I am trying to use Oaxaca-type decomposition of a wage equation with
selection effects, as discussed in Neuman and Oaxaca, "Estimating labor
market discrimination with selectivity-corrected wage equations:
methodological considerations and an illustration from Israel", discussion
paper 2-2003 from the Pinhas Sapir Center for Development at Tel-Aviv U.
It seems that all the standard decomposers (like oaxaca) in Stata adjust
the wage equations for selectivity, and then decompose the adjusted
difference into explained and unexplained effect.
Say, I have the following model:
y1 = x1b1 + s1c1
y2 = x2b2 + s2c2,
where s is the selection variable. Then, the standard Stata procedure
would do the following, as far as I understand:
adjust y1-y2 with s1c1 - s2c2, and then decompose this adjusted difference
into:
(x1 - x2)b1 + x2(b1-b2)
However, as in the above paper, I want to have three decomposition terms:
(x1 - x2)b1 + x2(b1-b2) + (s1c1 - s2c2),
such that I can further decompose the selection term, (s1c1 - s2c2). This
involves calculating s0 = f(h2g1)/F(h2g1), where g1 is the estimated
parameter from the selection model of the sample 1 and h2 are the
characteristics that enter the selection model for sample 2, F is normal
CDF and f is normal PDF. (see paper above, pp. 5 and 8)
Could anyone assist me with how to calculate this f/F ratio in stata?