| clear,clc
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| addpath('files');
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| load('model')
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| n_e=1;
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| [n_nodes,nodes,weights] = Monomials_2(n_e,eye(n_e));
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| nodes=nodes'; % transpose to n_e-by-n_nodes
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| %--------------------------------------------
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| % parameter values (for the fixed parameters)
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| %--------------------------------------------
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| GAMMA=2; ALPHA=.3; RHO=.8; SIGMA=.02;
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| params=eval(symparams);
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| %--------------------------------------------------------------------
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| % Start with a perturbation solution for the case of fixed parameters
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| %--------------------------------------------------------------------
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| BETA=.96; DELTA=.1;
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| % Steady state values
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| kss=((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
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| zss=0;
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| css=kss^ALPHA-DELTA*kss;
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| nxss=[kss;zss];
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| nyss=css;
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| pert_order=model.order(2);
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| M=get_moments(nodes,weights,pert_order);
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| % Get a perturbation solution for the case of fixed parameters. You need to
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| % provide the fixed value of the ms parameters (the variable chi_fixed)
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| chi_fixed=eval(chi);
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| [derivs,stoch_pert,nonstoch_pert,model]=get_pert(model,params,M,nxss,nyss,chi_fixed);
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| %---------------------------------------
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| % Proceed to Markov-switching parameters
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| %---------------------------------------
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| % The values of the parameters in each regime (there are 2 regimes)
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| msparams=[BETA-.02,BETA+.02;% BETA varies across regimes
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| DELTA-.05,DELTA+.05]; % DELTA varies across regimes
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| transition=[.9,.1;
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| .8,.2];
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| initial_guess=stoch_pert; % the initial guess has n_regimes columns (one for each regime).
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| x0=nxss; % evaluate the system at the steady state
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| c0=nxss; % the center of the initial guess is the steady state.
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| tolX=1e-6;
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| tolF=1e-6;
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| maxiter=10;
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| [coeffs,model]=tpsolve(initial_guess,x0,model,params,msparams,transition,c0,nodes,weights,tolX,tolF,maxiter);
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| % compute the model residuals
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| [R_funMS,g_funMS,Phi_funMS,aux_funMS]=residual(coeffs,x0,params,msparams,transition,c0,nodes,weights);
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| % R_funMS is a n_y-by-n_regimes matrix of the model residuals.
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| % g_funMS is a n_y-by-n_regimes matrix of the endogenous control variables for each current regime.
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| % Phi_funMS is a n_x-by-n_nodes-by-n_regimes-by-n_regimes array of next period state variables for each future node and current and future regimes.
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| % aux_funMS is a similar array of the auxiliary functions (for each future
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| % node and current/future regimes)
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| % To compute the model residuals only for a specific regime, add the
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| % required regime as the last argument
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| specific_regime=1;
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| [R_specific,g_specific,Phi_specific,auxvars_specific]=residual(coeffs,x0,params,msparams,transition,c0,nodes,weights,specific_regime);
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| % Compute the function g given the state x0 and the regime specific_regime
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| g_fun=evalg(x0,specific_regime,coeffs,c0);
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| % Compute the function Phi given the state x0, the control y0, the current
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| % and future regimes and the future shock epsp
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| y0=g_fun;
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| current_regime=1;
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| future_regime=2;
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| epsp=0;
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| Phi_fun=evalPhi(x0,y0,epsp,future_regime,current_regime,params,msparams);
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| %---------------------------------
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| % simulate the model for T periods
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| %---------------------------------
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| T=10000;
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| shocks=randn(1,T+1);
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| rshock=rand(1,T+1); % to determine the regime
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| x_simul=zeros(model.n_x,T+1);
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| regime_simul=zeros(1,T+1);
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| y_simul=zeros(model.n_y,T);
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| R_simul=zeros(model.n_y,T);
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| coeffs=reshape(coeffs,[],model.n_regimes);
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| x_simul(:,1)=x0;
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| regime_simul(1)=1;
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| % option=1; % compute only simulated variables
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| option=2; % compute model residuals
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| for t=1:T
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| xt=x_simul(:,t); % current state
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| regimet=regime_simul(t); % current regime
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| epsp=shocks(t+1); % future shock
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| % future regime
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| regimet_next=1+model.n_regimes-sum(double(logical((rshock(t+1)-cumsum(transition(regimet,:)))<0)));
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| % Option 1 - compute only the simulated variables
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| if option==1
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| yt=evalg(xt,regimet,coeffs,c0);
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| y_simul(:,t)=yt;
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| x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
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| regime_simul(t+1)=regimet_next;
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| else
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| % Option 2 - compute also model residuals
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| [Rt,yt]=residual(coeffs,xt,params,msparams,transition,c0,nodes,weights,regimet);
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| y_simul(:,t)=yt;
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| x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
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| regime_simul(t+1)=regimet_next;
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| R_simul(:,t)=Rt;
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| end
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| end
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| % Note that the simulated capital level is considerably different than the
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| % initial approximation point that we used. To improve accuracy, we can solve the
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| % model at the mean of the ergodic distribution.
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| meank=mean(x_simul(1,:));
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| ergodic_x0=[meank;0]; % solve at the mean of the ergodic distribution
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| [coeffs,model]=tpsolve(coeffs,ergodic_x0,model,params,msparams,transition,c0,nodes,weights,tolX,tolF,maxiter);
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| % simulate again and store residuals in R_simul2
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| x_simul(:,1)=ergodic_x0;
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| regime_simul(1)=1;
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| R_simul2=R_simul;
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| for t=1:T
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| xt=x_simul(:,t);
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| regimet=regime_simul(t);
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| epsp=shocks(t+1);
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| % future regime
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| regimet_next=1+model.n_regimes-sum(double(logical((rshock(t+1)-cumsum(transition(regimet,:)))<0)));
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| % Option 1 - compute only the simulated variables
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| if option==1
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| yt=evalg(xt,regimet,coeffs,c0);
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| y_simul(:,t)=yt;
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| x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
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| regime_simul(t+1)=regimet_next;
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| else
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| % Option 2 - compute also model residuals
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| [Rt,yt]=residual(coeffs,xt,params,msparams,transition,c0,nodes,weights,regimet);
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| y_simul(:,t)=yt;
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| x_simul(:,t+1)=evalPhi(xt,yt,epsp,regimet_next,regimet,params,msparams);
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| regime_simul(t+1)=regimet_next;
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| R_simul2(:,t)=Rt;
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| end
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| end
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| % compare mean errors for the two simulations
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| mean(abs(R_simul))
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| mean(abs(R_simul2))
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| % the second simulation is more accurate |
