Диссертация (1137758), страница 23
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Симуляция Монте-Карло для случая функцииполезности в форме Эпштейна-Зина и наличия неторгуемого активаКод симуляции динамики потребления с использованием функцииполезности в форме Эпштейна-Зина и в случае наличия неторгуемого актива всреде Matlab[path, params] = simulations(T);pathNR = path;paramsNR = params;theta = (1-params.gamma)/(1-1/params.sigma);cF0 = path.cw(1);alpha = path.alpha(1);EulerW_NR = 0;EulerA_NR = 0;EulerH_NR = 0;for iRH = 1 : 2for iRA = 1 : 2pH = params.RHDisribution.p(iRH);RH = params.RHDisribution.x(iRH);pA = params.RADisribution.p(iRA);RA = params.RADisribution.x(iRA);RW = alpha*RH + (1-alpha)*RA;wF1 = (1-cF0)*RW;cF1 = cF0*wF1;EulerW_NR = EulerW_NR + pH*pA*(...(params.beta*(cF1/cF0)^(-1/params.sigma))^theta...*RW^theta);EulerA_NR = EulerA_NR + pH*pA*(...(params.beta*(cF1/cF0)^(-1/params.sigma))^theta...*RW^(theta-1)*RA);EulerH_NR = EulerH_NR + pH*pA*(...(params.beta*(cF1/cF0)^(-1/params.sigma))^theta...*RW^(theta-1)*RH);endend[path, params] = simulationsrestricted2(10);theta = (1-params.gamma)/(1-1/params.sigma);EulerW = zeros(size(params.alpha));EulerA = zeros(size(params.alpha));EulerH = zeros(size(params.alpha));EulerWArt = zeros(size(params.alpha));for iAlpha = 1 : length(params.alpha)alpha = params.alpha(iAlpha);cF0 = path.cw(1, iAlpha);for iRH = 1 : 2131for iRA = 1 : 2pH = params.RHDisribution.p(iRH);RH = params.RHDisribution.x(iRH);pA = params.RADisribution.p(iRA);RA = params.RADisribution.x(iRA);wF1 = alpha*RH + (1-cF0-alpha)*RA;alphaF1 = alpha/wF1;RW = wF1/(1-cF0);cF1 = wF1*interp1(params.alpha, path.cw(1, :), alphaF1);EulerW(iAlpha) = EulerW(iAlpha) + pH*pA*(...(params.beta*(cF1/cF0)^(-1/params.sigma))^theta...*RW^theta);EulerA(iAlpha) = EulerA(iAlpha) + pH*pA*(...(params.beta*(cF1/cF0)^(-1/params.sigma))^theta...*RW^(theta-1)*RA);EulerH(iAlpha) = EulerH(iAlpha) + pH*pA*(...(params.beta*(cF1/cF0)^(-1/params.sigma))^theta...*RW^(theta-1)*RH);EulerWArt(iAlpha) = EulerH(iAlpha)*alpha + EulerA(iAlpha)*(1-alpha);endend% disp([(EulerW-1) (EulerA-1) (EulerH-1)]);endtable = num2cell([params.alpha',smooth(EulerW',0.1,'rlowess'),...smooth(EulerH',0.1,'rlowess'), smooth(EulerA',0.1,'rlowess')]);header = {'H', 'EulerW', 'EulerA', 'EulerH'};xlwrite('result.xlsx', [header; table]);function [path, params] = simulations(T)% Initial parametersparams.beta = 0.9;params.sigma = 0.5; % Elasticityparams.gamma = 0.5; % Risk aversionparams.alpha = [(-2:0.1:-0.5) (-0.4:0.01:1.4) (1.5:0.1:3)];params.RHDisribution.pparams.RHDisribution.xparams.RADisribution.pparams.RADisribution.x====[0.49, 0.51];[0.95, 1.10];[0.49, 0.51];[1.00,1.05];% Path for consumption and value functionpath.cw= nan(T, length(params.alpha));path.vw= nan(T, length(params.alpha));% Last periond valuespath.cw(T, :) = 0.06;path.vw(T, :) = valuefunction(params, path.cw(T, :), 18.5);% Back iterationsopt = optimset('Display', 'Notify', 'TolX', 1e-7, 'TolFun', 1e-7);for t = (T - 1) : (-1) : 1for iAlpha = 1 : length(params.alpha)alpha = params.alpha(iAlpha);[cwOpt, vwOpt] = fmincon(...@(cw) objectivefunction(params, path, t, cw , alpha), ...[0.5], [], [], [], [], ...132[0], [1], [], opt);vwOpt = -vwOpt;path.cw(t, iAlpha)= cwOpt;path.vw(t, iAlpha)= vwOpt;endfprintf('%s t = %d is done...\n', datestr(now(), 'HH:MM:SS'), t);endendfunction vw = objectivefunction(params, path, t, cw, alpha)vwF1Expected = 0;for iRH = 1 : 2for iRA = 1 : 2pH = params.RHDisribution.p(iRH);RH = params.RHDisribution.x(iRH);pA = params.RADisribution.p(iRA);RA = params.RADisribution.x(iRA);wF1 = alpha*RH + (1-cw-alpha)*RA;alphaF1 = alpha/wF1;if alphaF1 > params.alpha(end)vwF1 = path.vw(t + 1, end);elseif alphaF1 < params.alpha(1)vwF1 = path.vw(t + 1, 1);elsevwF1 = interp1(params.alpha, path.vw(t + 1, :), alphaF1);endendvwF1Expected = vwF1Expected ...+ pH*pA*(wF1*vwF1)^(1 - params.gamma);%%%%endendendvw = -valuefunction(params, cw, vwF1Expected);if t == 1cw(1)vwF1Expectedendfunction vwNotOptimal = valuefunction(params, cw, vwExpected)vwNotOptimal = ...(...(1 - params.beta)*cw.^(1 - 1/params.sigma) ...+ params.beta*vwExpected...^((1 - 1/params.sigma)/(1 - params.gamma)) ...).^(1/(1 - 1/params.sigma));end133Приложение Б.
Код для выбора взвешивающей матрицы при оценкемодели с когортамиКод генерации данных, расчета дисперсии шоков и получения оценокдисперсии и ковариации шоков с помощью различных взвешивающих матриц всреде Matlab%% Data generation% Ny --- number of years% Nm --- number of months% Ni --- number of itemsNy = 10;Nm = 3;Ni = 10;% VariancesSu = 1;Sxi = 12;% Common monthly shocksu= normrnd(0, Su, (Ny + 1)*12, 1);uMA = u(12:end);% 12 months cumsumfor i = 1 : 11uMA = uMA + u((12 - i) : (end - i));end% Individual shocksxi = normrnd(0, Sxi, Ny*Nm, Ni);% Total shockse= xi;for y = 1 : Nyfor m = 1 : Nme((y - 1)*Nm + m, :) = e((y - 1)*Nm + m, :) + uMA(y*12 - (Nm - m));endend% Form PanelT= Ny*Nm;E= e;% StatisticW = sqrt(T)*mean(e);%% Monte CarloB = 10000;WArray = nan(B, Ni);OmegaHacImprovedArray = nan(Ni, Ni, B);OmegaSimpleArray = nan(Ni, Ni, B);OmegaHacArray = nan(Ni, Ni, B);for b = 1 : Bu= normrnd(0, Su, (Ny + 1)*12, 1);uMA = u(12:end);% 12 months cumsum134for i = 1 : 11uMA = uMA + u((12 - i) : (end - i));end% Individual shocksxi = normrnd(0, Sxi, Ny*Nm, Ni);% Total shockse= xi;for y = 1 : Nyfor m = 1 : Nme((y - 1)*Nm + m, :) = e((y - 1)*Nm + m, :) + uMA(y*12 - (Nm - m));endend% Form PanelT= Ny*Nm;E= e;% StatisticW = sqrt(T)*mean(E);WArray(b, :) = W;%[Omega, OmegaSimple, OmegaHac] = getomegapehac(E, 2);OmegaHacImprovedArray(:, :, b) = Omega;OmegaSimpleArray(:, :, b) = OmegaSimple;OmegaHacArray(:, :, b) = OmegaHac;end% Avg of varianceWVar = WArray'*WArray/B;disp(WVar(1, 1:2));HacImprovedVarHacImprovedVarHacImprovedCovHacImprovedCovSimpleVarSimpleVarSimpleCovSimpleCovHacVarHacVarHacCovHacCov============OmegaHacImprovedArray(1,1,:);HacImprovedVar(:);OmegaHacImprovedArray(1,2,:);HacImprovedCov(:);OmegaSimpleArray(1,1,:);SimpleVar(:);OmegaSimpleArray(1,2,:);SimpleCov(:);OmegaHacArray(1,1,:);HacVar(:);OmegaHacArray(1,2,:);HacCov(:);%% TableTable = [{'Estimator', 'Bias', 'Std.
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