This sounds like a multilevel model to me. I don't know the method at
all as proposed by Fama and MacBeth (can you provide a reference? I
know Fama is famous in finance, but I am not sure he is equally famous
in statistics...), but it seems to me that plugging the regression
coefficient estimates as the real time series observations will at
least give wrong standard errors. (Don't tell me you are going to use
the bootstrap to correct them. Just don't get me started...) I would
advocate constructing an appropriate two-level model and estimate it
with -gllamm-; that would be the closest analog of SAS' PROC MIXED, if
that's what you had in mind there. See http://www.gllamm.org, GLVM
book from Stata, and examples at
http://www.ats.ucla.edu/stat/stata/examples/mlm_ma_hox/.
Before saying that Fama-MacBeth is the de-facto method, remember that
you may become a founder of a new methodology, so that people in
business would refer to it as Edmans model :))
