st: Fixed effects model, Hausman test (panel data)

[Zia Hydari <hydari@post.harvard.edu>]

(1) I understand that to estimate a fixed-effect linear model,
independent variables (of interest) must have some variation.  Is it
necessary that there should be variation in each and every
cross-sectional unit?  If yes, should cross-sectional units with no
variation be eliminated from the dataset?

To be slightly more specific, we have data on products that may get
"impaired" at some point in their life.  Once impaired, the product
remains impaired for the rest of its life.  We use a dummy variable:
impaired==0 (not impaired yet) and impaired==1 (already impaired).

The problem is that some products are impaired from day 1, so there is
no variation for these specific products for the "impaired" dummy
variable.

The value of the product depreciates over time.  However, we are
trying to find if product impairment causes a further decline in the
value of the product (then there may benefit in delaying impairment).

(2) A Hausman test indicates that a random effects model is
appropriate.  We find it surprising that the individual-specific
effect has no correlation with independent variables.  What are some
things worth checking to make sure that a random effects is indeed
appropriate.

Regards,
Zia
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