Hello,
I am working with StataIC16, and with Panel Data, where i=550 and t=6. To determine the effect of expenditure on test schore performance (math4) I want to use fixed effects IV Regression. The coefficient 13 seems quite plausible but I really do not understand why the standard error is so high? If I apply normal IV Regression the standard deviation is 1/10 of it.
Can anyone explain me the mechanism behind the FE IV Regression standard error? The only explanation I have is that the correlation between the endogenous regressor and the instrument might be very small which would lead to large standard errors - but then the se in the normal IV model should also be really high?
[ivreg math4 (aexpp = lfound) $control y96 y97 y98, r]
Instrumental variables (2SLS) regression Number of obs = 2,159
F(8, 2150) = 147.21
Prob > F = 0.0000
R-squared = 0.3489
Root MSE = 12.352
------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
aexpp | 16.96577 2.467018 6.88 0.000 12.12778 21.80376
[xtivreg2 math4 (aexpp = lfound) $control $conyear, cluster(distid) fe 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 and clustering on distid
Number of clusters (distid) = 543 Number of obs = 2152
F( 8, 542) = 118.73
Prob > F = 0.0000
Total (centered) SS = 201356.9083 Centered R2 = 0.3801
Total (uncentered) SS = 201356.9083 Uncentered R2 = 0.3801
Residual SS = 124825.1118 Root MSE = 8.808
------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
aexpp | 13.30751 22.61193 0.59 0.556 -31.01106 57.62607
lunch | .4525351 .5155055 0.88 0.380 -.5578372 1.462907
lunchsq | -.0022127 .0054569 -0.41 0.685 -.012908 .0084826
lenrol | 81.38056 64.70469 1.26 0.208 -45.4383 208.1994
lenrolsq | -5.737292 4.439372 -1.29 0.196 -14.4383 2.963717
y94 | 0 (omitted)
y95 | -11.71218 2.781055 -4.21 0.000 -17.16295 -6.261413
y96 | -11.70345 1.202484 -9.73 0.000 -14.06027 -9.346621
y97 | -14.54061 .6900335 -21.07 0.000 -15.89305 -13.18817
y98 | 0 (omitted)
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 54.158
Chi-sq(1) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 151.876
(Kleibergen-Paap rk Wald F statistic): 67.722
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
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): 0.000
(equation exactly identified)
-endog- option:
Endogeneity test of endogenous regressors: 0.028
Chi-sq(1) P-val = 0.8673
Regressors tested: aexpp
------------------------------------------------------------------------------
Instrumented: aexpp
Included instruments: lunch lunchsq lenrol lenrolsq y95 y96 y97
Excluded instruments: lfound
Dropped collinear: y94 y98
------------------------------------------------------------------------------
I am working with StataIC16, and with Panel Data, where i=550 and t=6. To determine the effect of expenditure on test schore performance (math4) I want to use fixed effects IV Regression. The coefficient 13 seems quite plausible but I really do not understand why the standard error is so high? If I apply normal IV Regression the standard deviation is 1/10 of it.
Can anyone explain me the mechanism behind the FE IV Regression standard error? The only explanation I have is that the correlation between the endogenous regressor and the instrument might be very small which would lead to large standard errors - but then the se in the normal IV model should also be really high?
[ivreg math4 (aexpp = lfound) $control y96 y97 y98, r]
Instrumental variables (2SLS) regression Number of obs = 2,159
F(8, 2150) = 147.21
Prob > F = 0.0000
R-squared = 0.3489
Root MSE = 12.352
------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
aexpp | 16.96577 2.467018 6.88 0.000 12.12778 21.80376
[xtivreg2 math4 (aexpp = lfound) $control $conyear, cluster(distid) fe 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 and clustering on distid
Number of clusters (distid) = 543 Number of obs = 2152
F( 8, 542) = 118.73
Prob > F = 0.0000
Total (centered) SS = 201356.9083 Centered R2 = 0.3801
Total (uncentered) SS = 201356.9083 Uncentered R2 = 0.3801
Residual SS = 124825.1118 Root MSE = 8.808
------------------------------------------------------------------------------
| Robust
math4 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
aexpp | 13.30751 22.61193 0.59 0.556 -31.01106 57.62607
lunch | .4525351 .5155055 0.88 0.380 -.5578372 1.462907
lunchsq | -.0022127 .0054569 -0.41 0.685 -.012908 .0084826
lenrol | 81.38056 64.70469 1.26 0.208 -45.4383 208.1994
lenrolsq | -5.737292 4.439372 -1.29 0.196 -14.4383 2.963717
y94 | 0 (omitted)
y95 | -11.71218 2.781055 -4.21 0.000 -17.16295 -6.261413
y96 | -11.70345 1.202484 -9.73 0.000 -14.06027 -9.346621
y97 | -14.54061 .6900335 -21.07 0.000 -15.89305 -13.18817
y98 | 0 (omitted)
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 54.158
Chi-sq(1) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 151.876
(Kleibergen-Paap rk Wald F statistic): 67.722
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
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): 0.000
(equation exactly identified)
-endog- option:
Endogeneity test of endogenous regressors: 0.028
Chi-sq(1) P-val = 0.8673
Regressors tested: aexpp
------------------------------------------------------------------------------
Instrumented: aexpp
Included instruments: lunch lunchsq lenrol lenrolsq y95 y96 y97
Excluded instruments: lfound
Dropped collinear: y94 y98
------------------------------------------------------------------------------
