I assume that you are using panel data. (These days, it would be unusual to restrict the investigation of this topic to cross-section or time-series data.) In this case,  I have some good news and some bad news. The good news is that to estimate a dynamic linear model, most practitioners would recommend xtabond2, a superb user-written programme for Stata. The author, David Roodman, has also provided a great Help file and published a companion paper in the Stata Journal:

Roodman, D. (2009) How to do xtabond2: An introduction to difference and system GMM in Stata, The Stata Journal, 9(1), 86–136.

See also:

Roodman, D. (2007) A short note on the theme of too many instruments. Center for Global Development, Washington, Working paper 125. Available online at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1101731 (accessed 3 April 2009). This has now been published in a journal.

If your export data contains few zero flows then you could estimate a linear model and ignore the bad news. However, for technical reasons, using a linear model to estimate a (log-log) gravity model - the usual framework for your topic - is always problematic (because of the theoretical non-linear form, which gives rise to an intractable problem of heteroskedasticity in the empirical linear form). If you intend to publish your work, you will have to acknowledge this issue and address it with a dynamic Poisson model. The bad news is that this raises several difficult issues. However, this approach can be implemented using Stata. The key reference here is:

Wooldridge, Jeffrey M., 2005. Simple Solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics 20, 39-54.

See also:

Cameron and Trivedi (2013; 2nd Ed.) Regression Analysis of Count Data, Cambridge University Press. Stata syntax for the Wooldridge model may be available from the personal website of A. Colin Cameron:

http://cameron.econ.ucdavis.edu/racd2/racd07.txt

Best wishes!

Geoff

Thanks a Lot professor Geoff, 

Prof. Hiri:

Sometimes it could be interesting to complement GMM estimations with alternative DPD estimators like bias corrected LSDV.

It is a consistent estimator for DPD with better properties than GMM for small sample databases.

See; http://homepage.univie.ac.at/robert.kunst/pres09_pan_eigner.pdf

In stata, it could be implemented by using https://ideas.repec.org/c/boc/bocode/s450101.html.

Best regards.

Demian

https://fmwww.bc.edu/EC-C/S2013/823/EC823.S2013.nn05.slides.pdf

Martin - thanks for the link. As might be expected, Baum's lecture notes are valuable. (The final slide makes a particularly important point for practitioners - i.e. that GMM estimates of dynamic models can be very sensitive with respect to both specification and the instrument set.) However, could you explain how these notes address Demian's points?

https://www.stata.com/manuals13/xtxtdpd.pdf