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1. We have 

<img src='content_image/308309.jpg'>

where 

<img src='content_image/308308.jpg'>

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 

<img src='content_image/308307.jpg'>

<img src='content_image/308306.jpg'>

