close all set(groot, 'DefaultAxesLineWidth', 1.5); set(groot, 'DefaultLineLineWidth', 4); set(groot, 'DefaultAxesTickLabelInterpreter','latex'); set(groot, 'DefaultLegendInterpreter','latex'); set(groot, 'DefaultAxesFontSize',24); N = 25000; T = p.T; A = zeros(2*N, T + 1); % Liquid Assets O = zeros(2*N, T + 1); % fraction of loan outstanding Th = zeros(2*N, T + 1); % initial mortgage size H = zeros(2*N, T + 1); % house size C = zeros(2*N, T); % consumption L = zeros(2*N, T); % liquidity after making housing choice D = zeros(2*N, T); % discrete choice: 1 ... 5 Y = zeros(2*N, T); % income V = zeros(2*N, T); % value function Pall = zeros(2*N, 5, T); Vall = zeros(2*N, 5, T); % First simulate history of shocks to income rng(100); Z = zeros(2*N, T); E = zeros(2*N, T); index = nodeunif(N, 1e-14, 1 - 1e-14); unif = index(randperm(N)); unif = [unif; 1 - unif]; % mirror sampling Fzcum = [0; cumsum(Fz)]; % cumulative ergodic for initial conditions [~, bin] = histc(unif, Fzcum); % bin is the index of initial draw of z Z(:,1) = bin; unif = index(randperm(N)); unif = [unif; 1 - unif]; % mirror sampling Fecum = [0; cumsum(we)]; % cumulative ergodic for transitory shock [~, bin] = histc(unif, Fecum); % bin is the index of e transitory shock E(:,1) = bin; Y(:,1) = p.lambdat(1)*p.zgrid(Z(:,1)).*p.egrid(E(:,1)); for t = 2 : T unif = index(randperm(N)); unif = [unif; 1 - unif]; % mirror sampling Fzcum = [zeros(2*N, 1), cumsum(Fzz(Z(:,t-1), :), 2)]; Z(:,t) = ((unif < Fzcum(:, 2:end)).*(unif >= Fzcum(:,1:end-1)))*(1 : 1 : p.nz)'; unif = index(randperm(N)); unif = [unif; 1 - unif]; [~, bin] = histc(unif, Fecum); % bin is the index of e transitory shock E(:,t) = bin; Y(:,t) = p.lambdat(t)*p.zgrid(Z(:,t)).*p.egrid(E(:,t)); end U = rand(2*N, T); U = -log(U)/p.nu; % generate actual cost % period 1 all are renters with 0 wealth t = 1; 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'); state = A(:, t); % others irrelevant here [Lall, Oall, Thall, Hall, V(:,t), Pall(:, 1: 3, t), Vall(:, 1 : 3, t)] = solveh(state, Whinterp, Wrinterp, p, p.thetay(t), 'r', A(:, t), Y(:, t), Z(:, t)); Pcum = [zeros(2*N, 1), cumsum(Pall(:, 1: 3, t), 2)]; unif = rand(2*N, 1); [~, D(:, t)] = max([Vall(:, 1 : 2, t), Vall(:, 3, t) - U(:, t)], [], 2); ind = sub2ind([2*N, 3], (1 : 1 : 2*N)', D(:,t)); L(:, t) = Lall(ind); O(:, t + 1) = Oall(ind); Th(:, t + 1) = Thall(ind); H(:, t + 1) = Hall(ind); % Find consumption rent = H(:, t + 1) == 0; Chint = griddedInterpolant({p.lgrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid}, reshape(ch(:, t), p.nl, p.no, p.nt, p.nh, p.nz), intmeth, 'linear'); Crint = griddedInterpolant({p.lgrid, p.zgrid}, reshape(cr(:, t), p.nl, p.nz), intmeth, 'linear'); cmin = bisect('savings', 1e-13, 1e5, L(rent, t), p, 'r', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, L(rent, t), p, 'r', amin); % c that implies a' = amin C(rent, t) = max(min(Crint(L(rent, t), p.zgrid(Z(rent, t))), cmax), cmin); [~, A(rent, t+1)] = savings(C(rent,t), L(rent, t), p, 'r'); % none of the other state variables matter cmin = bisect('savings', 1e-13, 1e5, L(~rent, t), p, 'h', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, L(~rent, t), p, 'h', amin); % c that implies a' = amin C(~rent,t) = max(min(Chint(L(~rent, t), O(~rent, t+1), Th(~rent, t+1), H(~rent, t+1), p.zgrid(Z(~rent, t))), cmax), cmin); [~, A(~rent, t+1)] = savings(C(~rent,t), L(~rent,t), p, 'h'); for t = 2 : T 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'); rent = H(:, t) == 0; % Renters state = A(rent, t); % others don't matter directly ntemp = numel(find(rent)); [Lall, Oall, Thall, Hall, V(rent,t), Pall(rent, 1 : 3, t), Vall(rent, 1 : 3, t)] = solveh(state, Whinterp, Wrinterp, p, p.thetay(t), 'r', A(rent, t), Y(rent, t), Z(rent, t)); [~, D(rent, t)] = max([Vall(rent, 1 : 2, t), Vall(rent, 3, t) - U(rent, t)], [], 2); ind = sub2ind([ntemp, 3], (1 : 1 : ntemp)', D(rent, t)); L(rent, t) = Lall(ind); O(rent, t + 1) = Oall(ind); Th(rent, t + 1) = Thall(ind); H(rent, t + 1) = Hall(ind); % Homeowners ntemp = numel(find(~rent)); state = [A(~rent, t), O(~rent, t), Th(~rent, t), H(~rent, t)]; % others don't matter directly hind = lookup1(p.hgrid, H(~rent, t), 1); tind = lookup1(p.tgrid, Th(~rent, t), 1); [Lall, Oall, Thall, Hall, V(~rent,t), Pall(~rent, :, t), Vall(~rent, :, t)] = solveh(state, Whinterp, Wrinterp, p, p.thetay(t), 'h', A(~rent, t), Y(~rent, t), Z(~rent, t), hind, tind); Pcum = [zeros(ntemp, 1), cumsum(Pall(~rent, :, t), 2)]; [~, D(~rent, t)] = max([Vall(~rent, 1 : 2, t), Vall(~rent, 3 : 4, t) - U(~rent, t), Vall(~rent, 5, t)], [], 2); ind = sub2ind([ntemp, 5], (1 : 1 : ntemp)', D(~rent, t)); L(~rent, t) = Lall(ind); O(~rent, t + 1) = Oall(ind); Th(~rent, t + 1) = Thall(ind); H(~rent, t + 1) = Hall(ind); % Find consumption rent = H(:, t + 1) == 0; Chint = griddedInterpolant({p.lgrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid}, reshape(ch(:, t), p.nl, p.no, p.nt, p.nh, p.nz), intmeth, 'linear'); Crint = griddedInterpolant({p.lgrid, p.zgrid}, reshape(cr(:, t), p.nl, p.nz), intmeth, 'linear'); cmin = bisect('savings', 1e-13, 1e5, L(rent, t), p, 'r', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, L(rent, t), p, 'r', amin); % c that implies a' = amin C(rent, t) = max(min(Crint(L(rent, t), p.zgrid(Z(rent, t))), cmax), cmin); [~, A(rent, t+1)] = savings(C(rent,t), L(rent, t), p, 'r'); % none of the other state variables matter cmin = bisect('savings', 1e-13, 1e5, L(~rent, t), p, 'h', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, L(~rent, t), p, 'h', amin); % c that implies a' = amin C(~rent,t) = max(min(Chint(L(~rent, t), O(~rent, t+1), Th(~rent, t+1), H(~rent, t+1), p.zgrid(Z(~rent, t))), cmax), cmin); [~, A(~rent, t+1)] = savings(C(~rent,t), L(~rent,t), p, 'h'); end Asave = A; Osave = O; Thsave = Th; Hsave = H; Csave = C; Lsave = L; Dsave = D; Ysave = Y; Zsave = Z; Esave = E; Vsave = V; Pallsave = Pall; Vallsave = Vall; Usave = U; %{ figure(2) id = 1; subplot(2,2,1), plot([C(id, 1 : p.T)', Y(id, 1 : p.T)']); title('Consumption and Income', 'Interpreter','Latex'); h = legend('consumption', 'income'); set(gca, 'ygrid', 'on') set(h,'Interpreter','latex'); subplot(2,2,2), plot([A(id, 1 : p.T + 1)', H(id, 1 : p.T + 1)'.*(1 - O(id, 1 : p.T + 1)'.*Th(id, 1 : p.T + 1)')]); title('Wealth', 'Interpreter','Latex'); set(gca, 'ygrid', 'on') h = legend('liquid', 'illiquid'); set(h,'Interpreter','latex'); subplot(2,2,3), plot([H(id, 2 : p.T + 1)', (p.R/p.alpha)^(-1/p.sigma)*C(id, :)']) title('Housing', 'Interpreter','Latex'); xlabel('age', 'Interpreter','Latex'); set(gca, 'ygrid', 'on') subplot(2,2,4), plot(O(id, 1 : p.T + 1)'.*Th(id, 1 : p.T + 1)') title('LTV', 'Interpreter','Latex'); xlabel('age', 'Interpreter','Latex'); set(gca, 'ygrid', 'on') figure(3) subplot(2,2,1), plot([mean(C(:, 1 : p.T))', mean(Y(:, 1 : p.T))']); title('Consumption and Income', 'Interpreter','Latex'); xlabel('age', 'Interpreter','Latex'); legend('consumption', 'income') set(gca, 'ygrid', 'on') subplot(2,2,2), plot([mean(A)', mean(H.*(1 - Th.*O))']); title('Wealth', 'Interpreter','Latex'); set(gca, 'ygrid', 'on') h = legend('liquid', 'illiquid'); set(h,'Interpreter','latex'); subplot(2,2,3), plot([mean(H)']); title('Housing Stock', 'Interpreter','Latex'); set(gca, 'ygrid', 'on') subplot(2,2,4), plot([mean(Th.*H.*O)'./mean(H)']); title('LTV', 'Interpreter','Latex'); set(gca, 'ygrid', 'on') %} W = A + H.*(1 - Th.*O); Debt = H.*Th.*O; Yh = p.phi^(1 + 1/p.gamma)*C.^(-p.sigma/p.gamma); % home production Rent = p.R*(p.R/p.alpha)^(-1/p.sigma)*C.*(H(:, 2:end) == 0); Debttilde = zeros(2*N, T + 1); Debttilde(H > 0) = (Debt(H > 0) - p.F0m)./(1 + p.F1m); % % Fextractage = zeros(p.T, 1); % % for t = 2 : p.T % % Fextractage(t) = mean(D(:,t) == 4 & H(:,t-1) > 0 & Debt(:, /mean(vec(H(:, 1 : end-1) > 0 & Debt(:, 1 : end - 1) > 0 ))*4; % % % end % Check aggregate resource constraint % transaction costs: Ftrans = (H(:, 1 : end - 1) == 0).*(D == 3).*(p.F0m + p.F1m*Debttilde(:, 2:end)) + ... % mortgage origination cost for renters (H(:, 1 : end - 1) > 0).*(D <= 3).*(p.Fs*H(:, 1 : end - 1)) + ... % house selling costs for homeowners (H(:, 1 : end - 1) > 0).*(D == 3 | D == 4).*(p.F0m + p.F1m*Debttilde(:, 2:end)); % mortgage origination cost for homeowners %{ t = 1 : T; rl = 1./(1 + exp(-p.r1*(A(:, t) - p.r2)))*(p.rh - p.rl) + p.rl; err_agg = norm(vec(C(:,t) + H(:, t+1) + A(:, t+1) + (1 + p.rm)*Debt(:, t) + Rent(:,t) - Yh(:,t) - Y(:,t) - (1 + rl).*A(:, t) - H(:, t) - Debt(:, t+1) + Ftrans(:,t))) fprintf('Err in Agg Resource Constr = %9.2e \n', err_agg); %} fsell = mean(vec(D <= 3 & H(:, 1 : end-1) > 0))/ mean(vec(H(:, 1 : end-1) > 0))*4; fmortg = mean(vec(Th(:,1:end-1).*O(:,1:end-1) > 0 & H(:, 1 : end-1) > 0)) / mean(vec(H(:, 1 : end-1) > 0)); agewealthratio = mean(vec(W(:, 41*4 + 1 : end))) / mean(vec(W(:, 2 : 41*4))); reqpayment = p.mbar*Th(:, 1:end - 1).*H(:, 1:end - 1).*(O(:, 1:end - 1) > 0).*(D == 5); actpayment = ((1 + p.rm)*Debt(:, 1 : end - 1) - Debt(:, 2 : end)).*(D == 5); fcurtail = sum(actpayment(:) > 1e-4 + reqpayment(:) & reqpayment(:) > 0 & D(:) == 5)/sum(reqpayment(:) > 0 & D(:) == 5); PTI = reqpayment(reqpayment > 0)./Y(reqpayment > 0); HY = H(:, 2:end)./Y/4; Age = zeros(2*N, T); % mortgage age for t = 2 : T Age(:,t) = (Age(:,t-1) + 1/4).*(Age(:,t-1) > 0 & D(:,t) == 5) + 1/4.*(D(:,t) == 3 | D(:,t) == 4); end Age = Age - 1/4; Age = floor(Age); LTV = O(:, 2 : end).*Th(:, 2 : end); % Let's computa Bhutta-Keys stats by annualizing first data. % Suppose we see them in the last quarter of the year Debta = O(:, 4 : 4: end).*Th(:, 4: 4 : end).*H(:, 4 : 4 : end); Xtract = (Debta(:, 2:end) - Debta(:, 1 : end-1))./Debta(:, 1 : end-1); Debta(:, end) = []; Ha = H(:, 4 : 4 :end); notmove = Ha(:, 2 : end) == Ha(:, 1 : end-1); Ha(:, end) = []; Aa = A(:, 4 : 4 : end); Aa(:, end) = []; fextract = sum(Xtract(:)>=0.05 & Debta(:) > 0 & notmove(:))/sum(Debta(:) > 0 & notmove(:)); medextract = median(Xtract(Xtract >= 0.05 & Debta > 0 & notmove)); fextracttwice = sum(vec(Xtract(:,2:end) >=0.05 & Xtract(:,1:end-1) >=0.05 & Debta(:, 2: end) >0 & notmove(:, 2:end) & Debta(:, 1:end-1) >0 & notmove(:, 1:end-1)))/... sum(vec(Xtract(:,1:end-1) >=0.05 & Debta(:, 2: end) >0 & notmove(:, 2:end) & Debta(:, 1:end-1) >0 & notmove(:, 1:end-1))); moment_model = zeros(57, 1); moment_model(1) = mean(vec(H(:, 2 : end) > 0)); moment_model(2) = mean(vec(W(:, 2 : end))) /mean(vec(Y))/4; moment_model(3) = mean(vec(H(:, 2 : end))) /mean(vec(Y))/4; moment_model(4) = mean(vec(Debt(:, 2 : end))) /mean(vec(Y))/4; moment_model(5) = mean(vec(A(:, 2 : end))) /mean(vec(Y))/4; moment_model(6) = fextract; moment_model(7) = mean(vec(Yh))/mean(vec(C)); moment_model(8) = agewealthratio; moment_model(9 : 13) = prctile(vec(A(:, 2 : end)), [10; 25; 50; 75; 90])/mean(vec(Y))/4; moment_model(14 : 18) = prctile(A(H == 0), [10; 25; 50; 75; 90])/mean(vec(Y))/4; moment_model(19 : 23) = prctile(A(H > 0), [10; 25; 50; 75; 90])/mean(vec(Y))/4; moment_model(24) = fsell; moment_model(25) = fmortg; moment_model(26 : 30) = prctile(Th(H > 0 & Debt > 0).*O(H > 0 & Debt > 0), [10; 25; 50; 75; 90]); moment_model(31 : 35) = prctile((1 - Th(H > 0).*O(H > 0)).*H(H > 0)./W(H > 0), [10; 25; 50; 75; 90]); moment_model(36 : 40) = prctile(vec(W(:,2:end)), [10; 25; 50; 75; 90])/mean(vec(Y))/4; moment_model(41 : 45) = prctile(PTI, [10; 25; 50; 75; 90]); moment_model(46 : 50) = prctile(HY(HY > 0), [10; 25; 50; 75; 90]); moment_model(51 : 55) = prctile(Age(Age >=0 & LTV > 0), [10; 25; 50; 75; 90]); moment_model(56) = medextract; moment_model(57) = fextracttwice; moment_data = [0.64; 1.45; 1.82; 0.83; 0.46; 0.08; 0.23; 2.00; -0.04; 0; 0.07; 0.48; 1.50; -0.05; 0; 0.01; 0.15; 1; -0.04; 0.01; 0.15; 0.68; 1.69; 0.044; 0.71; 0.18; 0.39; 0.62; 0.77; 0.88; 0.36; 0.64; 0.87; 0.99; 1.04; 0; 0.04; 0.73; 2.34; 3.94; 0.05; 0.08; 0.11; 0.17; 0.24; 1.02; 1.62; 2.48; 3.78; 6.43; 0; 1; 3; 6; 10; 0.23; 0.08]; if printr fprintf('\n') fprintf('Homeownership Rate = %9.2f %9.2f\n', [moment_model(1), moment_data(1)]); fprintf('Aggregate Wealth to Income = %9.2f %9.2f\n', [moment_model(2), moment_data(2)]); fprintf('Aggregate Housing to Income = %9.2f %9.2f\n', [moment_model(3), moment_data(3)]); fprintf('Aggregate Debt to Income = %9.2f %9.2f\n', [moment_model(4), moment_data(4)]); fprintf('Aggregate Liquid assets to Income = %9.2f %9.2f\n', [moment_model(5), moment_data(5)]); fprintf('Fraction of Homeowners with Mortgage who extract = %9.2f %9.2f\n', [moment_model(6), moment_data(6)]); fprintf('Non-Market Production to Consumption = %9.2f %9.2f\n', [moment_model(7), moment_data(7)]); fprintf('Mean wealth retirees / workers = %9.2f %9.2f\n', [moment_model(8), moment_data(8)]); fprintf('\n') fprintf('10 pctile liquid assets to income = %9.2f %9.2f\n', [moment_model(9), moment_data(9)]); fprintf('25 pctile liquid assets to income = %9.2f %9.2f\n', [moment_model(10), moment_data(10)]); fprintf('50 pctile liquid assets to income = %9.2f %9.2f\n', [moment_model(11), moment_data(11)]); fprintf('75 pctile liquid assets to income = %9.2f %9.2f\n', [moment_model(12), moment_data(12)]); fprintf('90 pctile liquid assets to income = %9.2f %9.2f\n', [moment_model(13), moment_data(13)]); fprintf('\n') fprintf('\n') fprintf('10 pctile liquid assets renters = %9.2f %9.2f\n', [moment_model(14), moment_data(14)]); fprintf('25 pctile liquid assets renters = %9.2f %9.2f\n', [moment_model(15), moment_data(15)]); fprintf('50 pctile liquid assets renters = %9.2f %9.2f\n', [moment_model(16), moment_data(16)]); fprintf('75 pctile liquid assets renters = %9.2f %9.2f\n', [moment_model(17), moment_data(17)]); fprintf('90 pctile liquid assets renters = %9.2f %9.2f\n', [moment_model(18), moment_data(18)]); fprintf('\n') fprintf('10 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(19), moment_data(19)]); fprintf('25 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(20), moment_data(20)]); fprintf('50 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(21), moment_data(21)]); fprintf('75 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(22), moment_data(22)]); fprintf('90 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(23), moment_data(23)]); fprintf('\n') fprintf('Fraction of Homeowners who curtail = %9.3f \n', fcurtail); fprintf('Fraction of Homeowners who sell = %9.3f %9.3f\n', [moment_model(24), moment_data(24)]); fprintf('Fraction of Homeowners with mortgage = %9.2f %9.2f\n', [moment_model(25), moment_data(25)]); fprintf('Median increase in balance extract = %9.2f %9.2f\n', [moment_model(56), moment_data(56)]); fprintf('Fraction that extract twice in a row = %9.2f %9.2f\n', [moment_model(57), moment_data(57)]); fprintf('\n') fprintf('10 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(26), moment_data(26)]); fprintf('25 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(27), moment_data(27)]); fprintf('50 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(28), moment_data(28)]); fprintf('75 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(29), moment_data(29)]); fprintf('90 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(30), moment_data(30)]); fprintf('\n') fprintf('10 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(31), moment_data(31)]); fprintf('25 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(32), moment_data(32)]); fprintf('50 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(33), moment_data(33)]); fprintf('75 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(34), moment_data(34)]); fprintf('90 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(35), moment_data(35)]); fprintf('\n') fprintf('10 pctile Wealth = %9.2f %9.2f\n', [moment_model(36), moment_data(36)]); fprintf('25 pctile Wealth = %9.2f %9.2f\n', [moment_model(37), moment_data(37)]); fprintf('50 pctile Wealth = %9.2f %9.2f\n', [moment_model(38), moment_data(38)]); fprintf('75 pctile Wealth = %9.2f %9.2f\n', [moment_model(39), moment_data(39)]); fprintf('90 pctile Wealth = %9.2f %9.2f\n', [moment_model(40), moment_data(40)]); fprintf('\n') fprintf('10 pctile PTI = %9.2f %9.2f\n', [moment_model(41), moment_data(41)]); fprintf('25 pctile PTI = %9.2f %9.2f\n', [moment_model(42), moment_data(42)]); fprintf('50 pctile PTI = %9.2f %9.2f\n', [moment_model(43), moment_data(43)]); fprintf('75 pctile PTI = %9.2f %9.2f\n', [moment_model(44), moment_data(44)]); fprintf('90 pctile PTI = %9.2f %9.2f\n', [moment_model(45), moment_data(45)]); fprintf('\n') fprintf('10 pctile housing to income = %9.2f %9.2f\n', [moment_model(46), moment_data(46)]); fprintf('25 pctile housing to income = %9.2f %9.2f\n', [moment_model(47), moment_data(47)]); fprintf('50 pctile housing to income = %9.2f %9.2f\n', [moment_model(48), moment_data(48)]); fprintf('75 pctile housing to income = %9.2f %9.2f\n', [moment_model(49), moment_data(49)]); fprintf('90 pctile housing to income = %9.2f %9.2f\n', [moment_model(50), moment_data(50)]); fprintf('\n') fprintf('10 pctile mortgage age = %9.2f %9.2f\n', [moment_model(51), moment_data(51)]); fprintf('25 pctile mortgage age = %9.2f %9.2f\n', [moment_model(52), moment_data(52)]); fprintf('50 pctile mortgage age = %9.2f %9.2f\n', [moment_model(53), moment_data(53)]); fprintf('75 pctile mortgage age = %9.2f %9.2f\n', [moment_model(54), moment_data(54)]); fprintf('90 pctile mortgage age = %9.2f %9.2f\n', [moment_model(55), moment_data(55)]); % Calculate life time value Hs = H(:, 2 : p.T + 1).*(H(:, 2 : p.T + 1) > 0) + (p.R/p.alpha)^(-1/p.sigma)*C.*(H(:, 2 : p.T + 1) == 0); U = C.^(1 - p.sigma)/(1 - p.sigma) + p.alpha*Hs.^(1 - p.sigma)/(1 - p.sigma) - p.phi^(1 + 1/p.gamma)/(1 + p.gamma)*C.^(-p.sigma*(1 + 1/p.gamma)); rl = 1./(1 + exp(-p.r1*(A(:,p.T+1) - p.r2)))*(p.rh - p.rl) + p.rl; V = sum(p.beta.^(0 : 1 : p.T - 1).*U, 2) + p.beta^p.T*p.B*(p.wbar + (1 + p.rl)*A(:,p.T+1) + (1 - p.Fs - (1 + p.rm)*O(:,p.T+1).*Th(:,p.T+1)).*H(:,p.T+1)).^(1 - p.sigma)/(1 - p.sigma); V = ((1 - p.sigma)*(1 - p.beta)/(1 - p.beta^p.T)*mean(V))^(1/(1 - p.sigma)); fprintf('\n') fprintf('Life Time Value, CEV = %9.4f \n', V); end weights = ones(13, 1); weights = weights/sum(weights); err_mom = (moment_model(1:13) - moment_data(1:13))./(1 + moment_data(1:13)); err_mom = (weights'*err_mom.^2).^(1/2); if exist('x', 'var') fprintf('%5.6f %5.6f %5.6f %5.6f %5.6f %5.6f %5.6f %5.6f %5.6f %5.6f \n', [x(:)', err_mom]); else fprintf('\n'); fprintf('value of objective = %5.6f \n', err_mom); fprintf('\n'); end % Characteristics of those who refinance W = A + H.*(1 - O.*Th); Wtemp = W(:, 1 : end - 1); % only state variables Atemp = A(:, 1 : end - 1); LTV = O(:, 1 : end - 1).*Th(:, 1 : end - 1); Htemp = H(:, 1 : end - 1); LY = Atemp./Y; Sh = 1 - Atemp./Wtemp; Age = repmat((1 : 1 : T)/4 + 25, 2*N, 1); refin = D == 4 & Htemp > 0; owner = (D == 4 | D == 5) & Htemp > 0; time = 1; fprintf('\n'); fprintf('Characteristics of Refinancers in Initial Steady State\n'); fprintf('\n'); fprintf('All, Refinance, Dont Refinance\n'); fprintf('\n'); fprintf('\n'); fprintf('Mean Liquid Assets = %9.2f %9.2f %9.2f \n', [mean(Atemp(owner)), mean(Atemp(owner & refin)), mean(Atemp(owner & ~refin))]); fprintf('Mean Income = %9.2f %9.2f %9.2f \n', [mean(Y(owner)), mean(Y(owner & refin)), mean(Y(owner & ~refin))]); fprintf('Mean Liquid Asset to Income = %9.2f %9.2f %9.2f \n', [mean(LY(owner)), mean(LY(owner & refin)), mean(LY(owner & ~refin))]); fprintf('Mean Share Housing Wealth = %9.2f %9.2f %9.2f \n', [mean(Sh(owner)), mean(Sh(owner & refin)), mean(Sh(owner & ~refin))]); fprintf('Mean Wealth = %9.2f %9.2f %9.2f \n', [mean(Wtemp(owner)), mean(Wtemp(owner & refin)), mean(Wtemp(owner & ~refin))]); fprintf('Mean LTV = %9.2f %9.2f %9.2f \n', [mean(LTV(owner)), mean(LTV(owner & refin)), mean(LTV(owner & ~refin))]); fprintf('Mean House = %9.2f %9.2f %9.2f \n', [mean(Htemp(owner)), mean(Htemp(owner & refin)), mean(Htemp(owner & ~refin))]); fprintf('Mean Age = %9.2f %9.2f %9.2f \n', [mean(Age(owner)), mean(Age(owner & refin)), mean(Age(owner & ~refin))]); fprintf('\n'); fprintf('\n'); fprintf('\n'); fprintf('Median Liquid Assets = %9.2f %9.2f %9.2f \n', [median(Atemp(owner)), median(Atemp(owner & refin)), median(Atemp(owner & ~refin))]); fprintf('Median Income = %9.2f %9.2f %9.2f \n', [median(Y(owner)), median(Y(owner & refin)), median(Y(owner & ~refin))]); fprintf('Median Liquid Asset to Income = %9.2f %9.2f %9.2f \n', [median(LY(owner)), median(LY(owner & refin)), median(LY(owner & ~refin))]); fprintf('Median Share Housing Wealth = %9.2f %9.2f %9.2f \n', [median(Sh(owner)), median(Sh(owner & refin)), median(Sh(owner & ~refin))]); fprintf('Median Wealth = %9.2f %9.2f %9.2f \n', [median(Wtemp(owner)), median(Wtemp(owner & refin)), median(Wtemp(owner & ~refin))]); fprintf('Median LTV = %9.2f %9.2f %9.2f \n', [median(LTV(owner)), median(LTV(owner & refin)), median(LTV(owner & ~refin))]); fprintf('Median House = %9.2f %9.2f %9.2f \n', [median(Htemp(owner)), median(Htemp(owner & refin)), median(Htemp(owner & ~refin))]); fprintf('Median Age = %9.2f %9.2f %9.2f \n', [median(Age(owner)), median(Age(owner & refin)), median(Age(owner & ~refin))]); fprintf('\n'); fprintf('\n');