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Unformatted text preview: conometrics 71 / 93 Failure of SLR.2: An Example (Q.2.b)
We start by writing out E [U jX = 1] to explore what ZCMA imposes
on the underlying parameters (µA , µB , pA , pB ):
E [U jX = 1] = E [U jX = 1, A] Pr (AjX = 1) +E [U jX = 1, B ] Pr (B jX = 1)
Pr (X = 1jA) Pr (A)
= E [U jA]
Pr (X = 1)
Pr (X = 1jB ) Pr (B )
+E [U jB ]
Pr (X = 1)
pA fA
p ( 1 fA )
= µA
+ µB B
Pr (X = 1)
Pr (X = 1) Melissa Tartari (Yale) Econometrics (9) 72 / 93 Failure of SLR.2: An Example (Q.2.b)
We start by writing out E [U jX = 1] to explore what ZCMA imposes
on the underlying parameters (µA , µB , pA , pB ):
E [U jX = 1] = E [U jX = 1, A] Pr (AjX = 1) +E [U jX = 1, B ] Pr (B jX = 1)
Pr (X = 1jA) Pr (A)
= E [U jA]
Pr (X = 1)
Pr (X = 1jB ) Pr (B )
+E [U jB ]
Pr (X = 1)
pA fA
p ( 1 fA )
= µA
+ µB B
Pr (X = 1)
Pr (X = 1) (9) And similarly,
E [U jX = 0] = µA
Melissa Tartari (Yale) (1 pA ) fA
(1
+ µB
1 Pr (X = 1)
1
Econometrics pB ) (1 fA )
.
Pr (X = 1) (10) 72 / 93 Failure of SLR.2: An Example (Q.2.b)
The question is: what does E [U jX = 1] = E [U jX = 0] imply for
(µA , µB , pA , pB )? Melissa Tartari (Yale) Econometrics 73 / 93 Failure of SLR.2: An Example (Q.2.b)
The question is: what does E [U jX = 1] = E [U jX = 0] imply for
(µA , µB , pA , pB )?
Before answering that question we need to take care of a little issue:
we need to impose the normalization E [U ] = 0. Melissa Tartari (Yale) Econometrics 73 / 93 Failure of SLR.2: An Example (Q.2.b)
The question is: what does E [U jX = 1] = E [U jX = 0] imply for
(µA , µB , pA , pB )?
Before answering that question we need to take care of a little issue:
we need to impose the normalization E [U ] = 0.
Recall
E [U ] = E [U jA] Pr (A) + E [U jB ] Pr (B ) = µ A fA + µ B ( 1 Melissa Tartari (Yale) Econometrics fA ) 73 / 93 Failure of SLR.2: An Example (Q.2.b)
The question is: what does E [U jX = 1] = E [U jX = 0] imply for
(µA , µB , pA , pB )?
Before answering that question we need to take care of a little issue:
we need to impose the normalizatio...
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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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