fminbnd error while solving the neoclassical growth model

I am using fminbnd to solve the neoclassical growth model and I have the following code for main.m

clear all;
close all;
tic
global v0 beta delta alpha kmat k0 s

%set up the fixed paramters
alpha = 0.33; %capital share
beta = 0.95;%discount rate
delta = 0.1; %rate of depreciation of capital
s = 2;


tol = 0.01;%tolerance
maxits = 1000;%maximum iteration
dif = tol + 100;
its = 0;

kstar = (alpha/(1/beta-(1-delta)))^(1/(1-alpha));
cstar = kstar^(alpha)-delta*kstar;
istar = delta * kstar;
ystar = kstar ^ alpha;

kmin = 0.25*kstar;
kmax = 1.75*kstar;
kgrid = 99;
grid = (kmax - kmin)/kgrid;
kmat = kmin:grid:kmax;
kmat = kmat';
[N,n] = size(kmat);

polfun = zeros(kgrid+1,3);

while dif>tol && its < maxits
    for i = 1:N
        k0 = kmat(i,1);
        k1 = fminbnd(@valfun,kmin,kmax);%continuous choice set, so it will search over all values 
        %of k1 between kmin and kmax. For this reason, we need to
        %interpolate values of the value function off of the grid
        v1(i,1) = -valfun(k1);
        k11(i,1) = k1;
    end
    dif = norm(v1-v0);
    v0=v1;
    its = its + 1;
end
for i = 1:N
    con(i,1) = kmat(i,1)^alpha - k11(i,1) + (1-delta)*kmat(i,1);
    polfun(i,1) = kmat(i,1)^(alpha) - k11(i,1) + (1-delta)*kmat(i,1);
end
toc

The value function valfun.m is as follows:

function val=valfun(k)

% This program gets the value function for a neoclassical growth model with
% no uncertainty and CRRA utility

global v0 beta delta alpha kmat k0 s

g = interp1(kmat,v0,k,'linear'); % smooths out previous value function

c = k0^alpha - k + (1 - delta)*k0; % consumption
if c<=0
    val = - 888888888888888888 - 800*abs(c); % keeps it from going negative
else
    val=(1/(1 - s))*(c^(1-s)-1) + beta*g;
end
val = -val; 

When I run, I keep getting the following error:

Error using interp1>reshapeAndSortXandV (line 447)
LENGTH(X) and SIZE(V,1) must be the same.

Error in interp1 (line 128)
[X,V,orig_size_v] = reshapeAndSortXandV(X,V);

Error in valfun (line 8)
g = interp1(kmat,v0,k,'linear'); % smooths out previous value function

Error in fminbnd (line 232)
x= xf; fx = funfcn(x,varargin{:});

Error in main (line 38)
k1 = fminbnd(@valfun,kmin,kmax);%continuous choice set, so it will search over all values

I am not sure what I am doing wrong. I think I followed all the steps to set up fminbnd as in the online help.

Thanks

[Torsten]

kmat and v0 must be of the same size in order to use interp1.

Answer 1

[Akshat Dalal]

Hello Prerna,

I understand you are facing some issue in using the “fminbnd“ function while solving the neoclassical growth model.

I believe the error is occurring when the “fminbnd” function is invoked for the first time, i.e., during the first iteration of the while and for loops.

In MATLAB, all global variables are initialized as empty 0x0 matrices. During the first call of the “fminbnd” function, the value of the global variable “v0” has not been changed from its default initialized value. Consequently, when the "valfun" value function is called, the inputs "kmat" and "v0" provided to the "interp1" function have different sizes, resulting in an error.