Hi,

I am using Stata 16IC and working with Panel Data. Currently I am doing a FE - IV Regression. I used the command:

[xtivreg2 math4 (aexpp = lfound l96 l97 l98) $control $conyear, fe r endog(aexpp) ]

Warning - singleton groups detected. 7 observation(s) not used.
Warning - collinearities detected
Vars dropped: y94 y98

FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 543 Obs per group: min = 2
avg = 4.0
max = 4
Warning - collinearities detected
Vars dropped: y94 y98

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs = 2152
F( 8, 1601) = 116.00
Prob > F = 0.0000
Total (centered) SS = 201356.9083 Centered R2 = 0.3787
Total (uncentered) SS = 201356.9083 Uncentered R2 = 0.3787
Residual SS = 125112.809 Root MSE = 8.818

------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
aexpp | 4.336699 21.96206 0.20 0.843 -38.70814 47.38154
lunch | .454041 .3926596 1.16 0.248 -.3155577 1.22364
lunchsq | -.0023254 .0043843 -0.53 0.596 -.0109185 .0062677
lenrol | 76.45576 65.37296 1.17 0.242 -51.67288 204.5844
lenrolsq | -5.676062 4.378242 -1.30 0.195 -14.25726 2.905134
y94 | 0 (omitted)
y95 | -12.75551 2.686937 -4.75 0.000 -18.02181 -7.489212
y96 | -12.10136 1.165543 -10.38 0.000 -14.38578 -9.816936
y97 | -14.68949 .6654535 -22.07 0.000 -15.99376 -13.38523
y98 | 0 (omitted)
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 80.417
Chi-sq(4) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 43.158
(Kleibergen-Paap rk Wald F statistic): 25.287
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 16.85
10% maximal IV relative bias 10.27
20% maximal IV relative bias 6.71
30% maximal IV relative bias 5.34
10% maximal IV size 24.58
15% maximal IV size 13.96
20% maximal IV size 10.26
25% maximal IV size 8.31
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 14.831
Chi-sq(3) P-val = 0.0020
-endog- option:
Endogeneity test of endogenous regressors: 0.014
Chi-sq(1) P-val = 0.9062
Regressors tested: aexpp
------------------------------------------------------------------------------
Instrumented: aexpp
Included instruments: lunch lunchsq lenrol lenrolsq y95 y96 y97
Excluded instruments: lfound l96 l97 l98
Dropped collinear: y94 y98
------------------------------------------------------------------------------

I am not sure if I understand the results clearly:

1) The Underidentification test checks whether the instruments are relevant for the potential endogenous regressor in the meaning that the instruments are correlated with the endogenous regressor. From the result I conclude, that my instruments are correlated with aexpp.

2) The weak identification test checks whether the instruments are only weakly correlated with the endogenous regressors. Since the value of the statistic is large, I conclude the instruments appear to be strong.

3) The Hansen J Statistic tests whether my instruments are valid, meaning whether they are correlated with the error term. Since the P-Value is 0.0020 I conclude, that the H0: Instruments are exogenous is not rejected.

Can someone please check whether my interpretation is correct ?

Thank you very much!