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

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: Standard Error of a Wald Estimator and -nlcom- Date Thu, 15 Oct 2009 08:51:52 -0500

```I would say so. They have different underlying algorithms for numeric
approximations, but the relative error of 1e-5 is OK for nonlinear
stuff. Can you report -reldif- instead of -abs()-?

On Wed, Oct 14, 2009 at 7:58 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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--
Stas Kolenikov, also found at http://stas.kolenikov.name
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