Instruments that were not weak become weak when using fixed effects

[Flo Adriaansens]

Dear Stata-users,

I am working with panel data and I have the following issue. I first made a regression using the regular iv estimation, with 4 excluded instruments for one potential endogenous variable.
However, since I am working with panel data and I suspect the presence of time-invariant unobservables to create endogeneity, I also have performed a fixed-effects estimation (with the same instruments as above). I included clustered standard errors in both.

The problem is that my instruments are not weak when using regular IV, but they are weak when adding the fixed effects (Kleibergen-Paap rk Wald F statistic is much smaller than the critical values reported). Below I report my steps and the outcomes for the fixed effects.

ivreg2 some_variable (isntrumentedvariable =  5 instruments ) some _othervariables, cluster(hhidpn) ffirst


xtivreg2 some_variable (isntrumentedvariable =  5 instruments ) some _othervariables, cluster(hhidpn) ffirst fe

Underidentification test (Kleibergen-Paap rk LM statistic):             11.188
                                                   Chi-sq(3) P-val =    0.0108
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Weak identification test (Cragg-Donald Wald F statistic):                5.243
                         (Kleibergen-Paap rk Wald F statistic):          3.655
Stock-Yogo weak ID test critical values:  5% maximal IV relative bias    13.91
                                         10% maximal IV relative bias     9.08
                                         20% maximal IV relative bias     6.46
                                         30% maximal IV relative bias     5.39
                                         10% maximal IV size             22.30
                                         15% maximal IV size             12.83
                                         20% maximal IV size              9.54
                                         25% maximal IV size              7.80
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
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Hansen J statistic (overidentification test of all instruments):         1.310
                                                   Chi-sq(2) P-val =    0.5195
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My question is: is there something I can do to still use fixed effects together with instruments? I have already tried different instruments but my data set is limited and none of them improved the situation. I have done quite an extensive literature research but have not found a method that can do inference with weak instruments in IV. Please note, I am aware of the 'weakiv' module but this does inference only for the endogenous variable.

Please let me know if my question is unclear. Thank you for your time and consideration.