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Numerical methods in economicsJune, 2011

Instructor

Alfonso Irarrazabal, Norges Bank

air@norges-bank.no

http://sites.google.com/site/alfonsoirarrazabalsite/

Date and place

From June 20th to June 24th at Blindern campus, University of Oslo

Course contents

This course covers basic tools of numerical analysis that can be used in micro and

macroeconomics. These techniques are usually used to solve, simulate and estimate

economics models. We will cover basic methods to solve systems of non-linear equa-

tions, numerical integration, optimization, montecarlo integration and simulation of

stochastic processes. We will apply these methods to calibration, numerical estimation

(non-linear, GMM and maximum likelihood), solving transitional dynamic problems,

dynamic programming and others.

The course will be computationally intensive. There will be three problem sets,

which will require the student to work on computational issues and applications.

Students are expected to replicate (the computational part) a relevant paper as a

nal examination.

To make good use of the course, it is important to get some matlab practice before

you start. The third week of May I will post on my webpage a set of simple sample

matlab tutorials and a set of exercises to practice basic programming techniques inmatlab. Below you will nd a more detailed outline of the contents for this course.

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Outline

DAY1: Basic numerical methods I

Solving system of equations (equilibrium concepts)Numerical dierentiation and integration

Optimization

Lab 1: Simple examples: monopoly, simple general equilibrium, portfolio problem.

DAY2: Basic numerical methods II

Approximation methods

Montecarlo analysis

Solving dierential equations (shooting method)

Lab 2: Simulation of time series, markov chains, transitional dynamics in growth

models

DAY 3 Simulation

Distributions and montecarlo methods

Simulation of stochastic processes

Lab 3: simulation of markov chains,. random walks processes. Computing moments

from simulations.

DAY 4. Dynamic programmingFinite horizon dynamic programming (Cake eating problem)

Deterministic dynamic programming

Stochastic dynamic programming

Discrete choice and continuos choice examples

Lab 4: Stochastic growth model, resource economics problem, investment problem,

etc

DAY 5. Applications to economics

Application in micro and macroeconomics: A couple examples will be provided from

real applications.: Investment problem, models of rm dynamics, monetary models

with price adjustment etc.

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References

[1] Adda and Russell Cooper. Dynamic Programming: Theory and Applications. MIT

Press.

[2] Kenneth L. Judd. Numerical Methods in Economics. MIT Press, 1998.

[3] David R. Kincaid and E. Ward Cheney. Numerical Analysis. Mathematics of Sci-

entic Computing. Brooks Cole, 2001.

[4] Lars Ljungqvist and Thomas J. Sargent. Recursive Macroeconomic Theory.

[5] MIT Press, 2nd edition, 2004.

[6] Rust, J. (1993). Structural Estimation of Markov Decision Models. Chapter 51

in R. Engle and D.

[7] William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery.

Numerical Recipes. The Art of Scientic Computing. Third edition. Cambridge

University Press, 2007.

[8] Nancy L. Stokey and Robert E. Lucas. Recursive Methods in Economic Dynamics.

Harvard University Press, 1989.

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