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close all
set(groot, 'DefaultAxesLineWidth', 1.5);
set(groot, 'DefaultLineLineWidth', 4);
set(groot, 'DefaultAxesTickLabelInterpreter','latex');
set(groot, 'DefaultLegendInterpreter','latex');
set(groot, 'DefaultAxesFontSize',24);
N = 2500;
T = 450;
A = zeros(2*N, T + 1); % Liquid Assets
Th = zeros(2*N, T + 1); % initial mortgage size
C = zeros(2*N, T); % consumption
L = zeros(2*N, T); % liquidity after making housing choice
R = zeros(2*N, T); % decision to refinance
X = zeros(2*N, T); % amount extracted
Age = zeros(2*N, T); % age of loan
% First simulate history of shocks to income
rng(100);
Y = randn(N, T)*se;
Y = exp([Y; -Y]);
Th(:, 1) = p.thetam;
A(:, 1) = 0;
Age(:,1) = 1;
for t = 1 : T
unif = rand(2*N, 1);
state = [(1 + p.rl)*A(:,t) + Y(:,t), Th(:,t)];
[~, pall, ~, Lall, thetall] = solveh(state, Winterp, p);
R(:,t) = unif <= pall(:,1);
L(:,t) = Lall(:,1).*R(:,t) + Lall(:,2).*(1 - R(:,t)); % when many options: generate a single unif and ask which interval belongs to
Th(:, t+1) = thetall(:,1).*R(:,t) + thetall(:,2).*(1 - R(:,t));
cmax = bisect('savings', 1e-13, 1e5, L(:,t), p, amin); % c that implies a' = amin
cmin = bisect('savings', 1e-13, 1e5, L(:,t), p, amax); % c that implies a' = amax
C(:,t) = max(min(Cinterp(L(:,t), Th(:,t+1)), cmax), cmin);
[~, A(:, t+1)] = savings(C(:,t), L(:,t), p);
Age(:, t+1) = (Age(:,t) + 1).*(1 - R(:,t)) + R(:,t);
X(:,t) = (Th(:,t+1) - Th(:,t))./Th(:,t).*R(:,t);
end
A(:, 1 : 150) = [];
Th(:, 1 : 150) = [];
C(:, 1 : 150) = [];
R(:, 1 : 150) = [];
L(:, 1 : 150) = [];
Y(:, 1 : 150) = [];
X(:, 1 : 150) = [];
Age(:, 1 : 150) = [];
Asave = A;
Thsave = Th;
Csave = C;
Lsave = L;
Rsave = R;
Ysave = Y;
Xsave = X;
Agesave = Age;
A(:, end) = [];
Th(:, end) = [];
Age(:, end) = [];
Age = floor(Age/4);
D = Th.*p.hbar;
W = A + p.hbar - D;
Yh = p.phi^(1/p.gamma)*C.^(-p.sigma/p.gamma);
figure(2)
id = 1;
subplot(1, 3, 1), plot([C(id, :)', Y(id, :)']);
title('Consumption and Income', 'Interpreter','Latex');
h = legend('consumption', 'income');
set(gca, 'ygrid', 'on')
set(h,'Interpreter','latex');
subplot(1, 3, 2), plot([A(id, :)', p.hbar.*(1 - Th(id, :)')]);
title('Wealth', 'Interpreter','Latex');
set(gca, 'ygrid', 'on')
h = legend('liquid', 'illiquid');
set(h,'Interpreter','latex');
subplot(1, 3, 3), plot(Th(id, :)');
title('Debt', 'Interpreter','Latex');
set(gca, 'ygrid', 'on')
set(h,'Interpreter','latex');
fextract = mean(vec(X >= 0.05))*4;
medianextract = median(X(X >= 0.05));
HY = p.hbar./Y/4;
PTI = p.mbar*p.hbar./Y;
moment_model = zeros(60, 1);
moment_model(1) = mean(W(:)) /mean(vec(Y))/4;
moment_model(2) = p.hbar /mean(vec(Y))/4;
moment_model(3) = mean(D(:)) /mean(vec(Y))/4;
moment_model(4) = mean(A(:)) /mean(vec(Y))/4;
moment_model(5) = fextract;
moment_model(6) = mean(vec(Yh))/mean(vec(C));
moment_model(7 : 11) = prctile( A(:), [10; 25; 50; 75; 90])/mean(vec(Y))/4;
moment_model(12 : 16) = prctile(Th(:), [10; 25; 50; 75; 90]);
moment_model(17 : 21) = prctile((1 - Th(:)).*p.hbar./W(:), [10; 25; 50; 75; 90]);
moment_model(22 : 26) = prctile( W(:), [10; 25; 50; 75; 90])/mean(vec(Y))/4;
moment_model(27 : 31) = prctile(PTI(:), [10; 25; 50; 75; 90]);
moment_model(32 : 36) = prctile(HY(:), [10; 25; 50; 75; 90]);
moment_model(37 : 41) = prctile(Age(:), [10; 25; 50; 75; 90]);
moment_model(42) = medianextract;
moment_data = [1.45; 1.82; 0.83; 0.46; 0.08; 0.23; -0.04; 0.01; 0.15; 0.68; 1.69;
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];
fprintf('\n')
fprintf('Aggregate Wealth to Income = %9.2f %9.2f\n', [moment_model(1), moment_data(1)]);
fprintf('Aggregate Housing to Income = %9.2f %9.2f\n', [moment_model(2), moment_data(2)]);
fprintf('Aggregate Debt to Income = %9.2f %9.2f\n', [moment_model(3), moment_data(3)]);
fprintf('Aggregate Liquid assets to Income = %9.2f %9.2f\n', [moment_model(4), moment_data(4)]);
fprintf('Non-Market Production to Consumption = %9.2f %9.2f\n', [moment_model(6), moment_data(6)]);
fprintf('\n')
fprintf('Fraction Borrowers who extract = %9.2f %9.2f\n', [moment_model(5), moment_data(5)]);
fprintf('Median Change in the Balance = %9.2f %9.2f\n', [moment_model(42), moment_data(42)]);
fprintf('\n')
fprintf('10 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(7), moment_data(7)]);
fprintf('25 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(8), moment_data(8)]);
fprintf('50 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(9), moment_data(9)]);
fprintf('75 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(10), moment_data(10)]);
fprintf('90 pctile liquid assets owners = %9.2f %9.2f\n', [moment_model(11), moment_data(11)]);
fprintf('\n')
fprintf('10 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(12), moment_data(12)]);
fprintf('25 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(13), moment_data(13)]);
fprintf('50 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(14), moment_data(14)]);
fprintf('75 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(15), moment_data(15)]);
fprintf('90 pctile LTV, borrowers = %9.2f %9.2f\n', [moment_model(16), moment_data(16)]);
fprintf('\n')
fprintf('10 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(17), moment_data(17)]);
fprintf('25 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(18), moment_data(18)]);
fprintf('50 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(19), moment_data(19)]);
fprintf('75 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(20), moment_data(20)]);
fprintf('90 Share Housing Wealth in Owner Wealth = %9.2f %9.2f\n', [moment_model(21), moment_data(21)]);
fprintf('\n')
fprintf('10 pctile Wealth = %9.2f %9.2f\n', [moment_model(22), moment_data(22)]);
fprintf('25 pctile Wealth = %9.2f %9.2f\n', [moment_model(23), moment_data(23)]);
fprintf('50 pctile Wealth = %9.2f %9.2f\n', [moment_model(24), moment_data(24)]);
fprintf('75 pctile Wealth = %9.2f %9.2f\n', [moment_model(25), moment_data(25)]);
fprintf('90 pctile Wealth = %9.2f %9.2f\n', [moment_model(26), moment_data(26)]);
fprintf('\n')
fprintf('10 pctile PTI = %9.2f %9.2f\n', [moment_model(27), moment_data(27)]);
fprintf('25 pctile PTI = %9.2f %9.2f\n', [moment_model(28), moment_data(28)]);
fprintf('50 pctile PTI = %9.2f %9.2f\n', [moment_model(29), moment_data(29)]);
fprintf('75 pctile PTI = %9.2f %9.2f\n', [moment_model(30), moment_data(30)]);
fprintf('90 pctile PTI = %9.2f %9.2f\n', [moment_model(31), moment_data(31)]);
fprintf('\n')
fprintf('10 pctile housing to income = %9.2f %9.2f\n', [moment_model(32), moment_data(32)]);
fprintf('25 pctile housing to income = %9.2f %9.2f\n', [moment_model(33), moment_data(33)]);
fprintf('50 pctile housing to income = %9.2f %9.2f\n', [moment_model(34), moment_data(34)]);
fprintf('75 pctile housing to income = %9.2f %9.2f\n', [moment_model(35), moment_data(35)]);
fprintf('90 pctile housing to income = %9.2f %9.2f\n', [moment_model(36), moment_data(36)]);
fprintf('\n')
fprintf('10 pctile mortgage age = %9.2f %9.2f\n', [moment_model(37), moment_data(37)]);
fprintf('25 pctile mortgage age = %9.2f %9.2f\n', [moment_model(38), moment_data(38)]);
fprintf('50 pctile mortgage age = %9.2f %9.2f\n', [moment_model(39), moment_data(39)]);
fprintf('75 pctile mortgage age = %9.2f %9.2f\n', [moment_model(40), moment_data(40)]);
fprintf('90 pctile mortgage age = %9.2f %9.2f\n', [moment_model(41), moment_data(41)]);
% Calculate life time value
T = size(C, 2);
U = C.^(1 - p.sigma)/(1 - p.sigma) - p.phi^(1 + 1/p.gamma)/(1 + p.gamma)*C.^(-p.sigma*(1 + 1/p.gamma));
V = sum(p.beta.^(0 : 1 : T -1).*U, 2);
V = ((1 - p.sigma)*(1 - p.beta)*mean(V))^(1/(1 - p.sigma));
fprintf('\n')
fprintf('Life Time Value, CEV = %9.4f \n', V);
% Compare characteristics of those who refinance and don't
S = (1 - Th(:)).*p.hbar./W(:);
R = R(:) == 1;
fprintf('\n');
fprintf('Mean Liquid Assets = %9.2f %9.2f %9.2f \n', [mean(A(:)), mean(A(R)), mean(A(~R))]);
fprintf('Mean Income = %9.2f %9.2f %9.2f \n', [mean(Y(:)), mean(Y(R)), mean(Y(~R))]);
fprintf('Mean Liquid Asset to Income = %9.2f %9.2f %9.2f \n', [mean(A(:)./Y(:)), mean(A(R)./Y(R)), mean(A(~R)./Y(~R))]);
fprintf('Mean Share Housing Wealth = %9.2f %9.2f %9.2f \n', [mean(S(:)), mean(S(R)), mean(S(~R))]);
fprintf('Mean Wealth = %9.2f %9.2f %9.2f \n', [mean(W(:)), mean(W(R)), mean(W(~R))]);
fprintf('Mean LTV = %9.2f %9.2f %9.2f \n', [mean(Th(:)), mean(Th(R)), mean(Th(~R))]);
fprintf('Mean Age = %9.2f %9.2f %9.2f \n', [mean(Age(:)), mean(Age(R)), mean(Age(~R))]);
fprintf('\n');
fprintf('\n');
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