Lagged Dependent Variables with Random Effects

Henrik Lindemann would like to come back to our advice not to use fixed effects and
a lagged dependent variable at the same time (see chapter 5.3/5.4 as
well as your blog entry of October 6, 2009).
Is it possible to use at least a random effects model in case I decide
to use the lagged variable or does the latter always require a pooled
regression?  In other words: Is it somehow possible to take the data
structure into account (the panel consists of 30 OECD countries)?

Good question Henrik.  If you have, say, random country effects in a
country panel then the lagged dependent variable will be correlated with
the random effect in your error term.  So you can't estimate that model
by OLS and get what you want.  This is a lot like
the complications that arise in panel models with fixed effects and
serial correlation - they get messy and hard to identify, perhaps even 
harmful. Random effects are just as troubling as fixed effects in the
lagged dependent variable case. Better to just add more lags and hope
this soaks up any serial correlation that messes up inference.  
Otherwise, it's oil and water.
JA