
From  "Michael S. Hanson" <mshanson@mac.com> 
To  statalist@hsphsun2.harvard.edu 
Subject  Re: st: RE: RE: More on F test and the translog 
Date  Thu, 13 Apr 2006 13:00:15 0400 
On Apr 13, 2006, at 10:05 AM, Gauri Khanna wrote:
The translog described in my email does not estimate Beta21, Beta31 and Beta32. The reason is because when one estimates the translog,, LnX1.LnX2 is the same as Ln.X2.LnX1, similarly for LnX2.LnX3=LnX3.LnX2 etc.. These cross products are not viewed as different from each other and hence only one of the pair is estimated.If I understand you correctly, you have already imposed \beta_{ij} = \beta_{ji}  that is, symmetry  in your estimation. Hence, you cannot test your "fourth" restriction, as it holds by assumption. Hope that helps.
But the homogeneity test requires equality between Beta(12)=Beta (21) etc in addition to the others..
> > More on the F test for homogeniety: Although I was able to > > run the first > > three test using the test, accumulate command, I was stumped > > at the fourth > > one(see below). Note I am using a translog production > > function with three > > inputs > > > > The restrictions that must be jointly imposed are: > > > > 1. Beta11+Beta12+Beta13=0 > > 2. Beta12+Beta22+Beta23=0 > > 3. Beta13+Beta23+Beta33=0 > > 4. Beta12=Beta21; Beta13=Beta31, Beta23=Beta32
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