# Q-Exam Syllabi

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## Econometrics Q-Exam Syllabus

## 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

## Macroeconomics Q-Exam Syllabus

The qualifying exam in macroeconomics is offered twice each year, in the spring and again in late summer. The qualifying exam is not a final exam for the macroeconomics sequence, nor is it the explicit goal of the courses to teach the exam. The exam covers the topics on the following outline.

While students might expect that much of this material will be covered in Economics 6130 and 6140, not all of it will be, and the instructors may choose to devote time to topics not on the Q syllabus. Students are advised to clarify early on with their instructors what on this list will and will not be covered, so they can plan their studying accordingly.

### 1. Introduction to Dynamic Programming

- Deterministic saving model
- Endogenous labor supply
- Aggregation
- Stochastic saving model with quadratic preferences

### 2. Dynamic Programming

- Concepts: metric spaces, contraction maps, fixed points
- Equivalence of recursive and sequential formulations
- Existence, uniqueness, monotonicity, concavity and differentiability of value functions

### 3. Search Model

- McCall's model
- Unemployment and worker flows
- McNeil's career choice model
- Mortensen-Pissarides-Diamond matching model

### 4. Discrete Markov Processes

### 5. Competitive Equilibrium with Complete Markets

- Planner's problem
- Date-0 and sequential trading competitive equilibrium
- Recursive planner's problem and competitive equilibrium
- Ricardian equivalence and the Modigliani-Miller Theorem

### 6. Asset Pricing

- Equity premium puzzle
- Disaster risk
- Distorted beliefs
- Endogenously incomplete markets

### 7. Overlapping Generations

- Offer curve and stationary equilibria
- Non-stationary monetary equilibria
- Inflationary taxation and social security
- Stochastic overlapping generation models

### 8. Stochastic Saving Model

- Lucas and Prescott's island model
- Mortensen-Pissarides-Diamond matching model
- Kiyotaki-Wright model of money

### 9. Optimal Taxation

- Primal approach and implementability constraints
- History independence of optimal taxes
- Lucas-Stokey model: tax smoothing and contingent government debt

### 10. Introduction to Macroeconomic Data

- Extracting and measuring cyclical fluctuations
- Stylized facts of economic growth
- Business cycle stylized facts
- Deterministic detrending
- Hodrick-Prescott filter

### 11. Properties and Solution of the Basic Real Business Cycle Model

- Dynamic optimization
- Dynamic programming
- General equilibrium growth model
- Social planner’s problem vs. competitive equilibrium
- Balanced growth path
- Growth accounting
- Solow residual
- Stationarity-inducing transformation
- Calibration
- Certainty equivalence
- Log-linear approximation
- Method of undetermined coefficients
- QZ decomposition
- Optimal linear regulator
- Technology shocks
- Impulse response functions
- Model simulation
- Autoregressive processes
- Stationarity

### 12. Performance and Some Extensions of the RBC Model

- Indivisible labor
- Investment technology shocks
- Variable capacity utilization
- Home production
- Government consumption shocks
- Labor and capital adjustment costs

### 13. Money and Output: Basic Facts and Flexible Price Models

- Long and short-run monetary facts
- Neutrality and superneutrality
- Money demand
- Shopping time and transaction cost models
- Cash-in-advance
- Money-in-utility
- Liquidity effects
- Speculative hyperinflations
- Classical dichotomy
- Money growth shocks

### 14. Measurement without Much Theory

- Vector autoregressions
- Wold decomposition theorem
- Invertibility
- State space representation
- Identification
- Long and short-run identification restrictions
- Structural vector autoregressions
- Time series representations of dynamic stochastic general equilibrium models
- Narrative approach
- Evidence on technology shocks
- Evidence on monetary policy shocks
- Evidence on fiscal policy shocks

### 15. Models of Nominal Rigidities

- Monopolistic competition
- Dixit-Stiglitz aggregator
- Sticky price model
- Phillips curve
- Calvo pricing
- Quadratic cost of price adjustment
- Taylor contracts
- Menu costs

## Microeconomics Q-Exam Syllabus

The qualifying exam in microeconomic theory is offered twice each year, in the spring and again in late summer. The 'Q' exam is not a final exam for the microeconomic theory sequence; nor is it the explicit goal of the courses to teach the exam. The exam covers the topics on the following outline.

While students might expect that much of this material will be covered in Economics 6090 and 6100, not all of it will be, and the instructors may choose to devote time to topics not on the Q syllabus. Students are advised to clarify early on with their instructors what on this list will and will not be covered, so they can plan their studying accordingly.

### 1. Consumer Theory

- Preferences and representation with utility functions
- Budget sets
- Revealed preference
- Choice based on preferences and on utility
- Demand functions–derivation (maximization) and properties of demand
- Comparative statics
- Duality–indirect utility, expenditure functions and Hicksian demand
- Integrability
- Consumer surplus
- Aggregation and properties of aggregate demand

### 2. Theory of the Firm

- Objective of the firm
- Technology
- Cost functions
- Profit maximization
- Input demand and output supply–derivation and properties
- Duality–profit functions and cost functions
- Aggregation

### 3. Decision Making under Uncertainty

- Objective uncertainty–probabilities as objects of choice
- Objective expected utility representation
- Risk aversion and measures of risk aversion
- Insurance and gambling
- Subjective uncertainty—Anscombe and Aumann structure
- Subjective expected utility representation

### 4. General Equilibrium — Analysis

- The existence problem
- Welfare analysis — Pareto optimality
- Comparative statics
- Equilibrium of plans, prices and price expectations (Radner equilibrium)

### 5. General Equilibrium — Examples

- Single agent economies
- Bilateral pure exchange
- The 2 × 2 production model
- Linear economies
- State-preference equilibrium models of uncertainty
- Intertemporal equilibrium
- Overlapping generations models

### 6. Externalities and Market Failure

- Public goods
- Information
- Non-convexities
- Market power

### 7. Non-cooperative Games

- The normal form
- Domination and iterative dominance
- Nash equilibrium
- Games of incomplete information and Bayesian-Nash equilibria
- Repeated games and the Folk Theorem
- Dynamic games of complete information and Subgame Perfect Nash Equilibria