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OBC_App_1_sims_PF_LOOP.m
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OBC_App_1_sims_PF_LOOP.m
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%Example 1' from the OBC paper (Asset Pricing Model, Supp Appendix)
%To study a different example, simply change the parameters and matrices
%Model structures are defined in the 'Insert' files
%Written by Michael Hatcher ([email protected]). Any errors are my own.
clc; clear; %close all;
T_guess = 6; % Final date before terminal solution (guess)
T_sim = T_guess + 5; % Simulation length
N_guess = 30; %No. of guesses
T_news = 5;
N_policy = 60; %No. of points for policy function
%Housekeeping
no_solutions = NaN(1,T_sim-1); ind_sol = NaN(N_guess,T_sim-1);
Time = 1:T_sim-1; r_plot = NaN(N_policy,1); q_plot = r_plot;
% Model and calibration
run Insert_App_1
%No. of variables
nvar = length(B1(:,1));
nx = 1; % %No. exogenous variables in x
% Find terminal solution (Cho and Moreno 2011, JEDC)
run Cho_and_Moreno
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);
%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+1
ind_stack(:,i) = [zeros(i-1,1); ones(T_guess-(i-1),1)];
end
vec_1 = ones(T_sim-T_guess,1);
%Shocks
e(2:T_news) = 0; %Specified news shocks
e1_stack = linspace(-0.2,0.2,N_policy);
for j=1:length(e1_stack)
e(1) = e1_stack(j);
e_vec = [e(1) e(2:T_news) zeros(1,T_sim+1-T_news)]; X_init = zeros(nvar,1); %Initial values
x_fin = NaN(nvar,T_sim-1);
mstar = zeros(N_guess,1);
run PF_insert.m
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
no_solutions(j) = k;
r_plot(j) = 100*(x_fin(1,1)-X1_min);
q_plot(j) = 100*x_fin(2,1);
end
figure(1)
subplot(2,1,1), plot(e1_stack,r_plot,'k'), ylabel('Percent'), title('Policy function for Interest Rate - Level'), hold on,
axis([-inf inf -inf inf])
subplot(2,1,2), plot(e1_stack,q_plot,'k'), ylabel('Percent'), title('Policy function for Asset Price - Percent Dev. from Steady State'), hold on,
axis([-inf inf -inf inf]), xlabel('Shock size')