XTABOND2: Stata module to extend xtabond dynamic panel data estimator

xtabond2 can fit two closely related dynamic panel data models. The first is the Arellano-Bond (1991) estimator, which is also available with xtabond without the two-step finite-sample correction described below. The second is an augmented version outlined in Arellano and Bover (1995) and fully developed in Blundell and Bond (1998). Arellano and Bond (1991) developed a Generalized Method of Moments estimator that treats the model as a system of equations, one for each time period. The equations differ only in their instrument/moment condition sets. The predetermined and endogenous variables in first differences are instrumented with suitable lags of their own levels. Strictly exogenous regressors, as well as any other instruments, can enter the instrument matrix in the conventional instrumental variables fashion: in first differences, with one column per instrument. A problem with the original Arellano-Bond estimator is that lagged levels are often poor instruments for first differences, especially for variables that are close to a random walk. Arellano and Bover (1995) described how, if the original equations in levels were added to the system, additional moment conditions could be brought to bear to increase efficiency. In these equations, predetermined and endogenous variables in levels are instrumented with suitable lags of their own first differences. Blundell and Bond (1998) articulated the necessary assumptions for this augmented estimator more precisely and tested it with Monte Carlo simulations. The original estimator is sometimes called "difference GMM," and the augmented one, "system GMM." Bond (2002) is a good introduction to these estimators and their use. xtabond2 implements both estimators. As GMM estimators, the Arellano-Bond estimators have one- and two-step variants. But though asymptotically more efficient, the two-step estimates of the standard errors tend to be severely downward biased (Arellano and Bond 1991; Blundell and Bond 1998). To compensate, xtabond2, unlike xtabond, makes available a finite-sample correction to the two-step covariance matrix derived by Windmeijer (2000). This can make twostep robust more efficient than onestep robust, especially for system GMM. Note: the routine requires an up-to-date version of Stata 7 (with the 21jun2002 update installed). Users of Stata version 10 (25feb2008 update) or later can take advantage of speed improvements due to Mata.