IV Regression Panel Data - xtivreg - lagged Variables

[Lea Birm]

Hello,

I am working with StataIC16 and the panel data set mathpnl**, for the years 1992 - 1998-
I want to analyze the effect of real expenditure per pupil (lrexpp) on the pass rate of a standardized math test (math4).
First I have done a fixed effects regression.
Now I want to use the policy change (the law concerning school financing has changed in 1995) to perform an IV Regression, using the exogenous foundation Grant (found / fnd_1) as an instrument for my (potential endogenous) spending variables.

The first stage regression gives me a large R2 and F statistic, but unfortunately I am not getting convincing results when applying the xtivreg command.
I think that I have a potential problem with the instruments, and moreover I am unsure how to handle the lagged effect of lrexpp_1 in an IV Regression.

I also considered to use the average of spending as an explanatory variable.

Does anybody know, how to do an IV Regression with two potential endogenous variables that are lagged?



1.
global control y94 y95 y96 y97 y98 lunch lunchsq lenrol lenrolsq

. [xtreg math4 lrexpp lrexpp_1 $control , fe]

Fixed-effects (within) regression Number of obs = 3,300
Group variable: distid Number of groups = 550

R-sq: Obs per group:
within = 0.6029 min = 6
between = 0.0323 avg = 6.0
overall = 0.3132 max = 6

F(11,2739) = 378.06
corr(u_i, Xb) = -0.0610 Prob > F = 0.0000

------------------------------------------------------------------------------
math4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lrexpp | .449403 2.564402 0.18 0.861 -4.578955 5.477761
lrexpp_1 | 7.309974 2.384014 3.07 0.002 2.635326 11.98462
y94 | 6.116057 .5627774 10.87 0.000 5.012546 7.219568
y95 | 17.91013 .7078583 25.30 0.000 16.52214 19.29812
y96 | 17.71773 .7803005 22.71 0.000 16.18769 19.24776
y97 | 14.95576 .8245826 18.14 0.000 13.3389 16.57263
y98 | 29.65786 .8596281 34.50 0.000 27.97227 31.34344
lunch | .0730933 .1196749 0.61 0.541 -.1615689 .3077556
lunchsq | -.0002439 .0016056 -0.15 0.879 -.0033922 .0029044
lenrol | 10.09453 8.467345 1.19 0.233 -6.508501 26.69756
lenrolsq | -.7154355 .6097558 -1.17 0.241 -1.911063 .4801923
_cons | -58.92273 43.51133 -1.35 0.176 -144.2411 26.39561
-------------+----------------------------------------------------------------
sigma_u | 11.587473
sigma_e | 8.9971971
rho | .62387373 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(549, 2739) = 5.75 Prob > F = 0.0000


2.

[xtivreg math4 (lrexpp lrexpp_1 = lfound lfnd_1 ) $controliv y96 y97 , fe vce(cluster distid)]

Fixed-effects (within) IV regression Number of obs = 1,602
Group variable: distid Number of groups = 538

R-sq: Obs per group:
within = 0.3133 min = 1
between = 0.0053 avg = 3.0
overall = 0.0260 max = 3


Wald chi2(9) = 2191.22
corr(u_i, Xb) = -0.8524 Prob > chi2 = 0.0000

(Std. Err. adjusted for 538 clusters in distid)
------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lrexpp | -10.48314 226.7776 -0.05 0.963 -454.959 433.9927
lrexpp_1 | 137.3179 262.9871 0.52 0.602 -378.1274 652.7632
lunch | .2588259 .6851738 0.38 0.706 -1.08409 1.601742
lunchsq | .0009495 .0094053 0.10 0.920 -.0174844 .0193835
lenrol | -27.92626 205.4506 -0.14 0.892 -430.602 374.7495
lenrolsq | 2.565563 10.14549 0.25 0.800 -17.31922 22.45035
y96 | -6.357215 3.641985 -1.75 0.081 -13.49537 .7809439
y97 | -11.55872 4.019192 -2.88 0.004 -19.43619 -3.681246
_cons | -973.5975 823.6287 -1.18 0.237 -2587.88 640.6851
-------------+----------------------------------------------------------------
sigma_u | 27.482767
sigma_e | 9.9361013
rho | .88439953 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Instrumented: lrexpp lrexpp_1
Instruments: lunch lunchsq lenrol lenrolsq y96 y97 lfound lfnd_1

[Phil Bromiley]

You didn't get a quick answer. You will increase your chances of a useful answer by following the FAQ on asking questions – provide Stata code in code delimiters, readable Stata output (fixed spacing fonts help), and sample data using dataex.

While I can't say exactly why the results differ, one difference is you have only two year dummies in one, and more in the other. But the big difference is you've got twice as many observations in one estimation then you do in the other. Double the sample size, and you shouldn't be surprised you get different results.

Let me suggest you look into factor variable notation and lag notation which would save you from creating lags and squares prior to the estimate (and makes it easier for margins to work with the results). You might also consider xtivreg2 which has more diagnostics.