Quantifier Elimination for Deduction in Econometrics

Casey Mulligan

No 24601, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: When combined with the logical notion of partially interpreted functions, many nonparametric results in econometrics and statistics can be understood as statements about semi-algebraic sets. Tarski’s quantifier elimination (QE) theorem therefore guarantees that a universal algorithm exists for deducing such results from their assumptions. This paper presents the general framework and then applies QE algorithms to Jensen’s inequality, omitted variable bias, partial identification of the classical measurement error model, point identification in discrete choice models, and comparative statics in the nonparametric Roy model. This paper also discusses the computational complexity of real QE and its implementation in software used for program verification, logic, and computer algebra. I expect that automation will become as routine for abstract econometric reasoning as it already is for numerical matrix inversion.

JEL-codes: C01 C63 C65 (search for similar items in EconPapers)
Date: 2018-05
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: LS TWP
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.nber.org/papers/w24601.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:24601

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w24601

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().