OBC_RBC_sims_PF.m

%Extra Example (RBC model + investment constraint) in the Supplementary Appendix.
%This code plots the perfect foresight solution following a negative TFP
%shock. To study a different example, simply change the parameters and matrices
%Model structures are defined in the 'Insert' files
%Written by Michael Hatcher (m.c.hatcher@soton.ac.uk). Any errors are my own.

clc; clear; %close all;

T_guess = 20; % Final date before terminal solution (guess)
T_sim = 51; % Simulation length
T_news = 3;
N_guess = 50;  %No. of guesses 

%Guessed structure
rng(1)
ind_stack = randi([0 1],T_guess,N_guess);
ind_stack(:,1) = ones(T_guess,1); 
for i=2:T_guess
    ind_stack(:,i) = [zeros(i-1,1); ones(T_guess-(i-1),1)]; 
end
vec_1 = ones(T_sim-T_guess,1);
    
% Model and calibration
run Insert_RBC

%No. of variables
nvar = length(B1(:,1));
nx = 1;  %No. exog vars in x

% Find terminal solution (Cho and Moreno 2011, JEDC)
run Cho_and_Moreno

%Shocks
e(1) = -0.04; e(2:T_news) = 0; %Specified news shocks
e_vec = [e(1) e(2:T_news) zeros(1,T_sim+1-T_news)]; 
X_init = zeros(nvar,1);   %Initial values

mstar = zeros(N_guess,1);

Omeg_t = NaN(size(Omega_bar,1), size(Omega_bar,2), T_sim);
Gama_t = NaN(size(Gama_bar,1), size(Gama_bar,2), T_sim);
Psi_t = NaN(size(Psi_bar,1), size(Psi_bar,2), T_sim);

%Check if M is a P matrix
X_init = zeros(nvar,1);   %Initial values
run M_matrix
run P_matrix
    
run PF_insert

mstar(mstar==0) = [];

if isempty(mstar) 
    
    disp('No solution found. Check T_guess and N_guess are not too small.')
    
elseif ~isempty(mstar) 

X_sol_exc = X_sol_exc(:,:,mstar);    
solutions =  reshape(permute(X_sol_exc,[1,3,2]),[],size(X_sol_exc,2));
ind_solutions = ind_sol(mstar,:);
X_sol = X_sol(:,:,mstar);
X_exog = X_sol(nvar-nx+1:nvar,:,1);  

%Solution paths
x_fin = unique(solutions,'rows','stable');
x_fin = [x_fin; X_exog];
sol_ind = unique(ind_solutions,'rows','stable');
ind_fin = sol_ind(1,:); 

%No. of solutions
k = length(x_fin(:,1))/nvar;

     if k==1
        disp('Unique solution found')
    else
        disp('Multiple solutions found')
     end
    
end

T_plot = 51; %Time horizon in plot
T_sim2 = (T_sim<=T_plot)*T_sim + (T_sim>T_plot)*T_plot; 
Time = 1:T_sim2-1;  %Counter for time

%figure(1)
subplot(1,3,1), plot(Time,100*x_fin(1,1:T_sim2-1),'k'),  xlabel('Time'), title('Investment'), hold on,
subplot(1,3,2), plot(Time,x_fin(2,1:T_sim2-1),'k'),  xlabel('Time'), title('Capital'), hold on, 
subplot(1,3,3), plot(Time,x_fin(3,1:T_sim2-1),'k'),  xlabel('Time'), title('Consumption'), hold on,