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Abstract
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.
References (12)
- 5.2 Analysis of the Difference Estimator 277
- 5.3 Application of Difference Estimation: Project STAR
- 5.5 The Differences-in-Differences Estimator
- 5.2 Estimating an AR(1) Error Model 358
- 5.2a Properties of an AR(1) Error 359
- 5.2b Nonlinear Least Squares Estimation 361
- 5.2c Generalized Least Squares Estimation 362
- 5.3 Estimating a More General Model 362
- Appendix 9A The Durbin-Watson Test 9A. 1 The Durbin-Watson Bounds Test Appendix 9B Properties of an AR(1) Error Chapter 11 Simultaneous Equations Models Learning Objectives Keywords 11.1 A Supply and Demand Model 11.2 The Reduced-Form Equations 11.3 The Failure of Least Squares Estimation 11.4 The Identification Problem 11.5 Two-Stage Least Squares Estimation 11.5.1 The General Two-Stage Least Squares Estimation Procedure 11.5.2 The Properties of the Two-Stage Least Squares Estimator 11.6 An Example of Two-Stage Least Squares Estimation 11.6.1 Identification 11.6.2 The Reduced-Form Equations
- Appendix 11A An Algebraic Explanation of the Failure of Least Squares 12.3.5 The Dickey Fuller Testing Procedures 12.3.6 The Dickey-Fuller Tests: An Example 12.3.7 Order of Integration 12.4 Cointegration 12.4.1 An Example of a Cointegration Test 12.4.2 The Error Correction Model 12.5 Regression When There Is No Cointegration 12.5.1 First Difference Stationary 12.
- A Microeconomic Panel 539 15.2 Pooled Model 540 15.2.1 Cluster-Robust Standard Errors 541 15.2.2 Pooled Least Squares Estimates of Wage Equation 542 15.3 The Fixed Effects Model 543 15.3.1 The Least Squares Dummy Variable Estimator for Small N 544 15.3.2 The Fixed Effects Estimator 547 15.3.2a Fixed Effects Estimates of Wage Equation for N = 10 548 15.3.3 Fixed Effects Estimates of Wage Equation from Complete Panel 549 15.4 The Random Effects Model 551 15.4.1 Error Term Assumptions 15.4.2 Testing for Random Effects 15.4.3 Estimation of the Random Effects Model 15.
- 4 Random Effects Estimation of the Wage Equation 15.5 Comparing Fixed and Random Effects Estimators 15.5.1 Endogeneity in the Random Effects Model 15.5.2 The Fixed Effects Estimator in a Random Effects Model 15.5.3 A Hausman Test 15.6 The Hausman-Taylor Estimator 15.7 Sets of Regression Equations 15.7.1 Grunfeld's Investment Data 15.7.2 Estimation: Equal Coefficients, Equal Error Variances 15.7.3 Estimation: Different Coefficients, Equal Error Variances 15.7.4 Estimation: Different Coefficients, Different Error Variances 15.7.5 Seemingly Unrelated Regressions 15.7.5a Separate or Joint Estimation? 15.7.5b Testing Cross-Equation Hypotheses 15.8 Exercises 15.8.1 Problems 15.8.2 Computer Exercises Appendix 15A Cluster-Robust Standard Errors: Some Details 16.1.4 Maximum Likelihood Estimation of the Probit Model 16.1.5 A Transportation Example 16.1.6 Further Post-estimation Analysis 16.2 The Logit Model for Binary Choice 16.2.1 An Empirical Example from Marketing 16.