*
* Example 17.7 from page 505
*
open data tablef9-2[1].txt
data(format=prn,org=columns) 1 25 valueadd capital labor nfirm
*
set logq = log(valueadd)
set logk = log(capital)
set logl = log(labor)
*
linreg logq
# constant logk logl
*
* Original parameterization
*
nonlin b0 bk bl sigma lambda
compute b0=%beta(1),bk=%beta(2),bl=%beta(3),sigma=.7*sqrt(%seesq),lambda=1
frml resid = logq-b0-bk*logk-bl*logl
frml frontier = eps=resid,-log(sigma)-.5*(eps/sigma)**2+log(%cdf(-eps*lambda/sigma))
maximize(method=bhhh,vcv) frontier
*
* Reparameterization. We'll start from the same initial conditions.
*
linreg logq
# constant logk logl
nonlin g0 gk gl theta lambda
compute theta=1.4/sqrt(%seesq),g0=%beta(1)*theta,gk=%beta(2)*theta,gl=%beta(3)*theta,lambda=1
frml resida = theta*logq-g0-gk*logk-gl*logl
frml frontier = alpha=resida,log(theta)-.5*alpha**2+log(%cdf(-lambda*alpha))
maximize(method=bhhh,vcv) frontier
compute theta=1/sigma,g0=b0*theta,gl=bl*theta,gk=bk*theta