Hi,
This is a really interesting discussion. I think Rodrigo is right in
saying that the standard Fama-MacBeth procedure is not appropriate
here because of the endogeneity problem. However, Antoni Sureda
provides a version of the Fama-MacBeth approach which is based on the
IV-estimator rather than on the OLS estimator. His -fmivreg- program
is available from
http://www.antonisureda.com/blog/files/category-6.html
What could also be an interesting path to proceed is to estimate the
regression model with Driscoll-Kraay standard errors. Why? If the
panel is unbalanced then the panel might well be a microeconometric
panel and these panels are likely to be cross-sectionally dependent
(due to things like social norms, neighborhood effects, and all sorts
of behavioral biases). Because Driscoll-Kraay standard errors are
heteroscedasticity consistent and robust to very general forms of
temporal and cross-sectional dependence, they might be interesting in
this respect. I implemented the Driscoll-Kraay estimator for use with
both balanced and unbalanced panels in my -xtscc- program (in Stata
type -net search xtscc-). Unfortunately, however, the -xtscc- program
currently does not allow for estimation of IV regression models but it
would be straightforward to generalize the -xtscc- program such that
it includes the 2SLS estimator. Please let me know if this would be of
interest for anyone.
Finally, if there is no cross-sectional dependence, then I think it
could be a simple but tractable way to estimate the regression model
by aid of the 2SLS estimator with panel-robust ("clustered" or Rogers)
standard errors. Monte Carlo simulations have shown that panel-robust
standard errors are robust to subject specific fixed effects.
Best,
Dan
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