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23A_IV_handout

# 23A_IV_handout - Endogeneity I 73-261 Econometrics October...

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Endogeneity - I 73-261 Econometrics October 18 Reading: Wooldridge 15, 3.3, 9.4-5

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p. 2 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Overview Topic 2: Problems and Fixes Problem: Endogeneity X correlated with u Missing variables, Measurement error Selection issues, true simultaneity Consequence: bias Reduces or increases effect of a variable Could create significance Fix: Instrumental variables
p. 3 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Endogeneity: definitions Violation of Assumption 4 E[ u | x ] . . . cov( u , x ) 0 x is affected by u x is (partially) determined within the model Hence, x is endogenous u is affected by (included) x ‘s x has indirect effect . . . . . . . . . Omitted variable (next slide)

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p. 4 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Omitted variable – setup True model: y = β 0 + β 1 x 1 + β 2 x 2 + u (∗) x 1 and x 2 are correlated: x 2 = δ 0 + δ 1 x 1 + e Let v = β 2 x 2 + u , then (∗) becomes y = . . . . . . . . . (∗∗) We do not observe x 2 So we estimate (∗∗) ; note that cov( x 1 , v ) 0 The estimate of β 1 is 1 ~ β e & u are independent of x
p. 5 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Omitted variable - bias Let’s compute the mean of : 1 ~ β 2 1 , 1 , 1 ) ( ) )( ( E ~ E X X Y Y X X i i i Σ Σ = β 2 1 , 1 1 0 1 , 1 0 1 1 , ) ( ) )( ( E X X V X V X X X i i i i Σ + + Σ = β β β β 2 1 , 1 1 , 2 1 , 1 1 , 1 1 1 , ) ( ) )( ( E ) ( ) ( ) ( E X X

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