X and Z are two jointly distributed random variables. Suppose you know the value of Z , but not the value of X. Let 11eb817c_771c_198d_84e6_d3a483d0d12a_SM2685_00 denote a guess of the value of X using the information on Z , and let 11eb817c_771c_198e_84e6_d93be02559b9_SM2685_00 denote the error associated with this guess. a. Show that E ( W ) = 0. b. Show that E ( WZ ) = 0. c. Let 11eb817c_771c_409f_84e6_37ae22685d25_SM2685_00 denote another guess of X using Z, and 11eb817c_771c_40a0_84e6_556c48b62483_SM2685_11 denote its error. Show that 11eb817c_771c_40a1_84e6_57bd8f97030f_SM2685_11 .

Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Edition 3ISBN: 978-9352863501

Edition 3ISBN: 978-9352863501

Exercise 23

X and Z are two jointly distributed random variables. Suppose you know the value of Z , but not the value of X. Let

denote a guess of the value of X using the information on Z , and let

denote the error associated with this guess.
a. Show that E ( W ) = 0.
b. Show that E ( WZ ) = 0.
c. Let

denote another guess of X using Z, and

denote its error. Show that

Explanation

Verified

It is told that:
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