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Numerical Methods for Macroeconomists

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Abstract

This primer will cover some of the numerical methods that are used in modern macroeconomics. You will learn how to: (1) solve nonlinear equations via bisection and Newton's method; (2) compute maximization problems via golden section search, discretization, and the particle swarm algorithm; (3) simulate difference equations using the extended path and multiple shooting algorithms; (4) differentiate and integrate functions numerically; (5) conduct Monte Carlo simulations by drawing random variables; (6) construct Markov chains; (7) interpolate functions and smooth data; (8) compute dynamic programming problems; (9) solve for policy functions using the Coleman, endogenous grid, and parameterized expectation algorithms; (10) study the Aiyagari heterogeneous agent model with and without aggregate uncertainty. This will be done while studying economic problems, such as the determination of labor supply, economic growth, and business cycle analysis. Calculus is an integral part of the primer and some elementary probability theory will be drawn upon. The MATLAB programming language will be used. It is time to move into the modern age and learn these techniques. Besides, using computers to solve economic models is fun. The primer is self contained so little prior knowledge is required. This is work in progress. Comments are welcome.

Suggested Citation

  • Jeremy Greenwood & Ricardo Marto, 2022. "Numerical Methods for Macroeconomists," Economie d'Avant Garde Research Reports 36, Economie d'Avant Garde.
    • Handle: RePEc:eag:rereps:36
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    File URL: http://www.jeremygreenwood.net/Book/NM4M.pdf
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    References listed on IDEAS

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    1. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    2. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    3. Jeremy Greenwood & Karen A. Kopecky, 2013. "Measuring The Welfare Gain From Personal Computers," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 336-347, January.
    4. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2011. "Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models," Quantitative Economics, Econometric Society, vol. 2(2), pages 173-210, July.
    5. Boppart, Timo & Krusell, Per & Mitman, Kurt, 2018. "Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
    6. J. R. Hicks, 1941. "The Rehabilitation of Consumers' Surplus," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 8(2), pages 108-116.
    7. Gary D. Hansen & Edward C. Prescott, 2002. "Malthus to Solow," American Economic Review, American Economic Association, vol. 92(4), pages 1205-1217, September.
    8. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    9. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
    10. Greenwood, Jeremy & Hercowitz, Zvi & Huffman, Gregory W, 1988. "Investment, Capacity Utilization, and the Real Business Cycle," American Economic Review, American Economic Association, vol. 78(3), pages 402-417, June.
    11. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
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    More about this item

    Keywords

    Aiyagari model; calibration; Coleman algorithm; difference equations; dynamic programming; endogenous grid method; interpolating functions; linearization; Markov chains; maximization problems; Monte Carlo simulation; nonlinear equations; numerical differentiation and integration; parameterized expectations; random number generation;
    All these keywords.

    JEL classification:

    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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