QExam Syllabi
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 Lpconvergence
 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, interpretation, and finite sample properties
 Large sample properties.
 Inference
2 Generalized Method of Moments
 Overview, linear singleequation GMM
 Hypothesis and specification tests
 2SLS as special case
 Multipleequation GMM.
 SUR, FIVE, and RE as special cases
 Panel data: Fixed vs Random Efefcts
3 Extremum Estimators
 Identification: A more formal approach
 Extremum estimators. Overview, consistency, asymptotic normality
 Hypothesis testing: the trinity
 Applications
4 The Bootstrap
 What is the bootstrap?
 When does it work?
 When does it improve on asymptotic approximation?
 Bootstrap tests and confidence regions
5 Nonand Semiparametric Estimation
 Kernel density estimation. Optimal rates and kernels. Inference.
 Nonparametric mean regression.
 Semiparametric Regression: Partially Linear Model, MINPIN Theory
Macroeconomics QExam 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.
PART I: Material taught by Professor TaschereauDumouchel
Endowment Economy with Complete Markets and under uncertainty
 Social planner’s problem and Pareto efficiency
 ArrowDebreu equilibrium
 Sequential markets equilibrium
 Asset pricing
References
 Instructors notes
 LS, Chapter 8.
 SLP, Chapter 15
Math, Dynamic Programing and Numerical Methods
 Recursive formulation and Bellman equations
 Guess and verify, value function iterations
 Transversality conditions
 Contraction Mapping Theorem
 Blackwell’s Theorem
 Theorem of the Maximum
 Principle of Optimality
 Dynamic Programming with bounded returns
 Benveniste Scheinkman
References
 Instructors notes
 LS, Chapters 25.
 SLP, Chapter 35.
Production, Investment and the Neoclassical Growth model
 Neoclassical Growth model in discrete time and under uncertainty
 Social planner’s allocation
 ArrowDebreu and sequential markets equilibrium
 Balanced growth path
References
 Instructors notes
 Romer, Chapter 8
 LS, Chapter 11.111.3, 11.9. 15.115.3, 15.5.
Overlapping Generations Models
 ArrowDebreu and sequential markets equilibrium
 Samuelson and classical economies. BalaskoShell
 Ricardian Equivalence
References
 Instructors notes
 LS Chapter 9
Textbooks
LS: Lars Ljunqvist and Thomas J. Sargent. Recursive Macroeconomic Theory, 3rd edition, MIT Press, 2012.
SLP: Nancy Stokey and Robert Lucas, with Edward Prescott, Recursive Methods in Economic Dynamics, Harvard University Press, 1989.
David Romer, Advanced Macroeconomics, 3rd edition, McGraw Hill, 2006.
PART II: Material taught by Professor Nimark
THE NEW KEYNESIAN BUSINESS CYCLE FRAMEWORK
The classical monetary model
 The representative household
 Firms and production
References

Gali Ch. 2
The basic New Keynesian model
 Monopolistic competition
 CES demand systems
 Calvo pricing and the New Keynesian Phillips Curve
 Monetary nonneutrality
References
 Instructor’s notes
 Gali Ch. 3
Monetary policy
 Fluctuations, welfare, efficiency
– Gali Ch. 4
Policy tradeoffs
 Costpush shocks
 Discretion vs commitment
– Gali Ch. 5
TIME SERIES TOOLS
Time Series
 Linear Difference Equations
 Lag operators
References
 Hamilton Ch.12.
 Brockwell and Davis Ch.1
Hilbert space, projections
 Time series as objects of a Hilbert space
 The projection theorem
References
 Brockwell and Davis Ch.2
State space models and the Kalman filter
 State Space Models
 The Kalman Filter
References
 Instructor’s notes
Textbooks
Brockwell, P.J. and Davis, R.A., Time series: theory and methods, Springer Science & Business Media, 2005.
Gali, Jordi, Monetary Policy, Inflation, and the Business Cycle, Princeton University Press, 2015.
PART III: Material taught by Professor Caunedo
Dynamic Optimization
 Convex analysis
 Necessary and Sufficient Conditions
 Applications KuhnTucker Theorem
 Welfare Theorems
– References: M(1), HM2(1)
One Sector Growth Model (Ramsey  Cass  Koopmans)
 Intro to the One sector Growth Model
 Extension to Infinite Horizon Economies
 Steady state
 Saddle path, existence and uniqueness of a stable manifold.
 Recursive representation, existence of equilibrium.
 Shooting algorithms and dynamic programming
– References: M(2, 3), HM2(1),HM1(26), BSiM (3, Appendix, Math Methods).
Competitive Equilibrium and Heterogeneity
 Competitive equilibrium, ArrowDebreu economies
 Recursive equilibrium
 Heterogeneity and Gorman Aggregation
– References: M(4), LS(5), HM1(11,26).
Exogenous Long Run Growth
 Pontryagrin’s maximum principle.
 AK model.
 Saddle path, uniqueness and stability.
 Recursive representation in continuous time.
 Application: Human capital accumulation (BenPorath).
– References: BSiM(3), A(7,8), AH(2)
Endogenous Long Run Growth
 Increasing Returns (Romer, 1986)
 Externalities in Human Capital (Lucas, 1988)
– References: A(10, 11), AH (3), HM2 (1).
Innovation and Long Run Growth
 Variety innovation (Romer, 1990)
 Technology ladder (AguionHowitt, 1992)
– References: A(11), AH (4, 5), K(9.4.3).
Textbooks
Handbook of Macroeconomics Vol. 1 (1999) (HM1)
Handbook of Macroeconomics Vol. 2 (2016) (HM2)
Rody Manuelliâ˘AZ´ s notes, Notes on Discrete Time Economic Models (M)
Stokey, Lucas and Prescott (1989), Recursive Methods in Economic Dynamics (SLP)
Ljungqvist and Sargent (2004), Recursive Macroeconomics Theory (LS)
Barro and SalaiMartin (2004), Economic Growth (BSiM)
Aghion and Howitt (2008), The Economics of Growth (AH)
Acemoglu (2009), Introduction to Modern Macroeconomic Growth (A)
Krueger (2012), Macroeconomic Theory (K)
PART IV: Material taught by Professor Huckfeldt
Search and Matching
 The McCall search model
 The Diamond, Mortensen, and Pissarides model of equilibrium unemployment
References: Instructor notes, LS (6, 29)
Aggregation of technology and preferences
 Elementary results on aggregation of technology and preferences
 Gorman aggregation
 (In)determinacy of the wealth distribution
 The Negishi method
References: Instructor notes, GLV, LS (8)
Consumption insurance and the permanent income hypothesis
 Full risksharing versus autarky
 Complete markets versus partial risksharing via a single riskfree bond
 Marginal utility of consumption as a random walk
 Consumption dynamics under parametric income processes
 Identification of income shocks from panel data
References: Instructor notes, GLV, LS (18)
Precautionary savings and the income fluctuation problem
 Prudence
 Borrowing constraints
 The natural borrowing limit
 Consumption dynamics under deterministic income fluctuations
 Consumption dynamics under stochastic income fluctuations
References: Instructor notes, GLV, LS (17)
Stationary equilibrium in an economy with idiosyncratic risk and incomplete markets
 Definition of recursive competitive equilibrium
 Existence and (lack of) uniqueness
 Computational strategies for computing stationary equilibrium
 Model calibration
References: Instructor notes, GLV, LS (2,18)
Applications of Bewley models
 Contribution of precautionary savings to aggregate capital stock
 Contribution of precautionary savings to wealth inequality
 Entrepreneurship
 Optimal taxation
 Optimal quantity of government debt
References: Instructor notes, GLV
Transitional dynamics in a Bewley model
 Backwards induction and computation of transition path
 Applications (i.e., welfare change from tax reform)
 Decomposition of welfare changes
References: Instructor notes, GLV, LS (10)
Bewley models with aggregate uncertainty
 Formulation of economic environment, state space, household problem
 Approximate equilibrium and computational algorithm
 Nearaggregation in KrusellSmith
References: Instructor notes, GLV, LS (18)
More extensions of Bewley models
 Indivisible labor and insurance within households
 Lifecycle economies
 Endogenous borrowing constraints
 Constrained efficiency in the Bewley model
References: Instructor notes, GLV
Textbooks
LS: Lars Ljunqvist and Thomas J. Sargent. Recursive Macroeconomic Theory, 4th edition, MIT Press, 2018.
GLV: Gianluca Violante. Lecture notes on heterogeneous agent models, mimeo, 2014.
Microeconomics QExam 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
 Statepreference equilibrium models of uncertainty
 Intertemporal equilibrium
 Overlapping generations models
6. Externalities and Market Failure
 Public goods
 Information
 Nonconvexities
 Market power
7. Noncooperative Games
 The normal form
 Domination and iterative dominance
 Nash equilibrium
 Games of incomplete information, and normal and extensive form equilibrium concepts
 Repeated games and the Folk Theorem
 Dynamic games of complete information and Subgame Perfect Nash Equilibria