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Unformatted text preview: G (X ) Melissa Tartari (Yale) E [Y jX ] , Y = G (X ) + U where E [U jX ] = 0, Econometrics 12 / 93 Identi…cation: Food for Thought I Recall the end of Chapter 1 slides, we claimed that: G (X ) E [Y jX ] , Y = G (X ) + U where E [U jX ] = 0, That is, given the form of E [Y jX ], U is de…ned by Y
thus by de…nition E [U jX ] = 0. Melissa Tartari (Yale) Econometrics G (X ) and 12 / 93 Identi…cation: Food for Thought I Recall the end of Chapter 1 slides, we claimed that: G (X ) E [Y jX ] , Y = G (X ) + U where E [U jX ] = 0, That is, given the form of E [Y jX ], U is de…ned by Y
thus by de…nition E [U jX ] = 0. G (X ) and Consider now the recently stated ZCMA: E [U jX ] = 0 given model
Y = g (X ) + U . Melissa Tartari (Yale) Econometrics 12 / 93 Identi…cation: Food for Thought I Recall the end of Chapter 1 slides, we claimed that: G (X ) E [Y jX ] , Y = G (X ) + U where E [U jX ] = 0, That is, given the form of E [Y jX ], U is de…ned by Y
thus by de…nition E [U jX ] = 0. G (X ) and Consider now the recently stated ZCMA: E [U jX ] = 0 given model
Y = g (X ) + U . The calligraphic di¤erence between U and U is not by chance and we
also di¤erentiated between the function g and G . Melissa Tartari (Yale) Econometrics 12 / 93 Identi…cation: Food for Thought I Recall the end of Chapter 1 slides, we claimed that: G (X ) E [Y jX ] , Y = G (X ) + U where E [U jX ] = 0, That is, given the form of E [Y jX ], U is de…ned by Y
thus by de…nition E [U jX ] = 0. G (X ) and Consider now the recently stated ZCMA: E [U jX ] = 0 given model
Y = g (X ) + U . The calligraphic di¤erence between U and U is not by chance and we
also di¤erentiated between the function g and G .
We next understand better why E [U jX ] = 0 holds by de…nition while
E [U jX ] = 0 holds by assumption. We procede in three steps. Melissa Tartari (Yale) Econometrics 12 / 93 Identi…cation: Food for Thought II  step 1 We …rst restate the models for Y :
Y
Y Melissa Tartari (Yale) = g (X ) + U , E [U ] = 0
= G (X ) + U , E [ U jX ] = 0 Econometrics (2)
(3) 13 / 93 Identi…cation: Food for Thought II  step 2 Take (2) and add and subtract G (X ) on the RHS:
Y = G (X ) + (U + g (X ) Melissa Tartari (Yale) Econometrics G (X )) 14 / 93 Identi…cation: Food for Thought II  step 2 Take (2) and add and subtract G (X ) on the RHS:
Y = G (X ) + (U + g (X ) G (X )) From (3) we see that the term in brackets must equal U ; then it
should be that E [U + g (X ) G (X ) jX ] = 0 always...
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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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