Hello!

I am running an IV Fixed Effects Regression with Panel Data. I have t=4 (1995-1998), N=550 districts.
I use StataIC16 and the data set mathpnl.
I want to use the Foundation grant awarded to each district as an instrument for average expenditures per student. The First Stage regression leads to a F-Statistic of 520 and the coefficient is significant, R2 = 0,73. Therefore I assume that the Foundation grant is a good instrument for average expenditures.

However if I run the regression and control for heteroskedastic standard errors and autocorrelation, I receive really large standard errors and my coefficient is not significant at all.
Am I missing something here? Is it possible that I still have an OVB Problem?

I would really appreciate some hints


[xtivreg math4 (laexpp = lfound ) $control y96 y97 y98, fe vce(cluster distid)]

Fixed-effects (within) IV regression Number of obs = 2,159
Group variable: distid Number of groups = 550

R-sq: Obs per group:
within = 0.3795 min = 1
between = 0.0510 avg = 3.9
overall = 0.0000 max = 4


Wald chi2(8) = 2835.36
corr(u_i, Xb) = -0.7394 Prob > chi2 = 0.0000

(Std. Err. adjusted for 550 clusters in distid)
------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
laexpp | 13.51771 23.08835 0.59 0.558 -31.73462 58.77004
lunch | .4493226 .5138517 0.87 0.382 -.5578082 1.456453
lunchsq | -.0022053 .0054514 -0.40 0.686 -.0128899 .0084793
lenrol | 81.13202 64.95943 1.25 0.212 -46.18612 208.4502
lenrolsq | -5.723085 4.459832 -1.28 0.199 -14.4642 3.018026
y96 | .0312388 1.752555 0.02 0.986 -3.403706 3.466183
y97 | -2.806808 2.376711 -1.18 0.238 -7.465076 1.85146
y98 | 11.73295 2.758448 4.25 0.000 6.326497 17.13941
_cons | -345.2751 331.3799 -1.04 0.297 -994.7678 304.2176
-------------+----------------------------------------------------------------
sigma_u | 19.563319
sigma_e | 8.834208
rho | .83062311 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: laexpp
Instruments: lunch lunchsq lenrol lenrolsq y96 y97 y98 lfound
------------------------------------------------------------------------------