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st: RE: why coefficients change after ivreg2 partial out

From   "Schaffer, Mark E" <>
To   "" <>
Subject   st: RE: why coefficients change after ivreg2 partial out
Date   Mon, 10 Jun 2013 16:27:00 +0000


Apologies to you and to the list for the long delay in replying.

The claim in the help file is correct - partialling-out with 2-step GMM should leave the un-partialled-out coefficients unchanged - but only if nothing else changes.

The problem is that -ivreg2- with the -gmm2s- option is a bit too forgiving when encountering a covariance matrix of orthogonality conditions (call it S) that is less than full rank, or alternatively, the warning issued by -ivreg2- is incomplete.

To do 2-step efficient GMM, -ivreg2- has to invert S to obtain the weighting matrix used in the second step of GMM.  If S is not full rank, then either:

(a) -ivreg2- should warn that test results and coefficient estimates should be treated with caution, or
(b) -ivreg2- should exit with an error and explain why.

What it does at the moment is almost the same thing as (a) but not quite - it warns that the test results should be treated with caution, but says nothing about the coefficient estimates.

What's probably happening in your case is that the problematic S generates 2nd-step GMM estimates where one or more coefficients are zeroed out (and similarly in the VCV).  Zeroed out is not the same thing as partialled-out, so the 2nd-step GMM results are different (=wrong).

Here is an example using the toy auto dataset:

. sysuse auto, clear
(1978 Automobile Data)

. gen singleton=(_n==1)

. qui ivreg2 price singleton foreign (mpg=weight), rob gmm2s
Warning: estimated covariance matrix of moment conditions not of full rank.
         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.

. mat list e(b)

          mpg  singleton    foreign      _cons
y1  -504.0671          0  2805.2759  16066.523

. mat list e(S)

symmetric e(S)[4,4]
              weight  singleton    foreign      _cons
   weight  8.375e+13
singleton  1.259e-19  4.297e-23
  foreign  4.408e+09          0  1960107.8
    _cons  2.383e+10  4.297e-23  1960107.8  7343027.8

The singleton variable causes the heteroskedastic-robust S to be less than full rank.   Note the row/col of what are effectively zeros in S.  Note also the zero coefficient on singleton in e(b).

If you first partial out the singleton variable, then the problem disappears:

. qui ivreg2 price singleton foreign (mpg=weight), rob gmm2s partial(singleton)

. mat list e(b)

           mpg     foreign
y1  -502.21911   2778.8407

. mat list e(S)

symmetric e(S)[2,2]
             weight     foreign
 weight   6.767e+12
foreign  -2.011e+09   1445594.7

Note that the coefficients are different from those in the first estimation.  Note also that S is now full rank.

If you now partial out foreign as well, then the claim in the help file kicks in - the coefficient on mpg remains -502.21911:

. qui ivreg2 price singleton foreign (mpg=weight), rob gmm2s partial(singleton foreign)

. mat list e(b)

symmetric e(b)[1,1]
y1  -502.21911


> -----Original Message-----
> From: [mailto:owner-
>] On Behalf Of Ronghong Huang
> Sent: 22 May 2013 08:57
> To:
> Subject: st: why coefficients change after ivreg2 partial out
> Dear Statalisters,
> I am sorry if this has been discussed before, however, I have spent lots of time
> searching and none answers my questions.
> My question is rather short, why coefficients estimates change after I use the
> Partial Out function in ivreg2 with gmm2s (I am using the latest version of
> ivreg2)?
> From the help file, it states that " 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.  (NB: this does not hold for CUE or GMM iterated more than
> two steps.) ".
> I am runing the following regression
> ivreg2 y (x1=z1 z2 z3 z4) x2 x3... fe(industry) fe(year), cluster(firm) gmm2s
> As there are many industry dummies, a warning message appears saying
> "Matrix not of full rank", from other posts, I know I can use Partial Out function
> to address this issue, therefore, I run the following regression again
> ivreg2 y (x1=z1 z2 z3 z4) x2 x3... fe(industry) fe(year), cluster(firm) gmm2s
> partial(industry)
> Suprisingly, the coefficients changed, which is not consistent with the help file. I
> retry with 2SLS and LIML, the coefficients actually are the  same after partial
> out.
> Any suggestion of what is going on here? Am I doing the right thing?
> Thank you for much in advance!
> Best Regards,
> Ronghong Huang
> *
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