Assumptions motivated by either logical or existing theory can be imposed during model estimation to restrict the feasible region of the parameters. The restrictions, implemented as shape constraints, may not provide any benefits in an asymptotic analysis, but will improve the estimator’s finite sample performance. This paper briefly reviews an illustrative set of research on shape constrained estimation in the economics and operations research literature. We highlight the methodological innovations and applications, with a particular emphasis on utility functions, production economics, and sequential decision making applications.
