st: Random Effects model with Dynamics

["Lee, Albert" <Albert.Lee@hud.gov>]

My dataset is an annual panel with many subjects (tens of thousands) and relatively short time period (at most 10 years).  This panel is very unbalanced (T ranges from 1 to 10).  Looking at some summary statistics, I'm convinced that it is best to model this as a random effects model with a lagged dependent variable as a regressor, i.e., 

y(i,t)=a+b*y(i, t-1)+e(i)+u(i,t), 

where e(i) is the subject random effects and u(i,t) is the noise.

I'm aware of the xtmixed and xtabond commands in stata.  But the model as specified may need a combination of the two estimation methods.

Questions:
1.  Does stata provide a routine that estimates dynamic model with random effects?
2.  Theoretically, is this an overkill to model dynamics and random effects in the same model?

Extra credit:
1.  I'm in fact estimating several equations like the one indicated above.  Is there a seemingly unrelated technique that I could use to exploit the correlations of the error terms from these equations.  I guess that it will be a simultaneous random effects panels with dynamics.  Any thoughts?

Many thanks in advance,

Albert Lee    

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