»  Home »  Products »  Features »  Dynamic panel data analysis

## Dynamic panel-data (DPD) analysis

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 first-differenced 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 moving-average 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:

. webuse abdata

. xtabond n L(0/2).(w k) yr1980-yr1984 year, vce(robust)

Arellano-Bond dynamic panel-data estimation     Number of obs     =        611
Group variable: id                              Number of groups  =        140
Time variable: year
Obs per group:
min =          4
avg =   4.364286
max =          6

Number of instruments =     40                  Wald chi2(13)     =    1318.68
Prob > chi2       =     0.0000
One-step results
(Std. Err. adjusted for clustering on id)

 Robust n Coef. Std. Err. z P>|z| [95% Conf. Interval] n L1. .6286618 .1161942 5.41 0.000 .4009254 .8563983 w --. -.5104249 .1904292 -2.68 0.007 -.8836592 -.1371906 L1. .2891446 .140946 2.05 0.040 .0128954 .5653937 L2. -.0443653 .0768135 -0.58 0.564 -.194917 .1061865 k --. .3556923 .0603274 5.90 0.000 .2374528 .4739318 L1. -.0457102 .0699732 -0.65 0.514 -.1828552 .0914348 L2. -.0619721 .0328589 -1.89 0.059 -.1263743 .0024301 yr1980 -.0282422 .0166363 -1.70 0.090 -.0608488 .0043643 yr1981 -.0694052 .028961 -2.40 0.017 -.1261677 -.0126426 yr1982 -.0523678 .0423433 -1.24 0.216 -.1353591 .0306235 yr1983 -.0256599 .0533747 -0.48 0.631 -.1302723 .0789525 yr1984 -.0093229 .0696241 -0.13 0.893 -.1457837 .1271379 year .0019575 .0119481 0.16 0.870 -.0214604 .0253754 _cons -2.543221 23.97919 -0.11 0.916 -49.54158 44.45514
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:

. xtdpdsys n L(0/2).(w k) yr1980-yr1984 year, vce(robust)

System dynamic panel-data estimation            Number of obs     =        751
Group variable: id                              Number of groups  =        140
Time variable: year
Obs per group:
min =          5
avg =   5.364286
max =          7

Number of instruments =     47                  Wald chi2(13)     =    2579.96
Prob > chi2       =     0.0000
One-step results

 Robust n Coef. Std. Err. z P>|z| [95% Conf. Interval] n L1. .8221535 .093387 8.80 0.000 .6391184 1.005189 w --. -.5427935 .1881721 -2.88 0.004 -.911604 -.1739831 L1. .3703602 .1656364 2.24 0.025 .0457189 .6950015 L2. -.0726314 .0907148 -0.80 0.423 -.2504292 .1051664 k --. .3638069 .0657524 5.53 0.000 .2349346 .4926792 L1. -.1222996 .0701521 -1.74 0.081 -.2597951 .015196 L2. -.0901355 .0344142 -2.62 0.009 -.1575862 -.0226849 yr1980 -.0308622 .016946 -1.82 0.069 -.0640757 .0023512 yr1981 -.0718417 .0293223 -2.45 0.014 -.1293123 -.014371 yr1982 -.0384806 .0373631 -1.03 0.303 -.1117111 .0347498 yr1983 -.0121768 .0498519 -0.24 0.807 -.1098847 .0855311 yr1984 -.0050903 .0655011 -0.08 0.938 -.1334701 .1232895 year .0058631 .0119867 0.49 0.625 -.0176304 .0293566 _cons -10.59198 23.92087 -0.44 0.658 -57.47602 36.29207
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:

. estat abond, artests(4)

Dynamic panel-data estimation                   Number of obs     =        751
Group variable: id                              Number of groups  =        140
Time variable: year
Obs per group:
min =          5
avg =   5.364286
max =          7

Number of instruments =     47                  Wald chi2(13)     =    2579.96
Prob > chi2       =     0.0000
One-step results
(Std. Err. adjusted for clustering on id)

 Robust n Coef. Std. Err. z P>|z| [95% Conf. Interval] n L1. .8221535 .093387 8.80 0.000 .6391184 1.005189 w --. -.5427935 .1881721 -2.88 0.004 -.911604 -.1739831 L1. .3703602 .1656364 2.24 0.025 .0457189 .6950015 L2. -.0726314 .0907148 -0.80 0.423 -.2504292 .1051664 k --. .3638069 .0657524 5.53 0.000 .2349346 .4926792 L1. -.1222996 .0701521 -1.74 0.081 -.2597951 .015196 L2. -.0901355 .0344142 -2.62 0.009 -.1575862 -.0226849 yr1980 -.0308622 .016946 -1.82 0.069 -.0640757 .0023512 yr1981 -.0718417 .0293223 -2.45 0.014 -.1293123 -.014371 yr1982 -.0384806 .0373631 -1.03 0.303 -.1117111 .0347498 yr1983 -.0121768 .0498519 -0.24 0.807 -.1098847 .0855311 yr1984 -.0050903 .0655011 -0.08 0.938 -.1334701 .1232895 year .0058631 .0119867 0.49 0.625 -.0176304 .0293566 _cons -10.59198 23.92087 -0.44 0.658 -57.47602 36.29207
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
 Order z Prob > z 1 -4.6414 0.0000 2 -1.0572 0.2904 3 -.19492 0.8455 4 .04472 0.9643
H0: no autocorrelation

### 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.

Explore more time-series features in Stata.