Econometric Theory

Econometrics is the branch of economics concerned with the use of mathematics to describe, model, prove, and predict economic theory and systems.

This book can be considered to be three parts.

Chapters 1-4

An introduction and mathematical base needed to perform basic and more advanced econometrics.

Chapters 5, 6

The basics of bivariate and multivariate regression analysis.

Chapters 7-16

Applications of basic econometrics and advanced topics.

Contents

1. Introduction to Econometric Theory
   1. Methodology of Econometrics
   2. Types of Econometrics
   3. Statistical Packages
   4. Prerequisites
2. Important Terms and Concepts of Regression Analysis
   1. What is Regression?
   2. Regression versus Causation and Correlation
   3. Terminology and Notation
   4. Data
3. Statistical Concepts
   1. Summation and Product Operators
   2. Sample Points, Sample Space and Events
   3. Probability Density Function (pdf)
   4. Concepts of Probability Distributions
   5. Theoretical Probability Distribution
   6. Asymptotic Convergence
   7. Statistical Inference
      1. Estimation
      2. Hypothesis Testing
4. Matrix Algebra
   1. Definitions
   2. Types of Matrices
   3. Matrix Operations
   4. Determinants
   5. Inverse of a square Matrix
   6. Matrix Differentiation
5. Classical Normal Linear Regression Model (CNLRM)
   1. Assumptions of Classical Linear Regression Model
   2. Properties of OLS Estimators
      1. Proofs of properties of β1
   3. Maximum Likelihood (ML)
   4. Ordinary Least Squares (OLS)
      1. Normal Equations Proof
6. Multiple Regression Analysis
   1. Ordinary Least Squares (OLS)
      1. Coefficients
      2. Variance
   2. General Least Squares (GLS)
      1. Coefficients
      2. Variance
   3. Inference
      1. t-Test
      2. F-Test
      3. The Coefficient of Determination: R
      4. The Likelihood Ratio (LR), Lagrange Multiplier (LM) and Wald (W) Tests
7. Dummy Variables
   1. Problems with Heteroskedasticity and Autocorrelation
8. Multicollinearity
   1. The Nature of Multicollinearity
   2. Theoretical Consequences in case of Multicollinearity
   3. Practical Consequences in case of Multicollinearity
   4. Tests for Multicollinearity
   5. Solutions to Multicollinearity
9. Heteroskedasticity
   1. The Nature of Heteroskedasticity
   2. Theoretical Consequences in case of Heteroskedasticity
   3. Practical Consequences in case of Heteroskedasticity
   4. Tests for Heteroskedasticity
   5. Solutions to Heteroskedasticity
10. Serial Correlation - Autocorrelation
11. Simultaneous-Equation Models
12. Time-Series Analysis
    1. First-Order Autocorrelation
    2. An Autoregressive (AR) Process
    3. A Moving-Average (MA) Process
    4. ARIMA Models
    5. Box-Jenkins Methodology of identifying, estimating and checking ARIMA Models
    6. Vector Autoregression
    7. ARCH
    8. GARCH
13. Model Specification and Diagnostic Testing
    1. Specification Errors
    2. Tests of Specification Errors
    3. Incorrect Specification of Error Term
    4. Nested and Non-nested Models
    5. Model Selection Criteria
14. Problems with Residuals: Robust Regression
    1. Outliers
    2. Leverage
    3. Heteroskedasticity-Consistent Estimators
15. Microeconometrics: Qualitative Dependent Variable Models
    1. Introduction
    2. Linear Probability Model (LPM)
    3. Binary Choice Models
       1. Logit
       2. Probit
    4. Tobit
    5. Poisson Regression
16. Study Aides and Equations
    1. Basic Statistics
    2. Hypothesis Testing
    3. SLR
    4. MLR

References

Ramanathan, Ramu. "Introductory Econometrics with Applications." South-western Thomson Learning, 2002.

Resources

• Gretl Gnu Regression, Econometrics and Time Series Library (open source and free software for econometric calculus)