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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 Mgt are large enough to

̂ ignore the estimation error in the gt; instead, the

uncertainty comes through vgt in (7). The MD approach from cluster sample notes effectively drops vgt from (7) and views gt t g xgtas 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 xgtvgt

12

(8)

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