Preface ix

Chapter 1 An Overview of Econometrics 1

1.1 The importance of econometrics 1

1.2 Types of economic data 2

1.3 Working with data: graphical methods 6

1.4 Working with data: descriptive statistics and correlation 11

1.5 Chapter summary 26

Exercises 26

Chapter 2 A Non-technical Introduction to Regression 29

2.1 Introduction 29

2.2 The simple regression model 30

2.3 The multiple regression model 42

2.4 Chapter summary 55

Exercises 57

Chapter 3 The Econometrics of the Simple Regression Model 59

3.1 Introduction 59

3.2 A review of basic concepts in probability in the context of the regression model 60

3.3 The classical assumptions for the regression model 64

3.4 Properties of the ordinary least-squares estimator of ß 67

3.5 Deriving a confidence interval for ß 75

3.6 Hypothesis tests about ß 77

3.7 Modifications to statistical procedures when ¿2 is unknown 78

3.8 Chapter summary 81

Exercises 82

Appendix 1: Proof of the Gauss-Markov theorem 84

Appendix 2: Using asymptotic theory in the simple regression model 85

Chapter 4 The Econometrics of the Multiple Regression Model 91

4.1 Introduction 91

4.2 Basic results for the multiple regression model 92

4.3 Issues relating to the choice of explanatory variables 96

4.4 Hypothesis testing in the multiple regression model 102

4.5 Choice of functional form in the multiple regression model 109

4.6 Chapter summary 115

Exercises 116

Appendix: Wald and Lagrange multiplier tests 117

Chapter 5 The Multiple Regression Model: Freeing Up the Classical Assumptions 121

5.1 Introduction 121

5.2 Basic theoretical results 122

5.3 Heteroskedasticity 124

5.4 The regression model with autocorrelated errors 138

5.5 The instrumental variables estimator 149

5.6 Chapter summary 164

Exercises 165

Appendix: Asymptotic results for the OLS and instrumental variables estimators 168

Chapter 6 Univariate Time Series Analysis 173

6.1 Introduction 173

6.2 Time series notation 175

6.3 Trends in time series variables 177

6.4 The autocorrelation function 179

6.5 The autoregressive model 181

6.6 Defining stationarity 195

6.7 Modeling volatility 197

6.8 Chapter summary 205

Exercises 207

Appendix: MA and ARMA models 210

Chapter 7 Regression with Time Series Variables 213

7.1 Introduction 213

7.2 Time series regression when X and Yare stationary 214

7.3 Time series regression when Y and X have unit roots 217

7.4 Time series regression when Y and X have unit roots but are NOTcointegrated 227

7.5 Granger causality 227

7.6 Vector autoregressions 233

7.7 Chapter summary 247

Exercises 248

Appendix: The theory of forecasting 251

Chapter 8 Models for Panel Data 255

8.1 Introduction 255

8.2 The pooled model 256

8.3 Individual effects models 256

8.4 Chapter summary 271

Exercises 272

Chapter 9 Qualitative Choice and Limited Dependent Variable Models 277

9.1 Introduction 277

9.2 Qualitative choice models 278

9.3 Limited dependent variable models 296

9.4 Chapter summary 304

Exercises 306

Chapter 10 Bayesian Econometrics 309

10.1 An overview of Bayesian econometrics 309

10.2 The normal linear regression model with natural conjugate prior and a single explanatory variable 315

10.3 Chapter summary 326

Exercises 326

Appendix: Bayesian analysis of the simple regression model with unknown variance 328

Appendix A: Mathematical Basics 333

Appendix B: Probability Basics 338

Appendix C: Basic Concepts in Asymptotic Theory 348

Appendix D: Writing an Empirical Project 353

Tables 359

Table 1. Area under the standard normal distribution Pr(0 ¿ Z ¿ z) 359

Table 2. Area under the Student t distribution for different degrees of freedom (DF), Pr(Z ¿ z) = ¿ 360

Table 3. Percentiles of the chi-square distribution 361

Table 4a. Area under the F-distribution for different degrees of freedom, ¿1 and ¿2, Pr(Z ¿ z) = 0.05 362

Table 4b. Area under the F-distribution for different degrees of freedom, ¿1 and ¿2, Pr(Z ¿ z) = 0.01 363

Bibliography 364

Index 365