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st: Re: Compositional data


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Compositional data
Date   Wed, 5 Mar 2008 15:20:54 -0500

>>I would like to estimate the following model:
i have n firms, each firm has a bundle of 3 products, characterized by
the different resource allocation for each product, measured in % which
sums up to 100%. That is, e.g.  firm 1 has 20% of production devoted to
product 1, 30% to product 2, etc., 100% in total. I would like to
explain the resource allocation choice by a firm.  Thus, the dependent
variable is actually 3 variables, which are continuous variables (% of
resources) and are interdependent.  

Which econometric model should I use and how to handle this in stata?
Thanks very much in advance, Regards, Elena<<

As Maarten noted, you have compositional data. Might I suggest looking
at the book by John Aitchison, Compositional Data Analysis (2003)? Also
Fry, J.M., Fry, T.R.L. and K.R. McLaren, (1996), "The Stochastic
Specification of Demand Share Equations: Restricting Budget Shares to
the Unit Simplex", Journal of Econometrics, 73, 377-385. 

The Dirichlet distribution is convenient but has a very restrictive
covariance structure, because it is fully determined by its marginals. 

Jay




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