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Melissa tartari yale econometrics 9 93 identication

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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...
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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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