st: replacing time effect from fixed effect panel regression with observed variables

[Nikunj Kapadia <nkapadia@som.umass.edu>]

I am running a two-way fixed effect (T, N) panel regression where the 
panel has data on firms over time as follows:

xi: areg Y X i.date, absorb(firm_identifier) robust cluster(firm_identifier)

Now, I also want to understand whether I can explain the time effect by 
a set of macroeconomic variables, M.

I was debating between the following three options.

1. Replace i.date by the macroeconomic variables, M.

areg Y X M, absorb(firm_identifier) robust cluster(firm_identifier)

But because my (limited) set of macro variables will not completely 
account for the time effect, it will bias
my standard errors on X. Now, I can use the standard errors from the 
original specification with i.date for X, so that is not a problem. But 
in the second specification above, will the standard errors on M itself 
be biased if there is additional unobserved time effect?

2. Use the T-1 dummy variables estimated from fixed effect panel 
regression and regress against macro variables as a second step regression.

3. I could average Y over N for each date, and then regress on macro 
variables.

What would be the pros and cons of the possible approaches?  Any 
comments will be appreciated!

Thanks!

NK


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