Becker Friedman Institute
for Research in Economics
The University of Chicago

Research. Insights. Impact. Advancing the Legacy of Chicago Economics.

machine learning

Automated Economic Reasoning with Quantifier Elimination

Casey Mulligan

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.

Random Projection Estimation of Discrete-Choice Models with Large Choice Sets

Khai X. Chiong, Matthew Shum

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation proceeds using cyclic monotonicity moment inequalities implied by the multinomial choice model; the estimation procedure is semi-parametric and does not require explicit distributional assumptions to be made regarding the random utility errors.