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Non-linear Real Arithmetic Benchmarks derived from Automated Reasoning in Economics

Author

Listed:
  • Casey B. Mulligan
  • Russell Bradford
  • James H. Davenport
  • Matthew England
  • Zak Tonks

Abstract

We consider problems originating in economics that may be solved automatically using mathematical software. We present and make freely available a new benchmark set of such problems. The problems have been shown to fall within the framework of non-linear real arithmetic, and so are in theory soluble via Quantifier Elimination (QE) technology as usually implemented in computer algebra systems. Further, they all can be phrased in prenex normal form with only existential quantifiers and so are also admissible to those Satisfiability Module Theory (SMT) solvers that support the QF_NRA logic. There is a great body of work considering QE and SMT application in science and engineering, but we demonstrate here that there is potential for this technology also in the social sciences.

Suggested Citation

  • Casey B. Mulligan & Russell Bradford & James H. Davenport & Matthew England & Zak Tonks, 2018. "Non-linear Real Arithmetic Benchmarks derived from Automated Reasoning in Economics," NBER Working Papers 24602, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:24602
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    References listed on IDEAS

    as
    1. Mulligan, Casey B., 2012. "The Redistribution Recession: How Labor Market Distortions Contracted the Economy," OUP Catalogue, Oxford University Press, number 9780199942213, Decembrie.
    2. Charles Steinhorn, 2008. "Tame Topology and O-Minimal Structures," Lecture Notes in Economics and Mathematical Systems, in: Computational Aspects of General Equilibrium Theory, pages 165-191, Springer.
    3. Li, Xiaoliang & Wang, Dongming, 2014. "Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 48-58.
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    Cited by:

    1. Casey B. Mulligan, 2018. "Quantifier Elimination for Deduction in Econometrics," NBER Working Papers 24601, National Bureau of Economic Research, Inc.

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    More about this item

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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