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


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Standard error correction when using control function approach to endogeneity
Date   Wed, 19 Jun 2013 12:41:18 -0400

Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de> :
did you read these?
http://www.stata.com/statalist/archive/2009-11/msg01485.html
http://www.stata.com/statalist/archive/2011-09/msg00284.html

On Wed, Jun 19, 2013 at 5:40 AM, Johannes Muck
<Johannes.Muck@dice.uni-duesseldorf.de> wrote:
> 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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