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Re: st: Negative Hausman


From   "Stas Kolenikov" <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Negative Hausman
Date   Wed, 24 Sep 2008 15:46:09 -0500

On 9/24/08, I. HESSELINK <I.Hesselink@uvt.nl> wrote:
>  For my master thesis I am analyzing a sample of panel data (y = whether a company diversified in year t, x = set of company characteristics). Because of the binary dependent variable I use xtlogit, and now want to apply a Hausman test to see whether fixed or random effects models are appropriate.
>
>  xtlogit y x, fe
>  est store fixed
>  xtlogit y x, re
>  est store random
>  hausman fixed random
>

I am not quite sure those models are directly comparable. Your
econometrics teacher should have explained that in binary dependent
variable models, only beta/sigma is identified. With fixed effects
logit (aka conditional logit aka McFadden's model), you don't really
talk about panel-level variance, so your total variance should
probably thought of as _pi^2/6 (the variance of the logistic
variable). In the random effects model, you explicitly allow your
sigma to go up by the value of the panel-level variance u_i, and hence
your coefficients get scaled by sqrt( (_pi^2/6 + Var[u])/(_pi^2/6) ).
See this: http://www.citeulike.org/user/ctacmo/article/3057661

Even if those models are comparable, I don't think their comparison
can have the same interpretation as in the linear models, that of
correlatedness of u_i with regressors. In linear models, those are
moment conditions, and linear models are all about moments. In binary
outcomes models, it's more of the likelihood and conditioning, and I
don't really know if there's much place for E[ux]=0 or !=0 in those.

Even further, biostatisticians would argue that sigma in those models
is a figment of econmetricians' imagination. We are talking about
probabilities, and they don't have to have the utility maximization
and binary choice foundation as econometricians like to think of. So
much for sigmaless/sigmamore story...

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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