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Unformatted text preview: he same among
2yr college students and 4yr college students. As long as the two
groups are not di¤erent in terms of their unobservables they can be
di¤erent in terms of their observables (pA 6= pB is allowed) and there
can be over/under sampling without either situation causing a bias in
the OLS estimator of β1 .
C.2: fA = 0 implies that there is only one subpop.: by construction
we cannot be over/under sampling. This condition su¢ ces b/c we
assumed E [U jX , A] = E [U jA] and E [U jX , B ] = E [U jB ], that is,
we assumed ZCMA within each group. Melissa Tartari (Yale) Econometrics 75 / 93 Failure of SLR.2: An Example (Q.2.b)
Let us comment on our …ndings:
C.1: µA = 0 implies µA = µB = 0  given the normalization  thus,
C.1 means that ZCMA holds whenever the distribution of U is the
same across the two subpop.s: mean ability/drive is the same among
2yr college students and 4yr college students. As long as the two
groups are not di¤erent in terms of their unobservables they can be
di¤erent in terms of their observables (pA 6= pB is allowed) and there
can be over/under sampling without either situation causing a bias in
the OLS estimator of β1 .
C.2: fA = 0 implies that there is only one subpop.: by construction
we cannot be over/under sampling. This condition su¢ ces b/c we
assumed E [U jX , A] = E [U jA] and E [U jX , B ] = E [U jB ], that is,
we assumed ZCMA within each group.
C.3: you can do some algebra and show that this condition requires
pA = pB = 1, that is, no variation in X : C.3 is irrelevant.
Melissa Tartari (Yale) Econometrics 75 / 93 The Variance of the OLS Estimator I
ˆˆ
How far can we expect β1 ( βo ) to be from β1 ( βo ) on average? Melissa Tartari (Yale) Econometrics 76 / 93 The Variance of the OLS Estimator I
ˆˆ
How far can we expect β1 ( βo ) to be from β1 ( βo ) on average?
ˆ
ˆ
The measure of spread in the distribution of β1 (and βo ) that is
ˆ jx (and Var β jx ) or its root, the
ˆ
easiest to work with is Var β1
o
standard deviation. Melissa Tartari (Yale) Econometrics 76 / 93 The Variance of the OLS Estimator I
ˆˆ
How far can we expect β1 (...
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 Fall '10
 DonaldBrown
 Econometrics

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