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Contents

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 s2 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) = a 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

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