slides_Ch2_W[1]

Slides_Ch2_W[1]

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Unformatted text preview: Y jB = (sA fA ) (E [Y jA] E [Y jB ]) ( Melissa Tartari (Yale) sA ) y B ] Econometrics 63 / 93 Failure of SLR.2: An Example (Q.1) The candidate estimator y is unbiased for E [Y ] i¤ E [y ] that is, i¤ 0 = E [ sA y A + ( 1 E [Y ] = 0, (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [y A ] + (1 sA ) E [y B ]) (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [Y jA] + (1 sA ) E [Y jB ]) (fA E [Y jA] + (1 fA ) E [Y jB = (sA fA ) (E [Y jA] E [Y jB ]) ( sA ) y B ] Based on expression (8) we conclude that there are two sets of su¢ cient conditions for unbiasedness of y : Melissa Tartari (Yale) Econometrics 63 / 93 Failure of SLR.2: An Example (Q.1) The candidate estimator y is unbiased for E [Y ] i¤ E [y ] that is, i¤ 0 = E [ sA y A + ( 1 E [Y ] = 0, (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [y A ] + (1 sA ) E [y B ]) (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [Y jA] + (1 sA ) E [Y jB ]) (fA E [Y jA] + (1 fA ) E [Y jB = (sA fA ) (E [Y jA] E [Y jB ]) ( sA ) y B ] Based on expression (8) we conclude that there are two sets of su¢ cient conditions for unbiasedness of y : sA = fA : there is no over or under sampling of one subpopulation. Melissa Tartari (Yale) Econometrics 63 / 93 Failure of SLR.2: An Example (Q.1) The candidate estimator y is unbiased for E [Y ] i¤ E [y ] that is, i¤ 0 = E [ sA y A + ( 1 E [Y ] = 0, (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [y A ] + (1 sA ) E [y B ]) (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [Y jA] + (1 sA ) E [Y jB ]) (fA E [Y jA] + (1 fA ) E [Y jB = (sA fA ) (E [Y jA] E [Y jB ]) ( sA ) y B ] Based on expression (8) we conclude that there are two sets of su¢ cient conditions for unbiasedness of y : sA = fA : there is no over or under sampling of one subpopulation. E [Y jA] = E [Y jB ]: there may be under/over sampling but mean grades are the same across the two subpopulations (that is, over/under sampling is based on a variable that does not a¤ect grades). Melissa Tartari (Yale) Econometrics 63 / 93 Failure of SLR.2: An Example (Q.1) We can, of cours...
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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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