Dear All,
I need to find a standard error of Z a ratio of two random
variables X and Y: Z=X/Y, where the means and SEs for X and Y are
known, as well as their corr coefficient. (In my particular case X and
Y are numbers of people that have such and such characteristics). I am
using delta-method according to [
http://www.math.umt.edu/patterson/549/Delta.pdf ] (see page 2(38)). I
then use svy:ratio to check my results and they don't match. I wonder
if I am doing something wrong, or is it any kind of precision-related
problem (the difference is about 7%, i.e. 1.7959 vs. 1.6795), or is my
check simply wrong and not applicable in this case.
I would appreciate if someone could look into the code and let me
know why the results are different.
Thank you,
Sergiy Radyakin
Below is a do file that one can Ctrl+C/Ctrl+V to Stata's command line:
**** BEGIN OF RV_RATIO.DO ****
sysuse auto, clear
generate byte www=1
svyset [pw=www]
capture program drop st_error_of_ratio
program define st_error_of_ratio, rclass
syntax varlist(min=2 max=2)
svy: mean `varlist'
matrix B=e(b)
local mux=B[1,1]
local muy=B[1,2]
matrix V=e(V)
local sigma2x=V[1,1]
local sigma2y=V[2,2]
local sigmax_sigmay=V[1,2]
svyset
corr `varlist' [aw`=r(wexp)']
local rho=r(rho)
return scalar se = sqrt((`mux')^2*`sigma2y'/(`muy')^4 +
`sigma2x'/(`muy')^2 - 2*`mux'/(`muy')^3*`rho'*`sigmax_sigmay')
end
st_error_of_ratio price length
display as text "Estimated SE=" as result r(se)
svy: ratio price / length
**** END OF RV_RATIO.DO ****
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