Dear Statalisters,
I would like to send a big thank you to Christopher Baum, Mark Schaffer and Steven Stillman for their excellent, very useful paper "Instrumental variables and GMM: Estimation and Testing", and for developing ivreg2.
Could someone help answer questions that arose when I tried to use ivreg2? Pls forgive me if they are basic questions.
1- In the examples shown in the help file for ivreg2, the test for heteroskedasticity in IV/GMM estimation is indicated with the option fitlev (fitted values). Why is this option needed ? I obtain different results when including (cannot reject null of homoskestaticity) and omitting (reject null of homoskestaticity) the fitlev option (see output below).
2- What are centered and uncentered R-square ? I do not understand why in some of the ivreg I ran, I also obtained negative r-squares.
3- I am using ivreg2 on a two-year panel data, on variables that have been first differenced. One variable may be endogenous (criyielA) and would need to be instrumented for. In their paper, Baum et al caution against the use of instrument with little explanatory power and propose a rule of thumb of an F-stat above 10. It is very difficult for me to find relevant excluded instruments and the F-stat is below 10. What would be your advice ?
Thanks a lot in advance for your help,
Best regards,
Thi Minh
PS: example of output below
First-stage regressions
-----------------------
First-stage regression of criyielA:
OLS regression with robust standard errors
------------------------------------------
Number of obs = 3370
F( 20, 3349) = 8.20
Prob > F = 0.0000
Total (centered) SS = 8667.132874 Centered R2 = 0.0414
Total (uncentered) SS = 9010.059308 Uncentered R2 = 0.0778
Residual SS = 8308.706362 Root MSE = 1.5751
------------------------------------------------------------------------------
| Robust
criyielA | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cprod92_lp~e | -1.64e-07 2.94e-07 -0.56 0.577 -7.41e-07 4.13e-07
clriceprice | -1.292931 .1453145 -8.90 0.000 -1.577845 -1.008017
lanupc92 | -.0143288 .0106115 -1.35 0.177 -.0351344 .0064769
chhsize | .0277972 .0179343 1.55 0.121 -.0073661 .0629605
chhsizesq | 6.56e-12 6.50e-12 1.01 0.313 -6.19e-12 1.93e-11
cf04s | .3489401 .2765587 1.26 0.207 -.1933009 .8911811
cf59s | .1901888 .2751527 0.69 0.489 -.3492955 .7296731
cf1014s | -.2640732 .254593 -1.04 0.300 -.7632467 .2351003
cm04s | .2340304 .3009332 0.78 0.437 -.356001 .8240618
cm59s | .7453756 .2718197 2.74 0.006 .2124262 1.278325
cm1014s | .5206262 .2808137 1.85 0.064 -.0299575 1.07121
croadnew8 | -.1269749 .0570803 -2.22 0.026 -.2388907 -.0150591
cmarketdis | .0301164 .0061014 4.94 0.000 .0181536 .0420793
croadist | -.0026464 .0052559 -0.50 0.615 -.0129515 .0076587
cm1555s | .3649849 .1925192 1.90 0.058 -.0124822 .742452
cirrignew8 | .2189353 .0634521 3.45 0.001 .0945265 .3433441
cpest4 | .3339898 .0771071 4.33 0.000 .182808 .4851715
cpest5 | -.1898401 .0683461 -2.78 0.006 -.3238443 -.0558359
cpest6 | -.092264 .0772317 -1.19 0.232 -.2436902 .0591621
cpest7 | -.1746922 .0659641 -2.65 0.008 -.3040261 -.0453583
_cons | .5711068 .075765 7.54 0.000 .4225564 .7196571
------------------------------------------------------------------------------
Partial R-squared of excluded instruments: 0.0122
Test of excluded instruments:
F( 6, 3349) = 6.71
Prob > F = 0.0000
Summary results for first-stage regressions:
Shea
Variable Partial R2 Partial R2 F( 6, 3349) P-value
criyielA 0.0122 0.0122 6.71 0.0000
NB: first-stage F-stat heteroskedasticity-robust
GMM estimation
--------------
Number of obs = 3370
F( 15, 3354) = 33.06
Prob > F = 0.0000
Total (centered) SS = 76.61568406 Centered R2 = 0.0439
Total (uncentered) SS = 107.2221951 Uncentered R2 = 0.3168
Residual SS = 73.24985164 Root MSE = .147431
------------------------------------------------------------------------------
| Robust
cpovgapsqi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
criyielA | -.0372633 .0151439 -2.46 0.014 -.0669447 -.0075819
cprod92_lp~e | -1.10e-07 1.62e-08 -6.77 0.000 -1.42e-07 -7.82e-08
clriceprice | -.0717184 .0223985 -3.20 0.001 -.1156187 -.027818
lanupc92 | .0008063 .0010795 0.75 0.455 -.0013095 .0029222
chhsize | .0211054 .0020391 10.35 0.000 .0171089 .0251019
chhsizesq | 4.74e-12 1.58e-12 3.01 0.003 1.65e-12 7.82e-12
cf04s | .2742387 .0270709 10.13 0.000 .2211807 .3272968
cf59s | .1364704 .0249785 5.46 0.000 .0875134 .1854273
cf1014s | .0050872 .0224207 0.23 0.821 -.0388565 .0490309
cm04s | .2357753 .0265897 8.87 0.000 .1836604 .2878901
cm59s | .1237924 .0246343 5.03 0.000 .07551 .1720747
cm1014s | .0513214 .0219281 2.34 0.019 .0083432 .0942996
croadnew8 | -.0090448 .0052677 -1.72 0.086 -.0193692 .0012797
cmarketdis | -.0017687 .0007171 -2.47 0.014 -.0031742 -.0003632
croadist | -.0009817 .0003324 -2.95 0.003 -.0016332 -.0003301
_cons | -.0559418 .0106129 -5.27 0.000 -.0767427 -.0351409
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 4.301
Chi-sq(5) P-val = 0.50693
-orthog- option:
Hansen J statistic for unrestricted equation: 0.000
Chi-sq(1) P-val = 0.98983
C statistic (exogeneity/orthogonality of specified instruments): 4.301
Chi-sq(4) P-val = 0.36681
Instruments tested: cpest4 cpest5 cpest6 cpest7
------------------------------------------------------------------------------
Instrumented: criyielA
Instruments: cm1555s cirrignew8 cpest4 cpest5 cpest6 cpest7 cprod92_lprice
clriceprice lanupc92 chhsize chhsizesq cf04s cf59s cf1014s cm04s
cm59s cm1014s croadnew8 cmarketdis croadist
------------------------------------------------------------------------------
. ivhettest, all
IV heteroskedasticity test(s) using levels and cross products of all IVs
Ho: Disturbance is homoskedastic
Pagan-Hall general test statistic : 311.008 Chi-sq(224) P-value = 0.0001
Pagan-Hall test w/assumed normality : 417.918 Chi-sq(224) P-value = 0.0000
White/Koenker nR2 test statistic : 469.100 Chi-sq(224) P-value = 0.0000
Breusch-Pagan/Godfrey/Cook-Weisberg : 636.519 Chi-sq(224) P-value = 0.0000
. ivhettest, all fitlev
IV heteroskedasticity test(s) using fitted value (X-hat*beta-hat)
Ho: Disturbance is homoskedastic
Pagan-Hall general test statistic : 1.444 Chi-sq(1) P-value = 0.2296
Pagan-Hall test w/assumed normality : 1.957 Chi-sq(1) P-value = 0.1619
White/Koenker nR2 test statistic : 1.495 Chi-sq(1) P-value = 0.2214
Breusch-Pagan/Godfrey/Cook-Weisberg : 2.029 Chi-sq(1) P-value = 0.1543
.
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