Dynamic Math for Economists

I'm using this page for a course at Quinnipiac on DSGE Modelling for advanced undergrads and to explore and build a course on economic dynamics

Spring 2020 QU Independent Study in

DSGE Modelling of CEE Economies

Outline for the Math of the Course

First Part of the Course

Introduction to Difference Equations: Basics
Introduction to Differential Equations: Basics

Introduction to Time Series: Basics
Introduction to Time Series: The Expectations Operator
Introduction to Time Series: Calculating Impulse Response Functions
Introduction to Time Series: AR to MA processes

Second Part of the Course

Optimization: Review of Static Lagrangians
Optimization: Two-Period Lagrangians
Optimization: Two-Period Insights into Infinite Horizons and Bellman
Optimization: Infinite Horizon Lagrangians in Discrete Time
Optimization: Infinite Horizon Hamiltonians in Continuous Time

Solving Models: Phase Diagrams in Continuous Time
Solving Models: Linearizing around Steady State
Solving Models: Systems of Difference Equations
Solving Models: Systems of Differential Equations

Economic Modelling Topics

Budget Constraints Part One: How To Think About and Model Them ... PDF
Budget Constraints Part Two

Graduate-Level Introduction to DSGE and Dynare

Eric Sims at Norte Dame has some of the best material to get into DSGE and to do it via Dynare.

Eric Sims Graduate Macro II class (2017)

Introductory Notes:

Preliminaries (Impluse Response Fns): pdf

Two period consumption-saving: pdf

Value function iteration: pdf

Using Dynare: pdf

More Advanced Material:

Review of neoclassical growth: pdf

Log-linearization: pdf

Solving linearized models: pdf

Matrix Algebra

Basic Matrix Terms and Definitions ... PDF
Professor Gilbert Strang's 2009 Linear Algebra Linear Algebra MIT 16.08 on Youtube
Prof. Strang's 2020 A 2020 Vision of Linear Algebra uses his new method for all the material in MIT 16.08. I encourage you to watch MIT 16.08 first, then these. Or, the first 2-3 lectures in 16.08, then Intro and Part 1 (below), then the next ones in 16.08, then Part 2 (below) and so on.
- Part 5: Singular Values and Singular Vectors
- Part 4: Eigenvalues and Eigenvectors
- Part 3: Orthogonal Vectors
- Part 2: The Big Picture of Linear Algebra
- Part 1: The Column Space of a Matrix
- Intro: A New Way to Start Linear Algebra
Prof. Strang's 2018 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning MIT 18.065

Gilbert Strang's Highlights of Calculus

Prof Gilbert Strang's short collection of videos and why he made these (click here)
MIT Courseware: click here
Prof Strang's Free Calculus textbook (download here).
Highlights and the Big Picture of Calculus
Derivatives

Probability and Stats

2010 MIT Course on Probability and Statistics includes processes.
Harvard's Statistics 110 (Probability) by Prof. Joe Blitzstein
- 34 Lectures on Youtube
MIT Course on Applied Math in Finance, including lectures on statistical processes.

Ronald Shone had two great textbooks on Economic Dynamics and Math. I think his approach was right: teach first how to solve the basic systems in excel and other programming languages, and then cover the math. I'm trying to build on his insight.

Introduction to Economic Dynamics (a "non-math" treatment where everything is solved in Excel)

Economic Dynamics (a more "applied" math coverage of the material needed for dynamic analysis in Economics with examples in excel and Maple)