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AW: 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   AW: st: Standard error correction when using control function approach to endogeneity
Date   Wed, 19 Jun 2013 11:40:47 +0200

Dear Austin,

thank you very much for your answer. 

As far as point (1) is concerned, I know that I could also use the 2SLS
estimator by running ivregress or ivreg2. The reason for why I want to use
the control function approach instead (where fitted residuals rather than
fitted values are used in the second stage) is the following: I estimate a
system of two simultaneous equations and need to test whether a combination
of parameters from both equations is significantly different from zero (for
further details see my earlier post to the statalist:
http://www.stata.com/statalist/archive/2013-06/msg00566.html). 

By using the control function approach I circumvent the problem that
combining two IV-estimations with the -suest- command does not work because
I only use the -reg- command. However, before combining the two estimations,
I want to make sure that the standard errors of my coefficients are correct.

Nevertheless, I am glad that bootstrapping the whole procedure would also do
the standard error correction. However, I guess it might be more elegant to
use the analytic standard error correction?

Best,

Johannes

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Austin Nichols
Gesendet: Dienstag, 18. Juni 2013 20:27
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: Standard error correction when using control function
approach to endogeneity

Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>:

1) yes, just run these to get the same answers:
ivreg y1 x1 x2 (y2 = z1 z2)
ivregress 2sls y1 x1 x2 (y2 = z1 z2)
ssc inst ivreg2
ivreg2 y1 x1 x2 (y2 = z1 z2)

2) yes, you can bootstrap the whole thing, but why would you?

On Tue, Jun 18, 2013 at 11:31 AM, Johannes Muck
<Johannes.Muck@dice.uni-duesseldorf.de> wrote:
> 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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