Dynamic panel-data analysis Stata

08/03/2022 14:48
Dynamic panel-data analysis | Stata
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Dynamic panel-data (DPD) analysis
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Stata has suite of tools for dynamic panel-data analysis:
xtabond implements the Arellano and Bond estimator, which uses moment conditions in which lags of
the dependent variable and first differences of the exogenous variables are instruments for the firstdifferenced equation.
xtdpdsys implements the Arellano and Bover/Blundell and Bond system estimator, which uses the
xtabond moment conditions and moment conditions in which lagged first differences of the dependent
variable are instruments for the level equation.
xtdpd, for advanced users, is a more flexible alternative that can fit models with low-order movingaverage correlations in the idiosyncratic errors and predetermined variables with a more complicated
structure than allowed with xtabond and xtdpdsys.
Postestimation tools allow you to test for serial correlation in the first-differenced residuals and test the
validity of the overidentifying restrictions.
Example
Building on the work of Layard and Nickell (1986), Arellano and Bond (1991) fit a dynamic model of labor
demand to an unbalanced panel of firms located in the United Kingdom. First we model employment on wages,
capital stock, industry output, year dummies, and a time trend, including one lag of employment and two lags of
wages and capital stock. We will use the one-step Arellano–Bond estimator and request their robust VCE:
https://www.stata.com/features/overview/dynamic-panel-data/
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Dynamic panel-data analysis | Stata
. webuse abdata
. xtabond n L(0/2).(w k) yr1980-yr1984 year, vce(robust)
Arellano–Bond dynamic panel-data estimation
Group variable: id
Time variable: year
Number of obs
Number of groups
=
=
Obs per group:
Number of instruments =
40
Wald chi2(13)
Prob > chi2
min =
avg =
max =
4.364
=
=
1318
0.0
One-step results
(Std. err. adjusted for clustering on
n
Coefficient
Robust
std. err.
z
P>|z|
[95% conf. interv
n
L1.
.6286618
.1161942
5.41
0.000
.4009254
.8563
w
--.
L1.
L2.
-.5104249
.2891446
-.0443653
.1904292
.140946
.0768135
-2.68
2.05
-0.58
0.007
0.040
0.564
-.8836592
.0128954
-.194917
-.1371
.5653
.1061
k
--.
L1.
L2.
.3556923
-.0457102
-.0619721
.0603274
.0699732
.0328589
5.90
-0.65
-1.89
0.000
0.514
0.059
.2374528
-.1828552
-.1263743
.4739
.0914
.0024
yr1980
yr1981
yr1982
yr1983
yr1984
year
_cons
-.0282422
-.0694052
-.0523678
-.0256599
-.0093229
.0019575
-2.543221
.0166363
.028961
.0423433
.0533747
.0696241
.0119481
23.97919
-1.70
-2.40
-1.24
-0.48
-0.13
0.16
-0.11
0.090
0.017
0.216
0.631
0.893
0.870
0.916
-.0608488
-.1261677
-.1353591
-.1302723
-.1457837
-.0214604
-49.54158
.0043
-.0126
.0306
.0789
.1271
.0253
44.45
Instruments for differenced equation
GMM-type: L(2/.).n
Standard: D.w LD.w L2D.w D.k LD.k L2D.k D.yr1980 D.yr1981 D.yr1982
D.yr1983 D.yr1984 D.year
Instruments for level equation
Standard: _cons
Because we included one lag of n in our regression model, xtabond used lags 2 and back as instruments.
Differences of the exogenous variables also serve as instruments.
Here we refit our model, using xtdpdsys instead so that we can obtain the Arellano–Bover/Blundell–Bond
estimates:
https://www.stata.com/features/overview/dynamic-panel-data/
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Dynamic panel-data analysis | Stata
. xtdpdsys n L(0/2).(w k) yr1980-yr1984 year, vce(robust)
System dynamic panel-data estimation
Group variable: id
Time variable: year
Number of obs
Number of groups
=
=
Obs per group:
Number of instruments =
47
Wald chi2(13)
Prob > chi2
min =
avg =
max =
5.364
=
=
2579
0.0
One-step results
n
Coefficient
Robust
std. err.
z
P>|z|
[95% conf. interv
n
L1.
.8221535
.093387
8.80
0.000
.6391184
1.005
w
--.
L1.
L2.
-.5427935
.3703602
-.0726314
.1881721
.1656364
.0907148
-2.88
2.24
-0.80
0.004
0.025
0.423
-.911604
.0457189
-.2504292
-.1739
.6950
.1051
k
--.
L1.
L2.
.3638069
-.1222996
-.0901355
.0657524
.0701521
.0344142
5.53
-1.74
-2.62
0.000
0.081
0.009
.2349346
-.2597951
-.1575862
.4926
.015
-.0226
yr1980
yr1981
yr1982
yr1983
yr1984
year
_cons
-.0308622
-.0718417
-.0384806
-.0121768
-.0050903
.0058631
-10.59198
.016946
.0293223
.0373631
.0498519
.0655011
.0119867
23.92087
-1.82
-2.45
-1.03
-0.24
-0.08
0.49
-0.44
0.069
0.014
0.303
0.807
0.938
0.625
0.658
-.0640757
-.1293123
-.1117111
-.1098847
-.1334701
-.0176304
-57.47602
.0023
-.014
.0347
.0855
.1232
.0293
36.29
Instruments for differenced equation
GMM-type: L(2/.).n
Standard: D.w LD.w L2D.w D.k LD.k L2D.k D.yr1980 D.yr1981 D.yr1982
D.yr1983 D.yr1984 D.year
Instruments for level equation
GMM-type: LD.n
Standard: _cons
Comparing the footers of the two commands’ output illustrates the key difference between the two estimators.
xtdpdsys included the lagged differences of n as instruments in the level equation; xtabond did not.
The moment conditions of these GMM estimators are valid only if there is no serial correlation in the
idiosyncratic errors. Because the first difference of white noise is necessarily autocorrelated, we need only
concern ourselves with second and higher autocorrelation. We can use estat abond to test for autocorrelation:
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Dynamic panel-data analysis | Stata
. estat abond, artests(4)
Dynamic panel-data estimation
Group variable: id
Time variable: year
Number of obs
Number of groups
=
=
Obs per group:
Number of instruments =
47
Wald chi2(13)
Prob > chi2
min =
avg =
max =
5.364
=
=
2579
0.0
One-step results
(Std. err. adjusted for clustering on
n
Coefficient
Robust
std. err.
z
P>|z|
[95% conf. interv
n
L1.
.8221535
.093387
8.80
0.000
.6391184
1.005
w
--.
L1.
L2.
-.5427935
.3703602
-.0726314
.1881721
.1656364
.0907148
-2.88
2.24
-0.80
0.004
0.025
0.423
-.911604
.0457189
-.2504292
-.1739
.6950
.1051
k
--.
L1.
L2.
.3638069
-.1222996
-.0901355
.0657524
.0701521
.0344142
5.53
-1.74
-2.62
0.000
0.081
0.009
.2349346
-.2597951
-.1575862
.4926
.015
-.0226
yr1980
yr1981
yr1982
yr1983
yr1984
year
_cons
-.0308622
-.0718417
-.0384806
-.0121768
-.0050903
.0058631
-10.59198
.016946
.0293223
.0373631
.0498519
.0655011
.0119867
23.92087
-1.82
-2.45
-1.03
-0.24
-0.08
0.49
-0.44
0.069
0.014
0.303
0.807
0.938
0.625
0.658
-.0640757
-.1293123
-.1117111
-.1098847
-.1334701
-.0176304
-57.47602
.0023
-.014
.0347
.0855
.1232
.0293
36.29
Instruments for differenced equation
GMM-type: L(2/.).n
Standard: D.w LD.w L2D.w D.k LD.k L2D.k D.yr1980 D.yr1981 D.yr1982
D.yr1983 D.yr1984 D.year
Instruments for level equation
GMM-type: LD.n
Standard: _cons
Arellano–Bond test for zero autocorrelation in first-differenced errors
H0: No autocorrelation
Order
1
2
3
4
z
-4.6414
-1.0572
-.19492
.04472
Prob > z
0.0000
0.2904
0.8455
0.9643
References
Arellano, M., and S. Bond. 1991.
Some tests of specification for panel data: Monte Carlo evidence and an application to employment
equations. The Review of Econometric Studies 58: 277–297.
Layard, R., and S. J. Nickell. 1986.
Unemployment in Britain. Economica 53: 5121–5169.
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