Contents

Preface xv

What Is Econometrics? I

1.1 What Is Econometrics? 1

1.2 Economic and Econometric Models 2

1.3 The Aims and Methodology of Econometrics 4

1.4 What Constitutes a Test of an Economic Theory? 6 Summary and an Outline of the Book 8

Statistical Background and Matrix Algebra 11

2.1 Introduction 12

2.2 Probability 12

2.3 Random Variables and Probability Distributions 17

2.4 The Normal Probability Distribution and Related Distributions 19

2.5 Classical Statistical Inference 21

2.6 Properties of Estimators 23

2.7 Sampling Distributions for Samples from a Normal Population 26

Simple Regression 59

3.1 Introduction 59

3.2 Specification of the Relationships 62

3.3 The Method of Moments 66

3.4 Method of Least Squares 68

3.5 Statistical Inference in the Linear Regression Model 76

3.6 Analysis of Variance for the Simple Regression Model 84

3.7 Prediction with the Simple Regression Model 85

3.8 Outliers 88

3.9 Alternative Functional Forms for Regression Equations 96

=.10 Inverse Prediction in the Least Squares

Regression Model 101 °.ll Stochastic Regressors 103 =.12 The Regression Fallacy 104

Summary 106

Exercises 108

Appendix to Chapter 3 114

Multiple Regression 127

4.1 Introduction 128

4.2 A Model with Two Explanatory Variables 129

4.3 Statistical Inference in the Multiple Regression Model 134

4.4 Interpretation of the Regression Coefficients 143

4.5 Partial Correlations and Multiple Correlation 146

2.8 Interval Estimation 27

2.9 Testing of Hypotheses 28

2.10 Relationship Between Confidence Interval Procedures and Tests of Hypotheses 32

Summary 33 Exercises 34 Appendix to Chapter 2 41

CONTENTS

4.6 Relationships Among Simple, Partial, and Multiple Correlation Coefficients 147

4.7 Prediction in the Multiple Regression Model 154

4.8 Analysis of Variance and Tests of Hypotheses 156

4.9 Omission of Relevant Variables and Inclusion of Irrelevant Variables 16j

4.10 Degrees of Freedom and 165

4.11 Tests for Stability 170

*4.12 The LR, W, and LM Tests 177 Summary 179 Exercises 181 Appendix to Chapter 4 187 Data Sets 194

Heteroskedasticity 201

5.1 Introduction 201

5.2 Detection of Heteroskedasticity 203

5.3 Consequences of Heteroskedasticity 209

5.4 Solutions to the Heteroskedasticity Problem 212

5.5 Heteroskedasticity and the Use of Deflators 215 *5.6 Testing the Linear Versus Log-Linear Functional

Form 220 Summary 223 Exercises 224 Appendix to Chapter 5 227

Autocorrelation • 229

6.1 Introduction 229

6.2 Durbin-Watson Test 230

6.3 Estimation in Levels Versus First Differences 232

6.4 Estimation Procedures with Autocorrelated Errors 236

6.5 Effect of AR(1) Errors on OLS Estimates 241

6.6 Some Further Comments on the DW Test 245

6.7 Tests for Serial Correlation in Models with Lagged Dependent Variables 248