I am attempting to apply GMM (xtabond2) to treat endogeneity and reverse causality. It is the first time that I use this model. In particular, I am trying to check the tests reported in the stata output, to be sure that everything is ok. I report below one of the models I have estimated.
Code:
xtabond2 SHROA_5w RepTrak Td_TE logTA Int_TA Bsize IndBoard Y1 Y2 Y3 Y4 Y5 Sector1 Sector2 Sector3 Sector4 Sector5 Country1-Country18 lag1GDPperCapita,
> robust gmm(SHROA_5w RepTrak Td_TE logTA Int_TA Bsize IndBoard, lag (2 2)) iv(Y1 Y2 Y3 Y4 Y5) iv(Sector1 Sector2 Sector3 Sector4 Sector5) iv(Country1-Cou
> ntry18) small
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate robust weighting matrix for Hansen test.
Difference-in-Sargan/Hansen statistics may be negative.
Dynamic panel-data estimation, one-step system GMM
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Group variable: Company1 Number of obs = 297
Time variable : Year Number of groups = 94
Number of instruments = 66 Obs per group: min = 1
F(35, 93) = 16.36 avg = 3.16
Prob > F = 0.000 max = 4
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| Robust
SHROA_5w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
RepTrak | .8240757 .3643529 2.26 0.026 .1005431 1.547608
Td_TE | -.0000894 .0008028 -0.11 0.912 -.0016836 .0015048
logTA | .5791236 .7792745 0.74 0.459 -.9683611 2.126608
Int_TA | -.1055613 .0948168 -1.11 0.268 -.2938487 .082726
Bsize | .2358727 .3432642 0.69 0.494 -.445782 .9175275
IndBoard | .0093846 .0422991 0.22 0.825 -.0746131 .0933822
Y1 | 0 (omitted)
Y2 | 5.76741 2.607804 2.21 0.029 .5888279 10.94599
Y3 | 4.945185 2.295553 2.15 0.034 .3866719 9.503697
Y4 | 4.3477 1.866018 2.33 0.022 .6421585 8.053242
Y5 | 0 (omitted)
Sector1 | 2.13721 1.75524 1.22 0.226 -1.348348 5.622769
Sector2 | 3.345858 2.051973 1.63 0.106 -.7289549 7.42067
Sector3 | 0 (omitted)
Sector4 | 1.926695 2.326126 0.83 0.410 -2.692531 6.545921
Sector5 | .2156303 1.772491 0.12 0.903 -3.304185 3.735445
Country1 | -.3803363 5.413125 -0.07 0.944 -11.12973 10.36906
Country2 | -1.267118 6.9272 -0.18 0.855 -15.02316 12.48893
Country3 | 0 (omitted)
Country4 | 2.981356 7.630048 0.39 0.697 -12.17041 18.13312
Country5 | 2.020135 5.026272 0.40 0.689 -7.961044 12.00131
Country6 | 1.050245 7.457543 0.14 0.888 -13.75896 15.85945
Country7 | .58333 7.467397 0.08 0.938 -14.24544 15.4121
Country8 | -1.265909 7.970619 -0.16 0.874 -17.09398 14.56216
Country9 | 7.628754 7.696808 0.99 0.324 -7.655581 22.91309
Country10 | 3.032004 12.82337 0.24 0.814 -22.43267 28.49668
Country11 | -1.848758 8.706837 -0.21 0.832 -19.13881 15.44129
Country12 | 1.560724 7.515723 0.21 0.836 -13.36401 16.48546
Country13 | 5.490397 8.946452 0.61 0.541 -12.27548 23.25628
Country14 | 5.398958 6.85746 0.79 0.433 -8.218599 19.01651
Country15 | 1.134326 5.682236 0.20 0.842 -10.14947 12.41812
Country16 | .7027418 6.13279 0.11 0.909 -11.47576 12.88125
Country17 | 0 (omitted)
Country18 | 2.949616 5.574061 0.53 0.598 -8.119365 14.0186
lag1GDPperCapita | -.0000125 .0001506 -0.08 0.934 -.0003116 .0002865
_cons | -72.54409 27.64953 -2.62 0.010 -127.4506 -17.6376
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Instruments for first differences equation
Standard
D.(Country1 Country2 Country3 Country4 Country5 Country6 Country7 Country8
Country9 Country10 Country11 Country12 Country13 Country14 Country15
Country16 Country17 Country18)
D.(Sector1 Sector2 Sector3 Sector4 Sector5)
D.(Y1 Y2 Y3 Y4 Y5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(SHROA_5w RepTrak Td_TE logTA Int_TA Bsize IndBoard)
Instruments for levels equation
Standard
Country1 Country2 Country3 Country4 Country5 Country6 Country7 Country8
Country9 Country10 Country11 Country12 Country13 Country14 Country15
Country16 Country17 Country18
Sector1 Sector2 Sector3 Sector4 Sector5
Y1 Y2 Y3 Y4 Y5
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(SHROA_5w RepTrak Td_TE logTA Int_TA Bsize IndBoard)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.07 Pr > z = 0.039
Arellano-Bond test for AR(2) in first differences: z = -0.32 Pr > z = 0.748
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(30) = 133.65 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(30) = 40.13 Prob > chi2 = 0.102
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(9) = 25.53 Prob > chi2 = 0.002
Difference (null H = exogenous): chi2(21) = 14.60 Prob > chi2 = 0.843
iv(Y1 Y2 Y3 Y4 Y5)
Hansen test excluding group: chi2(27) = 35.68 Prob > chi2 = 0.123
Difference (null H = exogenous): chi2(3) = 4.45 Prob > chi2 = 0.217
iv(Sector1 Sector2 Sector3 Sector4 Sector5)
Hansen test excluding group: chi2(26) = 35.05 Prob > chi2 = 0.111
Difference (null H = exogenous): chi2(4) = 5.08 Prob > chi2 = 0.279
iv(Country1 Country2 Country3 Country4 Country5 Country6 Country7 Country8 Country9 Country10 Country11 Country12 Country13 Country14 Country15 Country16
> Country17 Country18)
Hansen test excluding group: chi2(14) = 33.51 Prob > chi2 = 0.002
Difference (null H = exogenous): chi2(16) = 6.61 Prob > chi2 = 0.980
In particular:
- Significant F statistic (1) indicates that the model fitting should be ok. (ok)
- The insignificant Hansen statistics should indicate the validity of the adopted instruments in the model. (ok)
- The significance of Arellano–Bond test for AR(1) in first differences rejects the null of no first-order serial correlation. (ok)
- The test for AR(2) does not reject the null that there is no second-order serial correlation. (not ok) But I have noted that the main part of the papers adopting this model have the same results on this test.
- How should interpret the results of "Difference-in-Hansen tests of exogeneity of instrument subsets" ? Many articles do not even report it.
- I adopted the "small" option to use the small-sample adjustment. It should improve my results that could be biased by the small number of observations. Is it correct?
Any further observations on the validity/correctness of the applied model is really appreciated.
Thank you in advance for your precious support.
Nicola
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