where 2. If q ≥ 2 is the largest integer such that L$_{lr}$ = 0 for r = 1 , . . . , q − 1 , then the covariance of the estimates of the fixed effects ˆ π$_{2}$$_{l}$, . . . , ˆ π$_{ql}$, ˆ τ$_{1}$$_{l}$, . . . , ˆ τ$_{q}$$_{−}$$_{1}$$_{l}$ is identical to that it would be for L$_{l}$$_{1}$ = · · · = L$_{lD}$$_{−}$$_{1}$ = 0 . Moreover, the covariance between the estimates of ˆ π$_{2}$$_{l}$, . . . , ˆ π$_{ql}$, ˆ τ$_{1}$$_{l}$, . . . , ˆ τ$_{q}$$_{−}$$_{1}$$_{l}$ and the estimates of ˆ π$_{q}$$_{+1}$$_{l}$, . . . , ˆ π$_{Dl}$, ˆ τ$_{ql}$, . . . , ˆ τ$_{D}$$_{−}$$_{1}$$_{l}$ is also identical to that it would be for L$_{l}$$_{1}$ = · · · = L$_{lD}$$_{−}$$_{1}$ = 0 . Proof. 1. We begin with the result for the case L$_{l}$$_{1}$ = · · · = L$_{1}$$_{D}$$_{−}$$_{1}$ = 0. We demonstrate this by confirming By Lemma 4.2 we know that cov( ˆ β$_{l}$ , ˆ β$_{l}$ | L$_{l}$$_{1}$, . . . , L$_{lD}$$_{−}$$_{1}$ = 0 , L$_{lD}$ = l ) − 1 = ln$^{}$     A B T B T B C E B E C$^{}$     , cov( ˆ β$_{l}$ , ˆ β$_{l}$ | L$_{l}$$_{1}$, . . . , L$_{lD}$$_{−}$$_{1}$ = 0 , L$_{lD}$ = l ) − $^{1}$cov( ˆ β$_{l}$ , ˆ β$_{l}$ | L$_{l}$$_{1}$, . . . , L$_{lD}$$_{−}$$_{1}$ = 0 , L$_{lD}$ = l ) = I$_{2}$$_{D}$$_{−}$$_{1}$ . F = σ 2 b + 2 D − 1 D σ 2 $_{e}$, G$_{pq}$ = − σ 2 e ( p = 1 , . . . , D − 1; q = 1) , H$_{pq}$ = σ 2 $_{e}$(1 + δ$_{pq}$ ) ( p = 1 , . . . , D − 1; q = 1 , . . . , D − 1) . cov ( ˆ β$_{l}$ , ˆ β$_{l}$ | L$_{l}$$_{1}$, . . . , L$_{lD}$$_{−}$$_{1}$ = 0 , L$_{lD}$ = l ) =   ln | S$_{D}$ | | S$_{D}$ | ∑ i =1 X T $_{s$_{Di}$}$Σ − 1 D X$_{s}$$_{Di}$$^{}$  − 1 , = 1 ln     F G T G T G H 0$_{D}$$_{−}$$_{1}$$_{,D}$$_{−}$$_{1}$ G 0$_{D}$$_{−}$$_{1}$$_{,D}$$_{−}$$_{1}$ H     , (4.4) 1. We have 23