close all set(groot, 'DefaultAxesLineWidth', 1.5); set(groot, 'DefaultLineLineWidth', 4); set(groot, 'DefaultAxesTickLabelInterpreter','latex'); set(groot, 'DefaultLegendInterpreter','latex'); set(groot, 'DefaultAxesFontSize',24); S = 5; % Without intervention Asim = zeros(2*N, T, S + 1); Osim = zeros(2*N, T, S + 1); Thsim = zeros(2*N, T, S + 1); Hsim = zeros(2*N, T, S + 1); Csim = zeros(2*N, T, S); Lsim = zeros(2*N, T, S); Dsim = zeros(2*N, T, S); Ysim = zeros(2*N, T, S); Zsim = zeros(2*N, T, S); Esim = zeros(2*N, T, S); Vsim = zeros(2*N, T, S); Pallsim = zeros(2*N, 5, T, S); Vallsim = zeros(2*N, 5, T, S); Usim = zeros(2*N, T, S); Agesim = zeros(2*N, T, S); Asim(:, :, 1) = Asave(:, 1 : T); Osim(:, :, 1) = Osave(:, 1 : T); Thsim(:, :, 1) = Thsave(:, 1 : T); Hsim(:, :, 1) = Hsave(:, 1 : T); Csim(:, :, 1) = Csave(:, 1 : T); Lsim(:, :, 1) = Lsave(:, 1 : T); Dsim(:, :, 1) = Dsave(:, 1 : T); Ysim(:, :, 1) = Ysave(:, 1 : T); Zsim(:, :, 1) = Zsave(:, 1 : T); Esim(:, :, 1) = Esave(:, 1 : T); Vsim(:, :, 1) = Vsave(:, 1 : T); Usim(:, :, 1) = Usave(:, 1 : T); Deltasim(:, :, 1) = Deltasave(:, 1 : T); Pallsim(:, :, :, 1) = Pallsave; Vallsim(:, :, :, 1) = Vallsave; Agesim(:,:,1) = repmat((1 : 1 : T), 2*N, 1); index = nodeunif(N, 1e-14, 1 - 1e-14); % First simulate history of shocks to income for time = 2 : S Agesim(:, :, time) = rem(Agesim(:, : , time - 1), T) + 1; for initage = 1 : T % go over all initial age bins unif = index(randperm(N)); unif = [unif; 1 - unif]; % mirror sampling Fzcum = [zeros(2*N, 1), cumsum(Fzz(Zsim(:, initage, time - 1), :), 2)]; Zsim(:, initage, time) = ((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 Esim(:, initage, time) = bin; Ysim(:, initage, time) = p.lambdat(Agesim(:, initage, time)).*p.zgrid(Zsim(:, initage, time)).*p.egrid(Esim(:, initage, time)); end Usim(:, :, time) = rand(2*N, T); Deltasim(:, :, time) = rand(2*N, T); Deltasim(:, :, time) = p.delta(1)*(Deltasim(:, :, time) <= p.pidelta(1)) + p.delta(2)*(Deltasim(:, :, time) > p.pidelta(1)); end Asim(:, 1 : T - 1, 2) = Asave(:, 2 : T); Asim(:, T, 2) = 0; Osim(:, 1 : T - 1, 2) = Osave(:, 2 : T); Osim(:, T, 2) = 0; Thsim(:, 1 : T - 1, 2) = Thsave(:, 2 : T); Thsim(:, T, 2) = 0; Hsim(:, 1 : T - 1, 2) = Hsave(:, 2 : T); Hsim(:, T, 2) = 0; for time = 2 : S for initage = 1 : T age = Agesim(1, initage, time); Whinterp = griddedInterpolant({p.lgrid, (1: 1: p.no*p.nt*p.nh*p.nz)'}, reshape(wh(:, age), p.nl, p.no*p.nt*p.nh*p.nz), intmeth, 'linear'); Wrinterp = griddedInterpolant({p.lgrid, (1: 1: p.nz)'}, reshape(wr(:, age), p.nl, p.nz), intmeth, 'linear'); rent = Hsim(:, initage, time) == 0; % Renters state = (1 + interest(Asim(rent, initage, time), p)).*Asim(rent, initage, time); ntemp = numel(find(rent)); [Lall, Oall, Thall, Hall, Vsim(rent, initage, time), Pallsim(rent, 1 : 3, initage, time), Vallsim(rent, 1 : 3, initage, time)] = ... solveh(state, Whinterp, Wrinterp, p, p.thetay(age), 'r', state(:, 1), Ysim(rent, initage, time), Zsim(rent, initage, time)); Pcum = [zeros(ntemp, 1), cumsum(Pallsim(rent, 1 : 3, initage, time), 2)]; Dsim(rent, initage, time) = ((Usim(rent, initage, time) < Pcum(:, 2:end)).*(Usim(rent, initage, time) >= Pcum(:,1:end-1)))*(1 : 1 : 3)'; ind = sub2ind([ntemp, 3], (1 : 1 : ntemp)', Dsim(rent, initage, time)); Lsim(rent, initage, time) = Lall(ind); Osim(rent, initage, time + 1) = Oall(ind); Thsim(rent, initage, time + 1) = Thall(ind); Hsim(rent, initage, time + 1) = Hall(ind); % Homeowners Attemp = (1 + interest(Asim(~rent, initage, time), p)).*Asim(~rent, initage, time) - Deltasim(~rent, initage, time).*Hsim(~rent, initage, time); state = [Attemp, Osim(~rent, initage, time), Thsim(~rent, initage, time), Hsim(~rent, initage, time)]; % others don't matter directly hind = lookup1(p.hgrid, state(:, 4), 1); tind = lookup1(p.tgrid, state(:, 3), 1); ntemp = numel(find(~rent)); [Lall, Oall, Thall, Hall, Vsim(~rent, initage, time), Pallsim(~rent, :, initage, time), Vallsim(~rent, :, initage, time)] = ... solveh(state, Whinterp, Wrinterp, p, p.thetay(age), 'h', state(:, 1), Ysim(~rent, initage, time), Zsim(~rent, initage, time), hind, tind); Pcum = [zeros(ntemp, 1), cumsum(Pallsim(~rent, :, initage, time), 2)]; Dsim(~rent, initage, time) = ((Usim(~rent, initage, time) < Pcum(:, 2:end)).*(Usim(~rent, initage, time) >= Pcum(:,1:end-1)))*(1 : 1 : 5)'; ind = sub2ind([ntemp, 5], (1 : 1 : ntemp)', Dsim(~rent, initage, time)); Lsim(~rent, initage, time) = Lall(ind); Osim(~rent, initage, time + 1) = Oall(ind); Thsim(~rent, initage, time + 1) = Thall(ind); Hsim(~rent, initage, time + 1) = Hall(ind); % Find consumption rent = Hsim(:, initage, time + 1) == 0; Chint = griddedInterpolant({p.lgrid, p.ogrid, p.tgrid, p.hgrid, p.zgrid}, reshape(ch(:, age), p.nl, p.no, p.nt, p.nh, p.nz), intmeth, 'linear'); Crint = griddedInterpolant({p.lgrid, p.zgrid}, reshape(cr(:, age), p.nl, p.nz), intmeth, 'linear'); cmin = bisect('savings', 1e-13, 1e5, Lsim(rent, initage, time), p, 'r', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, Lsim(rent, initage, time), p, 'r', amin); % c that implies a' = amin Csim(rent, initage, time) = max(min(Crint(Lsim(rent, initage, time), p.zgrid(Zsim(rent, initage, time))), cmax), cmin); [~, Asim(rent, initage, time + 1)] = savings(Csim(rent, initage, time), Lsim(rent, initage, time), p, 'r'); % none of the other state variables matter cmin = bisect('savings', 1e-13, 1e5, Lsim(~rent, initage, time), p, 'h', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, Lsim(~rent, initage, time), p, 'h', amin); % c that implies a' = amin Csim(~rent, initage, time) = max(min(Chint(Lsim(~rent, initage, time), Osim(~rent,initage, time + 1), Thsim(~rent,initage, time + 1), Hsim(~rent,initage, time + 1), p.zgrid(Zsim(~rent, initage, time))), cmax), cmin); [~, Asim(~rent, initage, time + 1)] = savings(Csim(~rent, initage, time), Lsim(~rent, initage, time), p, 'h'); % none of the other state variables matter if age == T Asim(:, initage, time + 1) = 0; Osim(:, initage, time + 1) = 0; Thsim(:, initage, time + 1) = 0; Hsim(:, initage, time + 1) = 0; end end end Ct = zeros(S, 1); Yt = zeros(S, 1); At = zeros(S, 1); Ht = zeros(S, 1); Dt = zeros(S, 1); Rt = zeros(S, 1); MPRt = zeros(S, 1); % Beraja-Hurst propensity to refinance: amount of newly refinanced mortgages / outstanding stock of all existing mortgages Emt = zeros(S, 1); % median equity (1 - LTV) for borrowers for time = 1 : S Ct(time) = mean(vec(Csim(:, :, time))); Yt(time) = mean(vec(Ysim(:, :, time))); Ht(time) = mean(vec(Hsim(:, :, time))); At(time) = mean(vec(Asim(:, :, time))); Dt(time) = mean(vec(Osim(:, :, time).*Thsim(:, :, time).*Hsim(:, :, time))); Rt(time) = mean(vec(Dsim(:, :, time) == 4 & Hsim(:, :, time) > 0 & Osim(:, :, time).*Thsim(:, :, time) > 0))/mean(vec(Hsim(:, :, time) > 0 & Osim(:, :, time).*Thsim(:, :, time) > 0)); MPRt(time) = sum(vec((Dsim(:,:, time) == 4).*Osim(:, :, time + 1).*Thsim(:, :, time + 1).*Hsim(:, :, time + 1)))/... sum(vec( Osim(:, :, time ).*Thsim(:, :, time ).*Hsim(:, :, time ))); LTV = vec(Osim(:, :, time).*Thsim(:, :, time)); Emt(time) = 1 - median(LTV(LTV > 0)); end % With intervention start_new; Acsim = Asim; Ocsim = Osim; Thcsim = Thsim; Hcsim = Hsim; Ccsim = Csim; Lcsim = Lsim; Dcsim = Dsim; Vcsim = zeros(2*N, T, S); Pallcsim = Pallsim; Vallcsim = Vallsim; Rcsim = zeros(2*N, T, S + 1); Rcsim(:, :, 1 : 2) = 1; Ocsim(:, :, 2) = Osim(:,:,2)*p.adjustomega; for time = 2 : S for initage = 1 : T age = Agesim(1, initage, time); Whinterp = griddedInterpolant({p.lgrid, (1: 1: p.no*p.nt*p.nh*p.nr*p.nz)'}, reshape(wh(:, age), p.nl, p.no*p.nt*p.nh*p.nr*p.nz), intmeth, 'linear'); Wrinterp = griddedInterpolant({p.lgrid, (1: 1: p.nz)'}, reshape(wr(:, age), p.nl, p.nz), intmeth, 'linear'); rent = Hcsim(:, initage, time) == 0; % Renters state = (1 + interest(Acsim(rent, initage, time), p)).*Acsim(rent, initage, time); ntemp = numel(find(rent)); [Lall, Oall, Thall, Hall, Vcsim(rent, initage, time), Pallcsim(rent, 1 : 3, initage, time), Vallcsim(rent, 1 : 3, initage, time)] = ... solveh_new(state, Whinterp, Wrinterp, p, p.thetay(age), 'r', state(:,1), Ysim(rent, initage, time), Zsim(rent, initage, time)); Pcum = [zeros(ntemp, 1), cumsum(Pallcsim(rent, 1 : 3, initage, time), 2)]; Dcsim(rent, initage, time) = ((Usim(rent, initage, time) < Pcum(:, 2:end)).*(Usim(rent, initage, time) >= Pcum(:,1:end-1)))*(1 : 1 : 3)'; ind = sub2ind([ntemp, 3], (1 : 1 : ntemp)', Dcsim(rent, initage, time)); Lcsim(rent, initage, time) = Lall(ind); Ocsim(rent, initage, time + 1) = Oall(ind); Thcsim(rent, initage, time + 1) = Thall(ind); Hcsim(rent, initage, time + 1) = Hall(ind); % Homeowners Attemp = (1 + interest(Acsim(~rent, initage, time), p)).*Acsim(~rent, initage, time) - Deltasim(~rent, initage, time).*Hcsim(~rent, initage, time); state = [Attemp, Ocsim(~rent, initage, time), Thcsim(~rent, initage, time), Hcsim(~rent, initage, time), Rcsim(~rent, initage, time)]; % others don't matter directly hind = lookup1(p.hgrid, state(:, 4), 1); tind = lookup1(p.tgrid, state(:, 3), 1); rind = state(:, 5); % made this state variable an index (1, 2), or else doesn't respect monotonicity ntemp = numel(find(~rent)); [Lall, Oall, Thall, Hall, Vcsim(~rent, initage, time), Pallcsim(~rent, :, initage, time), Vallcsim(~rent, :, initage, time)] = ... solveh_new(state, Whinterp, Wrinterp, p, p.thetay(age), 'h', state(:,1), Ysim(~rent, initage, time), Zsim(~rent, initage, time), hind, tind, rind); Pcum = [zeros(ntemp, 1), cumsum(Pallcsim(~rent, :, initage, time), 2)]; unif = rand(ntemp, 1); Dcsim(~rent, initage, time) = ((Usim(~rent, initage, time) < Pcum(:, 2:end)).*(Usim(~rent, initage, time) >= Pcum(:,1:end-1)))*(1 : 1 : 5)'; ind = sub2ind([ntemp, 5], (1 : 1 : ntemp)', Dcsim(~rent, initage, time)); Lcsim(~rent, initage, time) = Lall(ind); Ocsim(~rent, initage, time + 1) = Oall(ind); Thcsim(~rent, initage, time + 1) = Thall(ind); Hcsim(~rent, initage, time + 1) = Hall(ind); inactive = Dcsim(:, initage, time) == 5; Rcsim(:, initage, time + 1) = Rcsim(:, initage, time).*inactive + p.nr.*(1 - inactive); % Find consumption rent = Hcsim(:, initage, time + 1) == 0; Chint = griddedInterpolant({p.lgrid, p.ogrid, p.tgrid, p.hgrid, (1 : 1 : p.nr)', p.zgrid}, reshape(ch(:, age), p.nl, p.no, p.nt, p.nh, p.nr, p.nz), intmeth, 'linear'); Crint = griddedInterpolant({p.lgrid, p.zgrid}, reshape(cr(:, age), p.nl, p.nz), intmeth, 'linear'); cmin = bisect('savings', 1e-13, 1e5, Lcsim(rent, initage, time), p, 'r', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, Lcsim(rent, initage, time), p, 'r', amin); % c that implies a' = amin Ccsim(rent, initage, time) = max(min(Crint(Lcsim(rent, initage, time), p.zgrid(Zsim(rent, initage, time))), cmax), cmin); [~, Acsim(rent, initage, time + 1)] = savings(Ccsim(rent, initage, time), Lcsim(rent, initage, time), p, 'r'); % none of the other state variables matter cmin = bisect('savings', 1e-13, 1e5, Lcsim(~rent, initage, time), p, 'h', amax); % c that implies a' = amin cmax = bisect('savings', 1e-13, 1e5, Lcsim(~rent, initage, time), p, 'h', amin); % c that implies a' = amin Ccsim(~rent, initage, time) = max(min(Chint(Lcsim(~rent, initage, time), Ocsim(~rent,initage, time + 1), Thcsim(~rent,initage, time + 1), Hcsim(~rent,initage, time + 1), Rcsim(~rent,initage, time + 1), p.zgrid(Zsim(~rent, initage, time))), cmax), cmin); [~, Acsim(~rent, initage, time + 1)] = savings(Ccsim(~rent, initage, time), Lcsim(~rent, initage, time), p, 'h'); % none of the other state variables matter if age == T Acsim(:, initage, time + 1) = 0; Ocsim(:, initage, time + 1) = 0; Thcsim(:, initage, time + 1) = 0; Hcsim(:, initage, time + 1) = 0; end end end Cct = zeros(S, 1); Yct = zeros(S, 1); Act = zeros(S, 1); Hct = zeros(S, 1); Dct = zeros(S, 1); Rct = zeros(S, 1); MPRct = zeros(S, 1); % Beraja-Hurst propensity to refinance: amount of newly refinanced mortgages / outstanding stock of all existing mortgages Emct = zeros(S, 1); % median equity (1 - LTV) for borrowers for time = 1 : S Cct(time) = mean(vec(Ccsim(:, :, time))); Hct(time) = mean(vec(Hcsim(:, :, time))); Act(time) = mean(vec(Acsim(:, :, time))); Dct(time) = mean(vec(Ocsim(:, :, time).*Thcsim(:, :, time).*p.Pgrid(Rcsim(:,:,time)).*Hcsim(:, :, time))); Rct(time) = mean(vec(Dcsim(:, :, time) == 4 & Hcsim(:, :, time) > 0 & Ocsim(:, :, time).*Thcsim(:, :, time) > 0))/mean(vec(Hcsim(:, :, time) > 0 & Ocsim(:, :, time).*Thcsim(:, :, time) > 0)); MPRct(time) = sum(vec((Dcsim(:,:, time) == 4).*Ocsim(:, :, time + 1).*Thcsim(:, :, time + 1).*p.Pgrid(Rcsim(:, :, time + 1)).*Hcsim(:, :, time + 1)))/... sum(vec( Ocsim(:, :, time ).*Thcsim(:, :, time ).*p.Pgrid(Rcsim(:, :, time )).*Hcsim(:, :, time ))); if time == 1 LTV = vec(Ocsim(:, :, time).*Thcsim(:, :, time)); else LTV = vec(Ocsim(:, :, time).*Thcsim(:, :, time).*p.Pgrid(Rcsim(:,:,time)))/p.Pgrid(p.nr); end Emct(time) = 1 - median(LTV(LTV > 0)); end % Characteristics of those who refinance: with and without the shock Wsim = Asim + Hsim.*(1 - Osim.*Thsim); time = 2; Wtemp = Wsim(:, :, time); % only state variables Atemp = Asim(:, :, time); LTV = Osim(:, :, time).*Thsim(:, :, time); Htemp = Hsim(:, :, time); LY = Atemp./Ysim(:, :, time); Sh = 1 - Atemp./Wtemp; Agetemp = Agesim(:, :, time)/4 + 25; Ytemp = Ysim(:, :, time); refin = Dsim(:, :, time) == 4 & Hsim(:, :, time) > 0; owner = Hsim(:, :, time) > 0; fprintf('\n'); fprintf('Characteristics of Refinancers Absent Shock\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(Ytemp(owner)), mean(Ytemp(owner & refin)), mean(Ytemp(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(Agetemp(owner)), mean(Agetemp(owner & refin)), mean(Agetemp(owner & ~refin))]); fprintf('\n'); fprintf('\n'); Wcsim = zeros(size(Acsim)); Wcsim(:,:, 1) = Acsim(:, :, 1) + p.Pgrid(1)*Hcsim(:, :, 1).*(1 - Ocsim(:, :, 1).*Thcsim(:, :, 1)); Wcsim(:, :, 2: end) = Acsim(:, :, 2 : end) + p.Pgrid(p.nr)*Hcsim(:,:,2:end) - p.Pgrid(Rcsim(:,:,2:end)).*Ocsim(:, :, 2:end).*Thcsim(:, :, 2:end); time = 2; Wtemp = Wcsim(:, :, time); % only state variables Atemp = Acsim(:, :, time); LTV = Ocsim(:, :, time).*Thcsim(:, :, time); Htemp = Hcsim(:, :, time); LY = Atemp./Ysim(:, :, time); Sh = 1 - Atemp./Wtemp; Agetemp = Agesim(:, :, time)/4 + 25; Ytemp = Ysim(:, :, time); refin = Dcsim(:, :, time) == 4 & Hcsim(:, :, time) > 0; owner = Hcsim(:, :, time) > 0; fprintf('\n'); fprintf('Characteristics of Refinancers With Shock\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(Ytemp(owner)), mean(Ytemp(owner & refin)), mean(Ytemp(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(Agetemp(owner)), mean(Agetemp(owner & refin)), mean(Agetemp(owner & ~refin))]); fprintf('\n'); fprintf('\n'); % MPC out of transfer in Ganong-Noel Experiment time = 2; Transfer = (p.mbargrid(p.nr) - p.mbargrid(Rcsim(:, :, time))).*Thcsim(:, :, time).*p.Pgrid(Rcsim(:,:,time)).*Hcsim(:,:,time).*(Dcsim(:, :, time) == 5).*(Osim(:,:,time) > 0); dC = (Ccsim(:, :, time) - p.phi^(1 + 1/p.gamma)*Ccsim(:, :, time).^(-p.sigma/p.gamma) - (Csim(:, :, time) - p.phi^(1 + 1/p.gamma)*Csim(:, :, time).^(-p.sigma/p.gamma))); dA = Acsim(:, :, time + 1) - Asim(:, :, time + 1); htm = Acsim(:, :, time + 1) <= 1/6.5*Ysim(:,:,time); gains = Vcsim(:, :, time) - Vsim(:, :, time); good = Transfer > 0 & Dcsim(:, :, time) == 5 & Dsim(:, :, time) == 5; MPC = dC(good)./Transfer(good); gains = gains(good); htm = htm(good); fbenefit = mean(gains > 0); fprintf('\n') fprintf('Fraction who benefit = %9.2f \n', fbenefit); fprintf('\n') fprintf('MPC, mean = %9.2f %9.2f %9.2f \n', [mean(MPC(gains > 0)), mean(MPC(gains > 0 & htm)), mean(MPC(gains > 0 & ~htm)) ]); fprintf('MPC, 10th pctile = %9.2f %9.2f %9.2f \n', [prctile(MPC(gains > 0), 10), prctile(MPC(gains > 0 & htm), 10), prctile(MPC(gains > 0 & ~htm), 10)]); fprintf('MPC, 25th pctile = %9.2f %9.2f %9.2f \n', [prctile(MPC(gains > 0), 25), prctile(MPC(gains > 0 & htm), 25), prctile(MPC(gains > 0 & ~htm), 25)]); fprintf('MPC, 50th pctile = %9.2f %9.2f %9.2f \n', [prctile(MPC(gains > 0), 50), prctile(MPC(gains > 0 & htm), 50), prctile(MPC(gains > 0 & ~htm), 50)]); fprintf('MPC, 75th pctile = %9.2f %9.2f %9.2f \n', [prctile(MPC(gains > 0), 75), prctile(MPC(gains > 0 & htm), 75), prctile(MPC(gains > 0 & ~htm), 75)]); fprintf('MPC, 90th pctile = %9.2f %9.2f %9.2f \n', [prctile(MPC(gains > 0), 90), prctile(MPC(gains > 0 & htm), 90), prctile(MPC(gains > 0 & ~htm), 90)]);