st: degrees of freedom correction: Frisch Waugh

[statalist <statalistrw@gmail.com>]

I am estimating a linear model with a large number of fixed effects  (e.g. worker/firm, student/teacher, etc...). 

One way to do this would be to use a two-way fixed effects estimator (e.g. a2reg, felsdvreg, etc...), but I am not really interested in the estimates of the fixed effects per se. 

An alternative would be to estimate the model in stages, using a wage equation as an example:
xtreg wage, fe i(worker_id)
predict wage_res1, e
xtreg experience, fe i(worker_id)
predict experience_res1, e

xtreg wage_res1, fe i(firm_id)
predict wage_res2, e
xtreg experience_res1, fe i(firm_id)
predict experience_res2, e

reg wage_res2 experience_res2

This should produce the exact same result as "xtreg wage experience i.firm_id, fe i(worker_id)" with the exception that the standard errors will be slightly smaller in the former example due to a degrees of freedom issue. 

My question is as follows: is there an easy way to correct the standard errors from the two+ stage model to mimic the one stage model? This obviously will not make a huge difference in large samples, but I want to know if such a solution exists. 






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