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OBC_Example_2_stoch_sims.m
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OBC_Example_2_stoch_sims.m
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%Example 2 in the paper -- `stochastic sims' using the algorithm. Model based on Example 2 in Holden (2023).
%Case of stochastic simulation as in Example 2 of the paper (Hatcher, 2024)
%To study a different example, simply change the parameters, matrices and nx
%Model matrices are defined in the 'Insert' files
%Written by Michael Hatcher ([email protected]). Any errors are my own.
clc; clear; %close all;
T_guess = 8; % Final date before terminal solution (guess)
T_guess = max(T_guess,3);
T_sim = T_guess + 17; % Simulation length
nat_num = 50; %Integer >=1
N_guess = nat_num*T_guess; %No. of guesses
T_sim = max(T_sim,T_guess + 30);
vec_1 = ones(T_sim-T_guess,1); %Vec of ones
% Model and calibration
run Insert_Example_2
%No. of variables
nvar = length(B1(:,1)); %No. vars in x
nx = 0; %No. exogenous vars in x
%For plots
Time = 1:20; T_plot = 20;
N_sims = 5; %No. of simulations
%Prior prob. of each solution
prob(1) = 0.95; prob(2) = 1 - prob(1);
%Housekeeping
X_sol = NaN(nvar,T_sim-1,N_guess); kstar_stack = NaN(N_sims,T_sim-1);
x_t1 = NaN(nvar,T_sim); ind_t1 = NaN(1,T_sim); X_stack = NaN(nvar,T_sim-1);
no_solutions = NaN(1,T_sim-1); no_uniq_solutions = no_solutions;
excess_solutions = no_solutions; ind_sol = NaN(N_guess,T_sim-1);
%Model and calibration
run Insert_Example_2
%Find terminal solution
run Cho_and_Moreno
%Initial values and matrices
X_init = [0; pi_0];
e(1) = -0.001; e(2) = -0.001; %A in periods 1 and 2
e_vec = [e(1) e(2) zeros(1,T_sim-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
not_P = NaN;
run M_matrix
run P_matrix
%Guessed structure
rng(1), ind_stack = randi([0 1],T_guess,N_guess); %Initialize with random guesses
run Guesses_master
%run Guesses_master_2
%-----------------------------
%Loop for random simulations
%-----------------------------
for i=1:N_sims
rng(19+i) %rng(19+i)
for t1=1:T_sim-1
mstar = zeros(N_guess,1);
if t1==1
X_init = [0; pi_0];
e(1) = -0.001; e(2) = -0.001; %Shock in period 1
e_vec = [e(1) e(2) zeros(1,T_sim-1)];
elseif t1>1
X_init = x_t1(:,t1-1);
e(1) = sigma_e*randn; e(2) = sigma_e*randn; %Shock in period 1
e_vec = [e(1) e(2) zeros(1,T_sim-1)];
end
run PF_insert.m
mstar(mstar==0) = [];
if isempty(mstar)
disp('No solution found. Check T_guess and N_guess are not too small.')
end
X_sol = X_sol(:,:,mstar);
solutions = reshape(permute(X_sol,[1,3,2]),[],size(X_sol,2));
ind_solutions = ind_sol(mstar,:);
x_fin = unique(solutions,'rows','stable');
sol_ind = unique(ind_solutions,'rows','stable');
%No. of solutions
k = length(x_fin(:,1,1))/nvar;
if k == 1
kstar = 1;
x_t1(:,t1) = x_fin(1:nvar,t1);
ind_t1(1,t1) = sol_ind(1,t1);
else
run Select_solution.m %Resolve indeterminacy
end
kstar_stack(i,t1) = kstar;
x_t1(:,t1) = x_fin((kstar-1)*nvar+1:kstar*nvar,1);
ind_t1(1,t1) = sol_ind(kstar,1);
no_solutions(t1) = length(mstar);
no_uniq_solutions(t1) = k;
end
subplot(2,2,1), plot([0 Time],[pi_0 x_t1(2,1:T_plot)],'k'), xlabel('Time'), title('Inflation \pi'), hold on,
subplot(2,2,2), plot(Time,x_t1(1,1:T_plot),'k'), xlabel('Time'), title('Nominal interest rate \it{i}'), hold on
end
run Print.m