slides_Ch2_W[1]

Slides_Ch2_W[1]

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Unformatted text preview: age where the weight of each observation equals the ratio of the theoretical frequency of the group to which it belongs and the sample frequency. Melissa Tartari (Yale) Econometrics 68 / 93 Failure of SLR.2: An Example (Q.1.a) To see that the unbiased estimator y W is intuitively sensible it is useful to do some algebra ... yW y = ... 1 = N = 1 N ( sA N fA ) ( y A fA N ∑ sA yi + N ∑ 1 fA yi sA ∑ ωi yi fj ( i ) sj ( i ) i =1 N i =1 1 yB ) 1 i =1 with ω i = We see that y W is a weighted sample average where the weight of each observation equals the ratio of the theoretical frequency of the group to which it belongs and the sample frequency. If there is no over/under sampling then ω i = 1 for all i and we verify that, as expected, the (unweighted ) sample average is an unbiased estimator of the population mean:y W = y . Melissa Tartari (Yale) Econometrics 68 / 93 Failure of SLR.2: An Example (Q.1.b) We …rst observe that given Y = γ + U , where γ is a parameter and U a (n unobserved) RV, the OLS estimator of γ is the sample average (just use the formula for bo ): β b γOLS = y . Melissa Tartari (Yale) Econometrics 69 / 93 Failure of SLR.2: An Example (Q.1.b) We …rst observe that given Y = γ + U , where γ is a parameter and U a (n unobserved) RV, the OLS estimator of γ is the sample average (just use the formula for bo ): β b γOLS = y . Thus, the biased estimator y is a OLS estimator: the example shows an instance in which failure of SLR.2 leads to bias. Melissa Tartari (Yale) Econometrics 69 / 93 Failure of SLR.2: An Example (Q.1.b) We …rst observe that given Y = γ + U , where γ is a parameter and U a (n unobserved) RV, the OLS estimator of γ is the sample average (just use the formula for bo ): β b γOLS = y . Thus, the biased estimator y is a OLS estimator: the example shows an instance in which failure of SLR.2 leads to bias. We will see that y W is also a LS estimator: the WLS estimator. Melissa Tartari (Yale) Econometrics 69 / 93 Failure of SLR.2: An Example...
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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.

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