File size: 12,801 Bytes
2a8276b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 | function [Lall, omegaall, thetaall, hall, v, pall, vall] = solveh(s, Whinterp, Wrinterp, p, pti, type, At, Y, znow, hnow, tnow)
ns = size(s, 1);
if strcmp(type, 'r')
Lall = zeros(ns, 3);
omegaall = zeros(ns, 3);
thetaall = zeros(ns, 3);
hall = zeros(ns, 3);
vall = zeros(ns, 3);
for branch = 1 : 1 : 3
if branch == 1 % Remain Renter
Lall(:, branch) = At + Y;
omegaall(:, branch) = 0;
thetaall(:, branch) = 0;
hall(:, branch) = 0;
vall(:, branch) = Wrinterp(Lall(:, branch), znow);
elseif branch == 2 % Purchase New Home Without Mortgage
vtemp = zeros(ns, p.nh) - 1e12;
Ltemp = zeros(ns, p.nh);
Cash = At + Y;
for i = 1 : p.nh
Ltemp(:,i) = Cash - p.hgrid(i); % liquidity after housing choice
ind2 = (znow - 1)*p.no*p.nt*p.nh + (i - 1)*p.no*p.nt + (1 - 1) *p.no + 1;
good = Ltemp(:, i) >= p.lgrid(1); % avoid extrapolation
if any(good)
vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
end
end
[vall(:, branch), htemp] = max(vtemp, [], 2);
hind = sub2ind([ns, p.nh], (1 : 1 : ns)', htemp);
Lall(:, branch) = Ltemp(hind);
omegaall(:, branch) = 0;
thetaall(:, branch) = 0;
hall(:, branch) = p.hgrid(htemp);
elseif branch == 3 % Purchase New Home with Mortgage
% create a grid of possible houses and initial LTVs
ht = gridmake((1 : 1 : p.nh)', (1 : 1 : p.nt)');
vtemp = zeros(ns, p.nh*p.nt) - 1e12;
Ltemp = zeros(ns, p.nh*p.nt);
Cash = At + Y;
for i = 1 : p.nh*p.nt
ttilde = (p.tgrid(ht(i, 2)) - p.F0m/p.hgrid(ht(i, 1)))/(1 + p.F1m);
Ltemp(:, i) = Cash - (1 - ttilde).*p.hgrid(ht(i, 1)); % liquidity after housing choice
ind2 = (znow - 1)*p.no*p.nt*p.nh + (ht(i, 1) - 1)*p.no*p.nt + (ht(i, 2) - 1) *p.no + p.no;
good = (ttilde <= min(p.thetam, pti*Y/p.mbar/p.hgrid(ht(i, 1)))) & (Ltemp(:,i) > p.lgrid(1));
if any(good)
vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
end
end
[vall(:, branch), htemp] = max(vtemp, [], 2);
hind = sub2ind([ns, p.nh*p.nt], (1 : 1 : ns)', htemp);
Lall(:, branch) = Ltemp(hind);
omegaall(:, branch) = 1;
thetaall(:, branch) = p.tgrid(ht(htemp, 2));
hall(:, branch) = p.hgrid(ht(htemp, 1));
end
end
% Compute pall and v
[vn, in] = max(vall(:, 1 : 2), [], 2);
vb = vall(:,3);
pb = (1 - exp(-p.nu*max(vb - vn, 0))).*(vb >= vn); % avoid NaN
pall = zeros(ns, 3);
pall(:, 1) = (1 - p.rr)*(1 - pb).*(in == 1) + p.rr; % no choice but to remain renter with p.rr
pall(:, 2) = (1 - p.rr)*(1 - pb).*(in == 2);
pall(:, 3) = (1 - p.rr)*pb;
v = (1 - p.rr)*(vn.*(vb < vn) + (vb - pb/p.nu).*(vb >= vn)) + p.rr*vall(:,1);
else
Lall = zeros(ns, 5);
omegaall = zeros(ns, 5);
thetaall = zeros(ns, 5);
hall = zeros(ns, 5);
vall = zeros(ns, 5);
for branch = 1 : 1 : 5
if branch == 1 % Switch to Renting
Lall(:, branch) = At + Y + (1 - p.Fs)*s(:,4) - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4); % liquidity after housing choice
omegaall(:, branch) = 0;
thetaall(:, branch) = 0;
hall(:, branch) = 0;
vall(:, branch) = Wrinterp(Lall(:, branch), znow);
elseif branch == 2 % Purchase home without mortgage
vtemp = zeros(ns, p.nh) - 1e12;
Ltemp = zeros(ns, p.nh);
Cash = At + Y + (1 - p.Fs)*s(:,4) - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4);
for i = 1 : p.nh
Ltemp(:,i) = Cash - p.hgrid(i); % liquidity after housing choice
ind2 = (znow - 1)*p.no*p.nt*p.nh + (i - 1)*p.no*p.nt + (1 - 1) *p.no + 1;
good = Ltemp(:, i) >= p.lgrid(1); % avoid extrapolation
if any(good)
vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
end
end
[vall(:, branch), htemp] = max(vtemp, [], 2);
hind = sub2ind([ns, p.nh], (1 : 1 : ns)', htemp);
Lall(:, branch) = Ltemp(hind);
omegaall(:, branch) = 0;
thetaall(:, branch) = 0;
hall(:, branch) = p.hgrid(htemp);
elseif branch == 3 % Purchase home with mortgage
ht = gridmake((1 : 1 : p.nh)', (1 : 1 : p.nt)');
vtemp = zeros(ns, p.nh*p.nt) - 1e12;
Ltemp = zeros(ns, p.nh*p.nt);
Cash = At + Y + (1 - p.Fs)*s(:, 4) - (1 + p.rm)*s(:, 2).*s(:, 3).*s(:, 4);
for i = 1 : p.nh*p.nt
ttilde = (p.tgrid(ht(i, 2)) - p.F0m/p.hgrid(ht(i, 1)))/(1 + p.F1m);
Ltemp(:, i) = Cash - (1 - ttilde).*p.hgrid(ht(i, 1));
good = (ttilde <= min(p.thetam, pti*Y/p.mbar/p.hgrid(ht(i, 1)))) & Ltemp(:, i) >= p.lgrid(1);
ind2 = (znow - 1)*p.no*p.nt*p.nh + (ht(i, 1) - 1)*p.no*p.nt + (ht(i, 2) - 1) *p.no + p.no;
if any(good)
vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
end
end
[vall(:, branch), htemp] = max(vtemp, [], 2);
hind = sub2ind([ns, p.nh*p.nt], (1 : 1 : ns)', htemp);
Lall(:, branch) = Ltemp(hind);
omegaall(:, branch) = 1;
thetaall(:, branch) = p.tgrid(ht(htemp, 2));
hall(:, branch) = p.hgrid(ht(htemp, 1));
elseif branch == 4 % Refinance mortgage
vtemp = zeros(ns, p.nt) - 1e12;
Ltemp = zeros(ns, p.nt);
Cash = At + Y - (1 + p.rm)*s(:, 2).*s(:, 3).*s(:, 4);
for i = 1 : p.nt
ttilde = (p.tgrid(i) - p.F0m./s(:,4))/(1 + p.F1m);
Ltemp(:, i) = Cash + ttilde.*s(:, 4);
good = (ttilde <= min(p.thetam, pti*Y/p.mbar./s(:,4))) & Ltemp(:, i) >= p.lgrid(1);
ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (i - 1)*p.no + p.no;
if any(good)
vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
end
end
[vall(:, branch), htemp] = max(vtemp, [], 2);
hind = sub2ind([ns, p.nt], (1 : 1 : ns)', htemp);
Lall(:, branch) = Ltemp(hind);
omegaall(:, branch) = 1;
thetaall(:, branch) = p.tgrid(htemp);
hall(:, branch) = s(:, 4);
elseif branch == 5 % Stay inactive
vtemp = zeros(ns, p.no + 1) - 1e12;
Ltemp = zeros(ns, p.no + 1);
% Pay more than required
Cash = At + Y - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4);
for i = 1 : p.no
Ltemp(:, i) = Cash + p.ogrid(i).*s(:,3).*s(:,4);
good = (p.ogrid(i) < max((1 + p.rm)*s(:,2) - p.mbar, 0)) & (Ltemp(:, i) >= p.lgrid(1));
ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (tnow - 1)*p.no + i;
if any(good)
vtemp(good, i) = Whinterp(Ltemp(good, i), ind2(good));
end
end
% Pay minimum required
otemp = max((1 + p.rm)*s(:,2) - p.mbar, 0);
Ltemp(:, p.no + 1) = At + Y - (1 + p.rm)*s(:,2).*s(:,3).*s(:,4) + otemp.*s(:,3).*s(:,4);
good = (Ltemp(:, p.no + 1) >= p.lgrid(1));
if any(good)
% Interpolate
otempind = lookup1(p.ogrid, otemp, 3);
w = (p.ogrid(otempind + 1) - otemp)./(p.ogrid(otempind + 1) - p.ogrid(otempind));
ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (tnow - 1)*p.no + otempind;
vtemp(good, p.no + 1) = w(good).*Whinterp(Ltemp(good, p.no + 1), ind2(good));
ind2 = (znow - 1)*p.no*p.nt*p.nh + (hnow - 1)*p.no*p.nt + (tnow - 1)*p.no + otempind + 1;
vtemp(good, p.no + 1) = vtemp(good, p.no + 1) + (1 - w(good)).*Whinterp(Ltemp(good, p.no + 1), ind2(good));
end
[vall(:, branch), htemp] = max(vtemp, [], 2);
hind = sub2ind([ns, p.no + 1], (1 : 1 : ns)', htemp);
Lall(:, branch) = Ltemp(hind);
omegaall(htemp <= p.no, branch) = p.ogrid(htemp(htemp <= p.no));
omegaall(htemp > p.no, branch) = otemp(htemp > p.no);
thetaall(:, branch) = p.tgrid(tnow);
hall(:, branch) = s(:,4);
end
end
% Compute pall and v
[vn, in] = max(vall(:, [1, 2, 5]), [], 2);
[vb, ib] = max(vall(:, [3, 4]), [], 2);
pb = (1 - exp(-p.nu*max(vb - vn, 0))).*(vb >= vn);
pall = zeros(ns, 5);
pall(:, 1) = (1 - p.hr)*(1 - pb).*(in == 1) + p.hr; % forced into renting with p.hr
pall(:, 2) = (1 - p.hr)*(1 - pb).*(in == 2);
pall(:, 5) = (1 - p.hr)*(1 - pb).*(in == 3);
pall(:, 3) = (1 - p.hr)* pb.*(ib == 1);
pall(:, 4) = (1 - p.hr)* pb.*(ib == 2);
v = (1 - p.hr)*(vn.*(vb < vn) + (vb - pb/p.nu).*(vb >= vn)) + p.hr*vall(:, 1);
end
|