/* ERGODIC.G: procedure to compute the invariant distribution of
	      an ergodic markov chain.

	      John Rust, Yale University, May, 2001. 
	      
    Input: 

    an (n x n) Markov transition probability matrix p (each row must be
               positive and sum to 1)

    Output:

    an (n x 1) vector representing the invariant distribution of the
               Markov process, if it exists and is unique. If it does
	       not exist or is not unique, the procedure returns a
	       missing value code */


    proc ergodic(p);

      local n,ap,y;

      n=rows(p);

      ap=eye(n)-p';

      ap=ap|ones(1,n);

      ap=ap~ones(n+1,1);

      if (rank(ap) < n+1);

	 "Error: transition matrix P is not ergodic";
	 retp(miss(0,0));

      endif;

      y=ones(n,1)|2;

      y=inv(ap)*y;

      retp(y[1:n]);

    endp;