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First we need a random sample from the population:
f(yi , xi ) ji = 1, ..., ng.
Observe that we can write yi = βo + β1 xi + ui for each i (2.9) How do we use this data? There exist several estimation procedures:
Method of Moments Melissa Tartari (Yale) Econometrics 20 / 93 Three Estimation Methods
Having established the key assumption under which ( βo , β1 ) are
identi…able  ZCMA  we are now in the business of estimating these
unknown parameters. How can we do that?
First we need a random sample from the population:
f(yi , xi ) ji = 1, ..., ng.
Observe that we can write yi = βo + β1 xi + ui for each i (2.9) How do we use this data? There exist several estimation procedures:
Method of Moments
Least Squares Melissa Tartari (Yale) Econometrics 20 / 93 Three Estimation Methods
Having established the key assumption under which ( βo , β1 ) are
identi…able  ZCMA  we are now in the business of estimating these
unknown parameters. How can we do that?
First we need a random sample from the population:
f(yi , xi ) ji = 1, ..., ng.
Observe that we can write yi = βo + β1 xi + ui for each i (2.9) How do we use this data? There exist several estimation procedures:
Method of Moments
Least Squares
Maximum Likelihood Melissa Tartari (Yale) Econometrics 20 / 93 The MoM: the Basics
Observe that because of E [u jx ] = 0 we also have that
E [ux ] = E [E [ux jx ]] = E [xE [u jx ]] = E [x 0] = 0. Melissa Tartari (Yale) Econometrics 21 / 93 The MoM: the Basics
Observe that because of E [u jx ] = 0 we also have that
E [ux ] = E [E [ux jx ]] = E [xE [u jx ]] = E [x 0] = 0.
Thus, we have two moment conditions :
E [u ] = 0
)
E [xu ] = 0 Melissa Tartari (Yale) E [y βo β1 x ] = 0
E [x (y βo β1 x )] = 0 Econometrics (2.12 & 2.13) 21 / 93 The MoM: the Basics
Observe that because of E [u jx ] = 0 we also have that
E [ux ] = E [E [ux jx ]] = E [xE [u jx ]] = E [x 0] = 0.
Thus, we have two moment conditions :
E [u ] = 0
)
E [xu ] = 0 E [y βo β1 x ] = 0
E [x (y βo β1 x )] = 0 (2.1...
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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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