slides_Ch2_W[1]

1 thus the rst equation of the focs is property 230

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Unformatted text preview: mean) n n 1 ˆ ˆ ¯ ∑ ui = 0 , n ∑ yi = y i =1 (2.30) i =1 The sample covariance between the regressor and the OLS residual is zero (, the sample covariance between the …tted values and the OLS residual is zero) n ˆ ∑ ui xi = 0 , i =1 Melissa Tartari (Yale) Econometrics n ˆˆ ∑ ui yi = 0 (2.31) i =1 38 / 93 Algebraic Properties - Food for Thought I Is part 1 of property 2.30, and respectively of 2.31, obvious? Melissa Tartari (Yale) Econometrics 39 / 93 Algebraic Properties - Food for Thought I Is part 1 of property 2.30, and respectively of 2.31, obvious? Recall the FOCs of the OLS minimization problem - namely (5): ∑n=1 (yi i ∑n=1 (yi i Melissa Tartari (Yale) b βo b βo Econometrics b xi ) = 0 β1 b xi )xi = 0 . β1 39 / 93 Algebraic Properties - Food for Thought I Is part 1 of property 2.30, and respectively of 2.31, obvious? Recall the FOCs of the OLS minimization problem - namely (5): ∑n=1 (yi i ∑n=1 (yi i b βo b βo b xi ) = 0 β1 b xi )xi = 0 . β1 Thus, the …rst equation of the FOCs is property 2.30 and the second equation of the FOCs system is property 2.c. Melissa Tartari (Yale) Econometrics 39 / 93 Algebraic Properties - Food for Thought I Is part 1 of property 2.30, and respectively of 2.31, obvious? Recall the FOCs of the OLS minimization problem - namely (5): ∑n=1 (yi i ∑n=1 (yi i b βo b βo b xi ) = 0 β1 b xi )xi = 0 . β1 Thus, the …rst equation of the FOCs is property 2.30 and the second equation of the FOCs system is property 2.c. So, yes, these two properties are obvious. Melissa Tartari (Yale) Econometrics 39 / 93 Algebraic Properties - Food for Thought I Is part 1 of property 2.30, and respectively of 2.31, obvious? Recall the FOCs of the OLS minimization problem - namely (5): ∑n=1 (yi i ∑n=1 (yi i b βo b βo b xi ) = 0 β1 b xi )xi = 0 . β1 Thus, the …rst equation of the FOCs is property 2.30 and the second equation of the FOCs system is property 2.c. So, yes, these two properties are obvious. You may want to verify the two implications of property 2.30 and, respectively, 2.31. Melissa Tartari (Yale) Econometrics 39 / 93 Algebraic Properties: Goodness of Fit Recall yi = yi +...
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This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

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