∙ Sometimes one wishes to impose some homogeneity in the slopes – say, _{gt } _{g }or even

_{gt } – in which case pooling can be used to

impose such restrictions. ∙ In any case, proceed as if M_{gt }are large enough to

̂ ignore the estimation error in the _{gt}; instead, the

uncertainty comes through v_{gt }in (7). The MD approach from cluster sample notes effectively drops v_{gt }from (7) and views _{gt } _{t } _{g } x_{gt} as a set of deterministic restrictions to be imposed on _{gt}. Inference using the efficient MD estimator

̂ uses only sampling variation in the _{gt}. Here, we

proceed ignoring estimation error, and so act as if

(7)

is, for t 1, . . . , T, g 1, . . . , G, ̂

_{gt } _{t } _{g } x_{gt} v_{gt }

12

(8)