Hello !
I am trying to estimate the following model in both difference and system GMM. However, the results change significantly both in terms of significance and in terms of the coefficients. Moreover, in difference GMM AR(1)=0.8 whereas in system GMM AR(2)=0.979 but AR(3)=0.031. What does this suggest and how I can fix this problem?
I have 33 groups and a time period=5.
Difference GMM
xtabond2 diff_gdp log_initial log_Mcap log_Liab log_trade log_school log_govsize log_infl td*, gmm( log_initi
> al , collapse sp) gmm( L.( log_Mcap log_Liab log_trade log_govsize log_school log_infl ), collapse) iv( td*
> ) robust two small ar(3) nolevel
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
res}Warning: split has no effect in Difference GMM.
td5 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.
Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: Country_ Number of obs = 126
Time variable : period Number of groups = 33
Number of instruments = 26 Obs per group: min = 2
F(0, 33) = . avg = 3.82
Prob > F = . max = 4
------------------------------------------------------------------------------
| Corrected
diff_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_initial | -.0766945 .059806 -1.28 0.209 -.1983708 .0449818
log_Mcap | .0410073 .0179618 2.28 0.029 .0044639 .0775508
log_Liab | .0198893 .0579202 0.34 0.733 -.0979503 .1377289
log_trade | -.1288009 .1143785 -1.13 0.268 -.3615057 .1039039
log_school | -.0846866 .0904975 -0.94 0.356 -.2688052 .099432
log_govsize | .0193566 .0762848 0.25 0.801 -.135846 .1745592
log_infl | .0061522 .0101976 0.60 0.550 -.0145949 .0268993
td1 | -.0457857 .0314332 -1.46 0.155 -.109737 .0181657
td2 | -.0283545 .0247333 -1.15 0.260 -.0786748 .0219658
td3 | -.0247058 .0176698 -1.40 0.171 -.0606554 .0112437
td4 | -.0070187 .0076711 -0.91 0.367 -.0226256 .0085883
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(td1 td2 td3 td4 td5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/4).(L.log_Mcap L.log_Liab L.log_trade L.log_govsize L.log_school
L.log_infl) collapsed
L(1/4).log_initial collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -0.25 Pr > z = 0.804
Arellano-Bond test for AR(2) in first differences: z = 0.56 Pr > z = 0.576
Arellano-Bond test for AR(3) in first differences: z = -1.07 Pr > z = 0.285
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(15) = 12.90 Prob > chi2 = 0.610
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(15) = 14.73 Prob > chi2 = 0.471
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
gmm(log_initial, collapse lag(1 .))
Hansen test excluding group: chi2(11) = 11.10 Prob > chi2 = 0.435
Difference (null H = exogenous): chi2(4) = 3.62 Prob > chi2 = 0.459
iv(td1 td2 td3 td4 td5)
Hansen test excluding group: chi2(11) = 8.51 Prob > chi2 = 0.667
Difference (null H = exogenous): chi2(4) = 6.22 Prob > chi2 = 0.183
System GMM
xtabond2 diff_gdp log_initial log_Mcap log_Liab log_trade log_school log_govsize log_infl td*, gmm( log_initi
> al , collapse sp) gmm( L.( log_Mcap log_Liab log_trade log_govsize log_school log_infl ), collapse) iv( td*
> ) robust two small ar(3)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
td2 dropped due to collinearity
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: Country_ Number of obs = 160
Time variable : period Number of groups = 33
Number of instruments = 34 Obs per group: min = 3
F(11, 32) = 34.48 avg = 4.85
Prob > F = 0.000 max = 5
------------------------------------------------------------------------------
| Corrected
diff_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_initial | -.0108161 .0085561 -1.26 0.215 -.0282444 .0066121
log_Mcap | .0029089 .0072577 0.40 0.691 -.0118746 .0176924
log_Liab | -.0101865 .0105349 -0.97 0.341 -.0316455 .0112725
log_trade | .0107354 .0097941 1.10 0.281 -.0092146 .0306853
log_school | .0400703 .0233032 1.72 0.095 -.0073967 .0875373
log_govsize | .0007092 .0124605 0.06 0.955 -.0246721 .0260904
log_infl | -.0005491 .0050937 -0.11 0.915 -.0109245 .0098264
td1 | -.0057598 .0053446 -1.08 0.289 -.0166465 .0051269
td3 | -.0054331 .0042171 -1.29 0.207 -.014023 .0031569
td4 | -.006852 .0052233 -1.31 0.199 -.0174916 .0037875
td5 | -.0181138 .0077344 -2.34 0.026 -.0338683 -.0023593
_cons | .025506 .1402732 0.18 0.857 -.2602211 .3112332
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(td1 td2 td3 td4 td5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/4).(L.log_Mcap L.log_Liab L.log_trade L.log_govsize L.log_school
L.log_infl) collapsed
L(1/4).log_initial collapsed
Instruments for levels equation
Standard
td1 td2 td3 td4 td5
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.log_Mcap L.log_Liab L.log_trade L.log_govsize L.log_school
L.log_infl) collapsed
D.log_initial collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.87 Pr > z = 0.062
Arellano-Bond test for AR(2) in first differences: z = 0.03 Pr > z = 0.979
Arellano-Bond test for AR(3) in first differences: z = -2.16 Pr > z = 0.031
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(22) = 43.85 Prob > chi2 = 0.004
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(22) = 25.91 Prob > chi2 = 0.255
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(15) = 15.40 Prob > chi2 = 0.423
Difference (null H = exogenous): chi2(7) = 10.52 Prob > chi2 = 0.161
gmm(log_initial, collapse eq(diff) lag(1 4))
Hansen test excluding group: chi2(18) = 23.43 Prob > chi2 = 0.175
Difference (null H = exogenous): chi2(4) = 2.49 Prob > chi2 = 0.647
gmm(log_initial, collapse eq(diff) lag(1 4)) eq(level) lag(0 0))
Hansen test excluding group: chi2(21) = 25.91 Prob > chi2 = 0.210
Difference (null H = exogenous): chi2(1) = -0.00 Prob > chi2 = 1.000
iv(td1 td2 td3 td4 td5)
Hansen test excluding group: chi2(18) = 24.99 Prob > chi2 = 0.125
Difference (null H = exogenous): chi2(4) = 0.92 Prob > chi2 = 0.921
I am trying to estimate the following model in both difference and system GMM. However, the results change significantly both in terms of significance and in terms of the coefficients. Moreover, in difference GMM AR(1)=0.8 whereas in system GMM AR(2)=0.979 but AR(3)=0.031. What does this suggest and how I can fix this problem?
I have 33 groups and a time period=5.
Difference GMM
xtabond2 diff_gdp log_initial log_Mcap log_Liab log_trade log_school log_govsize log_infl td*, gmm( log_initi
> al , collapse sp) gmm( L.( log_Mcap log_Liab log_trade log_govsize log_school log_infl ), collapse) iv( td*
> ) robust two small ar(3) nolevel
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
res}Warning: split has no effect in Difference GMM.
td5 dropped due to collinearity
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.
Dynamic panel-data estimation, two-step difference GMM
------------------------------------------------------------------------------
Group variable: Country_ Number of obs = 126
Time variable : period Number of groups = 33
Number of instruments = 26 Obs per group: min = 2
F(0, 33) = . avg = 3.82
Prob > F = . max = 4
------------------------------------------------------------------------------
| Corrected
diff_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_initial | -.0766945 .059806 -1.28 0.209 -.1983708 .0449818
log_Mcap | .0410073 .0179618 2.28 0.029 .0044639 .0775508
log_Liab | .0198893 .0579202 0.34 0.733 -.0979503 .1377289
log_trade | -.1288009 .1143785 -1.13 0.268 -.3615057 .1039039
log_school | -.0846866 .0904975 -0.94 0.356 -.2688052 .099432
log_govsize | .0193566 .0762848 0.25 0.801 -.135846 .1745592
log_infl | .0061522 .0101976 0.60 0.550 -.0145949 .0268993
td1 | -.0457857 .0314332 -1.46 0.155 -.109737 .0181657
td2 | -.0283545 .0247333 -1.15 0.260 -.0786748 .0219658
td3 | -.0247058 .0176698 -1.40 0.171 -.0606554 .0112437
td4 | -.0070187 .0076711 -0.91 0.367 -.0226256 .0085883
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(td1 td2 td3 td4 td5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/4).(L.log_Mcap L.log_Liab L.log_trade L.log_govsize L.log_school
L.log_infl) collapsed
L(1/4).log_initial collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -0.25 Pr > z = 0.804
Arellano-Bond test for AR(2) in first differences: z = 0.56 Pr > z = 0.576
Arellano-Bond test for AR(3) in first differences: z = -1.07 Pr > z = 0.285
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(15) = 12.90 Prob > chi2 = 0.610
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(15) = 14.73 Prob > chi2 = 0.471
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
gmm(log_initial, collapse lag(1 .))
Hansen test excluding group: chi2(11) = 11.10 Prob > chi2 = 0.435
Difference (null H = exogenous): chi2(4) = 3.62 Prob > chi2 = 0.459
iv(td1 td2 td3 td4 td5)
Hansen test excluding group: chi2(11) = 8.51 Prob > chi2 = 0.667
Difference (null H = exogenous): chi2(4) = 6.22 Prob > chi2 = 0.183
System GMM
xtabond2 diff_gdp log_initial log_Mcap log_Liab log_trade log_school log_govsize log_infl td*, gmm( log_initi
> al , collapse sp) gmm( L.( log_Mcap log_Liab log_trade log_govsize log_school log_infl ), collapse) iv( td*
> ) robust two small ar(3)
Favoring space over speed. To switch, type or click on mata: mata set matafavor speed, perm.
td2 dropped due to collinearity
Warning: Number of instruments may be large relative to number of observations.
Warning: Two-step estimated covariance matrix of moments is singular.
Using a generalized inverse to calculate optimal weighting matrix for two-step estimation.
Difference-in-Sargan/Hansen statistics may be negative.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: Country_ Number of obs = 160
Time variable : period Number of groups = 33
Number of instruments = 34 Obs per group: min = 3
F(11, 32) = 34.48 avg = 4.85
Prob > F = 0.000 max = 5
------------------------------------------------------------------------------
| Corrected
diff_gdp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_initial | -.0108161 .0085561 -1.26 0.215 -.0282444 .0066121
log_Mcap | .0029089 .0072577 0.40 0.691 -.0118746 .0176924
log_Liab | -.0101865 .0105349 -0.97 0.341 -.0316455 .0112725
log_trade | .0107354 .0097941 1.10 0.281 -.0092146 .0306853
log_school | .0400703 .0233032 1.72 0.095 -.0073967 .0875373
log_govsize | .0007092 .0124605 0.06 0.955 -.0246721 .0260904
log_infl | -.0005491 .0050937 -0.11 0.915 -.0109245 .0098264
td1 | -.0057598 .0053446 -1.08 0.289 -.0166465 .0051269
td3 | -.0054331 .0042171 -1.29 0.207 -.014023 .0031569
td4 | -.006852 .0052233 -1.31 0.199 -.0174916 .0037875
td5 | -.0181138 .0077344 -2.34 0.026 -.0338683 -.0023593
_cons | .025506 .1402732 0.18 0.857 -.2602211 .3112332
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(td1 td2 td3 td4 td5)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/4).(L.log_Mcap L.log_Liab L.log_trade L.log_govsize L.log_school
L.log_infl) collapsed
L(1/4).log_initial collapsed
Instruments for levels equation
Standard
td1 td2 td3 td4 td5
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.log_Mcap L.log_Liab L.log_trade L.log_govsize L.log_school
L.log_infl) collapsed
D.log_initial collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -1.87 Pr > z = 0.062
Arellano-Bond test for AR(2) in first differences: z = 0.03 Pr > z = 0.979
Arellano-Bond test for AR(3) in first differences: z = -2.16 Pr > z = 0.031
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(22) = 43.85 Prob > chi2 = 0.004
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(22) = 25.91 Prob > chi2 = 0.255
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(15) = 15.40 Prob > chi2 = 0.423
Difference (null H = exogenous): chi2(7) = 10.52 Prob > chi2 = 0.161
gmm(log_initial, collapse eq(diff) lag(1 4))
Hansen test excluding group: chi2(18) = 23.43 Prob > chi2 = 0.175
Difference (null H = exogenous): chi2(4) = 2.49 Prob > chi2 = 0.647
gmm(log_initial, collapse eq(diff) lag(1 4)) eq(level) lag(0 0))
Hansen test excluding group: chi2(21) = 25.91 Prob > chi2 = 0.210
Difference (null H = exogenous): chi2(1) = -0.00 Prob > chi2 = 1.000
iv(td1 td2 td3 td4 td5)
Hansen test excluding group: chi2(18) = 24.99 Prob > chi2 = 0.125
Difference (null H = exogenous): chi2(4) = 0.92 Prob > chi2 = 0.921
