Econ 504 / Stat 604
Computational Economics

Fall 2018

Professor: Mahmoud A. El-Gamal

Classes: MW 11:00-12:30, Room BKH 271

TA: Ibrahim Emirahmetoglu

Course Description:
This course introduces second-year Economics PhD students to the essential elements of numerical and Monte Carlo analysis methods for use in Economics and Finance. No prior programming experience is required, although, of course, such experience can be of value. Mostly, the course assignments and exams will be Matlab based, with links to AMPL and Knitro solver for large scale optimization, and to STAN for MCMC Bayesian methods. The last module of the course is more statistically oriented, and will thus be R based.

We will not have a formal textbook for the course, but elements of the following books will be used:

• Burden, R., D. Faires, and A. Burden Numerical Analysis(10th Ed.), Boston, MA: Cengage Learning, 2016.
• Judd, K. Numerical Methods in Economics, Cambridge, MA: MIT Press, 1998.
• Amman, H., D. Kendrick, and J. Rust. Handbook of Computational Economics (Vol.1), North Holand, 1996.
• Russell, S. and P. Norvig. Artificial Intelligence: A Modern Approach, Third Edition, Prentice Hall, 2010.
• Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning, Springer, 2nd ed., 2008.
• James, G., D. Witten, T. Hastie, and R. Tibshirani. An Introduction to Statistical Learning(using R), Springer, 2017.

Syllabus: 

Part 1: Basics, static solutions and optimization for equilibrium and estimation (Matlab based)

• Week 1 -- August 20, 22: Systems of linear equations, least squares, linear programming and zero-sum finite games
• Week 2 -- August 27, 29: Quadratic programming, optimal portfolio, Kalman Filter, L-Q optimal control
• September 3 -- Labor Day
• Week 3 -- September 5: Newton's & Quasi-Newton Method, nonlinear equations (equilibria, method of moments)
• Week 4 -- September 10, 12: Constrained and unconstrained optimization, GMM, N-person game Nash Equilibrium

Part 2: Dynamic and Stochastic Modeling (Matlab based)

• Week 5 -- September 17, 19: Dynamic Programming, function approximation, numerical & symbolic calculus
• Week 6 -- September 24, 26:  Simulation, stochastic processes, Monte Carlo integration, stochastic dynamic prog.
• Week 7 -- October 1, 3: Dynamic discrete choice models, MPEC, nested fixed point methods (+ AMPL, Knitro) 
• Midterm Recess -- October 8
• Week 8 -- October 10:  Dynamic discrete choice models, MPEC, nested fixed point methods (continued) 
• Week 9 -- October 15, 17: Stochastic games: Markov Perfect Equilibrium; stochastic & optimization algorithms
• Week 10 -- October 22, 24: Solving ordinary and Partial Differential Equations, option pricing
• Week 11 -- October 29, 31: Heterogeneous agent continuous time model solution (and estimation?)

Part 3: Bayesian Methods and Machine learning (R based)

• Week 12 -- November 5, 7: Bayesian methods, Markov Chain Monte Carlo methods (+STAN)
• Week 13 -- November 12, 14: Data-driven Model Selection, DAGs, Bayesian Networks (+ bnlearn)
• Week 14 -- November 19, 21: Artificial neural networks, supervised learning, self-organizing maps
• Week 15 -- November 26, 28: Causal inference, policy assessment (Average Treatment Effects via random forests)

Grading:

• Homeworks (take home projects wherein you may consult with colleagues): 50%
• Two exams (take home projects wherein you may not consult with anyone): 20% + 20%
• Class participation: 10%