st: Re: difference between estimated ratios of x/y and ax/ay

["Michael Blasnik" <michael.blasnik@verizon.net>]

..
It's not rounding and its not an error.  The ratio estimate is the sum of the 
numerator divided by the sum of the denominator (appropriately weighted if 
weights are specified), it is not the average of the ratio.  So, unless the 
variable trunk is a constant, it will most likely lead to a different estimate 
of the ratio.

Michael Blasnik

----- Original Message ----- 
From: "Zurab Sajaia" <zsajaia@hotmail.com>
To: "statalist" <statalist@hsphsun2.harvard.edu>
Sent: Wednesday, October 17, 2007 12:17 PM
Subject: st: difference between estimated ratios of x/y and ax/ay



> Dear All,
>
> I was estimating ratio of two variables (in fact, svy : ratio, but problem is 
> the same for both) and after noticing that both numerator and denominator 
> contained same component I decided to check whether canceling it would affect 
> the results. To my surprise it did.  Lets consider this example:
>
> sysuse auto, clear
>
> . ratio weight / length
> ...
>    _ratio_1 |   16.06673   .2807194      15.50726     16.6262
>
> ...
>
> .generate double wa = weight * trunk
> .generate double la  = length * trunk
>
> .ratio wa / la
> ...
>    _ratio_1 |   16.48413   .2797573      15.92658    17.04169
> ...
>
>
> Have anybody experienced similar case? does this thing come purely from 
> numerical, rounding issues or there is something bigger (I can't think of any 
> though)?
>
> Any insight would be appreciated.
> Thanks
> Zurab
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/