st: Re: Nonlinear Panel Data

[jacobb <adamcobb@umich.edu>]

Let's take the example you alluded to of an individual purchasing a new car. 
Let's say you have time (years 1 - 5) and you are interested in whether a
policy that was implemented in year 3 affects new car purchases.  A
fixed-effects regression focuses on within-individual variance.  The model
assumes that the unobservable factors that might stimulate an automobile
purchase are time-invariant (e.g. sex of the individual).  But a
fixed-effects model doesn't allow you to assess the effect of variables with
no within-individual variation.  

As it stands, it does not appear that you really have within-individual
variance across all 5 of your time periods.   You have variation between
years 2 and 3 (when the policy implementation took place) and possibly
variation in the DV (when the behavior is enacted -- be it in year 3, 4 or
5).  Going back to the car example, unless you have a covariate that varies
over time, you simply don't have within individual variance over time.  In
order for a fixed-effects model to be appropriate, you need to have at least
one variable that varies for the individual over time.  In our example,
individual income or the number of miles the person has driven their current
car, etc might be appropriate time-varying controls.       

In sum, because fixed-effects models rely on within-individual (or group,
firm, etc ...) action, you need repeated observations for each individual,
and a reasonable amount of variation of your key independent variables for
each individual.  

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