Why does it take a long time to run the program?

clear

diary jova.out

disp('Jovanovic model');

disp('');

%

%  set parameter values

%

A = 0.2;                       % production technology of human capital

fprob = 0.1*ones(10,1);        % uniform distribution of new job offers 

alpha = 60/100;                % production parameter

delta = 0.2;                   % depreciation rate in usual sense 

beta = 0.95;                   % discount rate 

%

%  form grid for human capital

%   

maxcap = 1;                    % maximum value of human capital   

mincap = 0.1;                  % minimum value of human capital

incap = 0.1;                   % size of grid increments

ncap= round(1/0.1);           % number of grid points

cap = linspace(mincap,maxcap,ncap);            % capital grids

%  form grid for search effort

maxs = 1;                    % maximum value of search effort   

mins = 0;                    % minimum value of search effort

ins = 0.1;                   % size of grid increments

ns = round(maxs/ins)+1;      % number of grid points

s = linspace(mins,maxs,ns);              % search effort grids

% the state variable is current human capital level

% the control variable is next period human capital level and search effort

     %  initialize some variables

     %

     v       = zeros(ncap,1);

     decis   = zeros(1,ncap);

     test1    = 10;

     test2    = 10;

     %  iterate on Bellman's equation and get the decision 

     %  rules and the value function at the optimum         

     while (test1 ~= 0) || (test2 > 0.1);

     %  tabulate the value function such that for phi + s > 1 or 

     %  phi > 1, value of the problem remains a large negative number 

     %  so that such values will never be chosen as value maximizing      

     %

     w = repmat(-1,[10 11 10]);

     %  the ith row of w denotes the next period capital level, the

     %  jth colume denots search effort, and the kth page denotes

     %  current human capital level. W is the value given above choices

     for k=ncap:-1:1

           for i=ncap:-1:1  

                for j=ns:-1:1

                   phi(i,k) = 1/cap(k)*((cap(i)-(1-delta)*cap(k))/A)^(1/alpha);% investment effort

                   Q(i) = max(v',v(i))*fprob;  % optimal value when having another offer

               if  0 <= phi(i,k) <= 1 && phi(i,k)+ s(j) <= 1 %&...

                     %cap(i)-(1-delta)*cap(k) > 0;  

                  % the last condition rules out the case of complex phi

                     w(i,j,k) = cap(k)*(1-phi(i,k)-s(j))+beta*(1-s(j)^0.5)*v(i)+beta*s(j)^0.5*Q(i);

                  end;

                end;

           end;

     end;

        vstack = reshape(w,[ncap*ns ncap]);

        [tvstack,tdecis] = max(vstack);

        tv = tvstack';    

        test1=max(any(tdecis-decis));

        test2=max(max(abs(tv - v)));

        v=tv;

        decis=tdecis;

     end;

     % note that the following recovering formula is specific for the case

     % ncap = 10, approximate changes should be made when otherwise

     sdecis = fix((decis-1)./10).*0.1;  % recover search effort form decis

     capdecis = (decis - fix((decis-1)/10)*10).*0.1; % recover future capital

     phidecis = ((capdecis' - (1-delta)*cap)./A).^(1/alpha)./cap; % recover optimal phi

     disp('value function and optimal decision rule')

     disp(' ')

     disp('     value     x_t+1      phi       s')

     disp('------------------------------------------')

     disp([v,capdecis',phidecis,sdecis'])    % ith row corresponds to current state

plot(cap,v,'r*',cap,capdecis','mo',cap,sdecis','bx',cap,phidecis,'r+')   

title('Graph of Jovanovic model, alpha = 60/100')

xlabel('current human capital')

ylabel('optimal phi +,optimal future capital o,optimal search effort x,value *')

grid on

diary off

[Rik]

Have a read here and here. It will greatly improve your chances of getting an answer.

[OCDER]

To figure out the slow part, make this script a function instead

 function testFunc
    ... %your code here
 end

and then run the profiler to figure out why it's slow https://www.mathworks.com/help/matlab/ref/profile.html

 profile on
 testFunc
 profile viewer

Then tell us what is taking the most time. It'll do an analysis of execution time per line of code. Vectorization & preallocation of variables are usually solutions to speeding up codes.