RE: st: fixed vs random effect model

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Ama,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> amatoallah ouchen
> Sent: 04 July 2010 18:31
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: fixed vs random effect model
> 
> David, David and Martin Thank you very much  for you  time 
> and answers, what makes me thought about using random instead 
> than fixed  in addition to the little variation issue is that 
> when i'm running random effects, i got very significant 
> results which are very compatible with the economic theory. 
> This is why  i've asked if  it is  possible to makethe  
> tradeoff of  loosing in efficiency for winning in consistancy.

The fixed-vs-random effects test is a vector of contrasts test: it's
based on the contrast between the coeffs from the FE estimator and the
coeffs from the RE estimator.

In fact, the RE estimator is a weighted average of the within (FE)
estimator and the between estimator, so the intuition is that the vector
of contrasts is between the coeffs estimated using only the within
variation (which the FE estimator gives you) and the coeffs estimated
using only the between variation (which the between estimator gives
you).

In GMM terms, the FE estimator using only orthogonality conditions
relating to the idiosyncratic error e_it.  The RE estimator also uses
orthogonality conditions relating to the group error u_i.

A big test stat is usually interpreted to mean that the orthogonality
conditions relating to e_it are OK but the orthogonlity conditions
relating to u_i fail.  This makes the RE and between estimators
inconsistent, and so you get a contrast between them and the FE
estimator.

It doesn't *have* to be this way - in some circumstances you might argue
that orthogonality conditions relating to u_i are valid and those
relating to e_it fail, and therefore the right estimator to use is some
variant of the between estimator.

It sounds like this *might* be the case in your situation.  If so, you
might want to use the between estimator.  Alternatively, you could use
the within variation (orthogonality conditions involving e_it) to
identify some coefficients and the between variation (orthogonality
conditions involving u_i) to identify other coefficients.  Angrist &
Pischke (2009), Mostly Harmless Econometrics, have a description of how
to do this, but I can't remember exactly where.

Cheers,
Mark

> 
> Ama
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