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Re: st: an estimation method question


From   Xiang Ao <xao@hbs.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: an estimation method question
Date   Wed, 17 Mar 2010 11:17:51 -0400

Hi Maarten,

Thanks for the suggestions. Indeed the categories need to have the same meaning across groups. In our case, that does not fit. If it's a market share study of, say five different brands of products, then it would make sense. We are interested in founder level. I am thinking whether we can do a maximum likelihood with some constraints by observation. That is, assume each share conforms to beta distribution, for example, then within each firm, the shares add up to one. Would that be valid?

I also like your idea of thinking of founders nested under firms. But we have to take care of the sum constraint somehow.

Xiang

Maarten buis wrote:
--- On Tue, 16/3/10, Xiang Ao  wrote:
There are different numbers of founders for each firm. The smallest number is 2, it can be as many as 10
co-founders.  As far as I understand, the number of
categories need to be fixed in the methods you
mentioned.

That is right, but more importantly the categories need
to have the same meaning across observations. For example
imangine we are looking at the proprotion of spending in a firm on labour and capital (I am no business economist so forgive me if this doesn't make substantive sense). Across firms the proportion spent on labour has (sorta) the same meaning. The aim of such an analysis is to find variables that make some firms spend more on labour and others more on capital goods.

I find it harder to come up with something similar for the different founders. Who would fall in the first category, who in the second, etc. (alphabetical order?). A solution would depend on what your unit of analysis is for your study, i.e. who do you want to study: the firms or their founders. If you want to study the firms, than I could imagine that you are interested in explaining differences in the "structure" of ownership. I would than try to operationalize that in one number per firm and use an appropriate regression like command to analyse that. For example, I could imagine someone interested in the share of the largest founder as a measure of concentration of ownership, in which case I would use the -glm- trick or -betafit- (zero or one proportions are no problem there as you stated that the minimum number of founders in your dataset is 2). Alternatively,
you could try other summaries of the concentration of
ownership like entropy. Don't take my reference to entropy too literaly, I only know that there are many
such measure, and entropy was the only one I could
remember.

If you want to study founders, I would for now forget
about the constaint that the proportions should add
up to one, and transform the data to a panel dataset where the observations are founders nested in firms. I would than try -xtgee- to model these proportions,
just like the -glm- trick. It will be a population
averaged model, so no individual level effects, which seems to be considered a problem in economics.
However, it would be a good place to start.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


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