st: Weak instrument tests in small panel data

["Xiao, Chong" <chong.Xiao@scheller.gatech.edu>]

Dear statalist users:

I have an unbalanced panel data that consists of about 40 groups in the cross section and 21 periods. I have two instruments and one endogenous variable that are all time-invariant. 
When I run the 2SLS regression, the Kleibergen-Paap F statistic is below the conventional critical value of 10, but the Shea Partial R2 is more than 10% and the Anderson-Rubin tests 
also show up strong. The first stage estimates for the instruments are also significant. I suspect that it is the small sample that drives the low F statistic. But could anyone 
provide more detailed explanations to reconcile the discrepancy between the various weak instrument test results? Thanks!

Number of clusters =      47                Number of obs =      876
Anderson-Rubin Wald test           F(2,46)=        6.27     P-val=0.0039
Anderson-Rubin Wald test           Chi-sq(2)=     12.98     P-val=0.0015
Underidentification test (Kleibergen-Paap rk LM statistic):             10.191
                                                    Chi-sq(2) P-val =    0.0061
Weak identification test (Cragg-Donald Wald F statistic):              114.638
                         (Kleibergen-Paap rk Wald F statistic):          8.952

sheapr2  .20971431

Best,
Steven Xiao


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