Consider the standard simple regression model y = 0 + 1 x + u under the Gauss-Markov Assumptions SLR.l through SLR.5. The usual OLS estimators 30 and J3X are unbiased for their respective population parameters. Let 11eb9ee2_f06a_f19d_8edd_9571fea2ca3f_SM2712_11 1 be the estimator of 1 obtained by assuming the intercept is zero (see Section 2.6). (i) Find E( 11eb9ee2_f06a_f19e_8edd_1960c3bacab0_SM2712_11 1 ) in terms of the x, 0 , and 1. Verify that 11eb9ee2_f06a_f19f_8edd_83c8b2373050_SM2712_11 1 is unbiased for 1 when the population intercept ( 0 ) is zero. Are there other cases where 1 is unbiased (ii) Find the variance of 11eb9ee2_f06b_18b0_8edd_b5f07bc67907_SM2712_11 1. (Hint: The variance does not depend on 1.) 11eb9ee2_f06b_18b1_8edd_57bae85ff289_SM2712_11 (iv)Comment on the trade off between bias and variance when choosing between 11eb9ee2_f06b_18b2_8edd_97bb704cd67c_SM2712_11 and 11eb9ee2_f06b_18b3_8edd_41097dfe5337_SM2712_11 .

Introductory Econometrics 4th Edition by Jeffrey Wooldridge

النسخة 4الرقم المعياري الدولي: 978-0324660609

Introductory Econometrics 4th Edition by Jeffrey Wooldridge

النسخة 4الرقم المعياري الدولي: 978-0324660609

تمرين 5

Consider the standard simple regression model y = 0 + 1 x + u under the Gauss-Markov Assumptions SLR.l through SLR.5. The usual OLS estimators 30 and J3X are unbiased for their respective population parameters. Let

1 be the estimator of 1 obtained by assuming the intercept is zero (see Section 2.6).
(i) Find E(

1 ) in terms of the x, 0 , and 1. Verify that

1 is unbiased for 1 when the population intercept ( 0 ) is zero. Are there other cases where 1 is unbiased
(ii) Find the variance of

1. (Hint: The variance does not depend on 1.)

(iv)Comment on the trade off between bias and variance when choosing between

and

التوضيح

موثّق

i)
To show the unbiasedness of the regre...