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The measure of spread in the distribution of 1 and o

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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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