params.phi;
delta_eta=params.delta_eta;
zeta=params.zeta;
alpha=params.alpha;
tax=params.tax;
dRoW=params.dRoW;
hardconstr_LTV = params.LTV;
hardconstr_PTI = params.PTI;
%hardconstr=params.hardconstr;
rental = params.rental;
if rental
kappaY = params.kappaY;
end
%%%%%%%%%%%%%%%%%%%%%%
% Parameters LTV,PTI %
%%%%%%%%%%%%%%%%%%%%%%
thetaM_LTV=params.thetaM_LTV;
thetaY_LTV=params.thetaY_LTV;
% Change the value of theta PTI here!
thetaM_PTI=params.thetaM_PTI;
thetaY_PTI=params.thetaY_PTI;
% extract endogeous variables
R=exp(solvec(1));
P=exp(solvec(2));
q=exp(solvec(3));
pY=exp(solvec(4));
pM=exp(solvec(5));
dM=exp(solvec(6));
dY=exp(solvec(7));
if rental
hY=solvec(10);
else
hY=exp(solvec(10));
end
mY=exp(solvec(11));
mM=exp(solvec(12));
vM=exp(solvec(14));
vY=exp(solvec(15));
muI=solvec(16);
RebMort=solvec(17);
var_number = 17;
if rental
var_number = var_number + 1;
muI_rentY=solvec(var_number);
end
if hardconstr_LTV || hardconstr_PTI
var_number = var_number + 1;
if hardconstr_LTV && hardconstr_PTI
lamM_LTV=solvec(var_number);
lamY_LTV=solvec(var_number+1);
lamM_PTI=solvec(var_number+2);
lamY_PTI=solvec(var_number+3);
var_number = var_number + 3;
elseif hardconstr_LTV && not(hardconstr_PTI)
lamM_LTV=solvec(var_number);
lamY_LTV=solvec(var_number+1);
var_number = var_number + 1;
elseif not(hardconstr_LTV) && hardconstr_PTI
lamM_PTI=solvec(var_number);
lamY_PTI=solvec(var_number+1);
var_number = var_number + 1;
end
end
exnpt=obj.Exogenv.exnpt;
if checkTrans
WMtrans_check = solvec(var_number+(1:exnpt));
eItrans_check = solvec(var_number+exnpt+(1:exnpt));
end
% allocate result
fx=zeros(obj.NSOL+checkTrans*2*exnpt,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Multiplier transformations %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Financial Intermediaries
muIplus=max(0,muI)^3;
muIminus=max(0,-muI)^3;
% Non-Negativity const. housing of the young agents.
if rental
muIplus_rentY=max(0,muI_rentY)^3;
muIminus_rentY=max(0,-muI_rentY)^3;
end
if hardconstr_LTV || hardconstr_PTI
if hardconstr_LTV && hardconstr_PTI
% LTV
lamMplus_LTV=max(0,lamM_LTV)^3;
lamMminus_LTV=max(0,-lamM_LTV)^3;
lamYplus_LTV=max(0,lamY_LTV)^3;
lamYminus_LTV=max(0,-lamY_LTV)^3;
% PTI
lamMplus_PTI=max(0,lamM_PTI)^3;
lamMminus_PTI=max(0,-lamM_PTI)^3;
lamYplus_PTI=max(0,lamY_PTI)^3;
lamYminus_PTI=max(0,-lamY_PTI)^3;
elseif hardconstr_LTV && not(hardconstr_PTI)
% LTV
lamMplus_LTV=max(0,lamM_LTV)^3;
lamMminus_LTV=max(0,-lamM_LTV)^3;
lamYplus_LTV=max(0,lamY_LTV)^3;
lamYminus_LTV=max(0,-lamY_LTV)^3;
% PTI
lamMplus_PTI=0;
lamYplus_PTI=0;
elseif not(hardconstr_LTV) && hardconstr_PTI
% LTV
lamMplus_LTV=0;
lamYplus_LTV=0;
% PTI
lamMplus_PTI=max(0,lamM_PTI)^3;
lamMminus_PTI=max(0,-lamM_PTI)^3;
lamYplus_PTI=max(0,lamY_PTI)^3;
lamYminus_PTI=max(0,-lamY_PTI)^3;
end
else
%LTV
lamMplus_LTV=0;
lamYplus_LTV=0;
% PTI
lamMplus_PTI=0;
lamYplus_PTI=0;
end
% extract some other state-dependent variables
envec=instr.addvars;
DI=envec.DI;
rhoM=envec.rhoM;
rhoY=envec.rhoY;
QYHH=envec.QYHH;
QMHH=envec.QMHH;
QY=envec.QY;
QM=envec.QM;
I=envec.I;
xI=envec.xI;
SM=envec.SM;
SY=envec.SY;
hM=envec.hM;
eI=instr.fullendogvars(2);
BO=envec.BO;
Y=envec.Y;
WM=envec.WM;
WY=envec.WY;
Rebate_today = envec.Rebate_today;
Y_star_today = envec.Y_star_today;
% Variables needed for the DTI constraints:
ym = (1-nu)*Y_star_today;
yy = nu*Y_star_today;
% probabilities and states to compute expectation terms
prnext=obj.Exogenv.mtrans(exst,:);
Ynext=obj.Exogenv.pts_perm(:,1);
sigeps_nextY=obj.Exogenv.pts_perm(:,2);
sigeps_nextM=obj.Exogenv.pts_perm(:,3);
mueps_nextY=-.5*sigeps_nextY.^2;
mueps_nextM=-.5*sigeps_nextM.^2;
% projection evaluation
if nargin>=8 && (~checkTrans)
% 8 or more arguments were passed.
% Means expectations have already been computed (fast
% solution mode)
Pol_next = varargin{1};
if mode==3
% credit surface computation
Yvar = varargin{2};
Mvar = varargin{3};
end
else
% Nothing passed in ((conditional moments and EE errors in
% simulation) or consistency equations
if checkTrans
nextst(:,2) = WMtrans_check;
nextst(:,3) = eItrans_check;
end
Pol_next = obj.evaluateVal(nextst)';
if size(Pol_next,1)==1
prnext=1;
end
forec = obj.evaluateForec([exst,instr.fullendogvars]);
Pol_next=[Pol_next,forec];
end
q_next = Pol_next(:,1);
I_next = Pol_next(:,2);
vM_next = Pol_next(:,3);
vY_next = Pol_next(:,4);
P_next = Pol_next(:,5);
pY_next = Pol_next(:,6);
pM_next = Pol_next(:,7);
BO_next = Pol_next(:,8);
R_next = Pol_next(:,9);
RebMort_next = Pol_next(:,10);
Reb_next = Pol_next(:,11);
xI_next=tau*nextst(:,3)-I_next;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% HERE I start using the equations %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Mortgage payoff and default for young
Ystar_next = Ynext + Reb_next + BO_next + RebMort_next;
ystar_next = (1-nu)*Ystar_next;
wYYdef_next = dY./G + nu*Ystar_next + pY_next;
% Change: eliminate BO_next
wYMdef_next = dY./G + (delta_eta*ystar_next)/piY;
epsbarYY_next = (mY/G - lambdaY*wYYdef_next)./((1-deltaH)*P_next*hY);
epsbarYM_next = (mY/G - lambdaY*wYMdef_next)./((1-deltaH)*P_next*hY);
% First for the individuals that stay young.
[Feps_nextYY,feps_nextYY,FepsplusYY,FepsminusYY,...
RFepsVFYY,RFepsFOC1YY,RFepsFOC2YY]= OLGIntermediaryModel.integEps(epsbarYY_next,mueps_nextY,sigeps_nextY,gamma,...
G*(1-deltaH)*P_next*hY/SY,(G*wYYdef_next-mY)/SY,obj.nodes,obj.weights,0);
[Feps_nextYM,feps_nextYM,FepsplusYM,FepsminusYM,...
RFepsVFYM,RFepsFOC1YM,RFepsFOC2YM]= OLGIntermediaryModel.integEps(epsbarYM_next,mueps_nextY,sigeps_nextY,gamma,...
G*(1-deltaH)*P_next*hY/SY,(G*wYMdef_next-mY)/SY,obj.nodes,obj.weights,0);
%%%%%%%%%%%%%%%%%%%%%%%
% Payoffs Calculations%
%%%%%%%%%%%%%%%%%%%%%%%
% YOUNG
Def_nextY = (1-piY)*Feps_nextYY + piY*Feps_nextYM;
FepsminusY = (1-piY)*FepsminusYY + piY*FepsminusYM;
Payoff_nextY = (1-Def_nextY).*mY./G + (1-deltaH)*P_next*hY.*(alpha + (1-xi)*FepsminusY);
wMdef_next = dM./G + q_next+xI_next + ((1-delta_eta)*ystar_next+pM_next);
epsbarM_next = (mM/G - lambdaM*wMdef_next)./((1-deltaH)*P_next*hM);
[Feps_nextM,feps_nextM,FepsplusM,FepsminusM,...
RFepsVFM,RFepsFOC1M,RFepsFOC2M]= OLGIntermediaryModel.integEps(epsbarM_next,mueps_nextM,sigeps_nextM,gamma,...
G*(1-deltaH)*P_next*hM/SM,(G*wMdef_next-mM)/SM,obj.nodes,obj.weights,0);
Payoff_nextM = (1-Feps_nextM).*mM./G + (1-deltaH)*P_next*hM.*(alpha + (1-xi)*FepsminusM);
%%%%%%%%%%%%%%%%%%
% Financial Int. %
%%%%%%%%%%%%%%%%%%
eInext = Payoff_nextY + Payoff_nextM - DI./G;
[min_eInext,minstate] = min(eInext);
min_PayoffY=Payoff_nextY(minstate);
min_PayoffM=Payoff_nextM(minstate);
%%%%%%%%%%%%%%%%%%%%%%
% Compute Middle SDF %
%%%%%%%%%%%%%%%%%%%%%%
Phi = (1/(1+ phi^(1/gamma)))^(1-gamma) + phi*(phi^(1/gamma)/(1+ phi^(1/gamma)))^(1-gamma) * betaO;
RMdef_next = G*(1-lambdaM)*wMdef_next/SM;
ThetaZ = ((1-theta)^(1-theta) * (theta/rhoM)^theta)^(1-gamma);
AZ = psiM*(dM/SM)^(1-gamma) + ...
beta*prnext*((RFepsVFM + Feps_nextM.*RMdef_next.^(1-gamma)) .* (piM*Phi + (1-piM)*vM_next));
BZ = AZ^(1/gamma)/( AZ^(1/gamma) + ThetaZ^(1/gamma));
MMnodef_m = beta * BZ^(-gamma)/vM * RFepsFOC1M .* (piM*Phi + (1-piM)*vM_next);
MMnodef_h = beta * BZ^(-gamma)/vM * RFepsFOC2M .* (piM*Phi + (1-piM)*vM_next);
MMdef = beta * BZ^(-gamma)/vM * RMdef_next.^(-gamma) .* (piM*Phi + (1-piM)*vM_next);
SDFM = MMnodef_m + (1-lambdaM)*Feps_nextM.*MMdef;
% With this we can compute the SDF of the financial
% intermediares.
SDFI = SDFM.*(tau + (1-tau)./(1-chi*I_next))*(1-chi*I);
% AZ = psiM*(dMhat)^(1-gamma) + beta*(piM*Phi + (1-piM)*vM)*(RepsVFM + FepsM*RMdef^(1-gamma));
% ThetaZ = ((1-theta)^(1-theta) * (theta/rhoM)^theta )^(1-gamma);
% SMshare = AZ^(1/gamma) / (AZ^(1/gamma) + ThetaZ^(1/gamma));
%%%%%%%%%%%%%%%%%%%%%%
% Derivatives of q_M %
%%%%%%%%%%%%%%%%%%%%%%
QMdiff_term = feps_nextM.*(mM - G*(1-xi)*(1-deltaH)*hM*P_next.*epsbarM_next);
% QMm_term = 1-Feps_nextM - QMdiff_term./(G*(1-deltaH)*P_next*hM);
QMm_term = QMdiff_term./(G*(1-deltaH)*P_next*hM) + (1-deltaH)*P_next*hM/mM .*(alpha + (1-xi)*FepsminusM);
QMh_term = G*(1-deltaH)*P_next.*(alpha + (1-xi)*FepsminusM + QMdiff_term.*epsbarM_next./(G*(1-deltaH)*P_next*hM));
QMd_term = lambdaM*QMdiff_term./(G*(1-deltaH)*P_next*hM);
QMb_term = QMd_term.*(q_next+xI_next)*G;
QMeta_term = QMd_term.*((1-delta_eta)*ystar_next+pM_next)*G;
QMh = (1+tax)*((1-ebarM)*muIplus*QMh_term(minstate) + prnext*(SDFI.*QMh_term))/(1+zeta);
QMm = (1+tax)*((1-ebarM)*muIplus*QMm_term(minstate) + prnext*(SDFI.*QMm_term))/(1+zeta);
QMd = (1+tax)*((1-ebarM)*muIplus*QMd_term(minstate) + prnext*(SDFI.*QMd_term))/(1+zeta);
QMb = (1+tax)*((1-ebarM)*muIplus*QMb_term(minstate) + prnext*(SDFI.*QMb_term))/(1+zeta);
QMeta = (1+tax)*((1-ebarM)*muIplus*QMeta_term(minstate) + prnext*(SDFI.*QMeta_term))/(1+zeta);
%%%%%%%%%%%%%%%%%%%%%%
% Compute Young SDF %
%%%%%%%%%%%%%%%%%%%%%%
RYYdef_next = G*(1-lambdaY)*wYYdef_next/SY;
RYMdef_next = G*(1-lambdaY)*wYMdef_next/SY;
ThetaY = ((1-theta)^(1-theta) * (theta/rhoY)^theta)^(1-gamma);
AY = psiY*(dY/SY)^(1-gamma) ...
+ beta*(1-piY)*prnext*((RFepsVFYY + Feps_nextYY.*RYYdef_next.^(1-gamma)) .* vY_next) ...
+ beta*piY*prnext*((RFepsVFYM + Feps_nextYM.*RYMdef_next.^(1-gamma)) .* vM_next);
BY = AY^(1/gamma)/( AY^(1/gamma) + ThetaY^(1/gamma));
MYnodef_m = beta * BY^(-gamma)/vY * ((1-piY)*RFepsFOC1YY.*vY_next + piY*RFepsFOC1YM.*vM_next);
MYnodef_h = beta * BY^(-gamma)/vY * ((1-piY)*RFepsFOC2YY.*vY_next + piY*RFepsFOC2YM.*vM_next);
MYdef = beta * BY^(-gamma)/vY * ((1-piY)*Feps_nextYY.*RYYdef_next.^(-gamma).*vY_next + piY*Feps_nextYM.*RYMdef_next.^(-gamma).*vM_next );
SDFY = MYnodef_m + (1-lambdaY)*MYdef;
MYY = beta * BY^(-gamma)/vY * (1-piY)*(RFepsFOC1YY + (1-lambdaY)*Feps_nextYY.*RYYdef_next.^(-gamma)) .* vY_next;
MYM = beta * BY^(-gamma)/vY * piY*(RFepsFOC1YM + (1-lambdaY)*Feps_nextYM.*RYMdef_next.^(-gamma)) .* vM_next;
%%%%%%%%%%%%%%%%%%%%%%
% Derivatives of q_Y %
%%%%%%%%%%%%%%%%%%%%%%
%Fhat_nextY = piY*(1-Feps_nextYM) + (1-piY)*(1-Feps_nextYY);
epshatYY = mY - G*(1-xi)*(1-deltaH)*hY*P_next.*epsbarYY_next;
epshatYM = mY - G*(1-xi)*(1-deltaH)*hY*P_next.*epsbarYM_next;
fhat_nextY = (piY*feps_nextYM.*epshatYM + (1-piY)*feps_nextYY.*epshatYY)./(G*(1-deltaH)*P_next*hY);
% QYm_term = Fhat_nextY - fhat_nextY;
QYm_term = fhat_nextY + (1-deltaH)*P_next*hY/mY .* (alpha + (1-xi)*FepsminusY);
QYd_term = lambdaY*fhat_nextY;
fhh_nextY = (piY*feps_nextYM.*epshatYM.*epsbarYM_next ...
+ (1-piY)*feps_nextYY.*epshatYY.*epsbarYY_next)./(G*(1-deltaH)*P_next*hY);
QYh_term = G*(1-deltaH)*P_next.*(alpha + FepsminusY*(1-xi)+ fhh_nextY);
% Change: eliminate BO_next
fhhh_nextY = (piY*((delta_eta*ystar_next)/piY).*feps_nextYM.*epshatYM ...
+ (1-piY)*feps_nextYY.*(nu*Ystar_next + pY_next).*epshatYY)./(G*(1-deltaH)*P_next*hY);
QYeta_term = G*lambdaY*fhhh_nextY;
QYeta = (1+tax)*((1-ebarY)*muIplus*QYeta_term(minstate) + prnext*(SDFI.*QYeta_term))/(1+zeta);
QYm = (1+tax)*((1-ebarY)*muIplus*QYm_term(minstate) + prnext*(SDFI.*QYm_term))/(1+zeta);
QYh = (1+tax)*((1-ebarY)*muIplus*QYh_term(minstate) + prnext*(SDFI.*QYh_term))/(1+zeta);
QYd = (1+tax)*((1-ebarY)*muIplus*QYd_term(minstate) + prnext*(SDFI.*QYd_term))/(1+zeta);
%%%%%%%%%%%%%%%%%%%%%%
% FOC's Middle aged %
%%%%%%%%%%%%%%%%%%%%%%
% Effective returns on housing
Rh_eff_next = G*(1-deltaH)*P_next/(P - rhoM - QMh);
% Effective returns to mortgages
Rm_eff_next = 1/(QMHH/mM - QMm);
% Effective returns to deposits. This is just one interest
% rate! Not next.
Rd_eff = R/(1-R*QMd);
% Effective returns to equity.
Re_eff_next = G*(q_next+xI_next)/(q - QMb);
% Effective returns to endowment.
Reta_eff_next = G*((1-delta_eta)*ystar_next+pM_next)/(pM - QMeta);
% This is the first element of equation (42)
cyieldM = psiM*(dM*BZ/SM)^(-gamma)/vM;
% The FOC written as no-excess return equations.
fx(1) = prnext*(SDFM.*Re_eff_next - MMnodef_h.*Rh_eff_next) ...
- lamMplus_LTV*thetaM_LTV*(BZ^(-gamma)/vM)*P/(P - rhoM - QMh);
fx(2) = Rd_eff*cyieldM + prnext*(SDFM.*(Rd_eff - Re_eff_next));
fx(3) = prnext*(MMnodef_h.*Rh_eff_next - MMnodef_m.*Rm_eff_next) ...
+lamMplus_LTV*(BZ^(-gamma)/vM)*(thetaM_LTV*P/(P - rhoM - QMh) - Rm_eff_next)...
-lamMplus_PTI*(BZ^(-gamma)/vM)*Rm_eff_next;
%payoffend_m = (1-delta_eta)*ym;
payoffend_m = ym;
fx(4) = prnext*(SDFM.*(Re_eff_next - Reta_eff_next))...
-lamMplus_PTI*payoffend_m*thetaM_PTI*(BZ^(-gamma)/vM)*(1/(pM - QMeta));
% Defintion of the savings for the middle aged.
fx(5) = SM - BZ*WM;
% vMcheck = AZ * ( AZ^(1/gamma) / (AZ^(1/gamma) + ThetaZ^(1/gamma)) )^(1-gamma) ...
% + ThetaZ * ( ThetaZ^(1/gamma) / (AZ^(1/gamma) + ThetaZ^(1/gamma)) )^(1-gamma);
% This is the defintion of v_m(Z) in the appenix.
fx(6) = vM - ThetaZ*(1-BZ)^(1-gamma) - AZ*BZ^(1-gamma);
%%%%%%%%%%%%%%%%%%%%%%%%
% FOC's Intermdiaries %
%%%%%%%%%%%%%%%%%%%%%%%%
fx(7)=1/R - muIplus/G - prnext*SDFI;
fx(8)=(1+zeta)*QY - (1-ebarY)*muIplus*min_PayoffY - G*prnext*(SDFI.*Payoff_nextY);
fx(9)=(1+zeta)*QM - (1-ebarM)*muIplus*min_PayoffM - G*prnext*(SDFI.*Payoff_nextM);
%%%%%%%%%%%%%%%%%%%%%%%%
% FOC's Young agents %
%%%%%%%%%%%%%%%%%%%%%%%%
% Effective returns on housing
RYh_eff_next = G*(1-deltaH)*P_next/(P - rhoY - QYh);
% Effective returns on mortgages.
RYm_eff_next = 1/(QYHH/mY - QYm);
% Effective returns on deposits (not an expectation!)
RYd_eff = R/(1-R*QYd);
% Effective returns of the endwoment asset if you don't age.
RYYeta_eff_next = G*(nu*Ystar_next + pY_next)/(pY - QYeta);
% Change: eliminate BO_next
% Effective returns of the endwoment asset if you age.
RYMeta_eff_next = G*((delta_eta*ystar_next)/piY)/(pY - QYeta);
% Auxiliary variable: first part of equation (42)
cyieldY = psiY*(dY*BY/SY)^(-gamma)/vY;
% The FOC written as no-excess return equations.
fx(10)= cyieldY*RYd_eff + prnext*(SDFY.*RYd_eff - MYnodef_m.*RYm_eff_next)...
- lamYplus_LTV*(BY^(-gamma)/vY)*RYm_eff_next...
- lamYplus_PTI*(BY^(-gamma)/vY)*RYm_eff_next;
if rental
fx(11)= prnext*(MYnodef_m.*RYm_eff_next - MYnodef_h.*RYh_eff_next) ...
+ lamYplus_LTV*(BY^(-gamma)/vY)*(RYm_eff_next - thetaY_LTV*P/(P - rhoY - QYh))...
+ lamYplus_PTI*(BY^(-gamma)/vY)*RYm_eff_next...
- (muIplus_rentY+(kappaY*(hY)^(-gamma))) * (BY^(-gamma)/vY)*(1/(P - rhoY - QYh));
else
fx(11)= prnext*(MYnodef_m.*RYm_eff_next - MYnodef_h.*RYh_eff_next) ...
+ lamYplus_LTV*(BY^(-gamma)/vY)*(RYm_eff_next - thetaY_LTV*P/(P - rhoY - QYh))...
+ lamYplus_PTI*(BY^(-gamma)/vY)*RYm_eff_next;
end
%payoffend_y = piY*(delta_eta*ym/piY) + (1-piY)*yy;
payoffend_y = yy;
if rental
fx(12)= prnext*(MYnodef_h.*RYh_eff_next - (MYY.*RYYeta_eff_next + MYM.*RYMeta_eff_next)) ...
+ lamYplus_LTV*(BY^(-gamma)/vY)*thetaY_LTV*P/(P - rhoY - QYh)...
- lamYplus_PTI*(BY^(-gamma)/vY)*thetaY_PTI*(payoffend_y/(pY - QYeta))...
+ (muIplus_rentY+(kappaY*(hY)^(-gamma))) * (BY^(-gamma)/vY)*(1/(P - rhoY - QYh));
else
fx(12)= prnext*(MYnodef_h.*RYh_eff_next - (MYY.*RYYeta_eff_next + MYM.*RYMeta_eff_next)) ...
+ lamYplus_LTV*(BY^(-gamma)/vY)*thetaY_LTV*P/(P - rhoY - QYh)...
- lamYplus_PTI*(BY^(-gamma)/vY)*thetaY_PTI*(payoffend_y/(pY - QYeta));
end
% Defintion of the savings for the middle aged.
fx(13)= SY - BY*WY;
% This is the defintion of v_y(Z) in the appenix.
fx(14)= vY - ThetaY*(1-BY)^(1-gamma) - AY*BY^(1-gamma);
% CC for the Intermediary
fx(15)=(1-ebarY)*min_PayoffY+(1-ebarM)*min_PayoffM - DI/G - muIminus;
% Budget Constraint of the Intermediary.
fx(16)= (1+zeta)*(QY + QM) - ((1-tau)*eI + I - chi*I^2/2 + DI/R);
% Rebates
fx(17)= RebMort - ( zeta*(QY+QM) - (QMHH-QM) - (QYHH-QY) );
eq_number = 17;
if rental
eq_number = eq_number+1;
fx(eq_number) = hY - muIminus_rentY;
end
if hardconstr_LTV || hardconstr_PTI
eq_number = eq_number+1;
if hardconstr_LTV && hardconstr_PTI
% LTV and PTI
fx(eq_number)=thetaM_LTV*P*hM - mM-lamMminus_LTV;
fx(eq_number+1)=thetaY_LTV*P*hY - mY-lamYminus_LTV;
fx(eq_number+2)=thetaM_PTI*payoffend_m - mM-lamMminus_PTI;
fx(eq_number+3)=thetaY_PTI*payoffend_y - mY-lamYminus_PTI;
eq_number = eq_number+3;
elseif hardconstr_LTV && not(hardconstr_PTI)
% LTV and PTI
fx(eq_number)=thetaM_LTV*P*hM - mM-lamMminus_LTV;
fx(eq_number+1)=thetaY_LTV*P*hY - mY-lamYminus_LTV;
eq_number = eq_number+1;
elseif not(hardconstr_LTV) && hardconstr_PTI
% LTV and PTI
fx(eq_number)=thetaM_PTI*payoffend_m - mM-lamMminus_PTI;
fx(eq_number+1)=thetaY_PTI*payoffend_y - mY-lamYminus_PTI;
eq_number = eq_number+1;
end
end
%%%%%%%%%%%%%%%
% Transitions %
%%%%%%%%%%%%%%%
% Aggregate income of the young defaulters:
WYYdef_next = (1-piY)*(dY./G + nu*Ystar_next + pY_next);
% Change: eliminate BO_next
WYMdef_next = piY*dY./G + (delta_eta*ystar_next);
% Aggregate income of the middle aged defaulters:
WMdef_next = dM./G + q_next+xI_next + (1-delta_eta)*ystar_next + pM_next;
RebateY = (1-piY)*lambdaY*Feps_nextYY.*WYYdef_next + lambdaY*Feps_nextYM.*WYMdef_next + (xi-xiDWL)*(1-deltaH)*FepsminusY.*P_next*hY;
RebateM = (xi-xiDWL)*(1-deltaH)*FepsminusM.*P_next*hM + lambdaM*Feps_nextM.*WMdef_next;
RebateI = -alpha*P_next*Hbar;
% Change: eliminate BO_next
WYMnext = (delta_eta*ystar_next + piY*dY/G).*(1-lambdaY.*Feps_nextYM)...
+ piY*((1-deltaH)*FepsplusYM.*P_next*hY - (1-Feps_nextYM)*mY/G);
% Total wealth of the middle age and old age people:
WMnext = WYMnext + (1-deltaH)*FepsplusM.*P_next*hM - (1-Feps_nextM)*mM/G + (1-lambdaM*Feps_nextM).*WMdef_next;
% This is the value of the state variable:
%Yhat_next = Ynext - lumptax_next;
WMtrans = WMnext - (q_next+xI_next) - pM_next;
eItrans = eInext;
if checkTrans
fx(eq_number+(1:exnpt)) = WMtrans - WMtrans_check;
fx(eq_number+exnpt+(1:exnpt)) = eItrans - eItrans_check;
end
% Jacobian computation (numeric)
if nargout > 1 && mode == 0 && ~isempty(obj.Jacobian)
% only for analytic Jacobian
else
J=[];
end
V=cell(3,1);
% marginal value functions
if mode==1
% Output new values for time iteration
Vnext=zeros(obj.Vfct.Nof,1);
Vnext(1)=q;
Vnext(2)=I;
Vnext(3)=vM;
Vnext(4)=vY;
Vnext(5)=P;
Vnext(6)=pY;
Vnext(7)=pM;
Vnext(8)=BO;
Vnext(9)=R;
Vnext(10)=RebMort;
V{1}=Vnext;
% state transition
V{2}=[WMtrans; eItrans]';
% forecasting function for rebates
V{3}=(RebateY+RebateM+RebateI)';
elseif mode==2
% Evaluation during simulation. Output conditional
% variables
% SDFs
SDF.SDFM = SDFM;
SDF.SDFI = SDFI;
SDF.SDFY = SDFY;
% Define returns
NetPayoff_nextM = Payoff_nextM - alpha.*(1-deltaH).*P_next*hM;
NetPayoff_nextY = Payoff_nextY - alpha.*(1-deltaH).*P_next*hY;
retMM = G*NetPayoff_nextM/QM;
retMY = G*NetPayoff_nextY/QY;
retH = G.*(1-deltaH)*P_next/(P-rhoM);
retBext = G.*(q_next + xI_next)/q;
retBin =(G*(Payoff_nextM+Payoff_nextY) - DI)./((1+zeta)*(QY+QM) - DI/R);
expR_MM = prnext * retMM;
expR_MY = prnext * retMY;
expR_H = prnext * retH;
expR_Bext = prnext * retBext;
expR_Bin = prnext * retBin;
% Expected default rates
EDefY = prnext * ((1-piY)*Feps_nextYY + piY*Feps_nextYM);
EDefM = prnext * Feps_nextM;
condvars = struct('expR_MM',expR_MM, ...
'expR_MY',expR_MY, ...
'expR_H',expR_H,...
'expR_Bext',expR_Bext,...
'expR_Bin',expR_Bin,...
'min_eInext',min_eInext,...
'cyieldM',cyieldM,...
'cyieldY',cyieldY,...
'EDefY',EDefY,...
'EDefM',EDefM);
% Wtrans.WY = WYtrans;
Wtrans.WM = WMtrans;
Wtrans.eI = eItrans;
V = {condvars,Wtrans,SDF};
elseif mode==3
% compute credit surface
% first young
npty=size(Yvar,1);
QYmat=zeros(npty,4);
for yi=1:npty
hYi = Yvar(yi,1);
levYi = Yvar(yi,2);
mYi=P*hYi*levYi;
levYWi = Yvar(yi,3);
% dYi=mYi/levYWi - nu;
% wYYdef_next = dYi./G + nu*Ystar_next+pY_next;
% wYMdef_next = dYi./G + ((1-nu)*Ystar_next+BO_next);
wYYdef_next = mYi/levYWi;
wYMdef_next = mYi/levYWi;
epsbarYY_next = (mYi/G - lambdaY*wYYdef_next)./((1-deltaH)*P_next*hYi);
epsbarYM_next = (mYi/G - lambdaY*wYMdef_next)./((1-deltaH)*P_next*hYi);
[Feps_nextYY,~,~,FepsminusYY]= OLGIntermediaryModel.integEps(epsbarYY_next,mueps_nextY,sigeps_nextY,gamma,[],[],obj.nodes,obj.weights,1);
[Feps_nextYM,~,~,FepsminusYM]= OLGIntermediaryModel.integEps(epsbarYM_next,mueps_nextY,sigeps_nextY,gamma,[],[],obj.nodes,obj.weights,1);
Def_nextY = (1-piY)*Feps_nextYY + piY*Feps_nextYM;
FepsminusY = (1-piY)*FepsminusYY + piY*FepsminusYM;
Payoff_nextYi = (1-Def_nextY).*mYi./G + (1-xi)*(1-deltaH)*FepsminusY.*P_next*hYi;
% price this mortgage
QYmat(yi,1)=(1-ebarY)*muIplus*Payoff_nextYi(minstate) + G*prnext*(SDFI.*Payoff_nextYi);
QYmat(yi,2)=mYi; % mortgage
QYmat(yi,3)=mYi/QYmat(yi,1); % spread
QYmat(yi,4)=mYi/QYmat(yi,1) - R; % spread
end
% then middle aged
nptm=size(Mvar,1);
QMmat=zeros(nptm,4);
for mi=1:nptm
hMi = Mvar(mi,1);
levMi = Mvar(mi,2);
mMi=P*hMi*levMi;
levMWi = Mvar(mi,3);
% dMi=mMi/levMWi - xI-q;
% wMdef_next = dMi./G + q_next+xI_next;
wMdef_next = mMi/levMWi;
epsbarM_next = (mMi/G - lambdaM*wMdef_next)./((1-deltaH)*P_next*hMi);
[Feps_nextM,~,~,FepsminusM]= OLGIntermediaryModel.integEps(epsbarM_next,mueps_nextM,sigeps_nextM,gamma,[],[],obj.nodes,obj.weights,1);
Payoff_nextMi = (1-Feps_nextM).*mMi./G + (1-xi)*(1-deltaH)*FepsminusM.*P_next*hMi;
% price this mortgage
QMmat(mi,1)=(1-ebarM)*muIplus*Payoff_nextMi(minstate) + G*prnext*(SDFI.*Payoff_nextMi);
QMmat(mi,2)=mMi;
QMmat(mi,3)=mMi/QMmat(mi,1);
QMmat(mi,4)=mMi/QMmat(mi,1) - R;
end
V={QYmat,QMmat};
end
end
function [errmat,solmat,condmat,Wshtrans,SDFmat]=calcEEError(obj,pointmat)
% function to compute Euler equation error at points in state
% space given by pointmat
nst=size(obj.Exogenv.pts_all,1);
errmat=zeros(size(pointmat,1),obj.Pfct.Nof);
solmat=zeros(size(errmat));
condmat=zeros(size(pointmat,1),obj.NCOND);
SDFmat=zeros(size(pointmat,1),3*nst);
Wshtrans=zeros(size(pointmat,1),obj.NSTEN*nst);
evaluatePol = @(point)obj.evaluatePol(point);
calcStateTransition = @(point,soltmp)obj.calcStateTransition(point,soltmp,0);
calcEquations = @(exst,nextst,soltmp,outstr)obj.calcEquations(exst,nextst,soltmp,outstr,2,0);
params=obj.Params;
% Should be parfor. Use for when debugging only
parfor i=1:size(errmat,1)
% for i=1:size(errmat,1)
point=pointmat(i,:);
soltmp=evaluatePol(point);
% transition
[nextst,outstr]=calcStateTransition(point,soltmp);
% equations
[fx,~,V]=calcEquations(point(1),nextst,soltmp,outstr);
R=exp(soltmp(1));
P=exp(soltmp(2));
vM=exp(soltmp(14));
vY=exp(soltmp(15));
Reb=soltmp(17);
QY=outstr.addvars.QY;
QM=outstr.addvars.QM;
DI=outstr.addvars.DI;
SM=outstr.addvars.SM;
SY=outstr.addvars.SY;
if params.rental
normvec=[R,R,R,R,SM,vM,1/R,QY,QM,R,R,R,SY,vY,DI,1,Reb,1];
else
normvec=[R,R,R,R,SM,vM,1/R,QY,QM,R,R,R,SY,vY,DI,1,Reb];
end
if params.PTI || params.LTV
if params.LTV && params.PTI
% LTV and PTI
normvec=[normvec,P,P,P,P];
elseif params.LTV && not(params.PTI)
% LTV and PTI
normvec=[normvec,P,P];
elseif not(params.LTV) && params.PTI
% LTV and PTI
normvec=[normvec,P,P];
end
end
condvars=V{1};
% WYtrans=V{2}.WY;
WMtrans=V{2}.WM;
eItrans=V{2}.eI;
SDFI=V{3}.SDFI;
SDFM=V{3}.SDFM;
SDFY=V{3}.SDFY;
errmat(i,:)=fx'./normvec;