Panel Date IV Regression, Fixed Effects

[Lea Birm]

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
------------------------------------------------------------------------------

[Phil Bromiley]

You may want to try to have a more readable presentation – fixed spacing fonts help for output tables. It is very hard to read your results table.

You may want to look at xtivreg2 which has more diagnostics. It has explicit tests for weak instruments. You might also want to test whether expenditures are endogenous. I might be tempted to look at expenditures over more lagged years – you are assuming a quick transfer from expenditures to math performance. However, it is quite possible that this form of expenditure doesn't influence your dependent variable. Another possibility to consider is whether your model should have a lagged dependent variable.

Note that you are estimating the effect of variation within panels on math4. It may be that large stable differences in expenditures do influence this variable even if small year-to-year variations don't.