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Econ375Homework2

# Econ375Homework2 - ECON 375 Introduction to Econometrics...

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ECON 375: Introduction to Econometrics Spring 2010 Problem Set 2 Due: April 29, 2010, 9:00PM NOTE: All assignments must be typed if you can not write it legibly. Graphs and calculations may be handwritten. No late homework will be accepted. Exercise 1 (10 Points) Consider two unbiased independent estimators h β and t β , constructed to estimate the parameter β . Suppose you construct a third estimator β * that is a convex combination of h β and t β , that is, β * = α h β +(1 - α ) t β , with α [0 , 1]. (a) Is β * an unbiased estimator? (b) Find the variance of β * and express it in terms of the variance of h β and t β . (c) Assume that the sampling distributions of h β and t β are normal. Describe the sampling distribution of β * . (d) What value of α would you choose to calculate β * ? Justify your answer. Exercise 2 (10 Points)

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Econ375Homework2 - ECON 375 Introduction to Econometrics...

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