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close all
% Inaction Region
figure(1)
[~, pall] = solveh(sv, Winterp, p);
data = [sv, pall(:,1)];
data = data(data(:,1) <= 3, :);
n1 = numel(unique(data(:,1)));
n2 = numel(unique(data(:,2)));
surf(reshape(data(:,1), n1, n2), reshape(data(:,2), n1, n2), reshape(data(:,3), n1, n2)); colorbar
xlabel('$w$', 'Interpreter', 'Latex');
ylabel('$\theta$', 'Interpreter', 'Latex');
title('probability refinance', 'Interpreter', 'Latex');
xlim([0, 3])
state = gridmake(nodeunif(100, 0.5, 4.5), 0.50);
[v, pall, vall, Lall, thetaall] = solveh(state, Winterp, p);
call = zeros(size(pall));
aprimeall = zeros(size(pall));
for i = 1 : 2
cmax = bisect('savings', 1e-13, 1e5, Lall(:, i), p, amin); % c that implies a' = amin
cmin = bisect('savings', 1e-13, 1e5, Lall(:, i), p, amax); % c that implies a' = amax
call(:,i) = solve_golden('wfunc', cmin, cmax, [Lall(:,i), thetaall(:,i)], EV, p);
[~, aprimeall(:,i)] = savings(call(:,i), [Lall(:,i), thetaall(:,i)], p);
end
%{
figure(2)
subplot(2, 3, 1)
plot(state(:,1), pall(:,1));
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('probability refinance', 'Interpreter', 'Latex');
subplot(2, 3, 2)
plot(state(:,1), Lall);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$l$', 'Interpreter', 'Latex');
legend('refinance', 'dont refinance')
subplot(2, 3, 3)
plot(state(:,1), thetaall);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$\theta^{\prime}$', 'Interpreter', 'Latex');
subplot(2, 3, 4)
plot(state(:,1), call);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$c$', 'Interpreter', 'Latex');
subplot(2, 3, 5)
plot(state(:,1), aprimeall);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$a^{\prime}$', 'Interpreter', 'Latex');
subplot(2, 3, 6)
plot(state(:,1), [vall, v]);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('values', 'Interpreter', 'Latex');
legend('refinance', 'dont refinance', 'envelope')
%}
figure(1)
subplot(2, 2, 1)
plot(state(:,1), [vall(:,1) - vall(:,2)]);
set(gca, 'ygrid', 'on')
xlabel('cash on hand', 'Interpreter', 'Latex');
title('$V^{R} - V^{N}$', 'Interpreter', 'Latex');
subplot(2, 2, 2)
plot(state(:,1), [call]);
set(gca, 'ygrid', 'on')
xlabel('cash on hand', 'Interpreter', 'Latex');
title('$c$', 'Interpreter', 'Latex');
legend('refinance', 'do not refinance')
subplot(2, 2, 3)
plot(state(:,1), [aprimeall]);
set(gca, 'ygrid', 'on')
xlabel('cash on hand', 'Interpreter', 'Latex');
title('$a^{\prime}$', 'Interpreter', 'Latex');
subplot(2, 2, 4)
plot(state(:,1), pall(:,1));
set(gca, 'ygrid', 'on')
xlabel('cash on hand', 'Interpreter', 'Latex');
title('probability of refinancing', 'Interpreter', 'Latex');
%{
figure(3)
state = gridmake(nodeunif(100, lmin, 3), 0.5);
cmax = bisect('savings', 1e-13, 1e5, state(:,1), p, amin); % c that implies a' = amin
cmin = bisect('savings', 1e-13, 1e5, state(:,1), p, amax); % c that implies a' = amax
c = solve_golden('wfunc', cmin, cmax, state, EV, p);
[~, aprime] = savings(c, state, p);
subplot(1, 2, 1)
plot(state(:,1), c);
set(gca, 'ygrid', 'on')
xlabel('$l$', 'Interpreter', 'Latex');
title('$c$', 'Interpreter', 'Latex');
subplot(1, 2, 2)
plot(state(:,1), aprime);
set(gca, 'ygrid', 'on')
xlabel('$w$', 'Interpreter', 'Latex');
title('$a^{\prime}$', 'Interpreter', 'Latex');
%}
figure(2)
gain = nodeunif(1000, -5000, 20000);
factor = 36500; % scaling factor to convert units in the model into u'(c) times 12896 in the data
plot(gain, [(1 - exp(-3*max(gain/factor, 0))).*(gain >=0), ...
(1 - exp(-10*max(gain/factor, 0))).*(gain >=0), ...
(1 - exp(-10000*max(gain/factor, 0))).*(gain >=0)])
title('probability of refinancing', 'Interpreter', 'Latex');
xlabel('welfare gains from refinancing', 'Interpreter', 'Latex');
legend('$\nu = 1/3$', '$\nu = 1/10$', '$\nu = 0$'); |