Economatrics Anakysis

ECONOMETRICS
Bruce E. Hansen c °2000, 20061 University of Wisconsin www.ssc.wisc.edu/~bhansen Revised: January 2006 Comments Welcome

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Contents
1 Introduction 1.1 Economic Data . . 1.2 Observational Data 1.3 Random Sample . 1.4 Economic Data . . 1 1 1 2 2 4 4 5 6 7 8 8 9 9 10 11 11 12 14 15 15 20 21 21 22 25 26 27 28 30 32 33 34 35

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2 Matrix Algebra 2.1 Terminology . . . . . . . . . . . . . . . . . 2.2 Matrix Multiplication . . . . . . . . . . . 2.3 Trace . . . . . . . . . . . . . . . . . . . . . 2.4 Inverse . . . . . . . . . . . . . . . . . . . . 2.5 Eigenvalues . . . . . . . . . . . . . . . . . 2.6 Rank and Positive Definiteness . . . . . . 2.7 Matrix Calculus . . . . . . . . . . . . . . . 2.8 Determinant . . . . . . . . . . . . . . . . . 2.9 Kronecker Products and the Vec Operator 3 Regression and Projection 3.1 Conditional Mean . . . . . 3.2 Regression Equation . . . 3.3 Conditional Variance . . . 3.4 Linear Regression . . . . . 3.5 Best Linear Predictor . . 3.6 Exercises . . . . . . . . . 4 Least Squares Estimation 4.1 Estimation . . . . . . . . 4.2 Least Squares . . . . . . . 4.3 Normal Regression Model 4.4 Model in Matrix Notation 4.5 Projection Matrices . . . . 4.6 Residual Regression . . . 4.7 Bias and Variance . . . . 4.8 Gauss-Markov Theorem . 4.9 Semiparametric Efficiency 4.10 Omitted Variables . . . . 4.11 Multicollinearity . . . . .

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