PhD Computational Methods Course
Lecture Slides
Lecture 1: Dynamic Programming (2023)
Introduction to Dynamic Programming, Guess and Verify, Value Function Iteration, Howard’s Policy Iteration, Acceleration with MacQueen-Porteus Bands, Endogenous Grid Method
Lecture 2: Function Interpolation (2023)
Interpolation vs Approximation, Polynomial interpolation, Cubic splines, Shape preserving splines, Expanding Grids, EZ Curvature reduction trick
Lecture 3: Integration (2023)
Integration by discretization, Rouwenhorst method, Gaussian Quadrature, Gauss-Kronrod, Automatic Integrators, de Doncker’s QAGS algorithm, Romberg integration, Benchmarking integration methods.
Lecture 4: Miscellaneous Tools (2023)
Root finding, 1-dimensional maximization, Brent’s method, Newton-Raphson, Newton’s fractals, Numerical differentiation
Lecture 5: Putting Algorithms to Work (Key Lecture) (2023)
Putting all we learned in Lectures 1-4 into work. Solving an income fluctuations problems with each method, Convergence criteria, Checking for accuracy, Pitfalls, Subtle failures.
Lecture 6: Local Optimization
1- and N-dimensional optimization, Newtons’ method: fast and furious, Nelder-Mead algorithm, DFNLS algorithm (sweet spot), Benchmarking optimizers.
Lecture 7: Global Optimization
Challenges and practical tips, plotting slices/surfaces of objective, Stochastic multi-start algorithms, TikTak TikTak fully parallelizable algorithm (fastest and most reliable), NLOPT algorithms.
Lecture 8: GE with Heterogeneity: No Aggregate Shocks (2023)
Aiyagari (1994) model, Substantive ideas , Computation, How to Simulate. Limits of inequality in Aiyagari style models. Introduction to Power Law Models and Pareto tails.
Lecture 9: GE with Heterogeneity and Aggregate Shocks, Part I (2023)
Incomplete markets models with aggregate shocks, Krusell-Smith (1998) model and method, Approximate aggregation, Essential accuracy plot, Checking for accuracy and convergence.
Lecture 10: GE with Heterogeneity, Part II
Incomplete markets models with 2 assets and bells and whistles, Guvenen (2009), Challenge of portfolio choice problems, Solving firms’ problems, Iterating on GE functions (prices & transitions).
“The thing, above all, that a teacher should endeavor to produce in his pupils, if democracy is to survive, is the kind of tolerance that springs from an endeavor to understand those who are different from ourselves. It is perhaps a natural human impulse to view with horror and disgust all manners and customs different from those to which we are used. Ants and savages put strangers to death. And those who have never traveled either physically or mentally find it difficult to tolerate the queer ways and outlandish beliefs of other nations and other times, other sects and other political parties. This kind of ignorant intolerance is the antithesis of a civilized outlook, and is one of the gravest dangers to which our overcrowded world is exposed.”
Bertrand Russell (1950)