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Unformatted text preview: p would entail solving the FOCs in (5) to get explicit
ˆ OLS ˆ OLS .
expressions for the βo , β1
Actually, we do not really need to go through the algebra because we
ˆ MM = βOLS .
ˆ
can claim that β
Are you surprised about this result?
You should not!
Why not?
ˆ MM and βOLS solve the same system of equations which in
ˆ
Because, β
the case of OLS are the FOCs of the minimization program and in the
case of MM are the sample analogues to the two moment conditions
E [u ] = 0 and E [ux ] = 0. Melissa Tartari (Yale) Econometrics 35 / 93 The Maximum Likelihood Estimator We postpone maximum likelihood estimation to when we cover
Chapter 6. Melissa Tartari (Yale) Econometrics 36 / 93 The Maximum Likelihood Estimator We postpone maximum likelihood estimation to when we cover
Chapter 6.
We do so because the MLE approach requires a distributional
assumption that neither MM nor OLS need. Melissa Tartari (Yale) Econometrics 36 / 93 The Maximum Likelihood Estimator We postpone maximum likelihood estimation to when we cover
Chapter 6.
We do so because the MLE approach requires a distributional
assumption that neither MM nor OLS need.
We preview that
ˆ MM = βOLS = βML .
ˆ
ˆ
β Melissa Tartari (Yale) Econometrics 36 / 93 The Maximum Likelihood Estimator We postpone maximum likelihood estimation to when we cover
Chapter 6.
We do so because the MLE approach requires a distributional
assumption that neither MM nor OLS need.
We preview that
ˆ MM = βOLS = βML .
ˆ
ˆ
β
ˆ OLS by β,
ˆ
Next, we concentrate on the OLS approach: we denote β
OLS by y , and u OLS by u since this simpler notation does not
yi
b
bi
bi
bi
create confusion and it is ... simpler. Melissa Tartari (Yale) Econometrics 36 / 93 The Mechanics of OLS We next describe a few properties of OLS. Melissa Tartari (Yale) Econometrics 37 / 93 The Mechanics of OLS We next describe a few properties of OLS.
We do so by distinguishing between algebraic or numerical properties
and statistical properties: Melissa Tartari (Yale) Econometrics 37 / 93 The Mechanics of OLS We next desc...
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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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