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st: Re: st: RE: Ratio of coefficients from two regressions and standard error‏.

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject st: Re: st: RE: Ratio of coefficients from two regressions and standard error‏. Date Sat, 3 Dec 2011 16:23:19 -0500

Bootstrapping the ratio should give good results with fewer assumptions about the regression coefficients.

Steve
*************CODE BEGINS*************
sysuse auto, clear
capture program drop myboot

program myboot, rclass
reg trunk length
scalar define b1 = _b[length]

reg weight length
scalar define b2 = _b[length]

return scalar ratio = b2/b1
end

bootstrap ratio =r(ratio) , reps(40): myboot
estat bootstrap, all
**************CODE ENDS**************

On Dec 2, 2011, at 10:44 AM, meenakshi beri wrote:

Thanks for your reply. One more question -- how to use  Fieller's theorem  and derive confidence limits using stata in this case?

Meenakshi Beri
Department of Economics
Wayne State University
dy5651@wayne.edu

From: Paul.Silcocks@liverpool.ac.uk
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: Ratio of coefficients from two regressions and standard error‏.
Date: Fri, 2 Dec 2011 09:23:04 +0000

On the assumption that the two regression coefficient estimates have a Normal distribution, their ratio would have a Cauchy distribution (with no defined variance) if their correlation is zero.  If the correlation is non-zero the exact distribution is complicated, though under certain conditions it tends to a Normal distribution.

You'd be better off instead using Fieller's theorem to obtain confidence limits rather than estimating the standard error

Paul Silcocks BM BCh, MSc , FRCPath, FFPH, CStat
Senior statistician,
Cancer Research UK Liverpool Cancer Trials Unit
University of Liverpool
Block C Waterhouse Building
1-3 Brownlow Street
L69 3GL

email:  paul.silcocks@liverpool.ac.uk
tel: 0151 7948802
mob: 0794 983 2775

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of meenakshi beri
Sent: 02 December 2011 06:08
To: statalist@hsphsun2.harvard.edu
Subject: st: Ratio of coefficients from two regressions and standard error‏.

Hello Statalist,
I am running a fixed effects regression followed by an auxiliary regression to capture the coefficient of time invariant variables. I want to estimate the ratio of two coefficients from these two regressions respectively along with the standard error of the ratio. How can I estimate the ratio and standard error?
Thanks,Meenakshi BeriWayne State University
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