clear all;
close all;
% Define the structural parameters of the model,
% i.e. policy invariant preference and technology parameters
% alpha : capital's share of output
% beta : time discount factor
% delta : depreciation rate 折旧率
% sigma : risk-aversion parameter, also intertemp. subst. param.
% gamma : unconditional expectation of the technology parameter
alpha = .35;
beta = .98;
delta = .025;
sigma = 2;
zbar = 5;
% Find the steady-state level of capital as a function of
% the structural parameters 稳态水平作为结构参数的函数
kstar = ((1/beta - 1 + delta)/(alpha*zbar))^(1/(alpha-1));
% Define the number of discrete values k can take
gk = 101;
k = linspace(0.95*kstar,1.05*kstar,gk);
% Compute a (gk x gk) dimensional consumption matrix c
% for all the (gk x gk) values of k_t, k_t+1
for h = 1 : gk
for i = 1 : gk
c(h,i) = zbar*k(h)^alpha + (1-delta)*k(h) - k(i);
if c(h,i) < 0
c(h,i) = 0;
end
% h is the counter for the endogenous state variable k_t
% i is the counter for the control variable k_t+1
end
end
% Compute a (gk x gk) dimensional consumption matrix u
% for all the (gk x gk) values of k_t, k_t+1
for h = 1 : gk
for i = 1 : gk
if sigma == 1
u(h,i) = log(c(h,i));
else
u(h,i) = (c(h,i)^(1-sigma) - 1)/(1-sigma);
end
% h is the counter for the endogenous state variable k_t
% i is the counter for the control variable k_t+1
end
end
% Define the initial matrix v as a matrix of zeros (could be anything)
v = zeros(gk,1);
% Set parameters for the loop
convcrit = 1E-9; % chosen convergence criterion
diff = 1; % arbitrary initial value greater than convcrit
iter = 0; % iterations counter
while diff > convcrit
% for each k_t
% find the k_t+1 that maximizes the sum of instantenous utility and
% discounted continuation utility
for h = 1 : gk
Tv(h,1) = max( u(h,:) + beta*v');
end
iter = iter + 1;
diff = norm(Tv - v);
v = Tv;
end
disp(iter)
% Find what gridpoint of the k_t+1 vector which gave the optimal value
for h = 1 : gk
[Tv,gridpoint] = max(u(h,:) + beta*v');
kgridrule(h) = gridpoint;
end
% Find what element of k_t+1 which gave the optimal value
kdecrule = k(kgridrule);
figure
plot(k,kdecrule,k,k);
xlabel('k_t')
ylabel('k_{t+1}')
print -djpeg kdecrule.jpg
% Compute the optimal decision rule for c as a function of the state
% variable
for h = 1 : gk
cdecrule(h) = zbar*k(h)^alpha + (1-delta)*k(h) - kdecrule(h);
end
figure
plot(k,cdecrule)
xlabel('k_t')
ylabel('c_t')
print -djpeg cdecrule.jpg
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