XtAbond

XtAbond is a Stata command that implements the Arellano-Bond difference GMM estimator for dynamic panel data models. It is used when the dependent variable depends on its own past values and on other regressors that may be endogenous, while unobserved individual effects are present. The estimator aims to provide consistent parameter estimates in short panels (large N, small T) where conventional fixed-effects or OLS would be biased.

The typical model addressed is y_it = alpha y_{i,t-1} + X_it' beta + mu_i + epsilon_it, where mu_i captures time-invariant individual effects. By first-differencing to remove mu_i, lagged levels of the endogenous variables become instruments for the differenced equation, along with exogenous variables and their lags. The method relies on assumptions about the absence of second-order serial correlation in the differenced errors and the validity of the chosen instruments to achieve consistency.

XtAbond offers options for one-step or two-step estimation, with robust standard errors and, in some implementations, finite-sample corrections. Diagnostic tests commonly used with xtabond include the Arellano-Bond tests for AR(1) and AR(2) in the differenced residuals and tests of overidentifying restrictions (Sargan or Hansen). A key practical concern is instrument proliferation, which can bias results and distort tests in small samples. Researchers often limit the instrument count or adjust specifications accordingly.

Limitations include potential weak instruments when the autoregressive parameter is near unity or when T is very small, and sensitivity to instrument choice. For improved efficiency and additional flexibility, researchers frequently turn to related tools like xtabond2, which implements system GMM (Arellano-Bover/Blundell-Bond) and offers extended diagnostics and instrument options.