Yes, Marcello is absolutely right. This is what I meant.
Excuse me for being sloppy.
ben
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> Marcello Pagano
> Sent: Monday, December 05, 2005 9:22 PM
> To: [email protected]
> Subject: Re: st: RE: constructing standard errors for the
> product of two estimates
>
>
> 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: [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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