/* -------------------------------------------------------------------------- */
/*                               proc makeik

Usage:  ik = makeik(delta,i);

Inputs:
        delta = depreciation rate (e.g., .01); may be a column vector
        i = investment series in levels; may be a time-series matrix.
Ouput:
        ik = investment/capital ratio, conformable to i.
Note:
        Accumulation is
            k(t+1) = (1-delta)(k(t) + i(t))
        Starts with ik[1] = E(i(t+1)/i(t)) / (1-delta) -1. This is the steady
        state with constant investment growth at its mean

                                                                             */
/* ------------------------------------------------------------------------- */

proc(1) = makeik(delta,i);
    local ik,j,T;
    T = rows(i);
    ik = zeros(rows(i),cols(i));
    ik[1,.] = meanc(i[2:T,.] ./ i[1:T-1,.])' ./ (1-delta') - 1 ;
    j = 2;
    do while j <= T;
        ik[j,.] = i[j,.]./i[j-1,.] .*
                        ik[j-1,.] ./ ( (1-delta') .* (1+ik[j-1,.]) );
        j = j+1;
    endo;
    retp(ik);
endp;