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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.
 Fall '10
 DonaldBrown
 Econometrics

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