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ECO341K Introduction to Econometrics Chapter 15: Endogeneity and Instrumental Variables Stephen Donald Stephen Donald () Chapter 15: IV 1 / 21
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Lecture 21 - Outline Endogeneity °violation of ZCM assumption Omitted Variables Instrumental variables Stephen Donald () Chapter 15: IV 2 / 21
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Endogeneity in the SLRM In the simple linear model, y = β 0 + β 1 x + u key assumption for unbiased (consistent) estimates of β 0 and β 1 is that, E ( u j x ) = 0 : ZCM ZCM implies E ( xu ) = 0 If E ( xu ) 6 = 0 then ZCM violatedand we have an endogenous regressor or and endogeneity problem Stephen Donald () Chapter 15: IV 3 / 21
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Endogeneity in the SLRM There are several reasons that could give rise to this problem 1 Omitted Variables Problems 2 Measurement Error in the regressor 3 Simultaneous causation (eg. supply and demand is a classic) We will consider 1.in detail and 3 by example Stephen Donald () Chapter 15: IV 4 / 21
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Omitted Variables Consider the following wage equation, log ( wage ) = β 0 + β 1 educ + β 2 ability + e If we omit ability then we run the regression of log ( wage ) on educ so that we have, log ( wage ) = β 0 + β 1 educ + u u = β 2 ability + e If education and ability are correlated then, E ( u . educ ) 6 = 0 Stephen Donald () Chapter 15: IV 5 / 21
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Omitted Variables - Proxy Variable Solution In Chapter 9.2 a solution to this problem is given via a proxy for ability Suppose that we have IQ in our data and that, E ( ability j educ , IQ ) = E ( ability j IQ ) = δ 0 + δ 1 IQ This means that educ does not help predict ability once you know IQ Then, E ( log ( wage ) j educ , IQ ) = β 0 + β 2 δ 0 + β 1 educ + β 2 δ 1 IQ + E ( e j educ , IQ ) Stephen Donald () Chapter 15: IV 6 / 21
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Omitted Variables - Proxy Variable Solution If also E ( e j educ , IQ ) = 0 then we have, E ( log ( wage ) j educ , IQ ) = β 0 + β 2 δ 0 + β 1 educ + β 2 δ 1 IQ Then we can get unbiased and consistent estimates of β 1 from the regression, log ( wage ) = β 0 + β 2 δ 0 + β 1 educ + β 2 δ 1 IQ + v E ( v j educ , IQ ) = 0 IQ is a ±proxy² for ability Important: Coe¢ cient on educ is β 1
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