Lecture 19 Linear Regression without strong exogeneity

Lecture 19 Linear Regression without strong exogeneity -...

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Unformatted text preview: Economics 326 Methods of Empirical Research in Economics Lecture 19: Linear regression without strong exogeneity Vadim Marmer University of British Columbia May 5, 2010 Strong exogeneity and the conditional expectation function (CEF) I Consider the linear regression model Y i = + 1 X i + U i . I When the errors are strongly exogenous , i.e. E ( U i j X i ) = 0, the linear regression model de&nes the CEF of Y conditional on X : CEF Y ( X i ) & E ( Y i j X i ) = E ( + 1 X i + U i j X i ) = + 1 X i + E ( U i j X i ) = + 1 X i . 1/9 Weak exogeneity Y i = + 1 X i + U i , EU i = I Suppose the errors are only weakly exogenous: E ( U i X i ) = . I In this case, CEF Y ( X i ) 6 = + 1 X i . I Question: What does the econometrician estimates when he runs a linear regression and the regressors are not strongly exogenous? 2/9 Linear regression as a misspeci&ed CEF I Suppose that E ( Y i j X i ) = g ( X i ) , where g is some unknown nonlinear function. Thus, the truefunction....
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Lecture 19 Linear Regression without strong exogeneity -...

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