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st: create data for frontier estimation


From   Cyrus Levy <levy.cyrus@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: create data for frontier estimation
Date   Fri, 11 Oct 2013 00:14:44 -0700

I'm trying to create a dataset using the true model specified below. The outcomes look good except the constant in lnsig2u. I am setting it to -1.2 in the program, but the estimation result is -0.197. I'm not sure what's wrong with the program. How can I fix this problem?

drop _all
set obs 10000
set seed 543210
gen x1 = rnormal(2)
gen x2 = rnormal(1)
gen x3 = rnormal(1)

gen lnsig2u = 1.4 * x3 - 1.2

gen sigu = sqrt(exp(lnsig2u))
gen nsig = sqrt(sigu^2 / (1 - 2/_pi))
gen u = abs(rnormal(0, nsig))
gen v = rnormal()

gen y = 0.5 * x1 + 0.5 * x2 + 0.5 + v + u

summ, sep(0)
frontier y x1 x2, cost uhet(x3)



Stoc. frontier normal/half-normal model           Number of obs =      10000
                                                  Wald chi2(2) =    2656.28
Log likelihood = -18811.039                       Prob > chi2 =     0.0000

------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y            |
          x1 |    .515271   .0137709    37.42   0.000 .4882805    .5422616
          x2 |   .4967352   .0137501    36.13   0.000 .4697854    .5236849
       _cons |   .4736053   .0428721    11.05   0.000 .3895775     .557633
-------------+----------------------------------------------------------------
lnsig2v      |
       _cons |  -.0455195     .03432    -1.33   0.185 -.1127855    .0217464
-------------+----------------------------------------------------------------
lnsig2u      |
          x3 |   1.407146   .0321241    43.80   0.000 1.344184    1.470108
_cons | -.1970581 .0729905 -2.70 0.007 -.3401169 -.0539994
-------------+----------------------------------------------------------------
     sigma_v |   .9774973   .0167738 .9451679    1.010933
------------------------------------------------------------------------------
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