| function err_mom = objective(x)
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| set(groot, 'DefaultAxesLineWidth', 1.5);
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| set(groot, 'DefaultLineLineWidth', 4);
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| set(groot, 'DefaultAxesTickLabelInterpreter','latex');
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| set(groot, 'DefaultLegendInterpreter','latex');
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| set(groot, 'DefaultAxesFontSize',22);
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| intmeth = 'linear';
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| printr = 0;
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| optset('bisect', 'tol', 1e-32);
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| p.beta = x(1);
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| p.alpha = x(2);
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| p.R = x(3);
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| p.phi = x(4);
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| p.F0m = x(5);
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| p.B = x(6);
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| p.rh = (1 + x(7))^(1/4) - 1;
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| p.r1 = x(8);
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| p.r2 = x(9);
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| p.rl = (1 - 0.028)^(1/4) - 1;
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| p.T = 61*4;
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| p.D = 30*4;
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| p.sigma = 2;
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| p.gamma = 1;
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| p.rm = (1 + 0.025)^(1/4) - 1;
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| p.Fs = 0.06;
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| p.F1m = 0.005;
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| p.wbar = 0.00001;
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| p.thetam = 0.85;
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| p.thetay = 0.214;
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| rhoz = 0.9908;
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| sz = 0.0761;
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| se = (1 - 0.55)^(1/2)*0.4869;
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| time = (1 : 1 : p.T)';
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| p.lambdat = exp(0.07982636 - 0.02322307 * (time/4 + 25) + 0.00105409 * (time/4 + 25).^2 - 0.00001028 * (time/4 + 25).^3);
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| p.thetay = p.thetay*(1 - 0.3126./(1 + exp(18.629 - 0.3049*(time/4 + 25))));
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| p.mbar = p.rm/(1 - (1 + p.rm)^(-p.D)); % minimum payment required per 1 of initial debt
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| % Quality of Approximation
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| p.na = 50; % number of nodes for liquid assets
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| p.nl = 75; % number of nodes for liquidity
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| p.no = 9; % number of nodes for omega (fraction of loan outstanding)
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| p.nt = 3; % number of possible initial LTV
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| p.nh = 7; % number of nodes for housing
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| p.nz = 9; % points for exogenous income z
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| p.ne = 3;
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| % Discretize Income Process
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| [zgrid, Fzz] = rouwenhorst(rhoz, sz, p.nz);
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| p.zgrid = exp(zgrid');
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| [Fz, d] = eigs(Fzz', 1, 'largestabs');
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| Fz = Fz/sum(Fz);
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| Fz = full(Fz); % ergodic distribution of z
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| [egrid, we] = qnwnorm(p.ne, 0, se^2);
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| p.egrid = exp(egrid);
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| % Discretize other state variables
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| amin = 0;
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| amax = 100;
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| p.agrid = amin + (amax - amin)*nodeunif(p.na, 0, 1).^2;
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| omin = 0;
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| omax = 1;
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| p.ogrid = omin + (omax - omin)*nodeunif(p.no, 0, 1);
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| tmin = 0.5;
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| tmax = p.thetam;
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| p.tgrid = tmin + (tmax - tmin)*nodeunif(p.nt, 0, 1);
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| hmin = 5; % minimum house size
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| hmax = 40; % maximum house size
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| p.hgrid = hmin + (hmax - hmin)*nodeunif(p.nh, 0, 1).^1.5;
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| ymax = max(p.lambdat)*zgrid(end)*egrid(end);
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| lmin = -0.1;
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| lmax = 125;
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| p.lgrid = lmin + (lmax - lmin)*nodeunif(p.nl, 0, 1).^1.5;
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| % Construct grids:
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| svbarh = gridmake(p.agrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid); % grid for expected value of homeowners
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| svbarr = gridmake(p.agrid, p.zgrid); % grid for expected value of renters
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| svh = gridmake(p.agrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid, p.egrid); % grid for value of homeowners prior to making h choice
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| svr = gridmake(p.agrid, p.zgrid, p.egrid); % grid for value of renters prior to making h choice
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| swh = gridmake(p.lgrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid); % grid for W functions
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| swr = gridmake(p.lgrid, p.zgrid);
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| ind2h = kron((1:1:p.no*p.nt*p.nh*p.nz)', ones(p.nl, 1));
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| ind2r = kron((1:1: p.nz)', ones(p.nl, 1));
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| vbarh = zeros(p.na*p.no*p.nt*p.nh*p.nz, p.T + 1); % expected values of homeowners
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| vbarr = zeros(p.na*p.nz, p.T + 1); % expected values of renters
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| 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)
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| vr = zeros(p.na*p.nz*p.ne, p.T); % value of renters prior to making h choice (envelope over possible options)
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| wh = zeros(p.nl*p.no*p.nt*p.nh*p.nz, p.T); % value of homeowners after making h choice
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| wr = zeros(p.nl*p.nz, p.T); % value of renters after making h choice
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| ch = zeros(p.nl*p.no*p.nt*p.nh*p.nz, p.T); % consumption homeowners after making h choice
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| cr = zeros(p.nl*p.nz, p.T); % consumption of renters after making h choice
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| aprimeh = zeros(p.nl*p.no*p.nt*p.nh*p.nz, p.T); % liquid savings of homeowners after making h choice
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| aprimer = zeros(p.nl*p.nz, p.T); % liquid savings of renters after making h choice
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| cmaxh = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'h', amin); % c that implies a' = amin
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| cmaxr = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'r', amin);
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| cminh = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'h', amax);
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| cminr = bisect('savings', 1e-13, 1e5, p.lgrid, p, 'r', amax);
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| cmaxh = repmat(cmaxh, p.no*p.nt*p.nh*p.nz, 1);
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| cmaxr = repmat(cmaxr, p.nz, 1);
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| cminh = repmat(cminh, p.no*p.nt*p.nh*p.nz, 1);
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| cminr = repmat(cminr, p.nz, 1);
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| lh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
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| lr = zeros(p.na*p.nz*p.ne, p.T);
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| omegaprimeh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
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| omegaprimer = zeros(p.na*p.nz*p.ne, p.T);
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| thetaprimeh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
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| thetaprimer = zeros(p.na*p.nz*p.ne, p.T);
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| hprimeh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
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| hprimer = zeros(p.na*p.nz*p.ne, p.T);
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| dh = zeros(p.na*p.no*p.nt*p.nh*p.nz*p.ne, p.T);
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| dr = zeros(p.na*p.nz*p.ne, p.T);
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| 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);
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| vbarr(:, p.T + 1) = p.B*(p.wbar + (1 + p.rl)*svbarr(:,1)).^(1 - p.sigma)/(1 - p.sigma);
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| for t = p.T : -1 : 1
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| 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');
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| EVr = griddedInterpolant({p.agrid, (1: 1: p.nz)'}, reshape(vbarr(:, t + 1), p.na, p.nz), intmeth, 'linear');
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| ch(:, t) = solve_golden('wfunc', cminh, cmaxh, swh, ind2h, EVh, p, 'h');
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| cr(:, t) = solve_golden('wfunc', cminr, cmaxr, swr, ind2r, EVr, p, 'r');
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| [~, aprimeh(:,t)] = savings(ch(:, t), swh, p, 'h');
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| [~, aprimer(:,t)] = savings(cr(:, t), swr, p, 'r');
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| wh(:, t) = wfunc(ch(:, t), swh, ind2h, EVh, p, 'h');
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| wr(:, t) = wfunc(cr(:, t), swr, ind2r, EVr, p, 'r');
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| 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');
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| Wrinterp = griddedInterpolant({p.lgrid, (1: 1: p.nz)'}, reshape(wr(:, t), p.nl, p.nz), intmeth, 'linear');
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| A = svr(:,1);
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| Y = p.lambdat(t)*svr(:,2).*svr(:,3);
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| znow = repmat(kron((1: 1 : p.nz)', ones(p.na, 1)), p.ne, 1); % index of z in (a, z, e) space for renters
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| [lr(:,t), omegaprimer(:,t), thetaprimer(:,t), hprimer(:,t), vr(:,t), dr(:,t)] = solveh(svr, Whinterp, Wrinterp, p, p.thetay(t), 'r', A, Y, znow);
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| % Solve discrete choice problem of housing
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| A = svh(:,1);
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| Y = p.lambdat(t)*svh(:,5).*svh(:,6);
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| znow = repmat(kron((1: 1 : p.nz)', ones(p.na*p.no*p.nt*p.nh, 1)), p.ne, 1);
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| 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
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| tnow = repmat(kron((1: 1 : p.nt)', ones(p.na*p.no, 1)), p.nh*p.nz*p.ne, 1);
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| [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);
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| for i = 1 : p.ne
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| 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));
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| vbarr(:,t) = vbarr(:,t) + we(i)*kronm({p.na, Fzz}, vr((i-1)*p.na*p.nz + 1 : i*p.na*p.nz, t));
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| end
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| end
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| simulate
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