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Econ418_ch15_instrumental variables

# Econ418_ch15_instrumental variables - ECON 418 Introduction...

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ECON 418 Introduction to Econometrics Anna Breman Univeristy of Arizona Part 4: Advanced Regression analysis Chapter 15: Instrumental Variables Anna Breman (Univeristy of Arizona) ECON 418 Fall 2008 1 / 19

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Chapter 15 I Instrumental Variables Endogeneity occurs whenever the error term, u , is correlated with the explanatory variable x j . Why is endogeneity a problem? We want to estimate a causal relationship between the independent variables and the dependent variable Endogeneity makes it di¢ cult to infer causality between y and x that is really due to other unobserved factors that a/ect y and also happen to be correlated with x It results in biased estimates Anna Breman (Univeristy of Arizona) ECON 418 Fall 2008 2 ± 19
What can cause endogeneity? 1 Omitted variables (Ch 3.3, 9) 2 Measurement Error (Chapter 9) 3 Simultaneity: the independent and dependent variables are jointly determined (Chapter 16) Anna Breman (Univeristy of Arizona) ECON 418 Fall 2008 3 / 19

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Multiple Linear Regression. Assumption 4 : Zero Conditional Mean The error u has an expected value of zero given any value of the explanatory variables. E ( u j x 1 , x 2 , ..., x k ) = 0 If SLR4 and MLR4 hold, we say that we have exogenous explanatory variables, and if it does not the variables are endogenous . If any explanatory variable x j is correlated with u for any reason, then x j is said to be endogenous. Anna Breman (Univeristy of Arizona) ECON 418 Fall 2008 4 / 19
How to deal with endogeneity 1 Omitted variables 1 Proxy variables 2 Panel data for time-constant omitted variables 3 Instrumental variables (IV) 2 Measurement Error (Chapter 9) 1 Instrumental variables (IV) 3 Simultaneity: the independent and dependent variables are jointly determined 1 Instrumental variables (IV) Anna Breman (Univeristy of Arizona) ECON 418 Fall 2008 5 / 19

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Instrumental variables 1 Intuition the error, but highly correlated with the endogenous explanatory variable 2 Extremely useful tool in dealing with endogeneity 3 Di¢ cult Anna Breman (Univeristy of Arizona) ECON 418 Fall 2008 6 / 19
Deriving the instrumental variables (IV) estimators Consider the problem of unobserved ability in the wage equation log ( wage ) = β 0 + β 1 educ + β 2 abil + e

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Econ418_ch15_instrumental variables - ECON 418 Introduction...

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