st: xtivreg2, clustered errors and F statistic

["Anna Rosso" <a.rosso@ucl.ac.uk>]

Dear list,

I am using Stata/MP 11.2 for Unix (Linux 64-bit x86-64)
Born 30 Mar 2011

I am running IV regressions using xtivreg2 (latest updated version) on a
panel of 16 regions and 11 years.

I estimate using regional fixed effects. My specification includes among the
RHS variables year dummies, 6 continuous control variables, and the
endogenous regressor of interest.
I use 90  IVs to instrument my endogenous regressor, and I cluster standard
errors at the regional level.

The problem is the following:
When I only include as RHS variables region and year dummies and the
endogenous regressor, my first stage F-stat for the significance of excluded
instruments goes to infinite. This is what I would expect given the degrees
of freedom are "negative": F stat is distributed as F(k,d-k)
Where k is the number of constraints (90 in my case, as I have 90
instruments to test), d is the number of clusters(16)  

When I add the additional six control variables: my first stage F-statistic
is more than normal: 14.76. 
Do you think it is possible? I don't understand why this is happening only
when I put controls in the regression.

I have also tried to "partial out" some variables, as suggested in Baum,
Schaffer and Stillman's paper("Enhanced routines for instrumental
variables/generalized method of moments" The Stata Journal (2007), 7, Number
4, pp. 465-506) when the number of clusters is less than the number of
exogenous regressors + excluded instruments. Partialling out some exogenous
regressors helps the covariance matrix of orthogonality
conditions to have full rank. Unfortunately, this still has not solved the
problem as I have many instruments.
Also, the Kleibergen-Paap Wald rk F statistic  (which is the one suggested
by the authors of the above paper in case of clustered errors) is reported
as missing.

I report the command used and the output of first stage statistics when I
only control for year dummies using fixed effect estimator (xtivreg2 with fe
and cluster() options)
----------------------------------------------------------------------------
---------------------------------------------------------------------------
xi: xtivreg2 netpay  (share_reg = GWmean40_UK_* GWmean40_USA_* GWmean40_DE_*
mean2004_40_UK_* mean2004_40_USA_* mean2004_40_DE_*) i.year if
year>=1997&year<=2007 ,fe cluster(won) first

.....

F test of excluded instruments:
  F( 90,    15) =  1.3e+13
  Prob > F      =   0.0000
Angrist-Pischke multivariate F test of excluded instruments:
  F( 90,    15) =  6.7e+12
  Prob > F      =   0.0000

Summary results for first-stage regressions
-------------------------------------------

                                           (Underid)            (Weak id)
Variable     | F( 90,    15)  P-val | AP Chi-sq( 90) P-val | AP F( 90,
15)
share_reg    |    1.3e+13    0.0000 |     1.5e+15   0.0000 |     6.7e+12

NB: first-stage test statistics cluster-robust

.....

Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(90)=.       P-val=     .

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                       2.99
Kleibergen-Paap Wald rk F statistic                                    .
.....

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(0,15)=           .     P-val=     .
Anderson-Rubin Wald test           Chi-sq(0)=         .     P-val=     .
Stock-Wright LM S statistic        Chi-sq(0)=         .     P-val=     .

....

Number of clusters             N_clust  =         16
Number of observations               N  =        176
Number of regressors                 K  =         11
Number of endogenous regressors      K1 =          1
Number of instruments                L  =        100
Number of excluded instruments       L1 =          0
----------------------------------------------------------------------------
----------------------------------------------------------------------------
And this is the command and output with extra controls:

----------------------------------------------------------------------------
----------------------------------------------------------------------------
xi: xtivreg2 netpay  public pop age sex shar_ed2 shar_ed3 (share_reg =
GWmean40_UK_* GWmean40_USA_* GWmean40_DE_* mean2004_40_UK_*
mean2004_40_USA_* mean2004_40_DE_*) i.year if year>=1997&year<=2007,fe
cluster(won) first

.......

F test of excluded instruments:
  F( 90,    15) =    14.73
  Prob > F      =   0.0000
Angrist-Pischke multivariate F test of excluded instruments:
  F( 90,    15) =    14.73
  Prob > F      =   0.0000

Summary results for first-stage regressions
-------------------------------------------

                                           (Underid)            (Weak id)
Variable     | F( 90,    15)  P-val | AP Chi-sq( 90) P-val | AP F( 90,
15)
share_reg    |      14.73    0.0000 |     3535.83   0.0000 |       14.73

NB: first-stage test statistics cluster-robust

.......

Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(90)=.       P-val=     .

Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                       2.53
Kleibergen-Paap Wald rk F statistic                                    .

......

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(6,15)=       16.04     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(6)=    256.57     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(6)=         .     P-val=     .

NB: Underidentification, weak identification and weak-identification-robust
    test statistics cluster-robust

Number of clusters             N_clust  =         16
Number of observations               N  =        176
Number of regressors                 K  =         17
Number of endogenous regressors      K1 =          1
Number of instruments                L  =        106
Number of excluded instruments       L1 =          6
----------------------------------------------------------------------------
----------------------------------------------------------------------------


Thanks for your consideration.

Best regards,

Anna Rosso


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