Department of Economics / Office: Heady 281
Fall 2016 / E-mail:
Mondays and Wednesdays, 9 – 10:50 am / Office hours: TR, 11 AM – 12:30 PM
Heady 272
Quantitative Methods in Economic Analysis II
(Econ 600)
OBJECTIVES
This part of the course is intended to serve as an introduction to infinite dimensional optimization. The course will focus on applying dynamic programming approach to formulate and solve economic problems recursively. We will apply dynamic programming approach to simple work-horse models of optimal growth and asset pricing, in deterministic as well as stochastic setups.
COURSE OUTLINE
The course will cover the following topics:
1) Introduction to dynamic optimization
2) Bellman equation; Contraction mapping theorem
3) Recursive formulation of dynamic problems:
- One sector growth (Ramsey) model
- Irreversible investment
- Balanced growth
4) Dynamic programming in stochastic environments: Ramsey model
5) Recursive competitive equilibrium:
- Exchange economies
- One sector growth model
- Asset pricing
6) Markov-perfect equilibrium
7) Search models (if time permits)
EXAM/GRADING
The grades will be based on the performance on problem sets (15%) and a two-hour exam (85%). Three of the problem sets will be graded. I may give you some problem sets for practice, which will not be graded. The problem sets will deal with extensions and variations of the models developed in class and should be viewed as an integral part of the course.
Textbooks
[A] Daron Acemoglu, Introduction to Modern Economic Growth, 2008, Princeton University Press
[LS] Ljungqvist, L., and T., Sargent, Recursive Macroeconomic Theory, 2012, MIT Press.
[SLP] Stokey, N. L, R.E. Lucas, Jr., and E. C. Prescott (1989). Recursive Methods in Economic Dynamics. Cambridge, Massachusetts: Harvard University Press.
COURSE OUTLINE AND READINGS
1. Introduction to Dynamic Optimization
(SLP Ch.1 -- general)
Optimal growth model as a social planning problem; a general formulation of a dynamic optimization problem; Lagrangian method; Finite and Infinite horizons.
2. Introduction to Dynamic Programming
(SLP Ch. 2; A Ch. 6)
Optimal growth model as a dynamic programming problem; Value Function; Functional Equation; Policy Functions.
3. Contraction Mapping Theorem
The Contraction Mapping Theorem; Blackwell’s sufficient conditions (SLP Ch. 3; A Ch. 6)
4. Dynamic programming under certainty
(SLP Ch. 4; A Ch. 6)
Principle of optimality; Bounded returns; Euler equations; Deterministic applications
5. Recursive formulations of dynamic programs under uncertainty
Dynamic programming under uncertainty (2.2, SLP); Markov chains (2.1-2.2 LS; A Ch. 16);
6. Recursive competitive equilibrium
Competitive equilibrium in exchange economies; Recursive competitive equilibrium (2.3 SLP, 7.1 – 7.4 LS)
7. Dynamic programming and asset pricing models
Asset pricing with complete markets (Ch 8.1-8.9 LS)
8. Markov perfect equilibrium
An example of Markov perfect equilibrium (Ch 7.4 LS)
9. Equilibrium search and matching
Chapter 28 LS
10. Dynamic Systems
Dynamic discrete systems; stability in planar systems; phase diagrams