slides_Ch2_W[1]

5 0 26 6 93 identication the claim the zero

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: tween X and U : for any given value x of X , the mean of U is the same hence it is equal to the mean of U in the entire population. Formally, E [U jX ] = E [U ] Melissa Tartari (Yale) Econometrics by 2.5 =0 (2.6) 6 / 93 Identi…cation: the claim The zero conditional mean assumption (ZCMA) Consider the following restriction on the relationship between X and U : for any given value x of X , the mean of U is the same hence it is equal to the mean of U in the entire population. Formally, E [U jX ] = E [U ] by 2.5 =0 (2.6) Claim Consider the SLRM Y = βo + β1 X + U , E [U ] = 0 and suppose that the RV X takes at least two values. If the ZCMA holds then ( βo , β1 ) are identi…ed. Melissa Tartari (Yale) Econometrics 6 / 93 Identi…cation: the claim The zero conditional mean assumption (ZCMA) Consider the following restriction on the relationship between X and U : for any given value x of X , the mean of U is the same hence it is equal to the mean of U in the entire population. Formally, E [U jX ] = E [U ] by 2.5 =0 (2.6) Claim Consider the SLRM Y = βo + β1 X + U , E [U ] = 0 and suppose that the RV X takes at least two values. If the ZCMA holds then ( βo , β1 ) are identi…ed. Working De…nition of Identi…cation: a parameter is identi…ed we can learn it from data on the entire population (or an in…nitely large sample from the population). Melissa Tartari (Yale) Econometrics 6 / 93 Identi…cation: the claim (proof) Let x be any value of X . Use ZCMA and the normalization E [U ] = 0 to obtain E [Y jX = x ] = βo + β1 x + 0. Melissa Tartari (Yale) Econometrics 7 / 93 Identi…cation: the claim (proof) Let x be any value of X . Use ZCMA and the normalization E [U ] = 0 to obtain E [Y jX = x ] = βo + β1 x + 0. Let x 0 and x 00 be two di¤erent values of X , then E Y jX = x 0 E Y jX = x 00 Melissa Tartari (Yale) = βo + β1 x 0 . = βo + β1 x 00 . Econometrics 7 / 93 Identi…cation: the claim (proof) Let x be any value of X . Use ZCMA and the normalization E [U ] = 0 to obtain E [Y jX = x ] = βo + β1 x + 0....
View Full Document

Ask a homework question - tutors are online