Structural Break Difference GMM

Difference GMM uses only lagged-level instruments and first-differenced equations, eliminating fixed effects. System GMM additionally exploits the levels equations with lagged-difference instruments, offering efficiency gains — especially when the autoregressive coefficient is large. With breaks, both approaches embed break dummies or split the sample, but System GMM generally dominates in persistence-heavy panels; Difference GMM is preferred when the stationarity conditions for the levels equations fail.

Prefer an externally motivated date (a known policy event, a crisis onset) or dates produced by a sequential Bai-Perron or sup-F test run on the first-differenced series before the main GMM estimation. Using the same data for break detection and GMM estimation without correction introduces pre-testing bias that inflates the apparent significance of the break.

Two-step GMM is asymptotically more efficient, but finite-sample standard errors are severely underestimated unless Windmeijer's (2005) correction is applied. With structural breaks the sample in each regime is smaller, amplifying this finite-sample problem, so the Windmeijer-corrected two-step estimator is strongly recommended.

Rejection typically signals that some instruments are invalid — either the lag instruments are correlated with the transformed error, or the break specification is incorrect. Try collapsing the instrument matrix, reducing the lag depth, re-examining the break date, or considering whether the assumed parametric break form (additive dummy) is too restrictive.

Yes, sub-period estimation is a valid and often more flexible alternative. It allows all slope coefficients — not just the intercept — to differ across regimes, and it avoids inflating the instrument count in a single pooled model. The trade-off is a smaller effective sample in each regime, which reduces the instrument depth available for lagged variables.