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Let bo , b1 denote the OLS estimators of such regression. Are they
ββ
unbiased? Under what assumptions?
We answer the above questions in two steps: Q.2.a we suppose that ZCMA holds
Q.2.b we identify the su¢ cient conditions for ZCMA to hold. Melissa Tartari (Yale) Econometrics 70 / 93 Failure of SLR.2: An Example (Q.2.a) As always we have (just use the standard formula)
b = β + ∑ ui (xi x ) .
β1
1
2
∑ (xi x ) Melissa Tartari (Yale) Econometrics 71 / 93 Failure of SLR.2: An Example (Q.2.a) As always we have (just use the standard formula)
b = β + ∑ ui (xi x ) .
β1
1
2
∑ (xi x ) Thus, we are bound to conclude that if ZCMA holds (E [U jX ] = 0)
then b1 is an unbiased estimator even if the sample is not random.
β Melissa Tartari (Yale) Econometrics 71 / 93 Failure of SLR.2: An Example (Q.2.a) As always we have (just use the standard formula)
b = β + ∑ ui (xi x ) .
β1
1
2
∑ (xi x ) Thus, we are bound to conclude that if ZCMA holds (E [U jX ] = 0)
then b1 is an unbiased estimator even if the sample is not random.
β
The above result begs the question: Melissa Tartari (Yale) Econometrics 71 / 93 Failure of SLR.2: An Example (Q.2.a) As always we have (just use the standard formula)
b = β + ∑ ui (xi x ) .
β1
1
2
∑ (xi x ) Thus, we are bound to conclude that if ZCMA holds (E [U jX ] = 0)
then b1 is an unbiased estimator even if the sample is not random.
β
The above result begs the question: under what conditions does ZCMA hold? Melissa Tartari (Yale) Econometrics 71 / 93 Failure of SLR.2: An Example (Q.2.a) As always we have (just use the standard formula)
b = β + ∑ ui (xi x ) .
β1
1
2
∑ (xi x ) Thus, we are bound to conclude that if ZCMA holds (E [U jX ] = 0)
then b1 is an unbiased estimator even if the sample is not random.
β
The above result begs the question: under what conditions does ZCMA hold?
in particular, may ZCMA hold and there still be di¤erences in the two
subpopulations and there still be over/under sampling? Formally, may
E [U jX ] = 0 and µA 6= µB and/or pA 6= pB ? Melissa Tartari (Yale) E...
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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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