Dear Economist,
Mathematical techniques and computational experiments have always been tools to complement and interpret data and models.
Quantifier elimination, recognized by Alfred Tarski in the late 1940s as a computable task when working at RAND, was initially considered impractical because of its high complexity (doubly exponentially).
But the task is conceptually quite simple: instead of solving an equation or a system of equations, say x2 + bx + c with respect to x, find the conditions on the parameters b and c such that the solutions for x are always positive (or negative or within a given range).
Quantifier elimination can be an incredibly useful tool. The last decades have brought quantifier elimination from a pie-in-the-sky method to a practical tool. Mathematicians were the first to adapt it, then it was used in quantum theory. Over the last three years, the number of applications in economics has been on the rise.
A recent paper from the National Economic Bureau of Research gives example problems for quantifier elimination and compares the available software products to do the actual computation. The paper concludes:
Of the tools we tried, only Mathematica was able to decide all problems in the benchmark set. In fact all 135 could be tackled by Mathematica [in] less than a minute on a laptop computer, with only three of those taking more than ten seconds, ...And just a few weeks after the aforementioned publication, a preprint was published on the arXiv preprint server that describes a new Mathematica package called TheoryGuru. The package is dedicated to quantifier elimination applications in economics and the social sciences.
We hope this package will be useful for economists. To further foster the use of quantifier elimination, we are offering temporary Mathematica licenses for select researchers in economics and related fields to get you started with the Wolfram Language. If you or your colleagues would be interested in a license, please let us know.
Sincerely,
The Wolfram Publication Watch Team
