Quantile regression and linprog

I'm trying to implement the linear program at page 2 of this link http://faculty.arts.ubc.ca/pschrimpf/628/hw5-quantile.pdf . I can't seem to get it to work though. As far as I have understood the estimate should be retrievable as the last element of the solution, but this is very small (<10e-10) and it should be 1.0675 according to another quantile regression algorithm (basically the true parameter is set to 1). Any thoughts?

   % set seed
   rng(1);
   % set parameters
   n=30;
   tau=0.5;
   % create regressor and regressand
   x=rand(n,1);
   y=x+rand(n,1)/10;
   % number of regressors (1)
   m=size(x,2);
   % vektors and matrices for linprog
   f=[tau*ones(n,1);(1-tau)*ones(n,1);zeros(m,1)]; 

   A=[eye(n),-eye(n),x;
     -eye(n),eye(n),-x;
     -eye(n),zeros(n),zeros(n,m);
     zeros(n),-eye(n),zeros(n,m)];
   b=[y;
     y
     zeros(n,1);
     zeros(n,1)];
   % get solution bhat=[u,v,beta] and exitflag (1=succes)
   [bhat,~,exflag]=linprog(f',A,b);

Answer 1

[Gittetier]

Hello Patrick, probably this no longer of any interest to you. But I think there is a mistake in the proposition you cite. When you split up the equality condition into two inequalities one of the Y should turn negative. So there is a mistake in your matrix b. In front of the second Y there should be a minus sign. Best Gittetier

[Patrick]

Hello Gittetier, well you are quite right. I had actually forgotten this question. I solved it not long after, but had already forgotten about this.

I have the corrected code on my computer at home, and should probably post the corrections. Thanks for reminding me. Patrick