First-year Ph.D. courses
Math Methods for Economists
First-Year Ph.D. course as part of the Columbia Economics Core curriculum.
Introduction to Recursive Mathematical Methods for economists.
Syllabus, Fall 2025
Course Outline and Reading List, Fall 2025
Lecture 1. Analysis
Lecture 2. The Contraction Mapping Theorem
Lecture 3. Eventual Application of the CMT
Lecture 4. Optimization and Convexity
Lecture 5. Theorem of the Maximum
Lecture 6. Dynamic Programming
Lecture 7. The Kalman Filter
description
Macro Analysis I
description
First-Year Ph.D. course as part of the Columbia Economics Core curriculum.
Introduction to business cycle facts, theory, and methods.
I cover business cycle facts, the Real Business Cycle (RBC) model, applications of dynamic programming to the NGM and RBC, calibration/evaluation of the RBC, early extensions of the RBC, complete markets, aggregation, asset pricing, the consumption CAPM, welfare costs of business cycles, incomplete markets, self-insurance and precautionary savings, and heterogeneous agent models.
Syllabus, Fall 2025
Course Outline and Reading List, Fall 2025
The following lecture notes for Macro Analysis 1 build directly on the dynamic programming lecture notes that I teach in Math Methods found above.