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Dear Stata users,
I believe stata's xtdpd and Roodman's xtabond2 produce different
results when estimating a just-identified model.
Below I present a set of estimations of the same model using
alternatively xtabond2 and xtdpd and abdata.dta . All estimation
generate the same coefficient estimates, except for the
just-identified model (the last three tables below). I can't figure
out what's going on. Do you have suggestion?
. xtdpd n w k yr*, dgmmiv(w k, l(2 10)) div( yr*) vce(robust) twostep nocons
note: yr1976 dropped from div() because of collinearity
note: D.yr1976 dropped because of collinearity
Dynamic panel-data estimation Number of obs = 891
Group variable: id Number of groups = 140
Time variable: year
Obs per group: min = 6
avg = 6.364286
max = 8
Number of instruments = 64 Wald chi2(10) = 263.63
Prob > chi2 = 0.0000
Two-step results
------------------------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w | -.5251849 .1867368 -2.81 0.005 -.8911822 -.1591875
k | .6931066 .1156379 5.99 0.000 .4664605 .9197527
yr1977 | -.0468811 .0224064 -2.09 0.036 -.0907969 -.0029653
yr1978 | -.079391 .0260936 -3.04 0.002 -.1305336 -.0282485
yr1979 | -.0908402 .0294539 -3.08 0.002 -.1485689 -.0331115
yr1980 | -.1082455 .028502 -3.80 0.000 -.1641083 -.0523827
yr1981 | -.1367655 .0256726 -5.33 0.000 -.1870828 -.0864482
yr1982 | -.1329874 .0307649 -4.32 0.000 -.1932854 -.0726893
yr1983 | -.1100415 .0381101 -2.89 0.004 -.184736 -.035347
yr1984 | -.0741515 .0441612 -1.68 0.093 -.1607057 .0124028
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/10).w L(2/10).k
Standard: D.yr1977 D.yr1978 D.yr1979 D.yr1980 D.yr1981
D.yr1982 D.yr1983 D.yr1984
. drop _est_dpd _est_ab2
. estimates store dpd
. xtabond2 n w k yr*, gmm(w k, l(2 10)) iv(yr*) robust twostep nolevel
Favoring speed over space. To switch, type or click on mata: mata set
matafavor space, perm.
yr1984 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: id Number of obs = 891
Time variable : year Number of groups = 140
Number of instruments = 64 Obs per group: min = 6
Wald chi2(10) = 263.63 avg = 6.36
Prob > chi2 = 0.000 max = 8
------------------------------------------------------------------------------
| Corrected
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w | -.5251849 .1867368 -2.81 0.005 -.8911822 -.1591875
k | .6931066 .1156379 5.99 0.000 .4664605 .9197527
yr1976 | .0741515 .0441612 1.68 0.093 -.0124028 .1607057
yr1977 | .0272704 .046981 0.58 0.562 -.0648106 .1193514
yr1978 | -.0052396 .0514405 -0.10 0.919 -.1060611 .095582
yr1979 | -.0166887 .0541152 -0.31 0.758 -.1227526 .0893751
yr1980 | -.034094 .0519545 -0.66 0.512 -.135923 .067735
yr1981 | -.0626141 .03934 -1.59 0.111 -.1397191 .014491
yr1982 | -.0588359 .0246208 -2.39 0.017 -.1070917 -.0105801
yr1983 | -.03589 .0152096 -2.36 0.018 -.0657003 -.0060797
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/10).(w k)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -0.40 Pr > z = 0.689
Arellano-Bond test for AR(2) in first differences: z = -1.70 Pr > z = 0.088
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(54) = 100.69 Prob > chi2 = 0.000
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(54) = 61.06 Prob > chi2 = 0.237
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
Hansen test excluding group: chi2(46) = 51.97 Prob > chi2 = 0.253
Difference (null H = exogenous): chi2(8) = 9.09 Prob > chi2 = 0.335
. estimates store ab2
. esttab dpd ab2
--------------------------------------------
(1) (2)
n n
--------------------------------------------
w -0.525** -0.525**
(-2.81) (-2.81)
k 0.693*** 0.693***
(5.99) (5.99)
yr1977 -0.0469* 0.0273
(-2.09) (0.58)
yr1978 -0.0794** -0.00524
(-3.04) (-0.10)
yr1979 -0.0908** -0.0167
(-3.08) (-0.31)
yr1980 -0.108*** -0.0341
(-3.80) (-0.66)
yr1981 -0.137*** -0.0626
(-5.33) (-1.59)
yr1982 -0.133*** -0.0588*
(-4.32) (-2.39)
yr1983 -0.110** -0.0359*
(-2.89) (-2.36)
yr1984 -0.0742
(-1.68)
yr1976 0.0742
(1.68)
--------------------------------------------
N 891 891
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. drop _est_dpd _est_ab2
. xtdpd n w k yr*, dgmmiv(w k, l(2 3)) div( yr*) vce(robust) twostep nocons
note: yr1976 dropped from div() because of collinearity
note: D.yr1976 dropped because of collinearity
Dynamic panel-data estimation Number of obs = 891
Group variable: id Number of groups = 140
Time variable: year
Obs per group: min = 6
avg = 6.364286
max = 8
Number of instruments = 34 Wald chi2(10) = 345.89
Prob > chi2 = 0.0000
Two-step results
------------------------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w | -.3776668 .2218938 -1.70 0.089 -.8125707 .0572371
k | .5092317 .1684431 3.02 0.003 .1790893 .8393742
yr1977 | -.0312372 .0242268 -1.29 0.197 -.078721 .0162465
yr1978 | -.0533206 .0304038 -1.75 0.079 -.1129109 .0062697
yr1979 | -.0617977 .0331106 -1.87 0.062 -.1266932 .0030978
yr1980 | -.0896192 .032657 -2.74 0.006 -.1536258 -.0256127
yr1981 | -.1448843 .0292449 -4.95 0.000 -.2022033 -.0875652
yr1982 | -.1697914 .0378177 -4.49 0.000 -.2439128 -.0956701
yr1983 | -.1665457 .0492459 -3.38 0.001 -.2630659 -.0700256
yr1984 | -.1511347 .0648747 -2.33 0.020 -.2782867 -.0239827
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/3).w L(2/3).k
Standard: D.yr1977 D.yr1978 D.yr1979 D.yr1980 D.yr1981
D.yr1982 D.yr1983 D.yr1984
. estimates store dpd
. xtabond2 n w k yr*, gmm(w k, l(2 3)) iv(yr*) robust twostep nolevel
Favoring speed over space. To switch, type or click on mata: mata set
matafavor space, perm.
yr1984 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: id Number of obs = 891
Time variable : year Number of groups = 140
Number of instruments = 34 Obs per group: min = 6
Wald chi2(10) = 345.89 avg = 6.36
Prob > chi2 = 0.000 max = 8
------------------------------------------------------------------------------
| Corrected
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w | -.3776668 .2218938 -1.70 0.089 -.8125707 .0572371
k | .5092317 .1684431 3.02 0.003 .1790893 .8393742
yr1976 | .1511347 .0648747 2.33 0.020 .0239827 .2782867
yr1977 | .1198974 .0689463 1.74 0.082 -.0152348 .2550297
yr1978 | .0978141 .0758716 1.29 0.197 -.0508914 .2465197
yr1979 | .089337 .0789305 1.13 0.258 -.065364 .244038
yr1980 | .0615155 .0736248 0.84 0.403 -.0827866 .2058175
yr1981 | .0062504 .0554414 0.11 0.910 -.1024127 .1149135
yr1982 | -.0186567 .0355157 -0.53 0.599 -.0882662 .0509527
yr1983 | -.015411 .0205404 -0.75 0.453 -.0556695 .0248474
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/3).(w k)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = 0.44 Pr > z = 0.660
Arellano-Bond test for AR(2) in first differences: z = -0.86 Pr > z = 0.390
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(24) = 43.27 Prob > chi2 = 0.009
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(24) = 25.01 Prob > chi2 = 0.405
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
Hansen test excluding group: chi2(16) = 16.30 Prob > chi2 = 0.432
Difference (null H = exogenous): chi2(8) = 8.71 Prob > chi2 = 0.367
. estimates store ab2
. esttab dpd ab2
--------------------------------------------
(1) (2)
n n
--------------------------------------------
w -0.378 -0.378
(-1.70) (-1.70)
k 0.509** 0.509**
(3.02) (3.02)
yr1977 -0.0312 0.120
(-1.29) (1.74)
yr1978 -0.0533 0.0978
(-1.75) (1.29)
yr1979 -0.0618 0.0893
(-1.87) (1.13)
yr1980 -0.0896** 0.0615
(-2.74) (0.84)
yr1981 -0.145*** 0.00625
(-4.95) (0.11)
yr1982 -0.170*** -0.0187
(-4.49) (-0.53)
yr1983 -0.167*** -0.0154
(-3.38) (-0.75)
yr1984 -0.151*
(-2.33)
yr1976 0.151*
(2.33)
--------------------------------------------
N 891 891
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
. xtdpd n w k yr*, dgmmiv(w k, l(2 2)) div( yr*) vce(robust) twostep nocons
note: yr1976 dropped from div() because of collinearity
note: D.yr1976 dropped because of collinearity
Dynamic panel-data estimation Number of obs = 891
Group variable: id Number of groups = 140
Time variable: year
Obs per group: min = 6
avg = 6.364286
max = 8
Number of instruments = 22 Wald chi2(10) = 282.19
Prob > chi2 = 0.0000
Two-step results
------------------------------------------------------------------------------
| WC-Robust
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w | -.5975386 .22683 -2.63 0.008 -1.042117 -.15296
k | .8595294 .2587153 3.32 0.001 .3524567 1.366602
yr1977 | -.0548315 .0248217 -2.21 0.027 -.1034811 -.0061819
yr1978 | -.0999575 .0341455 -2.93 0.003 -.1668814 -.0330336
yr1979 | -.1194597 .0385212 -3.10 0.002 -.19496 -.0439595
yr1980 | -.12629 .0349355 -3.61 0.000 -.1947623 -.0578176
yr1981 | -.1332924 .0315413 -4.23 0.000 -.1951123 -.0714726
yr1982 | -.1101542 .0543083 -2.03 0.043 -.2165964 -.0037119
yr1983 | -.073628 .0737858 -1.00 0.318 -.2182454 .0709895
yr1984 | -.038052 .0967039 -0.39 0.694 -.2275881 .1514842
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/2).w L(2/2).k
Standard: D.yr1977 D.yr1978 D.yr1979 D.yr1980 D.yr1981
D.yr1982 D.yr1983 D.yr1984
. estimates store dpd
. xtabond2 n w k yr*, gmm(w k, l(2 2)) iv(yr*) robust twostep nolevel
Favoring speed over space. To switch, type or click on mata: mata set
matafavor space, perm.
yr1984 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: id Number of obs = 891
Time variable : year Number of groups = 140
Number of instruments = 22 Obs per group: min = 6
Wald chi2(10) = 265.24 avg = 6.36
Prob > chi2 = 0.000 max = 8
------------------------------------------------------------------------------
| Corrected
n | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
w | -.5482155 .1914433 -2.86 0.004 -.9234375 -.1729936
k | .7211971 .3095853 2.33 0.020 .1144209 1.327973
yr1976 | .0840834 .1057541 0.80 0.427 -.1231909 .2913577
yr1977 | .0351314 .1117762 0.31 0.753 -.1839458 .2542087
yr1978 | -.0016077 .1249189 -0.01 0.990 -.2464443 .2432289
yr1979 | -.017301 .1322428 -0.13 0.896 -.2764921 .2418901
yr1980 | -.0296638 .1200275 -0.25 0.805 -.2649135 .2055858
yr1981 | -.051615 .08634 -0.60 0.550 -.2208382 .1176082
yr1982 | -.0477458 .0482995 -0.99 0.323 -.142411 .0469194
yr1983 | -.025815 .0244998 -1.05 0.292 -.0738337 .0222037
------------------------------------------------------------------------------
Instruments for first differences equation
Standard
D.(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(w k)
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -0.48 Pr > z = 0.631
Arellano-Bond test for AR(2) in first differences: z = -1.36 Pr > z = 0.173
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(12) = 28.17 Prob > chi2 = 0.005
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(12) = 14.79 Prob > chi2 = 0.253
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984)
Hansen test excluding group: chi2(4) = 5.46 Prob > chi2 = 0.243
Difference (null H = exogenous): chi2(8) = 9.33 Prob > chi2 = 0.315
. estimates store ab2
. esttab dpd ab2
--------------------------------------------
(1) (2)
n n
--------------------------------------------
w -0.598** -0.548**
(-2.63) (-2.86)
k 0.860*** 0.721*
(3.32) (2.33)
yr1977 -0.0548* 0.0351
(-2.21) (0.31)
yr1978 -0.1000** -0.00161
(-2.93) (-0.01)
yr1979 -0.119** -0.0173
(-3.10) (-0.13)
yr1980 -0.126*** -0.0297
(-3.61) (-0.25)
yr1981 -0.133*** -0.0516
(-4.23) (-0.60)
yr1982 -0.110* -0.0477
(-2.03) (-0.99)
yr1983 -0.0736 -0.0258
(-1.00) (-1.05)
yr1984 -0.0381
(-0.39)
yr1976 0.0841
(0.80)
--------------------------------------------
N 891 891
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
Thanks in advance,
Daniel
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