AU kursuskatalog arkiv

2951: Advanced Macroeconomics ( forår 2010 - 10 ECTS )

Rammer for udbud

• Uddannelsessprog: engelsk
• Niveau: PhD course, elective MSc course  
• Semester/kvarter: SEMESTER FOR WHICH THE COURSE DESCRIPTION APPLIES: Spring 2010  
• Timer per uge: NUMBER OF HOURS PER WEEK: 4 hours (2+2) per week for 12 weeks.  
• Deltagerbegrænsning: RESTRICTIONS ON ADMISSION: None.  
• Undervisningssted: Århus
• Hovedområde: Det Samfundsvidenskabelige Fakultet
• Udbud ID: 17521

Formål

LEARNING OBJECTIVES:

Having completed this course, the student will be able to

• reflect on advanced dynamic models
• reflect on solution techniques in discrete and continuous-time
• theorize on dynamic stochastic optimal control problems
• reflect on models of optimal saving under uncertainty
• relate basic concepts of probability theory
• apply numeric solution techniques to continuous-time macroeconomic models

Indhold

COURSE DESCRIPTION:

This course provides a toolbox for solving dynamic optimization problems in (stochastic) economic models. In particular, we review most of the mathematical tools required for typical graduate courses in economics including the calculus of variations, optimal control theory, and dynamic programming. We then thoroughly study models in discrete and continuous time under uncertainty. Throughout the course, the optimization problems are illustrated using various examples. A particular focus will be on formulating and solving dynamic models in modern macroeconomics.

COURSE SUBJECT AREAS:

Part I: Basic mathematical
(i) Topics in integration and differential equations (rules of transformation, differentiation, solution techniques)
(ii) Qualitative theory (phase plane analysis, stability for nonlinear systems)
(iii) Calculus of variation (Euler equation, transversality condition)
(iv) Control theory (maximum principle, variable final time, infinite horizon)
(v) Dynamic programming (Bellman equation, envelope theorem, multiple control and state variables)
(vi) `Dynamic macroeconomic modeling with Matlab' on numerical solutions to continuous-time dynamic macroeconomic models.
(vii) Basic concepts of probability theory (probability model, stochastic processes, functions of random variables)

Part II: Stochastic models in discrete time
(i) Topics in difference equations (basic concepts, solution techniques)
(ii) Stochastic difference equations (state-space representation, indeterminacy)
(iii) Discrete-time optimization (dynamic programming, stochastic control problems)
(iv) Overlapping-generations, multi-period models (real-business-cycles)
(v) Asset pricing in a closed economy

Part III: Stochastic models in continuous time
(i) Stochastic differential equations and rules for differentials (Itô's formula)
(ii) Solution techniques (Option pricing)
(iii) Stochastic dynamic control problems (Bellman equation)
(iv) Optimal saving under uncertainty (Poisson uncertainty, Brownian motions)
(v) Matching models, capital asset pricing, real-business-cycles

Faglige forudsætninger

REQUIRED COURSES:

Macro 1 (7005).

Underviser

LECTURER: Olaf Posch.

Undervisnings- og arbejdsform

TEACHING METHOD:

Lectures and take-home problem sets.

English

Litteratur

LITERATURE:

• Chang, Fwu-Ranq, Stochastic Optimization in Continuous Time, Cambridge Univ. Press 2004
• Ljungqvist, Lars and Thomas Sargent, Recursive macroeconomic theory, MIT Press, 2004
• Spanos, A., Probability Theory and Statistical Inference, Cambridge Univ. Press, 1999
• Stokey, Nancy L. and Robert E. Lucas Jr. and Edward C. Prescott, Recursive Methods in Economic Dynamics, Harvard Univ. Press, 1989
• Sydsaeter, Knut., Peter Hammond, Atle Seierstad, and Arne Strøm, Further Mathematics for Economic Analysis, Prentice Hall, 2008
• Wälde, Klaus, Applied Intertemporal Optimization, Univ. of Glasgow, 2009

Reading list: The main text books are Sydsaeter et al. (2008, chap. 4-12, 290 pages) and Chang (2004, chap. 4, 50 pages). Readings of Stokey et al. (1989), Ljungqvist and Sargent (2004), Spanos (1999), and Wälde (2009) as well as articles will be suggested as complementary material during the course. Reflecting the lecture notes is compulsory.

Lecture notes: approx. 120 pages
Total: approx. 460 pages

Bedømmelse

• Hj.opg., bedømt efter 7-skala med intern censur
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FORM OF ASSESSMENT: Take-home exam.
- It is a prerequisite that four mandatory problemsets are handed in to the lecturer and are approved before the take-home exam.

EXAMINATION AIDS ALLOWED: All