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Unformatted text preview: tly replacing the population objects µy , µx , var (x ) , cov (x , y )
in (4) with their sample counterparts.
ˆ MM ˆ MM ...
Recall, β , β
o 1 regarded as functions of the RVs X and Y are estimators of ( βo , β1 );
Melissa Tartari (Yale) Econometrics 27 / 93 The Method of Moments Approach VI
More generally, the LLN allows us to rewrite the system (2.12 & 2.13)
in terms of the sample counterparts (or analogues) of E [u ] and
E [xu ]. We can thus de…ne the MoM estimators as the solution to the
system:
∑n=1 xi (yi βo β1 xi ) = 0
i
.
∑n=1 yi βo β1 xi = 0
i (2.14 & 2.15) It goes without saying that the estimators obtained as solutions to the
ˆ MM ˆ MM obtained by
system (2.14 & 2.15) are exactly the βo , β1
n
o
directly replacing the population objects µy , µx , var (x ) , cov (x , y )
in (4) with their sample counterparts.
ˆ MM ˆ MM ...
Recall, β , β
o 1 regarded as functions of the RVs X and Y are estimators of ( βo , β1 );
evaluated at a speci…c data sample are estimates of ( βo , β1 ).
Melissa Tartari (Yale) Econometrics 27 / 93 The Method of Moments Approach VI You may want to to do the following for practice: Melissa Tartari (Yale) Econometrics 28 / 93 The Method of Moments Approach VI You may want to to do the following for practice:
Assume ZCMA but allow E [U ] = λ 6= 0. Melissa Tartari (Yale) Econometrics 28 / 93 The Method of Moments Approach VI You may want to to do the following for practice:
Assume ZCMA but allow E [U ] = λ 6= 0.
Show that the moment condition E [(u E (u )) x ] = 0, implied by the
ZCMA, is su¢ cient to identify β1 . Melissa Tartari (Yale) Econometrics 28 / 93 The Method of Moments Approach VI You may want to to do the following for practice:
Assume ZCMA but allow E [U ] = λ 6= 0.
Show that the moment condition E [(u E (u )) x ] = 0, implied by the
ZCMA, is su¢ cient to identify β1 .
Derive the implied sample analoguebased MoM estimator of β1 . Melissa Tartari (Yale) Econometrics 28 / 93 The Method of Moments Approach VI You may want to to do the following for practi...
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 Fall '10
 DonaldBrown
 Econometrics

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