Mark,
You are right. Now how one can run the IV only for the TI using any
set Z of instruments? This is similar to Hausman-Taylor estimator
but only taking the first 2 steps. Pretend x4 and x5 are TI then
xtreg y x1 x2 x3, fe
predict aux1, r
bysort id: egen aux2=mean(aux1)
replace aux2=aux2+_b[_cons]
reg aux2 z1 z2 z3
Just this?? do we need std-errors adjustments? does this work for
unbalanced-data? I think that we don't need more adjustments.
Moreover the covariance of _b[x1] and _b[z1] is zero. Am I right?
She can take x4 and x5 in the Z set (FE+BE), run the model and
compare it with RE using Hausman test (RE is the efficient one).
Rodrigo.
PS: Do you have some ideas why GLS-RE and MLE-RE were
so different in my example?
Mark wrote:
Rodrigo,
Still not sure I understand the issue she faces.
FE - consistent estimates of the TV coefficients, but not the TI ones
because they drop out.
RE - consistent estimates of the TV and TI coefficients, if not
correlated with the group error component ("fixed/random effect").
Inconsistent estimates of both if endogenous effects.
FE+BE - consistent estimates of TV coefficients. Consistent estimates
of TI coefficients, if not correlated with group error component, i.e.,
like random effects; inconsistent estimates of TI coefficients if they
are.
She is particularly interested in the TI coefficients. In terms of
consistency, it doesn't matter if she goes down the RE or FE+BE route.
If one estimate of the TI coefficients is inconsistent, so is the other.
Did I get this right? If so, is one conclusion that she needs
instruments for her TI variables?
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