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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 15:33:02 -0400

Misha Spisok <misha.spisok@gmail.com> :

The Wald estimator with the correct standard error is here:

use http://pped.org/card.dta
ivreg lwage exper (educ=nearc4), nohe r

as shown in
http://www.stata.com/statalist/archive/2009-10/msg00498.html

You can also:

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]
di `b1'/`b2'

and use -suest- and so forth, but why would you?  Unless you are
estimating on two separate datasets...

On Thu, Oct 15, 2009 at 3:19 PM, Misha Spisok <misha.spisok@gmail.com> wrote:
> 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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