  This paper provides a necessary and sufficient instruments condition assuring
two-step generalized method of moments (GMM) based on the forward orthogonal
deviations transformation is numerically equivalent to two-step GMM based on
the first-difference transformation. The condition also tells us when system
GMM, based on differencing, can be computed using forward orthogonal
deviations. Additionally, it tells us when forward orthogonal deviations and
differencing do not lead to the same GMM estimator. When estimators based on
these two transformations differ, Monte Carlo simulations indicate that
estimators based on forward orthogonal deviations have better finite sample
properties than estimators based on differencing.
