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function err_mom = objective(x)
set(groot, 'DefaultAxesLineWidth', 1.5);
set(groot, 'DefaultLineLineWidth', 4);
set(groot, 'DefaultAxesTickLabelInterpreter','latex');
set(groot, 'DefaultLegendInterpreter','latex');
set(groot, 'DefaultAxesFontSize',22);
intmeth = 'linear';
printr = 0;
optset('bisect', 'tol', 1e-32);
% Calibrated Parameters
p.beta = x(1); % discount factor
p.alpha = x(2); % weight on housing in preferences
p.R = x(3);
p.phi = x(4); % productivity non-market
p.F0m = x(5); % fixed cost of refinancing
p.B = x(6);
p.rh = (1 + x(7))^(1/4) - 1; % interest rate
p.r1 = x(8);
p.r2 = x(9); % parameters governing shape of rl curve
% Assigned Parameters
p.rl = (1 - 0.028)^(1/4) - 1; % lower bound on liquid rate
p.T = 61*4; % last period of life
p.D = 30*4; % maturity of mortgages
p.sigma = 2; % CRRA
p.gamma = 1; % Frisch elasticity of non-market production
p.rm = (1 + 0.025)^(1/4) - 1; % interest rate
p.Fs = 0.06; % fixed cost of selling home
p.F1m = 0.005; % proportional cost of refinancing
p.wbar = 0.00001; % parameter governing luxuriousness of bequests
p.thetam = 0.85; % maximum LTV
p.thetay = 0.214; % maximum PTI
rhoz = 0.9908;
sz = 0.0761;
se = (1 - 0.55)^(1/2)*0.4869; % Krueger Perri (2011) show 55% of the variance of trans compon is measurement error so subtract
time = (1 : 1 : p.T)';
p.lambdat = exp(0.07982636 - 0.02322307 * (time/4 + 25) + 0.00105409 * (time/4 + 25).^2 - 0.00001028 * (time/4 + 25).^3);
p.thetay = p.thetay*(1 - 0.3126./(1 + exp(18.629 - 0.3049*(time/4 + 25))));
p.mbar = p.rm/(1 - (1 + p.rm)^(-p.D)); % minimum payment required per 1 of initial debt
% Quality of Approximation
p.na = 50; % number of nodes for liquid assets
p.nl = 75; % number of nodes for liquidity
p.no = 9; % number of nodes for omega (fraction of loan outstanding)
p.nt = 3; % number of possible initial LTV
p.nh = 7; % number of nodes for housing
p.nz = 9; % points for exogenous income z
p.ne = 3;
% Discretize Income Process
[zgrid, Fzz] = rouwenhorst(rhoz, sz, p.nz);
p.zgrid = exp(zgrid');
[Fz, d] = eigs(Fzz', 1, 'largestabs');
Fz = Fz/sum(Fz);
Fz = full(Fz); % ergodic distribution of z
[egrid, we] = qnwnorm(p.ne, 0, se^2);
p.egrid = exp(egrid);
% Discretize other state variables
amin = 0;
amax = 100;
p.agrid = amin + (amax - amin)*nodeunif(p.na, 0, 1).^2;
omin = 0;
omax = 1;
p.ogrid = omin + (omax - omin)*nodeunif(p.no, 0, 1);
tmin = 0.5;
tmax = p.thetam;
p.tgrid = tmin + (tmax - tmin)*nodeunif(p.nt, 0, 1);
hmin = 5; % minimum house size
hmax = 40; % maximum house size
p.hgrid = hmin + (hmax - hmin)*nodeunif(p.nh, 0, 1).^1.5;
ymax = max(p.lambdat)*zgrid(end)*egrid(end);
lmin = -0.1;
lmax = 125;
p.lgrid = lmin + (lmax - lmin)*nodeunif(p.nl, 0, 1).^1.5;
% Construct grids:
svbarh = gridmake(p.agrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid); % grid for expected value of homeowners
svbarr = gridmake(p.agrid, p.zgrid); % grid for expected value of renters
svh = gridmake(p.agrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid, p.egrid); % grid for value of homeowners prior to making h choice
svr = gridmake(p.agrid, p.zgrid, p.egrid); % grid for value of renters prior to making h choice
swh = gridmake(p.lgrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid); % grid for W functions
swr = gridmake(p.lgrid, p.zgrid);
ind2h = kron((1:1:p.no*p.nt*p.nh*p.nz)', ones(p.nl, 1)); % index of all other state-variables to speed up evaluations (Bangladesh)
ind2r = kron((1:1: p.nz)', ones(p.nl, 1));
vbarh = zeros(p.na*p.no*p.nt*p.nh*p.nz, p.T + 1); % expected values of homeowners
vbarr = zeros(p.na*p.nz, p.T + 1); % expected values of renters
vh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T); % value of homeowners prior to making h choice (envelope over 5 possible options)
vr = zeros(p.na*p.nz*p.ne, p.T); % value of renters prior to making h choice (envelope over possible options)
wh = zeros(p.nl*p.no*p.nt*p.nh*p.nz, p.T); % value of homeowners after making h choice
wr = zeros(p.nl*p.nz, p.T); % value of renters after making h choice
ch = zeros(p.nl*p.no*p.nt*p.nh*p.nz, p.T); % consumption homeowners after making h choice
cr = zeros(p.nl*p.nz, p.T); % consumption of renters after making h choice
aprimeh = zeros(p.nl*p.no*p.nt*p.nh*p.nz, p.T); % liquid savings of homeowners after making h choice
aprimer = zeros(p.nl*p.nz, p.T); % liquid savings of renters after making h choice
cmaxh = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'h', amin); % c that implies a' = amin
cmaxr = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'r', amin);
cminh = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'h', amax); % c that implies a' = amax
cminr = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'r', amax);
cmaxh = repmat(cmaxh, p.no*p.nt*p.nh*p.nz, 1);
cmaxr = repmat(cmaxr, p.nz, 1);
cminh = repmat(cminh, p.no*p.nt*p.nh*p.nz, 1);
cminr = repmat(cminr, p.nz, 1);
lh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T); % liquidity of homeowners after making h choice (envelope over 5 possible options)
lr = zeros(p.na*p.nz*p.ne, p.T); % liquidity of renters after making h choice (envelope over possible options)
omegaprimeh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
omegaprimer = zeros(p.na*p.nz*p.ne, p.T);
thetaprimeh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
thetaprimer = zeros(p.na*p.nz*p.ne, p.T);
hprimeh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
hprimer = zeros(p.na*p.nz*p.ne, p.T);
dh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
dr = zeros(p.na*p.nz*p.ne, p.T);
% Terminal value of bequests
vbarh(:, p.T + 1) = p.B*(p.wbar + (1 + p.rl)*svbarh(:,1) + (1 - p.Fs - svbarh(:,2).*svbarh(:,3)*(1 + p.rl)).*svbarh(:,4)).^(1 - p.sigma)/(1 - p.sigma);
vbarr(:, p.T + 1) = p.B*(p.wbar + (1 + p.rl)*svbarr(:,1)).^(1 - p.sigma)/(1 - p.sigma);
for t = p.T : -1 : 1
% tic
EVh = griddedInterpolant({p.agrid, (1: 1:p.no*p.nt*p.nh*p.nz)'}, reshape(vbarh(:, t + 1), p.na, p.no*p.nt*p.nh*p.nz), intmeth, 'linear');
EVr = griddedInterpolant({p.agrid, (1: 1: p.nz)'}, reshape(vbarr(:, t + 1), p.na, p.nz), intmeth, 'linear');
% solve consumption-savings choice
ch(:, t) = solve_golden('wfunc', cminh, cmaxh, swh, ind2h, EVh, p, 'h');
cr(:, t) = solve_golden('wfunc', cminr, cmaxr, swr, ind2r, EVr, p, 'r');
[~, aprimeh(:,t)] = savings(ch(:, t), swh, p, 'h');
[~, aprimer(:,t)] = savings(cr(:, t), swr, p, 'r');
wh(:, t) = wfunc(ch(:, t), swh, ind2h, EVh, p, 'h');
wr(:, t) = wfunc(cr(:, t), swr, ind2r, EVr, p, 'r');
Whinterp = griddedInterpolant({p.lgrid, (1: 1: p.no*p.nt*p.nh*p.nz)'}, reshape(wh(:, t), p.nl, p.no*p.nt*p.nh*p.nz), intmeth, 'linear');
Wrinterp = griddedInterpolant({p.lgrid, (1: 1: p.nz)'}, reshape(wr(:, t), p.nl, p.nz), intmeth, 'linear');
% Solve discrete choice problem of renters
A = svr(:,1);
Y = p.lambdat(t)*svr(:,2).*svr(:,3);
znow = repmat(kron((1: 1 : p.nz)', ones(p.na, 1)), p.ne, 1); % index of z in (a, z, e) space for renters
[lr(:,t), omegaprimer(:,t), thetaprimer(:,t), hprimer(:,t), vr(:,t), dr(:,t)] = solveh(svr, Whinterp, Wrinterp, p, p.thetay(t), 'r', A, Y, znow);
% Solve discrete choice problem of housing
A = svh(:,1);
Y = p.lambdat(t)*svh(:,5).*svh(:,6);
znow = repmat(kron((1: 1 : p.nz)', ones(p.na*p.no*p.nt*p.nh, 1)), p.ne, 1); % index of z in (a, omega, theta, h, z, e) space for owners
hnow = repmat(kron((1: 1 : p.nh)', ones(p.na*p.no*p.nt, 1)), p.nz*p.ne, 1); % index of h in (a, omega, theta, h, z, e) space for owners
tnow = repmat(kron((1: 1 : p.nt)', ones(p.na*p.no, 1)), p.nh*p.nz*p.ne, 1); % index of theta in (a, omega, theta, h, z, e) space for owners
[lh(:,t), omegaprimeh(:,t), thetaprimeh(:,t), hprimeh(:,t), vh(:,t), dh(:,t)] = solveh(svh, Whinterp, Wrinterp, p, p.thetay(t), 'h', A, Y, znow, hnow, tnow);
% Compute expected value and update vbar
for i = 1 : p.ne
vbarh(:,t) = vbarh(:,t) + we(i)*kronm({p.na*p.no*p.nt*p.nh, Fzz}, vh((i-1)*p.na*p.no*p.nt*p.nh*p.nz + 1 : i*p.na*p.no*p.nt*p.nh*p.nz, t));
vbarr(:,t) = vbarr(:,t) + we(i)*kronm({p.na, Fzz}, vr((i-1)*p.na*p.nz + 1 : i*p.na*p.nz, t));
end
%fprintf('%6i %6.3f\n',[t toc]);
end
simulate
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