slides_Ch2_W[1]

# Melissa tartari yale econometrics 9 93 identication

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( βo , β1 ) given a random sample f(xi , yi ) ji = 1, ..., N g. Melissa Tartari (Yale) Econometrics 8 / 93 Identi…cation: the ZCMA I Claim: E [U jX ] = 0 =) corr (X , U ) = 0 Melissa Tartari (Yale) Econometrics 9 / 93 Identi…cation: the ZCMA I Claim: E [U jX ] = 0 =) corr (X , U ) = 0 How would we prove this? Melissa Tartari (Yale) Econometrics 9 / 93 Identi…cation: the ZCMA I Claim: E [U jX ] = 0 =) corr (X , U ) = 0 How would we prove this? First, we notice that corr (u , x ) = 0 i¤ cov (u , x ) = 0 because: q corr (u , x ) cov (u , x ) / Var (x ) Var (u ) Melissa Tartari (Yale) Econometrics 9 / 93 Identi…cation: the ZCMA I Claim: E [U jX ] = 0 =) corr (X , U ) = 0 How would we prove this? First, we notice that corr (u , x ) = 0 i¤ cov (u , x ) = 0 because: q corr (u , x ) cov (u , x ) / Var (x ) Var (u ) Second, we observe that cov (u , x ) can be written as E [ux ] (among other expressions) so that cov (u , x ) = 0 i¤ E [ux ] = 0: cov (u , x ) Melissa Tartari (Yale) E [(u E [u ]) (x E [x ])] = E [u (x Econometrics E [x ])] = E [ux ] . 9 / 93 Identi…cation: the ZCMA I Claim: E [U jX ] = 0 =) corr (X , U ) = 0 How would we prove this? First, we notice that corr (u , x ) = 0 i¤ cov (u , x ) = 0 because: q corr (u , x ) cov (u , x ) / Var (x ) Var (u ) Second, we observe that cov (u , x ) can be written as E [ux ] (among other expressions) so that cov (u , x ) = 0 i¤ E [ux ] = 0: cov (u , x ) E [(u E [u ]) (x E [x ])] = E [u (x E [x ])] = E [ux ] . Third, we observe that E [x jx ] = x and that, by the Law of Iterated Expectation (LIE), E [E [u jx ]] = E [u ]. Melissa Tartari (Yale) Econometrics 9 / 93 Identi…cation: the ZCMA I Claim: E [U jX ] = 0 =) corr (X , U ) = 0 How would we prove this? First, we notice that corr (u , x ) = 0 i¤ cov (u , x ) = 0 because: q corr (u , x ) cov (u , x ) / Var (x ) Var (u ) Second, we observe that cov (u , x ) can be written as E [ux ] (among other expressions) so that cov (u , x ) = 0 i¤ E [ux ] = 0: cov (u , x ) E [(u E [u ]) (x E [x ])] = E [u (x E [x ])] = E [ux ] . Third, we observe that...
View Full Document

## This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

Ask a homework question - tutors are online