23B_IV_handout

# 23B_IV_handout - Instrumental variables 73-261 Econometrics...

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Instrumental variables 73-261 Econometrics October 20 Wooldridge 15.1-5 Stock & Watson 12

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p. 2 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Overview Problem: Endogeneity x correlated with u Consequence: bias Solutions Proxy variable for omitted x Instrumental Variable(s) for endogenous x Formulas Examples Testing
p. 3 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Endogeneity Several equivalent definitions Violation of Assumption 4 E[ u | x ] ≠ 0 cov( u , x ) ≠ 0 x is affected by u x is (partially) determined within the model Hence, x is endogenous u is affected by x (in our data) x has indirect effect though u

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p. 4 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Reasons for endogeneity y = β 0 + 1 x 1 + u Omitted variable x 2 correlated with x 1 Estimate reflects indirect effect of x 1 on x 2 , which then affects y Measurement error in x (but not y ) Present in both x 1 and u Selection bias For some x 1 , only the observations with high u are present in the sample Simultaneity: p, Q determined by supply and demand 1 ~
p. 5 © CMU / Y. Kryukov 73-261 2.3 Endogeneity Solutions to Endogeneity y = β 0 + 1 x + u, E[ u | x ] ≠ 0 1. Replace omitted variable with a “proxy” i.e. control variable Unknown ability – proxy by IQ or parents’ wage

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23B_IV_handout - Instrumental variables 73-261 Econometrics...

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