# ECON 4XX: Computational and Quantitative Macroeconomics

This is a newly proposed course which will be taught as ECON 407 in Spring 2023 as a pilot.

See below for additional strongly recommended prerequisites. To summarize: beyond the intermediate micro students are expected to have a ECON 323 or a similar programming course using Python, Matlab, or similar languages (i.e., Stata and R are insufficient). Finally, students should have MATH 221 or an equivalent course in matrix algebra - which would already fulfilled by those taking ECON 323.

## Calendar Description:

ECON 4XX: Computational Methods in Macroeconomics

(3 credits course) Computational tools used in macroeconomics and financial economics including applications to unemployment, inequality, asset pricing, and economic growth

Prerequisites: One of ECON 301, ECON 304, ECON 308 and one of ECON 302, ECON 305, ECON 309 and one of ECON 323, CPSC 103, CPSC 107, CPSC 110, MATH 210, COMM 337 and MATH 221

## Course Overview

This is an introductory course in the computational tools used in macroeconomics. Students are not required to have taken intermediate macroeconomics in order to enrol.

Models in macroeconomics and financial economics are constructed from a core set of tools which provide a model of individual decisions while still maintaining an internal consistency between the decisions of many individuals in an economy. Some of the common features of these models include

1. dynamic and forward looking decisions: If I consume less today, I can save more for tomorrow;
2. randomness and uncertainty about the future: If reject a job offer, I am not sure when the next offer will occur;
3. prices and resources reflecting the collective decisions of other agents: The wage I am offered depends on the number of similar workers I am competing with, the intensity which the unemployed search for jobs, and the demand for my skills from firms;
4. social learning from other agents’ with information aggregated through prices: If many others consider a particular equity or bond asset a good buy, then I can infer this by the price of the asset itself; and
5. distributions and heterogeneity in the economy itself influences decisions and prices: If the distribution of income is askew and there are many poor agents living hand-to-mouth, government policy such as sending out stimulus cheques has a different effect on inflation and customer welfare than if every person had similar incomes.

A difficulty inherent to macroeconomics is that often model features must hold at the same time, which makes it difficult to do counter-factual experiments with partial-equilibrium’'—i.e., changing one price or element of the model in isolation—because of the interconnection of decisions, prices, and distributions. However, by writing formal models in mathematics, you can conduct policy experiments and interpret the data while still ensuring self-consistency. Using precise mathematical language will (1) uncover unanticipated consequences implicit in your assumptions; (2) keep everyone honest; (3) provide a framework to investigate changes in assumptions; (4) provide a framework to nest models and add enough “reality” to do quantitative analysis.

The downside is that while this set of mathematical tools provides a rich set of economic theories that can be explored and tested against the data, the inherent difficulty of dynamic models means that we may usually need to solve them approximately and on a computer.

This course will explore these sorts of theoretical models in conjunction with the computational tools to solve and simulate them. We will learn using the Julia programming language - a modern language for scientific and technical computing which will also help teach a new, high-performance programming language to compliment their existing background in Python or Matlab from other courses.

## Learning Outcomes

By the end of the course, students will be able to

1. program using tools from linear algebra, probability, and optimization in the Julia programming language (LO1)
2. simulate and analyze stochastic processes and understand the evolution of the wealth distribution (LO2)
3. describe economic dynamics as a linear state space model and solve them numerically (LO3)
4. implement and analyze Markov chains, and apply them to models of unemployment and asset pricing (LO4)
5. learn the role of general equilibrium and prices in aggregating information and reflecting the real economy (LO5)
6. define economic problems recursively, such labor market search and consumption savings models, and solve them numerically (LO6)
7. define and implement dynamic models of growth (LO7)

## Textbook and Materials

The core textbook is the online, open-source textbook Quantitative Economics with Julia by Jesse Perla, Thomas J. Sargent and John Stachurski. While it has both graduate-level and undergraduate-level material, in cases where material in the course is too advanced, we will choose a subset and adapt lecture materials to be appropriate for the level—where advanced students can examine the topics in more formality and detail.

The textbook includes both theory and code, and a set of Jupyter notebooks.

## Course Format

The course will meet for two 1.5 hours lectures per week for an in-class lecture. While there will not be a formal “lab”, the instructor may go through coding examples in class. A teaching assistant will be available to help with the class size of approximately 50 students.

While the coding is intended to stay at as basic level as possible at first, students are expected to start reasonably proficient in Matlab, Python, Julia, and similar languages. After the first few weeks the lectures will tend to focus on teaching the theory where code implementations done largely in the assignments. At that point, much of the coding practice will be done in the problem sets, leaving sufficient time in-class for macroeconomic theory.

All materials will be provided on http://canvas.ubc.ca and the open-source materials are on GitHub. Students are expected to have a laptop for in-class exploration and exams.

## Assignments and Assessment

The only way to learn how to apply programming to economic problems is practice. To aid in this, a significant portion of the grade will be the six problem sets.

The midterm and final will be in class and combine both theory and computations, with the exam submitted via a Jupyter notebook.

The weighting in the grade is:

• Six Problem sets: 30% (total)
• Midterm exam: 30%
• Final exam: 40%

The problem sets will start off short and easy to help those with less programming experience, and then build in complexity.

## Computational Infrastructure and Programming Language

While students will have experience with another programming language such as Python or Matlab from their prerequisities, this course will be taught using Julia. Beyond being an excellent language for technical computing and popular among macroeconomists, Julia provides a new set of programming principles that will broaden the student’s knowledge of computing. This will help them students by both providing a better differentiated resume, broader skills, and more opportunities to work as a research assistant for researchers requiring significant computational expertise.

Students can install a Julia on their laptop by following these instructions. While one can use Julia entirely from just Jupyter notebook, we will also install VS Code and introduce basic GitHub and VS Code usage as well to help broaden the students exposure to computational tools.

## Course Outline (by Week)

Note: a few of the linked lectures are currently in Python, and a port is under way.

### Week 1: Introduction to Julia and programming for economics (LO1)

• Topics include: Getting Started and Julia Essentials
• At the end of the week students will have reviewed the basic setup of the Julia programming language and can comfortably accomplish simple tasks as they would in to Python or Matlab.

### Week 2: Linear algebra and basic scientific computing (LO1)

• Topics include Arrays and Related Types and related topics in implementing Linear Algebra. In addition, students will review Optimizers and Solvers. Interested students can review bonus material in Generic Programming but it wouldn’t be required or tested.
• At the end of the week students will feel comfortable working with matrices, vectors, and arrays; solving linear systems and calculating eigenvalues; optimizing unconstrained and constrained functions; and solving systems of equations.

### Week 3: Geometric Series and Stochastic Processes (LO2)

• Topics include Geometric Series Dynamics in One Dimension
• At the end of the week students will understand how to calculate present discounted values, work with Keynesian money-multipliers, and simulating random processes.
• Problem Set 1 Due - basic loops, linear algebra, and optimization problems.

### Week 4: Dynamics of Wealth and Distributions (LO2)

• Topics include AR1 Processes and Wealth Distribution Dynamics
• At the end of the week students will better understand ergodic distributions, measures of inequality, and how to simulate the dynamics of the wealth distribution.

### Week 5: Linear State Space Models Part (LO3)

• Topics include Linear State Space Models
• At the end of this week students will understand how to describe processes such as asset pricing and consumption smoothing as linear-state space models, simulate them, and calculate present-discounted values using those stochastic processes.
• Problem Set 2 Due - calculating present discounted values and simulating univariate asset pricing models, simulating and calculating dynamics of the wealth distribution.

### Week 6: Permanent Income Model (LO3)

• Topics include The Permanent Income Model
• At the end of the week students will understand how to implement the classic consumption-savings model with linear-quadratic preferences in the LSS framework of the previous lecture, and to simulate permanent and transitory shocks to income.

### Week 7: Markov Chains (LO4)

• Topics include Finite Markov Chains
• At the end of the week students will understand how to describe discrete-state stochastic processes as Markov chains and simulate models of unemployment for a worker.
• Problem Set 3 Due - solving and simulating multivariate asset pricing problems in a LSS setup and exploring the permanent income model.

### Week 8: Models of Unemployment (LO4)

• Topics include the Lake Model of Employment and Unemployment
• At the end of the week students will build on the previous tools of Markov chains to look at a aggregated models of employment and unemployment in the economy.
• Midterm in class

### Week 9: Rational Expectations and Firm Equilibria (LO5)

• Topics include Rational Expectations Equilibrium
• At the end of the week students will understand the core “big K, little k” insight for implementing rational expectations equilibria and apply it to models of firm dynamics.

### Week 10: Asset Pricing (LO5)

• Topics include Asset Pricing with Finite State Models
• At the end of the week students will understand pricing assets with payouts following a Markov-chain as derived in the previous lectures.
• Problem Set 4 Due - firm dynamic simulations and more on dynamics of Markov chains.

### Week 12: Recursive Equilibria and the McCall Search Model (LO6)

• Topics include The McCall Search Model
• At the end of the week students will be able to define and solve basic models of labor market search.
• Problem Set 5 Due - asset pricing examples and a labor market search.

### Week 14: Cass Koopmans/Neoclassical Growth (LO7)

• Topics include Cass Koopmans Planning Problem
• At the end of the week students will be able to solve for the transition dynamics of the planning problem for the Cass Koopmans/neoclassical growth model.

### Week 15: Optimal Growth Model (LO7)

• Topics include Stochastic Optimal Growth Model
• At the end of the week students will be able to solve growth models with a single type of good and stochastic productivity.
• Problem Set 6 Due - solving stochastic dynamic programming and simulating transition dynamics of growth models.
• Final Exam - according to calendar schedule

## Policies

Missed Exam Policy: You are responsible for ensuring that you take these exams as scheduled; no make-up exams will be given.

• Missing a midterm for ANY acceptable reason will result in its weight being automatically transferred to the final exam.
• The final exam date will be announced by Student Services about half-way through the term.
• There is no make-up final. Travel plans and/or cheap tickets are not a reason to miss the final. If you have a medical or other compelling reason why you cannot take the final exam at its scheduled time you must follow the formal process and get an Academic Concession from your Faculty Advising Office (see below)

Policy for Academic Concessions: Sometimes, things happen during the course of a semester that can affect your ability to succeed. There are three main categories:

• Medical – i.e. you got sick and missed class or a chronic illness got worse
• Compassionate – i.e. a friend or close relative had something bad happen to them, or something bad happened to you.
• Conflicting Responsibilities – i.e. something happened in your personal life which is affecting your ability to do the work, like childcare falling through

You can read more about specific examples and the whole policy at: http://www.calendar.ubc.ca/vancouver/index.cfm?tree=3,48,0,0

In all of these cases, UBC’s policy is to allow you to request an academic concession. My policy is that all requests for academic concession on exams should be handled through your faculty Advising office (unless your office advises otherwise). This is so that we can centrally track requests for concession and ensure they are fairly administered; it also helps protect your privacy. You can find the procedure here, for Arts:

If you need a concession, you should immediately speak to Advising, who will follow-up with me to handle the academic side of things. In-term concessions, which handle things like missed assignments or deadlines, are handled usually by extending the deadline or adjusting the final grading of the course (e.g. omitting an assessment). Alternative forms of assessment may also be used if suitable and recommended by Advising.

Concessions need to be made in a timely fashion, which I will define as “within 2 weeks of the missed assessment” unless this is not reasonable. You are also welcome to speak to me regarding your issue; I’m here to support you and help you get through things and be successful. If you’re not sure if it’s something you should/could get a concession for, I can also give you a quick sense of what Advising will likely suggest if you’re unable to make an appointment immediately.