Dear Statalisters,

I have made a new estimation command available for installation from my website:

xtdpdgmm estimates a linear (dynamic) panel data model with the generalized method of moments (GMM). The main value added of the new command is that is allows to combine the traditional linear moment conditions with the nonlinear moment conditions suggested by Ahn and Schmidt (1995) under the assumption of serially uncorrelated idiosyncratic errors. These additional nonlinear moment conditions can yield potentially sizeable efficiency gains and they also improve the finite-sample performance. Given that absence of serial correlation is usually a prerequisite also for other GMM estimators in the presence of a lagged dependent variable, the gains from the nonlinear moment conditions essentially come for free.

The extra moment conditions can help to overcome a weak instruments problem of the Arellano and Bond (1991) difference-GMM estimator when the autoregressive coefficient approaches unity. Furthermore, the Ahn and Schmidt (1995) estimator is also robust to deviations from mean stationarity, a situation that would invalidate the Blundell and Bond (1998) system-GMM approach.

Without these nonlinear moment conditions, xtdpdgmm replicates the results obtained with the familiar commands xtabond, xtdpd, xtdpdsys, and xtabond2, as well as my other recent command xtseqreg. Collapsing of GMM-type instruments and different initial weighting matrices are supported. The key option of xtdpdgmm that adds the nonlinear moment conditions is called noserial. For example:

The Gauss-Newton technique is used to minimize the GMM criterion function. With vce(robust), the Windmeijer (2005) finite-sample standard error correction is computed for estimators with and without nonlinear moment conditions.

For details about the syntax, the available options, and the supported postestimation commands, please see the help files:

Available postestimation command include the Arellano-Bond test for absence of serial correlation in the first-differenced errors, estat serial, and the familiar Hansen J-test of the overidentifying restrictions, estat overid. The results of the Arellano-Bond test differ slightly from xtdpd and xtabond2 for two-step robust estimators because I account for the finite-sample Windmeijer (2005) correction when computing the test statistic, while the existing commands do not. estat overid can also be used to perform difference-in-Hansen tests but it requires that the two models are estimated separately. In that regard, the results differ from the difference-in-Hansen test statistics reported by xtabond2; see footnote 24 in Roodman (2009) for an explanation. An alternative to difference-in-Hansen tests is a generalized Hausman test, implemented in estat hausman for use after xtdpdgmm.

Finally, the results with and without nonlinear moment conditions can in principle also be obtained with Stata's official gmm command. However, it is anything but straightforward to do so. While the official gmm command offers lots of extra flexibility, it does not provide a tailored solution for this particular estimation problem. While xtdpdgmm can easily handle unbalanced panel data, gmm tends to have some problems in that case. In addition, gmm tends to be very slow in particular with large data sets. I did not do a sophisticated benchmark comparison, but for a single estimation on a data set with 40,000 observations, it took me 43 minutes (!) to obtain the results with gmm, while xtdpdgmm returned the identical results after just 4 seconds!

I hope you enjoy the new command. As always, comments and suggestions are highly welcome, and an appropriate reference would be very much appreciated if my command proves to be helpful for your own research.

References:

I have made a new estimation command available for installation from my website:

Code:

. net install xtdpdgmm, from(http://www.kripfganz.de/stata/)

The extra moment conditions can help to overcome a weak instruments problem of the Arellano and Bond (1991) difference-GMM estimator when the autoregressive coefficient approaches unity. Furthermore, the Ahn and Schmidt (1995) estimator is also robust to deviations from mean stationarity, a situation that would invalidate the Blundell and Bond (1998) system-GMM approach.

Without these nonlinear moment conditions, xtdpdgmm replicates the results obtained with the familiar commands xtabond, xtdpd, xtdpdsys, and xtabond2, as well as my other recent command xtseqreg. Collapsing of GMM-type instruments and different initial weighting matrices are supported. The key option of xtdpdgmm that adds the nonlinear moment conditions is called noserial. For example:

Code:

. webuse abdata . xtdpdgmm L(0/1).n w k, noserial gmmiv(L.n, collapse model(difference)) iv(w k, difference model(difference)) twostep vce(robust) Generalized method of moments estimation Step 1 initial: f(p) = 6.9508498 alternative: f(p) = 1.917675 rescale: f(p) = .07590133 Iteration 0: f(p) = .07590133 Iteration 1: f(p) = .003352 Iteration 2: f(p) = .00274414 Iteration 3: f(p) = .00274388 Iteration 4: f(p) = .00274388 Step 2 Iteration 0: f(p) = .26774896 Iteration 1: f(p) = .20397319 Iteration 2: f(p) = .2011295 Iteration 3: f(p) = .20109259 Iteration 4: f(p) = .20109124 Iteration 5: f(p) = .2010912 Group variable: id Number of obs = 891 Time variable: year Number of groups = 140 Moment conditions: linear = 10 Obs per group: min = 6 nonlinear = 6 avg = 6.364286 total = 16 max = 8 (Std. Err. adjusted for clustering on id) ------------------------------------------------------------------------------ | WC-Robust n | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- n | L1. | .657292 .1381388 4.76 0.000 .3865449 .9280391 | w | -.7248798 .0996565 -7.27 0.000 -.9202029 -.5295568 k | .2399022 .0737048 3.25 0.001 .0954435 .3843609 _cons | 2.719216 .4015915 6.77 0.000 1.932111 3.506321 ------------------------------------------------------------------------------

For details about the syntax, the available options, and the supported postestimation commands, please see the help files:

Code:

. help xtdpdgmm . help xtdpdgmm postestimation

Finally, the results with and without nonlinear moment conditions can in principle also be obtained with Stata's official gmm command. However, it is anything but straightforward to do so. While the official gmm command offers lots of extra flexibility, it does not provide a tailored solution for this particular estimation problem. While xtdpdgmm can easily handle unbalanced panel data, gmm tends to have some problems in that case. In addition, gmm tends to be very slow in particular with large data sets. I did not do a sophisticated benchmark comparison, but for a single estimation on a data set with 40,000 observations, it took me 43 minutes (!) to obtain the results with gmm, while xtdpdgmm returned the identical results after just 4 seconds!

I hope you enjoy the new command. As always, comments and suggestions are highly welcome, and an appropriate reference would be very much appreciated if my command proves to be helpful for your own research.

References:

- Ahn, S. C., and P. Schmidt (1995). Efficient estimation of models for dynamic panel data.
*Journal of Econometrics*68: 5-27. - Arellano, M., and S. R. Bond (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations.
*Review of Economic Studies*58: 277-297. - Blundell, R., and S. R. Bond (1998). Initial conditions and moment restrictions in dynamic panel data models.
*Review of Economic Studies*87: 115-143. - Roodman, D. (2009). How to do xtabond2: An introduction to difference and system GMM in Stata.
*Stata Journal*9: 86-136. - Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators.
*Journal of Econometric*s 126: 25-51.

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