notes-iv - A. Introduction A. log( wage ) = 0 + 1educ + 2...

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A. Introduction A. Introduction Omitted variable violates MLR\3 biased/wrong estimates overcome : (1) ignore (2) suitable proxy exists proxy variable (3) suitable proxy does not exist instrumental variable 01 2 log( ) wage educ ability u β ββ = ++ + * 2 y xs u y x u =+ + + + (1) cov( , ) 0 (2)cov( , ) 0 zsu chtha t zu z is an instrumental variable for x zx =
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(1) … instrument exogeneity z is uncorrelated with u z has no partial effect on y (2) … instrument relevance z is correlated with x (1) is non-testable, but (2) is, i.e .: OLS cov( , ) 0 zu = cov( , ) 0 zx 01 xz v π =+ + 1 cov( , ) var( ) z π= 1 cov( , ) 0 0 ⇔≠ :0 H
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e.g .: 01 2 log( ) wage educ ability β ββ =+ + u + Yes Yes Yes # siblings ? Yes ? Mother’s educ No Yes No IQ No No Yes last 4-digit of SSN IV? IV candidate for educ cov( , ) 0 zx cov( , ) 0 zu =
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and serve to identify β _1 “identification” of a parameter means that we can write _1 in terms of pop. moments that can be estimated using a sample of data.
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notes-iv - A. Introduction A. log( wage ) = 0 + 1educ + 2...

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