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

 From Misha Spisok To statalist@hsphsun2.harvard.edu Subject Re: st: Standard Error of a Wald Estimator and -nlcom- Date Thu, 15 Oct 2009 12:19:13 -0700

```Prof. Nichols,

Please forgive my obtuseness, but I'm not sure what you mean by
"rather than aggregating quantities over multiple regressions."  I
think you are referring to using the results from separate regressions
on the same data set, as you point out in the first line of the post
to which you referred me.  Please correct me if I'm wrong.

Also, by having "three ways to get a SE," do you mean to include the
initial one from the code
(http://www.stata.com/statalist/archive/2009-10/msg00498.html) that
comes from the two separate OLS regressions and the following
calculation?

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

I would understand this to be incorrect for the reasons given in the
first line of the referenced post--i.e., it uses the results from
separate estimates on the same data--in addition to the fact that it
neglects to correct for any correlation between b1 and b2.

And, for the sake of clarity, the other two being:

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

which, I understand to be an approximate standard error formula with a
correction for non-zero covariance, and

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

which, if I understand the documentation correctly, uses some
numerical implementation of the delta method.

Thank you for your time and patience.  I appreciate you correcting my
misunderstandings and taking the time to provide tidy examples.

Best,

Misha

On Thu, Oct 15, 2009 at 8:49 AM, Austin Nichols <austinnichols@gmail.com> wrote:
> 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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