An Introduction to Econometric Theory

Book description

A guide to economics, statistics and finance that explores the mathematical foundations underling econometric methods

An Introduction to Econometric Theory offers a text to help in the mastery of the mathematics that underlie econometric methods and includes a detailed study of matrix algebra and distribution theory. Designed to be an accessible resource, the text explains in clear language why things are being done, and how previous material informs a current argument. The style is deliberately informal with numbered theorems and lemmas avoided. However, very few technical results are quoted without some form of explanation, demonstration or proof.

The author — a noted expert in the field — covers a wealth of topics including: simple regression, basic matrix algebra, the general linear model, distribution theory, the normal distribution, properties of least squares, unbiasedness and efficiency, eigenvalues, statistical inference in regression, t and F tests, the partitioned regression, specification analysis, random regressor theory, introduction to asymptotics and maximum likelihood. Each of the chapters is supplied with a collection of exercises, some of which are straightforward and others more challenging. This important text:

  • Presents a guide for teaching econometric methods to undergraduate and graduate students of economics, statistics or finance
  • Offers proven classroom-tested material
  • Contains sets of exercises that accompany each chapter
  • Includes a companion website that hosts additional materials, solution manual and lecture slides 

Written for undergraduates and graduate students of economics, statistics or finance, An Introduction to Econometric Theory is an essential beginner’s guide to the underpinnings of econometrics. 

 

Table of contents

  1. Cover
  2. List of Figures
  3. Preface
  4. About the Companion Website
  5. Part I: Fitting
    1. Chapter 1: Elementary Data Analysis
      1. 1.1 Variables and Observations
      2. 1.2 Summary Statistics
      3. 1.3 Correlation
      4. 1.4 Regression
      5. 1.5 Computing the Regression Line
      6. 1.6 Multiple Regression
      7. 1.7 Exercises
    2. Chapter 2: Matrix Representation
      1. 2.1 Systems of Equations
      2. 2.2 Matrix Algebra Basics
      3. 2.3 Rules of Matrix Algebra
      4. 2.4 Partitioned Matrices
      5. 2.5 Exercises
    3. Chapter 3: Solving the Matrix Equation
      1. 3.1 Matrix Inversion
      2. 3.2 Determinant and Adjoint
      3. 3.3 Transposes and Products
      4. 3.4 Cramer's Rule
      5. 3.5 Partitioning and Inversion
      6. 3.6 A Note on Computation
      7. 3.7 Exercises
    4. Chapter 4: The Least Squares Solution
      1. 4.1 Linear Dependence and Rank
      2. 4.2 The General Linear Regression
      3. 4.3 Definite Matrices
      4. 4.4 Matrix Calculus
      5. 4.5 Goodness of Fit
      6. 4.6 Exercises
  6. Part II: Modelling
    1. Chapter 5: Probability Distributions
      1. 5.1 A Random Experiment
      2. 5.2 Properties of the Normal Distribution
      3. 5.3 Expected Values
      4. 5.4 Discrete Random Variables
      5. 5.5 Exercises
    2. Chapter 6: More on Distributions
      1. 6.1 Random Vectors
      2. 6.2 The Multivariate Normal Distribution
      3. 6.3 Other Continuous Distributions
      4. 6.4 Moments
      5. 6.5 Conditional Distributions
      6. 6.6 Exercises
    3. Chapter 7: The Classical Regression Model
      1. 7.1 The Classical Assumptions
      2. 7.2 The Model
      3. 7.3 Properties of Least Squares
      4. 7.4 The Projection Matrices
      5. 7.5 The Trace
      6. 7.6 Exercises
    4. Chapter 8: The Gauss‐Markov Theorem
      1. 8.1 A Simple Example
      2. 8.2 Efficiency in the General Model
      3. 8.3 Failure of the Assumptions
      4. 8.4 Generalized Least Squares
      5. 8.5 Weighted Least Squares
      6. 8.6 Exercises
  7. Part III: Testing
    1. Chapter 9: Eigenvalues and Eigenvectors
      1. 9.1 The Characteristic Equation
      2. 9.2 Complex Roots
      3. 9.3 Eigenvectors
      4. 9.4 Diagonalization
      5. 9.5 Other Properties
      6. 9.6 An Interesting Result
      7. 9.7 Exercises
    2. Chapter 10: The Gaussian Regression Model
      1. 10.1 Testing Hypotheses
      2. 10.2 Idempotent Quadratic Forms
      3. 10.3 Confidence Regions
      4. 10.4 Statistics
      5. 10.5 Tests of Linear Restrictions
      6. 10.6 Constrained Least Squares
      7. 10.7 Exercises
    3. Chapter 11: Partitioning and Specification
      1. 11.1 The Partitioned Regression
      2. 11.2 Frisch‐Waugh‐Lovell Theorem
      3. 11.3 Misspecification Analysis
      4. 11.4 Specification Testing
      5. 11.5 Stability Analysis
      6. 11.6 Prediction Tests
      7. 11.7 Exercises
  8. Part IV: Extensions
    1. Chapter 12: Random Regressors
      1. 12.1 Conditional Probability
      2. 12.2 Conditional Expectations
      3. 12.3 Statistical Models Contrasted
      4. 12.4 The Statistical Assumptions
      5. 12.5 Properties of OLS
      6. 12.6 The Gaussian Model
      7. 12.7 Exercises
    2. Chapter 13: Introduction to Asymptotics
      1. 13.1 The Law of Large Numbers
      2. 13.2 Consistent Estimation
      3. 13.3 The Central Limit Theorem
      4. 13.4 Asymptotic Normality
      5. 13.5 Multiple Regression
      6. 13.6 Exercises
    3. Chapter 14: Asymptotic Estimation Theory
      1. 14.1 Large Sample Efficiency
      2. 14.2 Instrumental Variables
      3. 14.3 Maximum Likelihood
      4. 14.4 Gaussian ML
      5. 14.5 Properties of ML Estimators
      6. 14.6 Likelihood Inference
      7. 14.7 Exercises
  9. Part V: Appendices
    1. Appendix A: The Binomial Coefficients
    2. Appendix B: The Exponential Function
    3. Appendix C: Essential Calculus
    4. Appendix D: The Generalized Inverse
  10. Recommended Reading
    1. Preliminary Reading
    2. Additional Reading
    3. For Reference
    4. Further Reading
  11. Index
  12. End User License Agreement

Product information

  • Title: An Introduction to Econometric Theory
  • Author(s): James Davidson
  • Release date: October 2018
  • Publisher(s): Wiley
  • ISBN: 9781119484882