[STATA] Dynamic panel data (xtabond2)

08/03/2022 14:50
[STATA] Dynamic panel data (xtabond2)
Motivation
Following Arellano and Bond (1991), let us model firms’ employmentn using a partial adjustment
model to reflect the costs of hiring and firing.
To reflect this partial adjustment, we include two lags of employment: nt−1 and nt−2 .
Other variables are:
Current and lagged wage level: wt and wt−1 .
Current, once- and twice-lagged capital stock: kt , kt−1 , kt−2 .
Current, once- and twice-lagged output in the firm’s sector: yst , yst−1 , yst−2
All variablesare expressed as logarithms.
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[STATA] Dynamic panel data (xtabond2)
A set of time dummies is also included to capture business cycle effects.
Import data
*use "https://www.stata-press.com/data/r17/abdata.dta", clear
webuse abdata, clear
describe
year
float
%9.0g
emp
float
%9.0g
wage
float
%9.0g
cap
float
%9.0g
indoutpt
float
%9.0g
n
float
%9.0g
w
float
%9.0g
k
float
%9.0g
ys
float
%9.0g
rec
float
%9.0g
yearm1
float
%9.0g
id
float
%9.0g
nL1
float
%9.0g
nL2
float
%9.0g
wL1
float
%9.0g
kL1
float
%9.0g
kL2
float
%9.0g
ysL1
float
%9.0g
ysL2
float
%9.0g
yr1976
byte
%8.0g
year==1976
yr1977
byte
%8.0g
year==1977
yr1978
byte
%8.0g
year==1978
yr1979
byte
%8.0g
year==1979
yr1980
byte
%8.0g
year==1980
yr1981
byte
%8.0g
year==1981
yr1982
byte
%8.0g
year==1982
yr1983
byte
%8.0g
year==1983
yr1984
byte
%8.0g
year==1984
-------------------------------------------------------------------------------Sorted by: id
year
Describe data
sort id year
xtset id year
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[STATA] Dynamic panel data (xtabond2)
xtsum n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2
Panel variable: id (unbalanced)
Time variable: year, 1976 to 1984
Delta: 1 unit
Variable
|
Mean
Std. dev.
Min
Max |
Observations
-----------------+--------------------------------------------+---------------c1
overall |
.
.
.
. |
N =
0
between |
.
.
. |
n =
0
within
.
.
. |
T =
.
|
|
ind
overall |
|
5.123181
2.678095
1
9 |
N =
1031
2.677405
1
9 |
n =
140
0
5.123181
2.21607
1976
1984 |
N =
1031
between |
.6001349
1979
1981 |
n =
140
within
2.133869
1975.651
between |
within
|
5.123181 | T-bar = 7.36429
|
year
overall |
|
1979.651
|
1983.651 | T-bar = 7.36429
|
emp
overall |
|
15.93492
.104
108.562 |
N =
1031
between |
7.891677
16.16889
.12975
102.1901 |
n =
140
within
2.209997
-14.81247
|
34.76311 | T-bar = 7.36429
|
wage
overall |
between |
within
|
|
23.9188
5.648418
8.0171
45.2318 |
N =
1031
5.184036
8.713344
36.06047 |
n =
140
2.06765
11.72244
40.93513 | T-bar = 7.36429
|
|
Pooled OLS
regress n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, cluster(id)
note: yr1976 omitted because of collinearity.
note: yr1977 omitted because of collinearity.
note: yr1984 omitted because of collinearity.
Linear regression
Number of obs
=
751
F(16, 139)
=
13990.88
Prob > F
=
0.0000
R-squared
=
0.9944
Root MSE
=
.10158
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[STATA] Dynamic panel data (xtabond2)
(Std. err. adjusted for 140 clusters in id)
-----------------------------------------------------------------------------|
Robust
n | Coefficient
std. err.
t
P>|t|
[95% conf. interval]
-------------+---------------------------------------------------------------nL1 |
1.044643
.0517969
20.17
0.000
.9422313
1.147055
nL2 |
-.0765426
.0488082
-1.57
0.119
-.1730451
.0199598
w |
-.5236727
.1740911
-3.01
0.003
-.8678817
-.1794637
wL1 |
.4767538
.1717904
2.78
0.006
.1370937
.8164139
k |
.3433951
.048649
7.06
0.000
.2472074
.4395829
kL1 |
-.2018991
.0650327
-3.10
0.002
-.3304803
-.073318
kL2 |
-.1156467
.0358966
-3.22
0.002
-.1866206
-.0446727
ys |
.4328752
.17894
2.42
0.017
.079079
.7866715
ysL1 |
-.7679125
.2514336
-3.05
0.003
-1.265041
-.2707836
ysL2 |
.3124721
.1322678
2.36
0.020
.0509551
.5739891
yr1976 |
0
(omitted)
yr1977 |
0
(omitted)
yr1978 |
-.0153956
.0204269
-0.75
0.452
-.0557832
.024992
yr1979 |
.0004932
.0187355
0.03
0.979
-.0365503
.0375367
yr1980 |
.0065977
.0204613
0.32
0.748
-.033858
.0470534
yr1981 |
-.0375487
.0228406
-1.64
0.102
-.0827087
.0076113
yr1982 |
-.0304299
.0194649
-1.56
0.120
-.0689156
.0080557
yr1983 |
-.0080024
.020992
-0.38
0.704
-.0495073
.0335025
yr1984 |
0
(omitted)
_cons |
.2901212
.3136154
0.93
0.357
-.3299523
.9101947
------------------------------------------------------------------------------
Problems:
Ignore unobserved heterogeneity at the firm level
...
Within estimator
xtreg n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, fe cluster(id)
(Std. err. adjusted for 140 clusters in id)
-----------------------------------------------------------------------------|
Robust
n | Coefficient
std. err.
t
P>|t|
[95% conf. interval]
-------------+---------------------------------------------------------------nL1 |
.7329476
.0596831
12.28
0.000
.6149436
.8509516
nL2 |
-.1394773
.0781564
-1.78
0.077
-.2940065
.0150519
w |
-.5597445
.1596195
-3.51
0.001
-.8753406
-.2441484
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[STATA] Dynamic panel data (xtabond2)
wL1 |
.3149987
.1430587
2.20
0.029
.0321463
.5978511
k |
.3884188
.056928
6.82
0.000
.275862
.5009756
kL1 |
-.0805185
.0538774
-1.49
0.137
-.1870436
.0260066
kL2 |
-.0278013
.0426222
-0.65
0.515
-.1120728
.0564703
ys |
.468666
.1712492
2.74
0.007
.1300759
.8072561
ysL1 |
-.6285587
.2066106
-3.04
0.003
-1.037065
-.2200527
0.44
0.663
-.2043473
.3203001
ysL2 |
.0579764
.1326758
yr1976 |
0
(omitted)
yr1977 |
0
(omitted)
yr1978 |
.0119152
.0281652
0.42
0.673
-.0437723
.0676028
yr1979 |
.0165714
.0278495
0.60
0.553
-.038492
.0716348
yr1980 |
.0231479
.0266961
0.87
0.387
-.029635
.0759308
yr1981 |
-.013454
.0272058
-0.49
0.622
-.0672447
.0403366
yr1982 |
-.0224821
.0202344
-1.11
0.268
-.062489
.0175248
yr1983 |
-.0161192
.0208214
-0.77
0.440
-.0572868
.0250485
yr1984 |
0
(omitted)
_cons |
1.780205
.6303464
2.82
0.005
.5338981
3.026512
-------------+---------------------------------------------------------------sigma_u |
.22568151
sigma_e |
.09395847
rho |
.85227336
(fraction of variance due to u_i)
------------------------------------------------------------------------------
Problems:
Nickell bias: The first difference of the lag dependent variable is correlated with the first difference
of the error. The Nickell bias is more servere in short time series.
...
A consistent estimate should be between polled OLS (upper bound) and the within estimator (lower
bound)
Anderson-Hsiao
It works for the first-differenced equation. Let us instrument the lagged dependent variable with the
twice-lagged level
ivregress 2sls D.n (D.nL1 = nL2) D.(nL2 w wL1 k kL1 kL2 ///
ys ysL1 ysL2 yr1979 yr1980 yr1981 yr1982 yr1983)
. |
.
636
. 3
0
0.8
0.3 5
.68 6
. 5 3 5
2.14
0.032
.0830965
1.898064
|
ys |
D1. |
.9905803
.4630105
|
ysL1 |
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y
[STATA] Dynamic panel data (xtabond2)
|
D1. |
-1.937912
1.438225
-1.35
0.178
-4.75678
.8809566
.4870838
.5099415
0.96
0.339
-.5123832
1.486551
.0467148
.0448599
1.04
0.298
-.0412089
.1346385
.0761344
.0624919
1.22
0.223
-.0463474
.1986163
.022623
.0557394
0.41
0.685
-.0866242
.1318701
.0127801
.0548402
0.23
0.816
-.0947048
.120265
.0099072
.0456113
0.22
0.828
-.0794894
.0993037
.0159337
.0273445
0.58
0.560
-.0376605
.0695279
|
ysL2 |
D1. |
|
yr1979 |
D1. |
|
yr1980 |
D1. |
|
yr1981 |
D1. |
|
yr1982 |
D1. |
|
yr1983 |
D1. |
|
_cons |
-----------------------------------------------------------------------------Instrumented: D.nL1
Instruments: D.nL2 D.w D.wL1 D.k D.kL1 D.kL2 D.ys D.ysL1 D.ysL2 D.yr1979
Problems:
...
Difference GMM
Assume that endogeneity is only present in the first lagged dependent variable
xtabond2 n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, gmm(nL1) ///
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr*) nolevel robust small
|
ys |
.6085073
.1753161
3.47
0.001
.2618979
.9551167
ysL1 |
-.7111651
.2354565
-3.02
0.003
-1.176675
-.245655
ysL2 |
.1057969
.1434813
0.74
0.462
-.1778733
.3894671
yr1978 |
.0077033
.0319176
0.24
0.810
-.0553996
.0708062
yr1979 |
.0172578
.0295618
0.58
0.560
-.0411875
.0757031
yr1980 |
.0297185
.0281082
1.06
0.292
-.0258529
.0852899
yr1981 |
-.004071
.0303813
-0.13
0.894
-.0641364
.0559944
yr1982 |
-.0193555
.0232123
-0.83
0.406
-.0652474
.0265364
yr1983 |
-.0136171
.0191302
-0.71
0.478
-.0514386
.0242044
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[STATA] Dynamic panel data (xtabond2)
-----------------------------------------------------------------------------Instruments for first differences equation
Standard
D.(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981
yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).nL1
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-3.60
Pr > z =
0.000
Arellano-Bond test for AR(2) in first differences: z =
-0.52
Pr > z =
0.606
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(25)
=
67.59
Prob > chi2 =
0.000
Prob > chi2 =
0.177
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(25)
=
31.38
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr19
> 82 yr1983 yr1984)
Hansen test excluding group:
chi2(11)
=
12.01
Prob > chi2 =
0.363
Difference (null H = exogenous): chi2(14)
=
19.37
Prob > chi2 =
0.151
A more succint way of writing the same command:
xtabond2 n L(1/2).n L(0/1).w L(0/2).(k ys) yr*, gmm(L.n) ///
iv(L(0/1).w L(0/2).(k ys) yr*) nolevel robust small
--. |
.6085073
.1753161
3.47
0.001
.2618979
.9551167
L1. |
-.7111651
.2354565
-3.02
0.003
-1.176675
-.245655
L2. |
.1057969
.1434813
0.74
0.462
-.1778733
.3894671
yr1978 |
.0077033
.0319176
0.24
0.810
-.0553996
.0708062
yr1979 |
.0172578
.0295618
0.58
0.560
-.0411875
.0757031
yr1980 |
.0297185
.0281082
1.06
0.292
-.0258529
.0852899
yr1981 |
-.004071
.0303813
-0.13
0.894
-.0641364
.0559944
yr1982 |
-.0193555
.0232123
-0.83
0.406
-.0652474
.0265364
yr1983 |
-.0136171
.0191302
-0.71
0.478
-.0514386
.0242044
|
-----------------------------------------------------------------------------Instruments for first differences equation
Standard
D.(w L.w k L.k L2.k ys L.ys L2.ys yr1976 yr1977 yr1978 yr1979 yr1980
yr1981 yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).L.n
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-3.60
Pr > z =
0.000
Arellano-Bond test for AR(2) in first differences: z =
-0.52
Pr > z =
0.606
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(25)
=
67.59
Prob > chi2 =
0.000
(Not robust, but not weakened by many instruments.)
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[STATA] Dynamic panel data (xtabond2)
Hansen test of overid. restrictions: chi2(25)
=
31.38
Prob > chi2 =
0.177
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(w L.w k L.k L2.k ys L.ys L2.ys yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr
> 1982 yr1983 yr1984)
Hansen test excluding group:
iff
(
ll
chi2(11)
)
hi (
=
12.01
Prob > chi2 =
)
b
0.363
hi
Let us study the senstivity of the results to the choice of “GMM-style” lag specification
Restrict the maximun lags to 5 periods
xtabond2 n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, gmm(nL1, lag(2 5)) ///
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr*) nolevel robust small
ys |
.6399356
.2082587
3.07
0.003
.2281969
1.051674
ysL1 |
-.7762311
.3621577
-2.14
0.034
-1.492236
-.0602258
ysL2 |
.0195998
.1916987
0.10
0.919
-.3593988
.3985985
yr1978 |
-.0264333
.0272127
-0.97
0.333
-.0802342
.0273677
yr1979 |
-.0087855
.025915
-0.34
0.735
-.0600208
.0424498
yr1980 |
.0103422
.028649
0.36
0.719
-.0462984
.0669828
yr1981 |
-.0197328
.0358396
-0.55
0.583
-.0905897
.0511241
yr1982 |
-.0298074
.0307328
-0.97
0.334
-.0905677
.030953
yr1983 |
-.0112002
.0204428
-0.55
0.585
-.0516167
.0292162
-----------------------------------------------------------------------------Instruments for first differences equation
Standard
D.(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981
yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/5).nL1
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-1.41
Pr > z =
0.158
Arellano-Bond test for AR(2) in first differences: z =
-2.08
Pr > z =
0.037
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(16)
=
24.69
Prob > chi2 =
0.075
Prob > chi2 =
0.676
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(16)
=
12.95
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr19
> 82 yr1983 yr1984)
Hansen test excluding group:
chi2(2)
=
1.40
Prob > chi2 =
0.497
Restrict the maximun lags to 4 periods
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[STATA] Dynamic panel data (xtabond2)
xtabond2 n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, gmm(nL1, lag(2 4)) ///
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr*) nolevel robust small
nL2 |
.2314476
.1747848
1.32
0.188
-.1141113
.5770065
w |
-.7087804
.2175647
-3.26
0.001
-1.138918
-.2786434
wL1 |
.6080322
.2624007
2.32
0.022
.0892518
1.126812
k |
.3094885
.0680321
4.55
0.000
.1749855
.4439916
kL1 |
-.2112921
.122904
-1.72
0.088
-.4542799
.0316957
kL2 |
-.2016251
.0656621
-3.07
0.003
-.3314426
-.0718076
ys |
.6982485
.2025977
3.45
0.001
.297702
1.098795
ysL1 |
-.986704
.34575
-2.85
0.005
-1.67027
-.3031376
ysL2 |
.1115407
.1988029
0.56
0.576
-.2815033
.5045848
yr1978 |
-.0397756
.0323797
-1.23
0.221
-.103792
.0242408
yr1979 |
-.0148331
.0322496
-0.46
0.646
-.0785923
.0489261
yr1980 |
.0100056
.0351291
0.28
0.776
-.0594465
.0794576
yr1981 |
-.021134
.043033
-0.49
0.624
-.1062125
.0639445
yr1982 |
-.0261283
.0347394
-0.75
0.453
-.09481
.0425534
yr1983 |
-.0049688
.0241235
-0.21
0.837
-.0526622
.0427247
-----------------------------------------------------------------------------Instruments for first differences equation
Standard
D.(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981
yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(2/4).nL1
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-2.04
Pr > z =
0.041
Arellano-Bond test for AR(2) in first differences: z =
-1.93
Pr > z =
0.054
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(13)
=
10.22
Prob > chi2 =
0.676
Prob > chi2 =
0.714
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(13)
=
9.75
(Robust, but can be weakened by many instruments.)
The estimate of the lagged dependent variable’s coefficient appears to be quite sensitive to thechoice
of lag length.
One disadvantage of this difference GMM approach is that it magnifies gaps in unbalanced panels. This
motivates an alternative transformation: the forward orthogonal deviations (FOD) transformation
(Arellano and Bover, 1995). The FOD transformation subtracts the average of all available future
observations from the current value. We apply this transformation below.
xtabond2 n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, gmm(nL1) ///
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr*) nolevel orthogonal robust small
|
ys |
.4687189
.1720838
2.72
0.007
.1285001
.8089377
ysL1 |
-.6254982
.2187189
-2.86
0.005
-1.057917
-.1930792
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[STATA] Dynamic panel data (xtabond2)
ysL2 |
.0419738
.1422114
0.30
0.768
-.2391858
.3231334
yr1978 |
.0091826
.0272736
0.34
0.737
-.0447388
.063104
yr1979 |
.0145949
.0267841
0.54
0.587
-.0383588
.0675485
yr1980 |
.0216254
.0258883
0.84
0.405
-.0295572
.072808
yr1981 |
-.0145863
.0268631
-0.54
0.588
-.0676961
.0385235
yr1982 |
-.023622
.0203417
-1.16
0.248
-.0638385
.0165946
yr1983 |
-.0159339
.0209197
-0.76
0.448
-.0572932
.0254254
-----------------------------------------------------------------------------Instruments for orthogonal deviations equation
Standard
FOD.(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980
yr1981 yr1982 yr1983 yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).nL1
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-4.09
Pr > z =
0.000
Arellano-Bond test for AR(2) in first differences: z =
-0.31
Pr > z =
0.758
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(25)
=
61.85
Prob > chi2 =
0.000
Prob > chi2 =
0.170
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(25)
=
31.61
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(w wL1 k kL1 kL2 ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr19
> 82 yr1983 yr1984)
Hansen test excluding group:
chi2(11)
=
11.09
Prob > chi2 =
0.436
Let us assume that the lag of employment, wages, and capital are endogenous (GMM-style)
xtabond2 n nL1 nL2 w wL1 k kL1 kL2 ys ysL1 ysL2 yr*, gmm(nL1 wL1 kL1) ///
iv(ys ysL1 ysL2 yr*) nolevel robust small
kL2 |
-.0304529
.0321355
-0.95
0.345
-.0939866
.0330807
ys |
.6509498
.189582
3.43
0.001
.276136
1.025764
ysL1 |
-.9162028
.2639274
-3.47
0.001
-1.438001
-.3944042
ysL2 |
.2786584
.1855286
1.50
0.135
-.0881415
.6454584
yr1978 |
.0238987
.0367972
0.65
0.517
-.0488513
.0966487
yr1979 |
.0352258
.0351846
1.00
0.318
-.034336
.1047876
yr1980 |
.0502675
.0365659
1.37
0.171
-.0220252
.1225602
yr1981 |
.0102721
.0349996
0.29
0.770
-.058924
.0794683
yr1982 |
-.0111623
.0264747
-0.42
0.674
-.0635042
.0411797
yr1983 |
-.0069458
.0191611
-0.36
0.718
-.0448283
.0309368
-----------------------------------------------------------------------------Instruments for first differences equation
Standard
D.(ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983
yr1984)
GMM-type (missing=0, separate instruments for each period unless collapsed)
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[STATA] Dynamic panel data (xtabond2)
L(1/.).(nL1 wL1 kL1)
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-5.39
Pr > z =
0.000
Arellano-Bond test for AR(2) in first differences: z =
-0.78
Pr > z =
0.436
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(74)
= 120.62
Prob > chi2 =
0.001
Prob > chi2 =
0.487
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(74)
=
73.72
(Robust, but can be weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
iv(ys ysL1 ysL2 yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984
> )
Hansen test excluding group:
chi2(65)
System GMM
Diff
(
ll H
)
hi2(9)
=
56.99
Prob > chi2 =
0.750
16 72
P
0 053
b
hi2
Let us follow Blundell and Bond, who used a simpler model, dropping the second lags and removing
sectoral demand. We consider wages and capital as potentially endogenous, with GMM-style
instruments
xtabond2 n L.n L(0/1).(w k) yr*, gmm(L.(n w k)) iv(yr*, equation(level)) ///
robust small
yr1980 |
-.0173995
.0221715
-0.78
0.434
-.0612366
.0264376
yr1981 |
-.0435283
.0193348
-2.25
0.026
-.0817565
-.0053
yr1982 |
-.0096193
.0186829
-0.51
0.607
-.0465588
.0273201
yr1983 |
.0038132
.0171959
0.22
0.825
-.0301861
.0378126
_cons |
.5522011
.1971607
2.80
0.006
.1623793
.9420228
-----------------------------------------------------------------------------Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L(1/.).(L.n L.w L.k)
Instruments for levels equation
Standard
_cons
yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984
GMM-type (missing=0, separate instruments for each period unless collapsed)
D.(L.n L.w L.k)
-----------------------------------------------------------------------------Arellano-Bond test for AR(1) in first differences: z =
-5.46
Pr > z =
0.000
Arellano-Bond test for AR(2) in first differences: z =
-0.25
Pr > z =
0.804
Carlos Mendez / [STATA] Dynamic panel data
(xtabond2)
Published
at Aug 22, 2021
= 186.90
Prob > chi2
= 0.000
-----------------------------------------------------------------------------Sargan test of overid. restrictions: chi2(100)
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(100)
= 110.70
Prob > chi2 =
0.218
(Robust, but can be weakened by many instruments.)
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(
,
y
y
[STATA] Dynamic panel data (xtabond2)
)
Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group:
chi2(79)
=
84.33
Prob > chi2 =
0.320
Difference (null H = exogenous): chi2(21)
=
26.37
Prob > chi2 =
0.193
iv(yr1976 yr1977 yr1978 yr1979 yr1980 yr1981 yr1982 yr1983 yr1984, eq(level))
Hansen test excluding group:
chi2(93)
Difference (null H = exogenous): chi2(7)
References
= 107.79
Prob > chi2 =
0.140
=
Prob > chi2 =
0 893
2 91
Arellano, M. and Bond, S. (1991) "Some tests of specification for panel data: Monte Carlo evidence
and an application to employment equations", The Review of Economic Studies, 58(2), 227-297,
doi: 10.2307/2297968
https://www.stata.com/features/overview/dynamic-panel-data/
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