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Automated Economic Reasoning with Quantifier Elimination

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  • Casey B. Mulligan

Abstract

Many theorems in economics can be proven (and hypotheses shown to be false) with “quantifier elimination.” Results from real algebraic geometry such as Tarski’s quantifier elimination theorem and Collins’ cylindrical algebraic decomposition algorithm are applicable because the economic hypotheses, especially those that leave functional forms unspecified, can be represented as systems of multivariate polynomial (sic) equalities and inequalities. The symbolic proof or refutation of economic hypotheses can therefore be achieved with an automated technique that involves no approximation and requires no problem-specific information beyond the statement of the hypothesis itself. This paper also discusses the computational complexity of this kind of automated economic reasoning, its implementation with Mathematica and REDLOG software, and offers several examples familiar from economic theory.

Suggested Citation

  • Casey B. Mulligan, 2016. "Automated Economic Reasoning with Quantifier Elimination," NBER Working Papers 22922, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:22922
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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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