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OBC_App_2_sims_PF_FG.m
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OBC_App_2_sims_PF_FG.m
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%Policy application from the OBC paper (NK model), find perfect forsight paths.
%Case of forward guidance modelled via `news shocks'
%To study a different example, simply change 'Insert' files 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 = 20; % Final date before terminal solution (guess)
T_guess = max(T_guess,3);
T_sim = T_guess + 10; % Simulation length
T_news = 6; %Set at 1 for no FG
nat_num = 350; %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
%Shocks
zero = zeros(2,T_sim+1);
% Model and calibration
%run Insert_App_2
run Insert_App_2_FG
%run Insert_App_2_PLT
%No. of variables
nvar = length(B1(:,1));
nx = 0; %No. exogenous variables in x
% Find terminal solution
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); %Initialize with random guesses
%run Guesses_master
run Guesses_master_2
%Shocks
e = zero(1,:); e_FG = zero(1,:);
e(1) = 0.01; %Specified news shocks
e_FG(1) = 0; e_FG(1,2:T_news) = - 0.01 - 0.005; %Forward guidance shocks
e_vec = [e(1:T_news) zeros(1,T_sim+1-T_news); e_FG(1:T_news) zeros(1,T_sim+1-T_news)];
%Check if M is a P matrix
X_init = zeros(nvar,1); %Initial values
not_P = NaN;
run M_matrix
run P_matrix
run PF_insert.m
run Solutions_insert_App_2.m
run Print.m
%Plot simulated series
T_plot = 21; %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)
for j=1:k
if j==1
subplot(2,3,1), plot(Time,x_fin(4+nvar*(j-1),1:T_sim2-1),'k','LineWidth',1), xlabel('Time'), title('Inflation'), xlim([1 inf]), hold on
subplot(2,3,2), plot(Time,x_fin(3+nvar*(j-1),1:T_sim2-1),'k','LineWidth',1), xlabel('Time'), title('Output gap'), xlim([1 inf]), hold on
subplot(2,3,3), plot(Time,100*(x_fin(1+nvar*(j-1),1:T_sim2-1)-X1_min),'k','LineWidth',1), xlabel('Time'), title('Interest rate (%)'), xlim([1 inf]), hold on,
else
subplot(2,3,4), plot(Time,x_fin(4+nvar*(j-1),1:T_sim2-1),'k','LineWidth',1), xlabel('Time'), title('Inflation'), xlim([1 inf]), hold on
subplot(2,3,5), plot(Time,x_fin(3+nvar*(j-1),1:T_sim2-1),'k','LineWidth',1), xlabel('Time'), title('Output gap'), xlim([1 inf]), hold on
subplot(2,3,6), plot(Time,100*(x_fin(1+nvar*(j-1),1:T_sim2-1)-X1_min),'k','LineWidth',1), xlabel('Time'), title('Interest rate (%)'), xlim([1 inf]), hold on,
end
end
ylim([-inf inf])