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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