RECURSIVE MACROECONOMICS

Modules I - II, 2002-03

Instructor: Alexei Deviatov

Course description: This is an advanced elective two-module sequence in macroeconomics. The course objective is twofold. First, students will be familiarized with the basics of dynamic programming including some of numerical techniques for solution of dynamic programming problems. Second, the tools will be applied to a wide range of recursive macroeconomic models. We shall address such issues as unemployment, long-term growth, asset pricing, and other selected topics to cover the most important developments in the field.

Textbooks:
• L. Ljungqvist and T. Sargent. Recursive macroeconomic theory. MIT Press, 2000.
• N. Stokey and R. Lucas with E. Prescott. Recursive methods in economic dynamics. Harvard University Press, 1989.
• K. Judd. Numerical methods in Economics. MIT Press, 1998. Papers:
• [AH]. Philippe Aghion and Peter Howitt. “A Model of Growth through Creative Destruction.” Econometrica, 60 (2), 1992, 323-351.
• [LPW]. Derek Laing, Theodore Palivos and Ping Wang. “Learning, Matching and Growth.” Review of Economic Studies, 62 (1), 1995, 115-129.

In addition to these papers students are strongly encouraged to read the original papers referred to by Ljungqvist and Sargent in the chapters on the reading list below. Note that no textbook can give full exposition of the material, and, therefore, students should find these readings very helpful.

Grading: In every module there will be 4 homeworks (40%), a midterm (20%) and a final exam (40%). Homeworks will be given once in approximately every ten days. Due dates and the dates of exams will be announced in class. Although attendance is not mandatory, students are responsible for the readings and for being aware of all oral announcements made in regard to this course. All homework is due to the beginning of class on the due date and will be collected at that time. Late homework will be accepted and graded, yet a substantial discount will be applied unless you have a valid excuse. As a general policy, no make-up midterm exams are given in this course. If you miss a midterm exam and have a valid excuse, your grade will be based on the remaining elements of the course. In most cases valid excuse is an unforeseen circumstance beyond student’s control such as illness or family emergency. If you are unable to participate in the important elements of this course because of a circumstance which qualifies as a valid excuse, please notify instructor as soon as possible. Please be ready to provide written evidence of your situation. Note that it is a responsibility of the instructor or of the Dean of Students to determine whether your particular situation qualifies as a valid excuse.

Course Outline.

MODULE I

Part 1. Tools. (4 lectures) Sequence Problems. Bellman equations. The contraction mapping theorem.
Value and policy function iteration. Euler equations. Transversality
conditions. Some examples. Dynamic programming under uncertainty. Practical
dynamic programming: discrete state, Howard improvement algorithm.
Examples. Numerical implementation in MATLAB.
LS, ch.2, 3; SLP, ch. 3-5; and Judd ch. 12.1-12.5.

Part 2. Search, matching and unemployment. (4 lectures)
McCall’s and bathtub models. Jovanovich’s model of unemployment.
The island model of Lucas and Prescott. The Diamond-Mortensen-Pissarides
model.
LS, ch. 5, 19 and SLP, ch. 10.7-10.10.

Part 3. Growth. (6 lectures)
Endogenous growth with reproducible factors. Knowledge spillovers. Horizontal
innovation: R&D and monopolistic competition. Vertical innovation:
the model of Aghion and Howitt. Growth with non-reproducible factors.
Search, unemployment and growth.
LS, ch. 11; SLP, ch. 10.1-10.3; AH; and LPW.

MODULE II
Part 4. Competitive equilibrium and asset pricing. (4 lectures)
Competitive equilibrium with complete markets. Arrow securities. Asset
pricing. Equity premium puzzle. Hansen-Jagannathan bounds.
LS, ch. 7, 10 and SLP, ch. 10.6.

Part 5. Optimal taxation. (2 lectures)
Ramsey problem. Optimal taxation under uncertainty.
LS, ch. 12.

Part 6. Incomplete markets. (2 lectures)
Savings with incomplete markets. Borrowing limits. IOU. Exchange rate
indeterminacy. Precautionary savings.
LS, ch. 14.

Part 7. Social insurance. (3 lectures)
Social insurance without commitment. Social insurance with asymmetric
information. Optimal unemployment compensation.
LS, ch. 15.

Part 8. Credit and currency. (3 lectures)
Case of complete markets. The turnpike model. The Friedman rule.
Legal restrictions. Two money case. Commodity money.
LS, ch. 18.