HW03_Econ140A_2011Fall

# HW03_Econ140A_2011Fall - Economics 140A Fall 2011 Professor...

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Economics 140A Fall 2011 Professor Startz Homework 3 1. The variance of the OLS estimator is ( ̂ ) , where . You're hired to estimate and you're going to be paid according to the accuracy of your estimate. Specifically, your revenue is ( ̂ ) . You can buy as many observations as you want at price . The sample variance of , , never changes. How many observations should you buy? 2. Suppose that you have observations on , that , that ( ) , ( ) , and that ( ) . Prove that the sample mean, ̂ , is the best, linear, unbiased estimator of . Feel free to cite previous results about the variance of ̂ , but carry out the proof rather than simply citing the Gauss-Markov theorem. 3 a. Find the formula for ( ̂ ̂ ) . b. Find the formula for ( ̂ ̂ ) 4. Use the data set cdcosts2010 to estimate the marginal cost of one more CD. (Regress costs on the number of CDS.) Test the hypothesis that the marginal cost equals 75 cents. How would the results of the hypothesis test change if cost was measured in cents rather than in dollars.

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