econometrics ch 8 - Introduction to Econometrics Chapter 8:...

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Unformatted text preview: Introduction to Econometrics Chapter 8: Nonlinear Regression Functions Geo rey Williams gwilliams@econ.rutgers.edu April 13, 2010 Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 8: Nonlinear Regress Test scores and district income Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 8: Nonlinear Regress Non-Linear Regression Models If a relation between Y and X is nonlinear: The e ect on Y of a change in X depends on the value of X - that is, the marginal e ect of X is not constant A linear regression is mis-speci ed - the functional form is wrong The estimator of the e ect on Y of X is biased - it needn't even be right on average. The solution to this is to estimate a regression function that is nonlinear in X Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 8: Nonlinear Regress Non-Linear Regression Models If a relation between Y and X is nonlinear: The e ect on Y of a change in X depends on the value of X - that is, the marginal e ect of X is not constant A linear regression is mis-speci ed - the functional form is wrong The estimator of the e ect on Y of X is biased - it needn't even be right on average. The solution to this is to estimate a regression function that is nonlinear in X Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 8: Nonlinear Regress Non-Linear Regression Models If a relation between Y and X is nonlinear: The e ect on Y of a change in X depends on the value of X - that is, the marginal e ect of X is not constant A linear regression is mis-speci ed - the functional form is wrong The estimator of the e ect on Y of X is biased - it needn't even be right on average. The solution to this is to estimate a regression function that is nonlinear in X Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 8: Nonlinear Regress Non-Linear Regression Models If a relation between Y and X is nonlinear: The e ect on Y of a change in X depends on the value of X - that is, the marginal e ect of X is not constant A linear regression is mis-speci ed - the functional form is wrong The estimator of the e ect on Y of X is biased - it needn't even be right on average. The solution to this is to estimate a regression function that is nonlinear in X Geo rey Williams gwilliams@econ.rutgers.edu Introduction to Econometrics Chapter 8: Nonlinear Regress Non-Linear Regression Models If a relation between Y and X is nonlinear: The e ect on Y of a change in X depends on the value of X - that is, the marginal e ect of X is not constant A linear regression is mis-speci ed - the functional form is wrong The estimator of the e ect on Y of X is biased - it needn't even be right on average....
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econometrics ch 8 - Introduction to Econometrics Chapter 8:...

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