st: Interactions between endogenous and exogenous variables using ivreg2

[sudha mani <prof.smani@gmail.com>]

Dear Satalist users:

I am using ivreg2 to estimate the following model and would like guidance
on the treatment of the interaction between an endogenous and exogenous
variable. The panel data includes approximately 300 firms over 15 years. I
am using Stata 11.2 for Windows and I would like to estimate the following
model:


Y=X1+X2+X3+X1X2+X1X3+X4+error
Where, X1 is endogenous.
X2 and X3 are exogenous
X1X2 and X1X3 are the interaction terms and are thus endogenous
X4 is a vector of control variables (included instruments).
Z1 and Z2 are valid excluded instruments for X1.

As I understand I can instrument the interaction terms using one of
the following methods.

First, if I understand Wooldridge's approach correctly, then I can use the
following strategy to instrument the interaction term.

Reg X1 X2 X3 X4 Z1 Z2
Predict X1hat
g X1hatX2=X1hat*X2
g X1hatX3=X1hat*X3
Ivreg2 Y X2 X3 X4 (X1 X1X2 X1X3=X1hat X1hatX2 X1hatX3), gmm2s cluster(firm)
robust

Is the above a correct implementation of Wooldridge's approach in Stata? Is
the instrumentation strategy valid under conditions of heteroscedasticity?

Second, an alternative instrumentation strategy for the interaction term is
as follows:

g X2Z1=X2*Z1
g X2Z2=X2*Z2
g X3Z1=X3*Z1
g X3Z2=X3*Z2
Ivreg2 Y X2 X3 X4(X1 X1X2 X1X3=Z1 Z2 X2Z1 X2Z2 X3Z1 X3Z2), gmm2s
cluster(firm) robust

Is there a loss of efficiency in the GMM case?

Finally, what if I instrument the interaction term with its lag, where
Z3 is the lag of (X1X2) and Z4 is the lag of (X1X3)?

Ivreg2 Y X2 X3 X4 (X1 X1X2 X1X3=(Z1 Z2 Z3 Z4), gmm2s cluster(firm) robust

I test the validity of the instruments Z3 and Z4 using the Sargan C test.
The results indicate the lagged variables of the interaction term were
uncorrelated with the error term in the second-stage regression. Is it fair
to say that the instruments Z3 and Z4 are valid, but there is further loss
of efficiency than with methods 1 and 2?

I would greatly appreciate if the list participants could weigh in on each
of the instrumentation strategies for the interaction term.

Thank you!
Sudha


--
_____________
Dr. Sudha Mani
William Paterson University
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