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From |
Marcello Pagano <[email protected]> |

To |
[email protected] |

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

Date |
Mon, 05 Dec 2005 15:21:49 -0500 |

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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