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


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Standard Error of a Wald Estimator and -nlcom-
Date   Thu, 15 Oct 2009 11:49:47 -0400

Misha Spisok <misha.spisok@gmail.com> :
Instead of focusing on the final line, look at the first sentence of the post:
http://www.stata.com/statalist/archive/2009-10/msg00498.html
You have 3 ways to get a SE, not 2, and -ivreg- or equivalent (I use
-ivreg2- from SSC) is the way to go, rather than aggregating
quantities over multiple regressions.

On Wed, Oct 14, 2009 at 8:58 PM, Misha Spisok <misha.spisok@gmail.com> wrote:
> 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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