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st: IV estimation of semi-endogenous interaction effect

Subject   st: IV estimation of semi-endogenous interaction effect
Date   Wed, 14 Dec 2011 21:18:48 +0100

Dear All,

I am concerned with the effect of the disclosure score DSCORE on the cost of equity capital COST. An OLS regression model of COST on DSCORE and a linear interaction effect between the number of analysts, ANALYST 

reg COST DSCORE dscore_analysts ANALYSTS XYZ

where dscore_analysts = DSCORE*ANALYSTS is the interaction variable and XYZ are control variables.

Now I want to test the theoretical proposition that DSCORE is an endogenous regressor, while ANALYSTS is known as exogenous. That is, the interaction variable dscore_analysts would be "semi-endogenous". It is clear from an IV estimation standpoint that the following procedure yields correct estimates when DSCORE is in fact endogenous


where UVW are additional excluded instruments.

However, this standard approach fails to capture the interaction effect observed in the basic OLS model. I am thus tempted to treat the semi-endogenous interaction variable as fully endogenous using the alternative 2SLS model

ivreg COST XYZ (DSCORE dscore_analysts = ANALYSTS UVW).

Of course, the second first stage variable dscore_analysts will be correlated with the excluded instrument ANALYSTS by construction. Could you please tell me if this approach is valid? Assuming further that ANALYSTS passes the IV redundancy test, and a subsequent ivendog test fails to reject the Null, does consistency with prior IV estimation require the variable ANALYSTS to be excluded in the OLS regression?

Your help will be greatly appreciated!

Best regards,
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