% VERSION 2.0, MARCH 1997, COPYRIGHT H. UHLIG.
% EXAMPL1.M calculates through Hansens benchmark real business
% cycle model in H. Uhlig, "A toolkit for solving nonlinear dynamic stochastic models easily".
% First, parameters are set and the steady state is calculated. Next, the matrices are
% declared.  In the last line, the model is solved and analyzed by calling DO_IT.M

% Copyright: H. Uhlig.  Feel free to copy, modify and use at your own risk.
% However, you are not allowed to sell this software or otherwise impinge
% on its free distribution.

disp('EXAMPLE 1: Hansen benchmark real business cycle model,');
disp('           see Hansen, G., "Indivisible Labor and the Business Cycle,"');
disp('           Journal of Monetary Economics, 16 (1985), 281-308.');

disp('Hit any key when ready...');
pause;

% Setting parameters:

N_bar     = 1.0/3;  % Steady state employment is a third of total time endowment
Z_bar     = 1; % Normalization
rho       = .36; % Capital share
delta     = .025; % Depreciation rate for capital
R_bar     = 1.01; % One percent real interest per quarter
eta       = 1.0; % constant of relative risk aversion = 1/(coeff. of intertemporal substitution)
psi       = .95; % autocorrelation of technology shock
sigma_eps = .712; % Standard deviation of technology shock.  Units: Percent.

% Calculating the steady state:

betta   = 1.0/R_bar;  % Discount factor beta
YK_bar  = (R_bar + delta - 1)/rho;  % = Y_bar / K_bar
K_bar   = (YK_bar / Z_bar)^(1.0/(rho-1)) * N_bar;
I_bar   = delta * K_bar;
Y_bar   = YK_bar * K_bar;
C_bar   = Y_bar - delta*K_bar;
A       =  C_bar^(-eta) * (1 - rho) * Y_bar/N_bar; % Parameter in utility function

% Declaring the matrices. 


VARNAMES = ['capital    ',
            'consumption',
            'output     ',
            'labor      ',
            'interest   ',
            'investment ',
            'technology '];

% Translating into coefficient matrices.  
% The equations are, conveniently ordered:
% 1) 0 = - I i(t) - C c(t) + Y y(t)
% 2) 0 = I i(t) - K k(t) + (1-delta) K k(t-1)
% 3) 0 = rho k(t-1) - y(t) + (1-rho) n(t) + z(t)
% 4) 0 = -eta c(t) + y(t) - n(t)
% 5) 0 = - rho Y/K k(t-1) + rho Y/K y(t) - R r(t)
% 6) 0 = E_t [ - eta c(t+1) + r(t+1) + eta c(t) ]
% 7) z(t+1) = psi z(t) + epsilon(t+1)
% CHECK: 7 equations, 7 variables.
%
% Endogenous state variables "x(t)": k(t)
% Endogenous other variables "y(t)": c(t), y(t), n(t), r(t), i(t)
% Exogenous state variables  "z(t)": z(t).
% Switch to that notation.  Find matrices for format
% 0 = AA x(t) + BB x(t-1) + CC y(t) + DD z(t)
% 0 = E_t [ FF x(t+1) + GG x(t) + HH x(t-1) + JJ y(t+1) + KK y(t) + LL z(t+1) + MM z(t)]
% z(t+1) = NN z(t) + epsilon(t+1) with E_t [ epsilon(t+1) ] = 0,

% for k(t):
AA = [ 0
       - K_bar
       0
       0
       0 ];

% for k(t-1):
BB = [ 0
       (1-delta)*K_bar
       rho
       0
       - rho * YK_bar ];

%Order:   consumption  output      labor     interest  investment
CC = [    -C_bar,      Y_bar,      0,        0,        -I_bar % Equ. 1)
          0,           0,          0,        0,        I_bar  % Equ. 2)
          0,           -1,         1-rho,    0,        0      % Equ. 3)      
          -eta,        1,          -1,       0,        0      % Equ. 4)
          0,           rho*YK_bar, 0,        - R_bar,  0 ];   % Equ. 5)

DD = [ 0
       0
       1
       0
       0 ];

FF = [ 0 ];

GG = [ 0 ];

HH = [ 0 ];

JJ = [ -eta,  0,  0,  1,  0];

KK = [ eta,   0,  0,  0,  0];

LL = [ 0 ];

MM = [ 0 ];

NN = [psi];

Sigma = [ sigma_eps^2  ];

% Setting the options:

[l_equ,m_states] = size(AA);
[l_equ,n_endog ] = size(CC);
[l_equ,k_exog  ] = size(DD);

  
PERIOD     = 4;  % number of periods per year, i.e. 12 for monthly, 4 for quarterly
GNP_INDEX  = 3; % Index of output among the variables selected for HP filter
IMP_SELECT = [1:5,7];
   %  a vector containing the indices of the variables to be plotted
DO_SIMUL   = 1; % Calculates simulations
SIM_LENGTH = 150;
DO_MOMENTS = 1; % Calculates moments based on frequency-domain methods
HP_SELECT  = 1:(m_states+n_endog+k_exog); % Selecting the variables for the HP Filter calcs.



% Starting the calculations:

do_it;


 
       

