st: RE: partialling out exogenous singleton fixed effects in iv-model (ivreg, ivregress)

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

Max,

See comments below.

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of max.ch.h.bode@gmail.com
> Sent: 30 March 2013 02:38
> To: statalist@hsphsun2.harvard.edu
> Subject: st: partialling out exogenous singleton fixed effects in iv-model
> (ivreg, ivregress)
> 
> Hi statlisters,
> 
> Some background:
> I am currently working on an IV model. The model is estimating the effect of
> access to microfinance (instrumented by distance to
> provider) on various outcome variables of interest (income etc.). So for the
> sack of an example suppose we have
> * 1st stage: take-up = b1 + b2*distancetoprovider + i.fe + e
> * 2nd stage: income = a1 + a2*predicted take-up + i.fe + e whereas i.fe are
> my raster fixed effects.
> 
> I included raster fixed effects (whereas rasters are x^2 meters areas) into
> the model in order to ensure the exogeneity of the instrument. It is
> unavoidable that with the raster sizes I would like to use (in order to
> minimize endogeneity) I'll get a few singleton dummies, i.e., a variable with
> one 1 and N-1 zeros.
> 
> Problem #1: So originally I used the -ivreg- command (as it easily tied into a
> program I wrote that produced stacked LaTeX tables). This command gave
> me an error message because I included singleton dummies (through the
> fixed effects) while requesting a robust covariance matrix. The error
> message further said I should try the -partial- option which I then did. Here
> the message:
> 
> Warning: estimated covariance matrix of moment conditions not of full rank.
>          standard errors and model tests should be interpreted with caution.
> Possible causes:
>          singleton dummy variable (dummy with one 1 and N-1 0s or vice
> versa) partial option may address problem

You aren't using ivreg - this is the output of ivreg2, a user-written program (I am the co-author).

Unlike official ivreg (which, as you note below, is now an out-of-date command), we still maintain and upgrade ivreg2 and and you can continue use it.

More below...

> Here is a description of what the partial option is:
> 
> The partial(varlist) option requests that the exogenous regressors in varlist
> are "partialled out" from all the other variables (other regressors and
> excluded instruments) in the estimation.  If the equation includes a constant,
> it is also automatically partialled out as well.  The coefficients corresponding
> to the regressors in varlist are not calculated. [...] A similar problem arises
> when the regressors include a variable that is a singleton dummy, i.e., a
> variable with one 1 and N-1 zeros or vice versa, if a robust covariance matrix
> is requested.  The singleton dummy causes the robust covariance matrix
> estimator to be less than full rank.  In this case, partialling-out the variable
> with the singleton dummy solves the problem.
> 
> Question #1: I don't fully understand what happens when variables are
> "partialled out" and I couldn't find much literature on it. Could somebody
> point me to relevant resources on this?

This is the Frisch-Waugh-Lovell theorem, which is discussed in most econometrics textbooks and various other places as well (including, dare I say it, Wikipedia).

> Is it even legit to use it in a standard
> 2sls model?

Dave Giles has a nice albeit rather advanced discussion on his blog of the FWL theorem and its application to IV:

http://davegiles.blogspot.co.uk/2011/03/dummies-for-dummies.html

and mentions in passing that he published a paper in 1984 showing that the FWL theorem applies to IV as well.  The reference is: Giles, D. E. (1984). Instrumental variables regressions involving seasonal data. Economics Letters, 14, 339-343.

> The description of the options mentions how "by the Frisch-
> Waugh-Lovell (FWL) theorem, in IV, two-step GMM and LIML estimation the
> coefficients for the remaining regressors are the same as those that would
> be obtained if the variables were not partialled out."  Does this hold for 2sls
> as well?

For linear models, 2SLS is the same thing as IV.

> More generally speaking, do you think it is okay for me to do this here? What
> are the consequences for my estimates.

This gets discussed on Statalist from time to time - have a look in the archives.  Here's an example:

http://www.stata.com/statalist/archive/2010-02/msg00573.html

> Problem #2: Because -ivreg- is an out-of-date command as of Stata 10, I now
> tried running my regressions with -ivregress-. What is
> different:
> * First of all, now the "singleton dummies - use partial out" error message
> does no longer occur.
> * Second, my first stage and therefore my second stage no longer have
> significant effects in a limited sample (in my bigger sample it still works).
> 
> Question #2:  Why does the error message not occur anymore?

If you re-run the regression using ivreg2 instead of ivregress, you will probably still get the message.

HTH,
Mark

> And under
> the condition that it even makes sense to partial out (i.e. question
> #1) could I somehow do it with ivregress?
> 
> Answers to my questions will be greatly appreciated. Thanks a lot!
> 
> Best,
> Max
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