options crt;  ? 9e3
in klem;
freq a;
smpl 47,71;
dot k l e m;
  a. = q./qy;
  pp = p.;
  dot k l e m;
    r.. = sqrt(pp/p.);  ? note:  rkk = 1, rll = 1, etc.
  enddot;
  frml eq. a. = dk.*rk. + dl.*rl. + de.*re. + dm.*rm. ;
  param dk. dl. de. dm.;
enddot;
dot k l e m;
  lsq eq.;  ? (a.1)
enddot;
lsq eqk eql eqe eqm;  ? (a.2) - IZEF

tc = 0;
ly = log(qy);
dot k l e m;
  v. = p.*q.;
  tc = tc + v.;
  lp. = log(p.);
  frml es. s. = alpha. + g.k*lpk + g.l*lpl + g.e*lpe + g.m*lpm + g.y*ly;
  param alpha. g.k g.l g.e g.m g.y;
enddot;
dot(index=i) k l e m;
  s. = v./tc;
  if (i<4); then; lsq es.;  ? (b.1)
enddot;
sur esk esl ese;  ? (b.2) - ZEF
lsq esk esl ese;  ? (b.2) - IZEF
? Now adjust the standard errors for degrees of freedom, to show that
? they will then equal those from OLS.
title 'IZEF SEs adjusted for DF equal those from OLS';
mat vcov = @vcov*(@nob/(@nob-6));
tstats(names=@rnms) @coef vcov;