Conditions that imply that B is asymptotically equivalent to B are lim and lim XQ-1 (x)=0 Theorem An asymptotically efficient FGls does not require that we have an efficient es- timator of 8; only a consistent one is required to achieve full efficiency for theConditions that imply that βˇ is asymptotically equivalent to β˜ are lim T→∞  1 T X0Ωˆ −1X  −  1 T X0Ω −1X  = 0 and lim T→∞  1 √ T X0Ωˆ −1 ε  −  1 √ T X0Ω −1 ε  = 0. Theorem: An asymptotically efficient FGLS does not require that we have an efficient es￾timator of θ; only a consistent one is required to achieve full efficiency for the FGLS estimator. 8