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st: Standard Error of a Wald Estimator and -nlcom-


From   Misha Spisok <misha.spisok@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Standard Error of a Wald Estimator and -nlcom-
Date   Wed, 14 Oct 2009 17:58:25 -0700

In brief, are the two following approaches for the standard error of a
Wald estimate equivalent?  If not, why not?

use http://pped.org/card.dta
reg lwage exper nearc4, nohe r
loc b1=_b[nearc4]
loc s1=_se[nearc4]
reg educ exper nearc4, nohe r
loc b2=_b[nearc4]
loc s2=_se[nearc4]
ivreg lwage exper (educ=nearc4), nohe r
di `b1'/`b2'
di `b1'/`b2'*sqrt((`s2'/`b2')^2+(`s1'/`b1')^2)

qui reg lwage exper nearc4
est sto r1
qui reg educ exper nearc4, nohe
est sto r2
suest r1 r2
mat v=e(V)
matrix cov=v["r1_mean:nearc4","r2_mean:nearc4"]
loc c=cov[1,1]


-----Approach 1-----

di `b1'/`b2'*sqrt((`s2'/`b2')^2+(`s1'/`b1')^2-2*`c'/`b1'/`b2')

This final line is the result of the approach suggested by Austin
Nichols (http://www.stata.com/statalist/archive/2009-10/msg00498.html)
to get the standard error for the Wald estimator.

Then, using the above results from -suest-,

-----Approach 2-----

nlcom [r1_mean]_b[nearc4]/[r2_mean]_b[nearc4]

The results for the standard error are close (the difference is
0.00001913), but not exactly the same.  Are the two approaches
analytically equivalent but different only numerically?

Thank you for your time and attention.

Misha
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