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Unformatted text preview: Let x 0 and x 00 be two di¤erent values of X , then
E Y jX = x 0 E Y jX = x 00 = βo + β1 x 0 .
= βo + β1 x 00 . Subtract the 2nd eq from the …rst and solve for β1 :
β1 = Melissa Tartari (Yale) E [Y jX = x 0 ]
(x 0 Econometrics E [Y jX = x 00 ]
.
x 00 ) 7 / 93 Identi…cation: the claim (proof)
Let x be any value of X . Use ZCMA and the normalization E [U ] = 0
to obtain
E [Y jX = x ] = βo + β1 x + 0.
Let x 0 and x 00 be two di¤erent values of X , then
E Y jX = x 0 E Y jX = x 00 = βo + β1 x 0 .
= βo + β1 x 00 . Subtract the 2nd eq from the …rst and solve for β1 :
β1 = E [Y jX = x 0 ]
(x 0 E [Y jX = x 00 ]
.
x 00 ) Take the …rst eq (or the 2nd) and solve for βo :
βo = E Y jX = x 0 Melissa Tartari (Yale) E [Y jX = x 0 ]
(x 0 Econometrics E [Y jX = x 00 ] 0
x.
x 00 ) 7 / 93 Identi…cation: the claim (proof)
Let x be any value of X . Use ZCMA and the normalization E [U ] = 0
to obtain
E [Y jX = x ] = βo + β1 x + 0.
Let x 0 and x 00 be two di¤erent values of X , then
E Y jX = x 0 E Y jX = x 00 = βo + β1 x 0 .
= βo + β1 x 00 . Subtract the 2nd eq from the …rst and solve for β1 :
β1 = E [Y jX = x 0 ]
(x 0 E [Y jX = x 00 ]
.
x 00 ) Take the …rst eq (or the 2nd) and solve for βo :
βo = E Y jX = x 0 E [Y jX = x 0 ]
(x 0 E [Y jX = x 00 ] 0
x.
x 00 ) Finally, observe that E [Y jX = x 0 ],E [Y jX = x 00 ] , and E [Y jX = x 0 ]
are known if we have access to the population (recall LLN).
Melissa Tartari (Yale) Econometrics 7 / 93 Identi…cation: the roadmap We just showed that in the SLRM the ZCMA is su¢ cient for
identication of ( βo , β1 ). Melissa Tartari (Yale) Econometrics 8 / 93 Identi…cation: the roadmap We just showed that in the SLRM the ZCMA is su¢ cient for
identi…cation of ( βo , β1 ).
We next delve into the meaning of the ZCMA. Melissa Tartari (Yale) Econometrics 8 / 93 Identi…cation: the roadmap We just showed that in the SLRM the ZCMA is su¢ cient for
identi…cation of ( βo , β1 ).
We next delve into the meaning of the ZCMA.
We …nally introduce three estimation methods, that is, three
procedures to obtain estimates of...
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 Fall '10
 DonaldBrown
 Econometrics

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