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Topics in Computational Economics

John Stachurski

This is the home page of ECON-GA 3002, a PhD level course on computational economics to be held at NYU in the spring semester of 2016.

(Note: This document is preliminary and still under development)

Semi-Random quote

All this technology carries risk. There is no faster way for a trading firm to destroy itself than to deploy a piece of trading software that makes a bad decision over and over in a tight loop. Part of Jane Street's reaction to these technological risks was to put a very strong focus on building software that was easily understood--software that was readable.

-- Yaron Minsky, Jane Street

Table of Contents:

News

Please note that the lecture room has changed to room 5-75 in the Stern Building.

The time is unchanged: Friday 9am--11am

Please be sure to bring your laptop

References

  • http://quant-econ.net/
  • Secondary / Useful / Related / Recommended texts
    • Kendall Atkinson and Weimin Han (2009). Theoretical Numerical Analysis (3rd ed)
    • Ward Cheney (2001). Analysis for Applied Mathematics
    • Nancy Stokey and Robert Lucas Jr. (1989) Recursive Methods in Economic Dynamics
    • John Stachurski (2009). Economic Dynamics: Theory and Computation

Prerequisites

I assume that you have

  • At least a bit of programming experience
    • E.g., some experience writing Matlab code or similar
  • Econ PhD level quantitative skills, including some familiarity with
    • Linear algebra
    • Basic analysis (sequences, limits, continuity, etc.)
    • Dynamics (diff equations, finite Markov chains, AR(1) processes, etc.)

If you would like to prepare for the course before hand please consider

  • Installing Linux on a VM or in a bootable partition on your laptop
    • Backup your data first!
    • Help available in the first class
  • Build up your Linux skills (and profit)
  • Do some exercises in real analysis if you are rusty
  • Read the first 3 chapters of RMT if you don't know any Markov chain theory or dynamic programming

Syllabus

Below is a sketch of the syllabus for the course. The details are still subject to some change.

Part I: Programming

Introduction

Coding Foundations

Core Python

Scientific Python I: SciPy and Friends

Scientific Python II: The Ecosystem

Julia

Part II: Comp Econ Foundations

Markov Dynamics I: Finite State

  • Asymptotics
  • The Dobrushin coefficient
  • A simple coupling argument
  • Code from QuantEcon
  • Applications

Functional Analysis

  • A dash of measure and integration
  • Metric / Banach / Hilbert space
    • Space of bounded functions (cbS is a closed subset)
    • The Lp spaces
  • Banach contraction mapping theorem
    • Blackwell's sufficient condition
  • Orthogonal projections
  • Neumann series lemma
  • Applications
    • The Lucas 78 asset pricing paper

Markov Dynamics II: General State

  • General state spaces
    • Feller chains, Boundedness in prob
    • Monotone methods
  • LLN and CLT
  • Look ahead method
    • examples in lae_extension?
    • examples in poverty traps survey?
  • Applications
    • ARCH, AZ, STAR, MCMC, etc.

Solving Forward Looking Models

  • L2 methods
  • Asset Pricing

Dynamic Programming

  • Fundamental theory
    • The principle of optimality
    • VFI
    • Howard's policy iteration algorithm
  • Approximation
    • Preserving the contraction property
    • MC for integrals
  • Weighted sup norm approach

Part III: Applications

DP II: Applications and Extensions

Optimal Stopping

  • Reservation rule operator
    • Theory
    • Applications

Coase's Theory of the Firm

  • Theory
  • Implementation

Assessment

See lecture 1 slides.

Notes on Class Presentations

All students enrolled in the course must give a 20 minute presentation. The presentation can be on your class project or on a code library or algorithm in Julia or Python that you find interesting. Here are some suggestions:

  • Profiling (see, e.g., this link or this one)
  • scikit-learn (a machine learning library)
  • Unit tests (see, e.g., here or here)
  • Alternative plotting libraries and their strengths / weaknesses
  • Distributions.jl (a well-written Julia library)
  • Some features of vim or vim plug-in(s) that you find particularly useful
  • Techniques for parallel processing
  • Interfacing with C and Fortran code in either Python or Julia

Notes on the Class Project

You should discuss your class project at least briefly with me before you start. I am flexible about topics and mainly concerned with quality.

All projects are due by midnight on June 3rd.

Structure of the Project

A completed class project is a GitHub repository containing

  • Code
  • A Jupyter notebook that pulls all the code together and runs it
  • A PDF document that provides analysis and reports results
    • like a short research paper

Good projects demonstrate proficiency with

  • Python or Julia
  • Good programming style
  • Ideally, the techical material discussed during the course

Random Ideas

Here are some very random ideas that I'll add to over the semester. The links are to papers, code or discussions of algorithms, quantitative work, etc. that could be implemented / replicated / improved using Python or Julia. Feel free to use or ignore. (Ideally you will find your own topic according to your own interests. Please discuss your topic with me either way).

Additional Resources

Vectorization: * http://blog.datascience.com/straightening-loops-how-to-vectorize-data-aggregation-with-pandas-and-numpy/

Good reads * http://undsci.berkeley.edu/article/cold_fusion_01 * https://msdn.microsoft.com/en-us/library/dn568100.aspx