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The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics

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  • Keyvan Eslami
  • Tom Phelan

Abstract

A recent literature within quantitative macroeconomics has advocated the use of continuous-time methods for dynamic programming problems. In this paper we explore the relative merits of continuous-time and discrete-time methods within the context of stationary and nonstationary income fluctuation problems. For stationary problems in two dimensions, the continuous-time approach is both more stable and typically faster than the discrete-time approach for any given level of accuracy. In contrast, for convex lifecycle problems (in which age or time enters explicitly), simply iterating backwards from the terminal date in discrete time is superior to any continuous-time algorithm. However, we also show that the continuous-time framework can easily incorporate nonconvexities and multiple controls—complications that often require either problem-specific ingenuity or nonlinear root-finding in the discrete-time context. In general, neither approach unequivocally dominates the other, making the choice of one over the other an art, rather than an exact science.

Suggested Citation

  • Keyvan Eslami & Tom Phelan, 2023. "The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics," Working Papers 23-10, Federal Reserve Bank of Cleveland.
    • Handle: RePEc:fip:fedcwq:96110
    DOI: 10.26509/frbc-wp-202310
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    Cited by:

    1. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.

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    More about this item

    Keywords

    Markov Chain Approximation; Dynamic programming; Numerical methods; Income fluctuation problems;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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