Consider the one-variable regression model Y i = 0 + 1 X i + u i and suppose that it satisfies the least squares assumptions in Key Concept 4.3. The regressor X i is missing, but data on a related variable Z i are available, and the value of X i is estimated using 11eb817c_77d2_49e9_84e6_43b50fd50af5_SM2685_00 a. Show that 11eb817c_77d2_49ea_84e6_8f57848e16c4_SM2685_00 is the minimum mean square error estimator of X i using Z i. That is, let 11eb817c_77d2_49eb_84e6_c9ec397dd205_SM2685_00 be some other guess of X i based on Z i and show that 11eb817c_77d2_49ec_84e6_dda9de26d197_SM2685_11 b. Show that 11eb817c_77d2_49ed_84e6_f507aaeb1eea_SM2685_11 . c. Suppose that E ( u|Z i ) = 0 and that 11eb817c_77d2_49ee_84e6_874377da4b86_SM2685_11 , is used as the regressor in place of X i. Show that 11eb817c_77d2_49ef_84e6_3bae080fa613_SM2685_11 is consistent. Is 11eb817c_77d2_7100_84e6_d58254424d37_SM2685_11 consistent

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

النسخة 3الرقم المعياري الدولي: 978-9352863501

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

النسخة 3الرقم المعياري الدولي: 978-9352863501

تمرين 13

Consider the one-variable regression model Y i = 0 + 1 X i + u i and suppose that it satisfies the least squares assumptions in Key Concept 4.3. The regressor X i is missing, but data on a related variable Z i are available, and the value of X i is estimated using