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Melissa tartari yale econometrics 65 93 failure of

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Unformatted text preview: wo subpop.s) the sample average is a biased estimator of the population mean. Under what circumstances can we construct an unbiased estimator of E [Y ] in the presence of under/over sampling? Melissa Tartari (Yale) Econometrics 65 / 93 Failure of SLR.2: An Example (Q.1) We have concluded that in the presence of over/under sampling (and true di¤erences b/w the two subpop.s) the sample average is a biased estimator of the population mean. Under what circumstances can we construct an unbiased estimator of E [Y ] in the presence of under/over sampling? We consider two conditions and show that, taken together, they su¢ ce: Melissa Tartari (Yale) Econometrics 65 / 93 Failure of SLR.2: An Example (Q.1) We have concluded that in the presence of over/under sampling (and true di¤erences b/w the two subpop.s) the sample average is a biased estimator of the population mean. Under what circumstances can we construct an unbiased estimator of E [Y ] in the presence of under/over sampling? We consider two conditions and show that, taken together, they su¢ ce: C.1 the econometrician knows the sampling proportions and the population proportions, namely, sA and pA ; Melissa Tartari (Yale) Econometrics 65 / 93 Failure of SLR.2: An Example (Q.1) We have concluded that in the presence of over/under sampling (and true di¤erences b/w the two subpop.s) the sample average is a biased estimator of the population mean. Under what circumstances can we construct an unbiased estimator of E [Y ] in the presence of under/over sampling? We consider two conditions and show that, taken together, they su¢ ce: C.1 the econometrician knows the sampling proportions and the population proportions, namely, sA and pA ; C.2 for each i we know whether i 2 A (j (i ) = A) or i 2 B (j (i ) = B ). Melissa Tartari (Yale) Econometrics 65 / 93 Failure of SLR.2: An Example (Q.1) Use what we showed to “guess” an unbiased estimator: E [ y ] = E [ Y ] + ( sA Melissa Tartari (Yale) fA ) ( E [ Y j A ] Econometrics E [Y jB ]) 66 / 93 Failure of SLR.2: An Example (Q.1) Use what we showed to “guess” an unbiased estimator: E [ y ] = E [ Y ] + ( sA Observe that by C.1 (sA Melissa Tartari (Ya...
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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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