I wish to estimate the following:
Y = b0 + b1X + b2Z + b3XZ + Control variables
I would like Z to be instrumented by Q. How does one deal
with the interaction? Is the interaction instrumented by Q
(as well as a second instrument)? Or, can I first regress Z
on Q, and then use Zhat above instead of Z (I suspect that
this solution will not provide correct standard errors given
that the control variables were not used in the first
stage).
I am not sure how I should proceed here because this
procedure is not commonly done.
Thanks in advance,
John.
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