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st: How to Approximae the Variance of Log Variable
From
"Zhang, Sisi" <[email protected]>
To
<[email protected]>
Subject
st: How to Approximae the Variance of Log Variable
Date
Tue, 8 Mar 2011 19:57:37 -0500
Hello,
Everyone knows that
Variance(y1+y2)=variance(y1)+variance(y2)+2*covariance(y1+y2)
My question is: How do we approximate Variance [log(y1+y2)] as a function
of first and second moments of y1 and y2?
I can think of using Taylor expansion or Delta method, Variance [log
(y)]=variance(y)/[E(y)^2] , as var[f(x)]=var(x)*(f'(E(x))^2.
(http://en.wikipedia.org/wiki/Taylor_expansions_for_the_moments_of_function
s_of_random_variables)
However, this approximation is very poor when mean of y is small or
variance of y is large. Is there a better way to approximate variance of
log variable? Thanks a lot!!!
Best,
Sisi
--------------------------------------
Sisi Zhang, Ph.D.
Research Associate/Economist
The Urban Institute
2100 M Street, NW
Washington, DC 20037
Phone: UI: (202) 261-5302
Fax: UI: (202) 463-8522
Email: [email protected]
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