Question: The parameter is defined in the model Y Xe where e is independent of X 0, E[e] 0, E e2

The parameter ¯ is defined in the model Y Æ X¤¯Åe where e is independent of X¤ ¸ 0, E[e] Æ 0, E

£

e2¤

Æ ¾2. The observables are (Y ,X) where X Æ X¤v and v È 0 is random scale measurement error, independent of X¤ and

e. Consider the least squares estimator b¯ for ¯.

(a) Find the plim of b¯ expressed in terms of ¯ and moments of (X, v,e).

(b) Can you find a non-trivial condition under which b¯ is consistent for ¯? (By non-trivial we mean something other than v Æ 1.)

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