(1a) Suppose you wish to predict Yi having observed Xi , but you tie your hands...

(1a) Suppose you wish to predict Yi having observed Xi , but you tie your hands to prediction rules of the form f(Xi) = g1Xi for some constant g1. Derive a formula for coefficient γ1 that minimizes the mean square prediction error M(g1) = E[(Yi − g1Xi) 2 ].

(1b) Now suppose you wish to estimate a regression model of the form Yi = β1Xi +ui . Derive a formula relating β1 and γ1.

(1c) Using your answer to part (b), show that γ1 = β1 if Assumption 1 holds. (d) Propose an estimator of γ1 and show it is consistent. State any additional assumptions.

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orchestra answered 1 year ago

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