CEF - Conditional Expectations and Linear Regressions...

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Conditional Expectations and Linear Regressions Walter Sosa-Escudero Econ 507. Econometric Analysis. Spring 2009 March 31, 2009 Walter Sosa-Escudero Conditional Expectations and Linear Regressions
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‘All models are wrong, but some are useful’ (George E. P. Box) Box, G. E. P. and Draper, N., 1987, Empirical Model-Building and Response Surfaces , Wiley, New York, p. 424. Walter Sosa-Escudero Conditional Expectations and Linear Regressions
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Motivation Our last attempt with the linear model So far we have assumed we ‘know’ the model and its structure. The OLS (or the GMM) estimator consistently estimates the unknown parameters. What is OLS estimating if the underlying model is completeley unknown (possibly non-linear, endogenous, heteroskedastic, etc.) We will argue that the OLS estimator provides a good linear aproximation of the (possibly non-linear) conditional expectation. Note: this lecture is highly inspired by Angrist and Pischke (2009). Walter Sosa-Escudero Conditional Expectations and Linear Regressions
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E ( y | x ) gives the expected value of y for given values of x . It provides a reasonable representation of how x alters y . If x is random, E ( y | x ) is a random function. LIE: E ( y ) = E [ E ( y | x )] . We need two more properties. Walter Sosa-Escudero
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This note was uploaded on 02/27/2012 for the course STATS 315A taught by Professor Tibshirani,r during the Spring '10 term at Stanford.

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CEF - Conditional Expectations and Linear Regressions...

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