Re: st: RE: constructing standard errors for the product of two estimates

[Marcello Pagano <pagano@hsph.harvard.edu>]

This does not make much sense since a variance is a number and the 
formula below has random variables on the right! I think what has been 
left out are expected values of the variables on the right.  I don't 
have my Mood and Graybill here, but I suspect that we can derive the 
formula from scratch using the conditional formula:
Var(Y) = E Var(Y|X) + Var[ E(Y|X)]
and that would yield:
Var(ab) = [E(a)]^2 * Var(b) + [E(b)]^2 * Var(a) + Var(a)*Var(b)

which, I am sure,  is what Jann meant.

m.p.



Jann Ben wrote:


> I would say, the variance of the product of two independent 
> random variables is
>
> V(a*b) = a^2*V(b) + b^2*V(a) + V(a)*V(b)
>
> where a and b are the random variables and V(a) and V(b) are
> their variances. See, for example, Mood et al. (1974:180).
>
> ben
>
> Mood, A. M., F. A. Graybill, and D. C. Boes (1974): 
> Introduction to the Theory of Statistics, 3 ed. New 
> York: McGraw-Hill.
>
>  
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu 
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> > Evans, David
> > Sent: Monday, December 05, 2005 8:03 PM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: constructing standard errors for the product of 
> > two estimates
> >
> >
> > Dear Statalist,
> >
> > I have an estimate of the reduction in disease risk based on a dietary
> > supplement, and I also have the estimate of the cost of disease
> > incidence.
> >
> > I want to multiply these two estimates in order to know the expected
> > reduction in medical costs as a result of taking the dietary 
> > supplement.
> >
> > The two estimates are from completely different, independent samples.
> >
> > Question: can I use Stata to estimate the standard errors for this
> > product? 
> > In my case, I'm not estimating the elements of the product 
> > myself (which
> > makes 'lincom' less helpful since I want to supply the estimates and
> > standard errors without running the regressions (which come from other
> > papers).
> >
> > Thanks so much for any thoughts,
> > David
> >
> > _______________________________
> > David Evans, Ph.D.
> > Associate Economist, RAND
> > 1776 Main Street, P.O. Box 2138
> > Santa Monica, CA 90407-2138
> > Phone: 310.393.0411 x6310
> > E-mail: devans@rand.org
> > Fax: 310.260.8156 
> >
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