HW2_S2010 - Problem Set 2 - Due Thursday 02/25/10 at the...

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Problem Set 2 - Due Thursday 02/25/10 at the beginning of class Econ 3200 - Introduction to Econometrics Spring 2010 Cornell University Prof. Molinari 1. Question 2.2 from Wooldridge p. 66. 2. Consider a simple linear regression model WITHOUT a constant (the true value of & 0 is 0 ) y i = 1 x i + u i : (1) This is the usual two variable regression model where it is known that & 0 = 0 : Suppose in n observations of ( y i ; x i ) : (a) Derive the formula for e 1 , the least squares estimator of 1 for model (1). (b) Compute the bias of e 1 . (c) Derive the variance formula for e 1 . (d) Suppose that averages of x i u i and x 2 i satisfy laws of large numbers. In other words, assume that p lim 1 n n X i =1 x i u i ! = 0 and p lim 1 n n X i =1 x 2 i ! = ± 2 = E ( x 2 i ) < 1 . Prove that e 1 is a consistent estimator of 1 . Now consider an alternative estimator of 1 obtained by the usual regression model where the intercept is included (the estimator we would use if we didn±t know that
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This note was uploaded on 04/14/2010 for the course ECON 3200 taught by Professor Neilsen during the Spring '08 term at Cornell University (Engineering School).

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HW2_S2010 - Problem Set 2 - Due Thursday 02/25/10 at the...

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