Table Of ContentQuantitative Economics with Julia
Jesse Perla, Thomas J. Sargent and John Stachurski
December 4, 2020
2
Contents
I Getting Started with Julia 1
1 Setting up Your Julia Environment 3
2 Interacting with Julia 9
3 Introductory Examples 17
4 Julia Essentials 45
5 Arrays, Tuples, Ranges, and Other Fundamental Types 75
6 Introduction to Types and Generic Programming 111
II Packages and Software Engineering in Julia 135
7 Generic Programming 137
8 General Purpose Packages 159
9 Data and Statistics Packages 167
10 Solvers, Optimizers, and Automatic Differentiation 177
11 Julia Tools and Editors 197
12 Git, GitHub, and Version Control 209
13 Packages, Testing, and Continuous Integration 227
14 The Need for Speed 249
III Tools and Techniques 271
15 Linear Algebra 273
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4 CONTENTS
16 Orthogonal Projections and Their Applications 297
17 LLN and CLT 313
18 Linear State Space Models 331
19 Finite Markov Chains 355
20 Continuous State Markov Chains 379
21 A First Look at the Kalman Filter 401
22 Numerical Linear Algebra and Factorizations 417
23 Krylov Methods and Matrix Conditioning 447
IV Dynamic Programming 479
24 Shortest Paths 481
25 Job Search I: The McCall Search Model 489
26 Job Search II: Search and Separation 503
27 A Problem that Stumped Milton Friedman 515
28 Job Search III: Search with Learning 527
29 Job Search IV: Modeling Career Choice 543
30 Job Search V: On-the-Job Search 557
31 Optimal Growth I: The Stochastic Optimal Growth Model 569
32 Optimal Growth II: Time Iteration 585
33 Optimal Growth III: The Endogenous Grid Method 601
34 LQ Dynamic Programming Problems 609
35 Optimal Savings I: The Permanent Income Model 637
36 Optimal Savings II: LQ Techniques 653
CONTENTS 5
37 Consumption and Tax Smoothing with Complete and Incomplete Markets 671
38 Optimal Savings III: Occasionally Binding Constraints 689
39 Robustness 707
40 Discrete State Dynamic Programming 727
V Modeling in Continuous Time 751
41 Modeling COVID 19 with Differential Equations 753
42 Modeling Shocks in COVID 19 with Stochastic Differential Equations 769
VI Multiple Agent Models 789
43 Schelling’s Segregation Model 791
44 A Lake Model of Employment and Unemployment 801
45 Rational Expectations Equilibrium 825
46 Markov Perfect Equilibrium 839
47 Asset Pricing I: Finite State Models 857
48 Asset Pricing II: The Lucas Asset Pricing Model 877
49 Asset Pricing III: Incomplete Markets 887
50 Uncertainty Traps 899
51 The Aiyagari Model 911
52 Default Risk and Income Fluctuations 919
53 Globalization and Cycles 937
VII Time Series Models 951
54 Covariance Stationary Processes 953
6 CONTENTS
55 Estimation of Spectra 971
56 Additive Functionals 985
57 Multiplicative Functionals 1003
58 Classical Control with Linear Algebra 1023
59 Classical Filtering With Linear Algebra 1043
VIII Dynamic Programming Squared 1063
60 Dynamic Stackelberg Problems 1065
61 Optimal Taxation in an LQ Economy 1091
62 Optimal Taxation with State-Contingent Debt 1111
63 Optimal Taxation without State-Contingent Debt 1143
Part I
Getting Started with Julia
1
Chapter 1
Setting up Your Julia Environment
1.1 Contents
• Overview 1.2
• A Note on Jupyter 1.3
• Desktop Installation of Julia and Jupyter 1.4
• Using Julia on the Web 1.5
• Installing Packages 1.6
1.2 Overview
In this lecture we will cover how to get up and running with Julia.
There are a few different options for using Julia, including a local desktop installation and
Jupyter hosted on the web.
If you have access to a web-based Jupyter and Julia setup, it is typically the most straightfor-
ward way to get started.
1.3 A Note on Jupyter
Like Python and R, and unlike products such as Matlab and Stata, there is a looser connec-
tion between Julia as a programming language and Julia as a specific development environ-
ment.
While you will eventually use other editors, there are some advantages to starting with the
Jupyter environment while learning Julia.
• The ability to mix formatted text (including mathematical expressions) and code in a
single document.
• Nicely formatted output including tables, figures, animation, video, etc.
• Conversion tools to generate PDF slides, static HTML, etc.
• Online Jupyter may be available, and requires no installation.
We’ll discuss the workflow on these features in the next lecture.
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4 CHAPTER 1. SETTING UP YOUR JULIA ENVIRONMENT
1.4 Desktop Installation of Julia and Jupyter
If you want to install these tools locally on your machine
• Download and install Julia, from download page , accepting all default options.
– We do not recommend JuliaPro.
• Open Julia, by either
1. Navigating to Julia through your menus or desktop icons (Windows, Mac), or
2. Opening a terminal and typing julia (Linux; to set this up on Mac, see end of
section)
You should now be looking at something like this
This is called the JULIA REPL (Read-Evaluate-Print-Loop), which we discuss more later.
• In the Julia REPL, hit ] to enter package mode and then enter.
add IJulia InstantiateFromURL
This adds packages for
• The IJulia kernel which links Julia to Jupyter (i.e., allows your browser to run Julia
code, manage Julia packages, etc.).
• The InstantiateFromURL which is a tool written by the QE team to manage pack-
age dependencies for the lectures.
Note: To set up the Julia terminal command on Mac, open a terminal and run sudo ln -
s <where_julia_app_is>/Contents/Resources/julia/bin/julia /usr/lo-
cal/bin/julia.
The full command might look like sudo ln -s /Applications/Julia-
1.4.app/Contents/Resources/julia/bin/julia /usr/local/bin/julia, if you
placed the app in your Applications folder.
Note: To obtain the full set of packages we use, at this stage you can run the following (see
the package setup section.)
using InstantiateFromURL
github_project("QuantEcon/quantecon-notebooks-julia", version = "0.8.0", instantiate = true, precompile = true)
1.4.1 Installing Jupyter
If you have previously installed Jupyter (e.g., installing Anaconda Python by downloading
the binary https://www.anaconda.com/download/) then the add IJulia installs
everything you need into your existing environment.
