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: [email protected]
> [mailto:[email protected]] On Behalf Of
> Evans, David
> Sent: Monday, December 05, 2005 8:03 PM
> To: [email protected]
> 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: [email protected]
> Fax: 310.260.8156
>
>
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