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.
I taught this in Fall 2023 & 2025
Syllabus, Fall 2025
Course Outline and Reading List, Fall 2025
Lecture Notes can be found below
description
Macroeconomic 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 taught this in Fall 2015, 2017, 2018, 2019, 2021, 2022, 2023, 2025
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 2023
Course Outline and Reading List, Fall 2023
Lecture Notes can be found below
(Recursive) Math Methods
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
Please note that the following lecture notes for Macro Analysis 1 build directly on the dynamic programming lecture notes that I teach in Math Methods.