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Introduction to Computational Economics
- Computational technology exploding...enormous impact on every field of science except economics!
- MIT Applied mathematician well acquainted with MIT economists:
Economists will soon be so far behind they will not be able to catch up.
Department chair of leading economics department in a discussion with applied mathematicians...
Nothing in numerical analysis is useful to economists
Recent job market candidate presenting at University of Chicago...
A new professor can easily learn computation after he finishes his thesis.
Elite journals put no value on bringing methods from the mathematics literature to economics.
- Very few economics departments off serious training in numerical methods.
- Top U.S. trained PhD students now nothing about numerical methods.
Ragnar Frisch developed interior-point methods for solving optimization problems.
Todd Munson author of best Computable General Equilibrium (CGE) software available will discuss linear and non-linear optimization methods.
CW: Don't trust black boxes! Numerical methods can be trusted...Knittel and Metaxoglou 2013 example of bad work!
Reality: Open your eyes and turn on the lights and black boxes cease to black!
Econometric Vol 75 Issue 1. Constrained optimization problem. Issue 5. Same claim. Econometrica 2012 issue 5? All about how solving dynamic games is hard. Using correct constrained optimization methods...these difficulties are NOT necessary. Only necessary if you use the wrong software/algorithms!
CW: Dynamic programming is hard! Difficult to write stable, efficient, and accurate code for solving DP models.
ZICE 2014: This is easy for concave problems once you learn a little math!
CW: Solving non-linear equations is hard.
ZICE 2014: Karl Schmedders will show you how to solve large systems of non-linear equations (useful for Dynamic games).
CW: Hard to finds all Nash equilibria of a dynamic game.
ZICE: 2014 Sevin Yeltkin: methods for finding all Nash equilibria in Dynamic games
CW: Hard to compute high-dimensional integrals CW: Monte Carlo good enough for econometrics CW: Bakhvalov (1959): curse of dimensionality in integration
ZICE 2014: Learn some applied math! Applied maths literature has much better methods for integration than flipping coins!
Macroeconomists love to linearize their models around a deterministic steady state: "It is reasonable to work with first order perturbations."
CW < 1940 "Linear approximations of Navier-Stokes equations are good enough for bridge design." CW > 1940 Linear approximations are not good enough!
C.F. Tacoma narrows bridge...Petrovsky book about engineering disasters? "Engineers learn one disaster at a time!"
ZICE 2014: Log-linearization is a bad way to build bridges or economic policy...will learn ways to provide global approximations...
- Economists spend too much time on computational problems...
- Come up with a nice idea
- Spend an enormous amount of time and effort figuring out a way to code up a model in Matlab.
- Change the Matlab code until you get the result you expected (i.e., consistent with your "intuition").
- Publish a paper that students can not replicate.
Applied/computational math approach...
- Find the kind of maths that expresses your problem.
- Identify the best computational algorithms and software for your problem and use them!
- Want to free up your time and mind to focus on economics.