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st: Standard error correction when using control function approach to endogeneity


From   Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Standard error correction when using control function approach to endogeneity
Date   Tue, 18 Jun 2013 17:31:20 +0200

Dear all,

I am trying to fit a linear regression model with one endogenous variable
using the control function approach (two stage residual inclusion estimator)
as described in Wooldridge (2010, pp. 126-129).

More specifically, I estimate something like:

(1)  reg y2 x1 x2 z1 z2
(2)  predict uhat, res
(3)  reg y1 y2 x1 x2 uhat

where y1 is my dependent variable of interest, y2 is the endogenous
variable, x1 and x2 are exogenous explanatory variables, and z1 and z2 are
valid instruments for y2.

Since the fitted residual from the first stage is included in the second
stage regression as an additional regressor, the standard errors need be to
corrected. Wooldridge (2010, pp. 157-160) derives the formula for the
corrected standard errors in his book in Appendix 6A, equation (6.58).

Now my two questions are:

(1) Has someone already implemented this standard error correction in Stata
or do I have to calculate equation (6.58) in Appendix 6A manually?

(2) Could I also obtain a "standard error correction" by bootstrapping
equations (1)-(3)?


Any help is greatly appreciated.

Best,

Johannes Muck

References:
Wooldridge, J. M. (2010), Econometric Analysis of Cross Section and Panel
Data, 2nd edition, MIT Press, Cambridge MA.

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