st: RE: Tricky IV-Problem and how do I correct Standard Errors in the Second Stage?

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Benjamin,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Benjamin Niug
> Sent: 29 May 2012 10:37
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Tricky IV-Problem and how do I correct Standard 
> Errors in the Second Stage?
> 
> Hi Stata-users,
> 
> Here is background information:
> 
> - Dataset: I have a T=2 panel dataset with approximately 5000 
> observations.
> 
> - Sampling: Observations are sampled across different localities (e.g.
> 20 observation per locality).
> 
> - Estimation Goal: I want to run a IV-regression accounting 
> for FE and clustering at the individual level.
> 
> - I am using Stata 11.
> 
> Here comes the issue:
> 
> The explanatory variable that is endogenous (to be 
> instrumented) takes on the same values for observations in 
> the same locality. Hence, I want to run the first stage 
> regression using averages of exogenous variables per locality 
> as exogenous instrumental variables. Hence, there would some 
> further level of aggregation in the first stage (with 
> 5000/20=250 observations).
> 
> Questions:
> 1. Is there a Stata command that can estimate this somewhat 
> tricky Two-Stage Regression? (no Stata command that I am aware of).

No, but it's not StataCorp's fault - it can't be done as specified.

The problem is that the endogenous variable to be instrumented doesn't
vary by locality.  Because it's locality-invariant, it will be absorbed
by the fixed effects.  There will be nothing left to instrument.  Put
another way, the FE estimator relies solely on within-locality
variation.  There is no such variation in your endogenous regressor.

Aside from finding a different explanatory variable that does have some
within-locality variation, your only option is to use an estimator that
exploits between-locality variation.  The between estimator does this,
as does the random effects estimator.  Hybrid estimators are also
possible (e.g., exploit only between variation for some regressors and
only within variation for others), but you'd have to do those by hand.

HTH,
Mark

> 2. If I run the first stage regression by hand: How do I 
> correct the standard errors in the second stage?
> 
> Thanks in advance.
> 
> Best regards,
> Benjamin
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