Hansen2009

Hansen2009 - ECONOMETRICS Bruce E. Hansen c...

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Unformatted text preview: ECONOMETRICS Bruce E. Hansen c & 2000, 2009 1 University of Wisconsin www.ssc.wisc.edu/~bhansen This Revision: January 14, 2009 Comments Welcome 1 This manuscript may be printed and reproduced for individual or instructional use, but may not be printed for commercial purposes. Contents 1 Introduction 1 1.1 Economic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Observational Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Economic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Regression and Projection 3 2.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Conditional Density and Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Conditional Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.6 Best Linear Predictor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.7 Technical Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Least Squares Estimation 14 3.1 Random Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 Normal Regression Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5 Model in Matrix Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.6 Projection Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.7 Residual Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.8 Bias and Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.9 Gauss-Markov Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.10 Semiparametric E ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.11 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.12 In&uential Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.13 Technical Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.14 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Inference 32 4.1 Sampling Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2 Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334....
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This note was uploaded on 05/04/2010 for the course ECON 551 taught by Professor Taisukeotsu during the Spring '10 term at Yale.

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Hansen2009 - ECONOMETRICS Bruce E. Hansen c...

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