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Principles of Econometrics

2007

Chapter 2 The Simple Linear Regression Model 39 Learning Objectives 39 Keywords 2.1 An Economic Model 2.2 An Econometric Model 2.2.1 Introducing the Error Term 2.3 Estimating the Regression Parameters 2.3.1 The Least Squares Principle 51 2.3.2 Estimates for the Food Expenditure Function 2.3.3 Interpreting the Estimates 2.3.3a Elasticities 2.3.3b Prediction 2.3.3c Computer Output 2.3.4 Other Economic Models 2.4 Assessing the Least Squares Estimators 2.4.1 The Estimator b 2 2.4.2 The Expected Values of b\\ and b 2 2.4.3 Repeated Sampling 2.4.4 The Variances and Covariance of b\\ and b 2 2.5 The Gauss-Markov Theorem 2.6 The Probability Distributions of the Least Squares Estimators 2.7 Estimating the Variance of the Error Term 2.7.1 Estimating the Variances and Covariance of the Least Squares Estimators 2.7.2 Calculations for the Food Expenditure Data 2.7.3 Interpreting the Standard Errors 2.8 Estimating Nonlinear Relationships 68 2.8.1 Quadratic Functions 69 2.8.2 Using a Quadratic Model 69 2.8.3 A Log-Linear Function 70 2.8.4 Using a Log-Linear Model 2.8.5 Choosing a Functional Form 73 2.9 Regression with Indicator Variables 74 2.10 Exercises 75 2.10.1 Problems 75 2.10.2 Computer Exercises 78 Appendix 2A Derivation of the Least Squares Estimates 83 Appendix 2B Deviation from the Mean Form of b 2 84 Appendix 2C b 2 Is a Linear Estimator 85 Appendix 2D Derivation of Theoretical Expression for b 2 85 Appendix 2E Deriving the Variance of b 2 86 Appendix 2F Proof of the Gauss-Markov Theorem 87 CONTENTS xiii Appendix 2G Monte Carlo Simulation 88 2G.1 The Regression Function 88 2G.2 The Random Error 89 2G.3 Theoretically True Values 90 2G.4 Creating a Sample of Data 91 2G.

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