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st: Reduced form specification for an interaction instrumented variable
This is a follow up to a response you gave on your website (on 26 August,
2004) to someone querying 'RE: Interaction with an instrumented variable -
The person with the query has the following specification and query,
"Y=b0 + b1*X1 + b2*X2 + b3*X3 + b4*X2*X3 + U
X2 is the endogenous variable, which is instrumented with Z.
X2 is itself interacted with X3.
How does one model the interaction between an instrumented variable (X2
instrumented with Z) and an exogenous variable (X3)?"
And this was your response,
"You've got two endogenous variables, just as if you had another endogenous
variable X4 and you did not realize that X4=X2*X3. But if Z is a valid
instrument, and X3 is truly exogenous, then Z*X3 is a valid instrument, too."
However, its not clear from this how you go about estimating the reduced
form. What would you use as your LHS variable in the reduced form.
Would the specification for the reduced form for the endogenous interaction
variable look as follows,
X2*X3=b0 + Z*X3 + b1*X1 + b2*X2 + b3*X3 + u?
University of Cape Town
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