Lectures on DirectX 9.0 3D Graphs and Game Programming in C_
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- mémoire
- cours magistral - matière potentielle : on directx 9.0 3 d
- virtual view point
- create cube
- map world map
- cube rendering
- dolphin animation
- normal vector data
- mesh
- point
Guillaume Vandenbroucke
Numerical Methods Spring 2012
Econ 645, USC, Spring 2012
Guillaume Vandenbroucke USC, Dept. of Economics KAP 316 A
The purpose of the class is to present computational techniques used in various areas of economics. Al though there is an emphasis on computing the solutions of models with optimizing agents, some of the techniques presented in the class are relevant for other fields.For example, we will discuss numerical integration and Monte Carlo simulations which are relevant in econometrics. This is not a numerical analysis class. We will study the logic underlying some numerical algorithms and why we expect them to approximate solutions arbitrarily well.Knowledge of computer programming is useful, but the class is not a programming class.Students are free to use whatever programming language they feel comfortable with.Matrix oriented softwares such as Matlab and Gauss are useful and intuitive. Compiled languages (C, C++ and Fortran) can also be used but. I will present examples written in Matlab and C. I will also use a combination of both where C codes are compiled and then called from within a Matlab code. Evaluation Students will prepare and present a project.Students can either choose to replicate the computations in an existing paper or present and compute the solution of a model of their own.Ideas for a project must be discussed with me beforeFebruary 9. There must be a short paper (about 10 pages) associated with the project. The grade will depend on the presentation (no more than 30 minutes) and the paper. Failing to handin the paper and/or to present it implies an F. Student with disabilities Students requesting academic accommodations based on a disability are required to register with Dis ability services and Programs (DSP) each semester.A letter of verification for approved accommoda tions can be obtained from DSP when adequate documentation is supplied. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible.DSP is open MondayFriday, 8:305:00. The office is in Student Union 301 and their phone is (213) 7400776.
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Guillaume Vandenbroucke
Outline
Econ 645, USC, Spring 2012
Root finding Numerical differentiation Approximation methods, Orthogonal polynomials and Numerical Integration Functional Equations
Applications
The deterministic optimal growth model –Linearization: Undetermined coefficients approach, BlanchardKahn –Relaxation algorithm –Discrete state space dynamic programming –Weighted residual methods Markov chains and discretizing an AR(1) process The stochastic growth model –The HodrickPrescott filter –Weighted residual methods –Parameterized expectations –Computing business cycle statistics –Occasionally binding constraints Heterogeneity –Idiosyncratic risk; Idiosyncratic risk and Aggregate Uncertainty; Overlapping Genera tions –Computing solutions with exogenous borrowing limits –Computing stationary distributions –Finding the equilibrium Multi sector models, Structural change, Transition paths, Asset Pricing Fitting model to data
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Guillaume Vandenbroucke
Useful list of references
Econ 645, USC, Spring 2012
Aiyagari, S. R. 1994, “Uninsured idiosyncratic risk and aggregate saving,”The Quarterly Journal of Eco nomics,109(3) 659–684
Cooley, T. F., ed. 1995.Frontiers of business cycle research,Princeton University Press, Princeton, NJ
Greenwood, J., Z. Hercowitz and G. Huffman.1988. “Investment,capacity utilization, and the real business cycle,”American Economic Review, 78(3), 402–417
Hansen, G. and E. C. Prescott.2002. “Malthusto Solow,”The American Economic Review,92(4), 1205– 1217
Hodrick, R. and E. C. Prescott. 1997 “Postwar U.S. Business Cycles: An Empirical Investigation,”Journal of Money, Credit and Banking,29(1), 1–16
Huggett, M. 1993. “The riskfree rate in heterogenousagent incomplete insuranceeconomies,”Journal of Economic Dynamics and Control,17(56), 953–969
Huggett, M. 1996. “Wealth distribution in lifecycle economiess,”Journal of Monetary Economics,38(3), 469–494
Judd, K. 1998.Numerical Methods in Economics, Cambridge MA: The MIT Press
Krusell, P. and A. Smith.1998. “Incomeand Wealth Heterogeneity in the Macroeconomy,”Journal of Political Economy106(5), 867–896
Marimon, R. and A. Scott (editors). 1999.Computational Methods for the Study of Dynamic Economies, New York, NY: Oxford University Press
Mehra, R. and E. C. Prescott.1985. “Theequity premium:A puzzle,”Journal of Monetary Economics, 15(2), 145–161
Ngai L. R. and C. A. Pissarides.2007. “Structuralchange in a multisector model of growth,”American Economic Review,97(1), 429–443
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Guillaume Vandenbroucke
Econ 645, USC, Spring 2012
Prescott, E. C. 1986. “Theory ahead of business cycle measurement,”Quarterly Review, vol. 10, pp. 9–22, Federal Reserve Bank of Minneapolis
Press, W., S. A. Teukolky, W. T. Vetterling and B. P. Flannery.1992.Numerical Recipes in C, Cambridge: Cambridge University Press (online at http://apps.nrbook.com/c/index.html)
RosRull, J. V. 1995. “Models with heterogeneous agents,” in Cooley (1995)
RosRull, J. V. 1999. “Equilibria in heterogeneousagent models,” in Marimon, R. and A. ScottComputa tional methods for the study of dynamic economies,Oxford University Press, Oxford
Tauchen, G. 1986. “Finite state Markov chain approximations to univariate and vector autoregressions,” Economics Letters,20(2), 177–181
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