Introduction to Econometric Theory

JAMES DAVIDSON is Professor of Econometrics at the University of Exeter. He has also held teaching posts at the University of Warwick, the London School of Economics, the University of Wales Aberystwyth and Cardiff University, as well as visiting positions at the University of California, Berkeley, the University of California, San Diego, and Central European University, Budapest.

• List of Figures ixPreface xiAbout the CompanionWebsite xvPart I Fitting 11 Elementary Data Analysis 31.1 Variables and Observations 31.2 Summary Statistics 41.3 Correlation 61.4 Regression 101.5 Computing the Regression Line 121.6 Multiple Regression 161.7 Exercises 182 Matrix Representation 212.1 Systems of Equations 212.2 Matrix Algebra Basics 232.3 Rules of Matrix Algebra 262.4 Partitioned Matrices 272.5 Exercises 283 Solving the Matrix Equation 313.1 Matrix Inversion 313.2 Determinant and Adjoint 343.3 Transposes and Products 373.4 Cramer’s Rule 383.5 Partitioning and Inversion 393.6 A Note on Computation 413.7 Exercises 434 The Least Squares Solution 474.1 Linear Dependence and Rank 474.2 The General Linear Regression 504.3 Definite Matrices 524.4 Matrix Calculus 564.5 Goodness of Fit 574.6 Exercises 59Part II Modelling 635 Probability Distributions 655.1 A Random Experiment 655.2 Properties of the Normal Distribution 685.3 Expected Values 725.4 Discrete Random Variables 755.5 Exercises 806 More on Distributions 836.1 Random Vectors 836.2 The Multivariate Normal Distribution 846.3 Other Continuous Distributions 876.4 Moments 906.5 Conditional Distributions 926.6 Exercises 947 The Classical RegressionModel 977.1 The Classical Assumptions 977.2 The Model 997.3 Properties of Least Squares 1017.4 The Projection Matrices 1037.5 The Trace 1047.6 Exercises 1068 The Gauss-Markov Theorem 1098.1 A Simple Example 1098.2 Efficiency in the General Model 1118.3 Failure of the Assumptions 1138.4 Generalized Least Squares 1148.5 Weighted Least Squares 1168.6 Exercises 118Part III Testing 1219 Eigenvalues and Eigenvectors 1239.1 The Characteristic Equation 1239.2 Complex Roots 1249.3 Eigenvectors 1269.4 Diagonalization 1289.5 Other Properties 1309.6 An Interesting Result 1319.7 Exercises 13310 The Gaussian RegressionModel 13510.1 Testing Hypotheses 13510.2 Idempotent Quadratic Forms 13710.3 Confidence Regions 14010.4 t Statistics 14110.5 Tests of Linear Restrictions 14410.6 Constrained Least Squares 14610.7 Exercises 14911 Partitioning and Specification 15311.1 The Partitioned Regression 15311.2 Frisch-Waugh-Lovell Theorem 15511.3 Misspecification Analysis 15611.4 Specification Testing 15911.5 Stability Analysis 16011.6 Prediction Tests 16211.7 Exercises 163Part IV Extensions 16712 Random Regressors 16912.1 Conditional Probability 16912.2 Conditional Expectations 17012.3 StatisticalModels Contrasted 17412.4 The Statistical Assumptions 17612.5 Properties of OLS 17812.6 The Gaussian Model 18212.7 Exercises 18313 Introduction to Asymptotics 18713.1 The Lawof Large Numbers 18713.2 Consistent Estimation 19213.3 The Central LimitTheorem 19513.4 Asymptotic Normality 19813.5 Multiple Regression 20113.6 Exercises 20314 Asymptotic Estimation Theory 20714.1 Large Sample Efficiency 20714.2 Instrumental Variables 20814.3 Maximum Likelihood 21014.4 Gaussian ML 21314.5 Properties of ML Estimators 21414.6 Likelihood Inference 21614.7 Exercises 218Part V Appendices 221A The Binomial Coefficients 223B The Exponential Function 225C Essential Calculus 227D The Generalized Inverse 229Recommended Reading 233Index 235