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

[max.ch.h.bode@gmail.com]

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


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? Is it even legit to
use it in a standard 2sls model? 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?
More generally speaking, do you think it is okay for me to do this
here? What are the consequences for my estimates.

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? 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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