# Econometrics Q-Exam Syllabus

The 2013 exam will cover the same material as the 6190 and 6200 lectures. The corresponding syllabi are reproduced below.

Probability Theory and Statistics for Economists

Required textbook: *Statistical Inference*, 2nd Edition, George Casella and Roger Berger, 2002.

### 1 Introduction to Statistics and Econometrics

### 2 Foundation of Probability Theory

- Random Experiments
- Basic Concepts of Probability
- Review of Set Theory
- Fundamental Probability Laws
- Methods of Counting
- Conditional Probability and Independence

### 3 Random Variables and Univariate Probability Distributions

- Random Variables and Distribution Functions
- Discrete Random Variable
- Continuous Random Variables
- Functions of a Random Variable
- Mathematical Expectations
- Moment Generating Function
- Characteristic Function

### 4 Important Parametric Distributions

- Introduction
- Discrete Distributions
- Continuous Probability Distributions

### 5 Random Vectors and Multivariate Probability Distribution

- Random vectors and Joint Probability Distributions
- Marginal Distributions
- Conditional Distributions
- Independence
- Empirical Applications
- Bivariate Transformation
- Expectations Under Multivariate Distributions
- Implications of Independence
- Conditional Expectations

### 6 Introduction to Sampling Theory and Statistics

- Population and Random Sample
- The Sampling Distribution of the Sample Mean
- The Sampling Distribution of the Sample Variance
- Student s t Distribution
- Snedecor s F Distribution
- Sufficient Statistics

### 7 Convergence Concepts and Limit Theories

- Limits and Orders of Magnitude: A Review
- Motivation for Convergence Concepts
- Convergence in Quadratic Mean and Lp-convergence
- Convergence in Probability
- Almost Sure Convergence
- Convergence in Distribution

### 8 Parameter Estimation and Evaluation

- Population and Distribution Model
- Maximum Likelihood Estimation
- Method of Moments and Generalized Method of Moments
- Mean Squared Error Criterion
- Best Unbiased Estimators

### 9 Hypothesis Testing

- Introduction to Hypothesis Testing
- The Wald Test
- The Lagrangian Multiplier Test
- The Likelihood Ratio Test
- A Simple Example

Principles of Estimation and Inference

Required textbook: *Econometrics*. Hayashi, F., Princeton University Press (2000)

### 1 Ordinary Least Squares

- Definition and finite sample properties
- Large sample properties in rather general setting.
- Robust test statistics

### 2 Generalized Method of Moments

- Overview, linear single-equation GMM
- OLS and IV as special cases
- Linear single equation
- Hypothesis and specification tests
- 2SLS as special case
- Multiple-equation GMM.
- SUR, FIVE, and RE as special cases
- Panel data: a GMM perspective
- FE, RE, first-difference as special cases

### 3 Extremum Estimators

- Identification: A more formal approach
- Extremum estimators. Overview, consistency, asymptotic normality
- Hypothesis testing: the trinity
- Maximum likelihood: some applications

### 4 The Bootstrap

- What is the bootstrap?
- When does it work?
- When does it improve on asymptotic approximation?
- Bootstrap confidence regions and bootstrap bias correction

[revised: February 2013]

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