Dynamic panel GMM (Arellano-Bond / Blundell-Bond) estimates a model with a lagged dependent variable and entity effects using instrumental-variable GMM, with over-identification and serial-correlation diagnostics.
When an outcome depends on its own past (y_i,t-1) and on unobserved entity effects, ordinary fixed-effects and OLS are both biased (the lagged outcome is correlated with the demeaned error — the Nickell bias). Difference GMM first-differences the model to remove the entity effect, then instruments the lagged difference with earlier levels of the outcome (y_i,t-2 and before) that are uncorrelated with the differenced error.
The one-step estimator uses a fixed weight matrix; the two-step estimator uses an optimal weight from the one-step residuals and reports finite-sample-corrected standard errors. System GMM augments the differenced moment conditions with level equations instrumented by lagged differences, which helps when the series are persistent.
Dependent variable + an entity index + a numeric, evenly spaced time index + optional exogenous regressors + one/two-step choice.
Coefficients (est / SE / z / p), the Sargan/Hansen over-identification test, Arellano-Bond AR(1) and AR(2) serial-correlation tests, and a joint Wald test.
A significant AR(1) but insignificant AR(2), together with a non-significant Sargan/Hansen test, supports the specification.
The lagged-dependent coefficient measures persistence; values near 1 indicate a highly persistent process.