199 lines
6.7 KiB
Modula-2
199 lines
6.7 KiB
Modula-2
/*
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Compare simulation results with pruning at second order
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*/
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var m P c e W R k d n l gy_obs gp_obs y dA ;
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varexo e_a e_m;
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parameters alp bet gam mst rho psi del;
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alp = 0.33;
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bet = 0.99;
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gam = 0.003;
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mst = 1.011;
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rho = 0.7;
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psi = 0.787;
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del = 0.02;
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model;
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dA = exp(gam+e_a);
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log(m) = (1-rho)*log(mst) + rho*log(m(-1))+e_m;
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-P/(c(+1)*P(+1)*m)+bet*P(+1)*(alp*exp(-alp*(gam+log(e(+1))))*k^(alp-1)*n(+1)^(1-alp)+(1-del)*exp(-(gam+log(e(+1)))))/(c(+2)*P(+2)*m(+1))=0;
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W = l/n;
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-(psi/(1-psi))*(c*P/(1-n))+l/n = 0;
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R = P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(-alp)/W;
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1/(c*P)-bet*P*(1-alp)*exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)/(m*l*c(+1)*P(+1)) = 0;
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c+k = exp(-alp*(gam+e_a))*k(-1)^alp*n^(1-alp)+(1-del)*exp(-(gam+e_a))*k(-1);
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P*c = m;
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m-1+d = l;
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e = exp(e_a);
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y = k(-1)^alp*n^(1-alp)*exp(-alp*(gam+e_a));
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gy_obs = dA*y/y(-1);
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gp_obs = (P/P(-1))*m(-1)/dA;
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end;
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steady_state_model;
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dA = exp(gam);
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gst = 1/dA;
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m = mst;
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khst = ( (1-gst*bet*(1-del)) / (alp*gst^alp*bet) )^(1/(alp-1));
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xist = ( ((khst*gst)^alp - (1-gst*(1-del))*khst)/mst )^(-1);
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nust = psi*mst^2/( (1-alp)*(1-psi)*bet*gst^alp*khst^alp );
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n = xist/(nust+xist);
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P = xist + nust;
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k = khst*n;
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l = psi*mst*n/( (1-psi)*(1-n) );
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c = mst/P;
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d = l - mst + 1;
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y = k^alp*n^(1-alp)*gst^alp;
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R = mst/bet;
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W = l/n;
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ist = y-c;
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q = 1 - d;
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e = 1;
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gp_obs = m/dA;
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gy_obs = dA;
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end;
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shocks;
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var e_a; stderr 0.014;
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var e_m; stderr 0.005;
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end;
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steady;
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T = 10;
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ex=randn(T,M_.exo_nbr);
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% 2nd order
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stoch_simul(order=2, nograph, irf=0);
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% simult_.m: implements KKSS
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options_.pruning = true;
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Y2_simult = simult_(M_,options_,oo_.dr.ys,oo_.dr,ex,options_.order);
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% local_state_space_iteration_2 mex: implements KKSS
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constant = oo_.dr.ys(oo_.dr.order_var)+0.5*oo_.dr.ghs2;
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ss = oo_.dr.ys(oo_.dr.order_var);
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Y1_local = zeros(M_.endo_nbr,T+1);
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Y1_local(:,1) = oo_.dr.ys;
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Y2_local = zeros(M_.endo_nbr,T+1);
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Y2_local(:,1) = oo_.dr.ys;
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state_var = oo_.dr.order_var(M_.nstatic+1:M_.nstatic+M_.nspred);
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for t=2:T+1
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u = ex(t-1,:)';
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yhat1 = Y1_local(state_var,t-1)-oo_.dr.ys(state_var);
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yhat2 = Y2_local(state_var,t-1)-oo_.dr.ys(state_var);
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[Y2, Y1] = local_state_space_iteration_2(yhat2, u, oo_.dr.ghx, oo_.dr.ghu, constant, oo_.dr.ghxx, oo_.dr.ghuu, oo_.dr.ghxu, yhat1, ss, options_.threads.local_state_space_iteration_2);
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Y1_local(oo_.dr.order_var,t) = Y1;
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Y2_local(oo_.dr.order_var,t) = Y2;
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end
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if (max(abs(Y2_local(:) - Y2_simult(:)))>1e-12)
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error('2nd-order output of simult_ and local_state_space_iteration_2 output are inconsistent.')
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end
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% pruned_state_space_system.m: implements Andreasen et al.
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pss = pruned_state_space_system(M_, options_, oo_.dr, [], 0, false, false);
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Y2_an = zeros(M_.endo_nbr,T+1);
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Y2_an(:,1) = oo_.dr.ys;
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% z = [xf;xs;kron(xf,xf)]
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% inov = [u;kron(u,u)-E_uu(:);kron(xf,u)]
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z = zeros(2*M_.nspred+M_.nspred^2, 1);
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z(1:2*M_.nspred, 1) = repmat(Y2_an(state_var,1)-oo_.dr.ys(state_var), 2, 1);
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z(2*M_.nspred+1:end, 1) = kron(z(1:M_.nspred, 1), z(M_.nspred+1:2*M_.nspred, 1));
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inov = zeros(M_.exo_nbr+M_.exo_nbr^2+M_.nspred*M_.exo_nbr, 1);
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for t=2:T+1
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u = ex(t-1,:)';
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inov(1:M_.exo_nbr, 1) = u;
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inov(M_.exo_nbr+1:M_.exo_nbr+M_.exo_nbr^2, 1) = kron(u, u) - M_.Sigma_e(:);
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inov(M_.exo_nbr+M_.exo_nbr^2+1:end, 1) = kron(z(1:M_.nspred, 1), u);
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Y = oo_.dr.ys(oo_.dr.order_var) + pss.d + pss.C*z + pss.D*inov;
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x1 = z(1:M_.nspred,1);
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x2 = z(M_.nspred+1:2*M_.nspred,1);
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z = pss.c + pss.A*z + pss.B*inov;
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Y2_an(oo_.dr.order_var,t) = Y;
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end
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if (max(abs(Y2_an(:) - Y2_local(:)))>1e-12)
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error('2nd-order output of pruned_state_space_system and local_state_space_iteration_2 output are inconsistent.')
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end
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% 3rd order
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stoch_simul(order=3, nograph, irf=0);
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% simult_.m
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Y3_simult = simult_(M_,options_,oo_.dr.ys,oo_.dr,ex,options_.order);
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% pruned_state_space_system.m
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pss = pruned_state_space_system(M_, options_, oo_.dr, [], 0, false, false);
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Y3_an = zeros(M_.endo_nbr,T+1);
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Y3_an(:,1) = oo_.dr.ys;
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% z = [xf; xs; kron(xf,xf); xrd; kron(xf,xs); kron(kron(xf,xf),xf)]
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% inov = [u; kron(u,u)-E_uu(:); kron(xf,u); kron(xs,u); kron(kron(xf,xf),u); kron(kron(xf,u),u); kron(kron(u,u),u))]
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x_nbr = M_.nspred;
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u_nbr = M_.exo_nbr;
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z_nbr = x_nbr + x_nbr + x_nbr^2 + x_nbr + x_nbr^2 + x_nbr^3;
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inov_nbr = u_nbr + u_nbr^2 + x_nbr*u_nbr + x_nbr*u_nbr + x_nbr^2*u_nbr + x_nbr*u_nbr^2 + u_nbr^3;
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z = zeros(z_nbr, 1);
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inov = zeros(inov_nbr, 1);
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for t=2:T+1
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u = ex(t-1,:)';
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xf = z(1:M_.nspred,1);
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xs = z(M_.nspred+1:2*M_.nspred,1);
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inov(1:u_nbr, 1) = u;
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ub = u_nbr;
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inov(ub+1:ub+u_nbr^2, 1) = kron(u, u) - M_.Sigma_e(:);
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ub = ub+u_nbr^2;
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inov(ub+1:ub+x_nbr*u_nbr, 1) = kron(xf, u);
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ub = ub+x_nbr*u_nbr;
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inov(ub+1:ub+x_nbr*u_nbr, 1) = kron(xs, u);
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ub = ub+x_nbr*u_nbr;
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inov(ub+1:ub+x_nbr^2*u_nbr) = kron(kron(xf,xf),u);
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ub = ub+x_nbr^2*u_nbr;
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inov(ub+1:ub+x_nbr*u_nbr^2) = kron(kron(xf,u),u);
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ub = ub+x_nbr*u_nbr^2;
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inov(ub+1:end) = kron(kron(u,u),u);
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Y = oo_.dr.ys(oo_.dr.order_var) + pss.d + pss.C*z + pss.D*inov;
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z = pss.c + pss.A*z + pss.B*inov;
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Y3_an(oo_.dr.order_var,t) = Y;
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end
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if (max(abs(Y3_an(:) - Y3_simult(:)))>1e-12)
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error('3rd-order outputs of pruned_state_space_system and simult_ are inconsistent.')
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end
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% local_state_space_iteration_3 mex
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Y3_local = zeros(M_.endo_nbr,T+1);
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Y3_local(:,1) = oo_.dr.ys;
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Ylat_local = zeros(3*M_.endo_nbr,T+1);
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Ylat_local(:,1) = repmat(oo_.dr.ys,3,1);
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for t=2:T+1
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u = ex(t-1,:)';
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yhat1 = Ylat_local(state_var,t-1)-oo_.dr.ys(state_var);
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yhat2 = Ylat_local(M_.endo_nbr+state_var,t-1)-oo_.dr.ys(state_var);
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yhat3 = Ylat_local(2*M_.endo_nbr+state_var,t-1)-oo_.dr.ys(state_var);
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ylat = [yhat1;yhat2;yhat3];
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[Y3,Y] = local_state_space_iteration_3(ylat, u, oo_.dr.ghx, oo_.dr.ghu, oo_.dr.ghxx, oo_.dr.ghuu, oo_.dr.ghxu, oo_.dr.ghs2, oo_.dr.ghxxx, oo_.dr.ghuuu, oo_.dr.ghxxu, oo_.dr.ghxuu, oo_.dr.ghxss, oo_.dr.ghuss, ss, options_.threads.local_state_space_iteration_3, true);
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Ylat_local(oo_.dr.order_var,t) = Y(1:M_.endo_nbr);
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Ylat_local(M_.endo_nbr+oo_.dr.order_var,t) = Y(M_.endo_nbr+1:2*M_.endo_nbr);
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Ylat_local(2*M_.endo_nbr+oo_.dr.order_var,t) = Y(2*M_.endo_nbr+1:end);
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Y3_local(oo_.dr.order_var,t) = Y3;
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end
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Y3_local_1 = Ylat_local(1:M_.endo_nbr,:);
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Y3_local_2 = Y3_local_1 + Ylat_local(M_.endo_nbr+1:2*M_.endo_nbr,:) - oo_.dr.ys;
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if (max(abs(Y3_local_1(:) - Y1_local(:)))>1e-12)
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error('1st-order outputs of local_state_space_iteration_3 and local_state_space_iteration_2 are inconsistent.')
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end
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if (max(abs(Y3_local_2(:) - Y2_local(:)))>4e-12)
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error('2nd-order outputs of local_state_space_iteration_3 and local_state_space_iteration_2 are inconsistent.')
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end
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if (max(abs(Y3_local(:) - Y3_simult(:)))>1e-12)
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error('3rd-order output of simult_ and local_state_space_iteration_3 output are inconsistent.')
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end
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