Goodness-of-fit and utility estimation: what's possible and what's not
Abstract
A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit index that is continuous and accurate, where the latter means that a perfect score is obtained if and only if a dataset can be rationalized by a well-behaved utility function. While many standard goodness-of-fit indices are inaccurate we show that these indices are (in a sense we make precise) essentially accurate. Goodness-of-fit indices are typically generated by loss functions and we find that standard loss functions usually do not yield a best-fitting utility function when they are minimized. Nonetheless, welfare comparisons can be made by working out a robust preference relation from the data.
Cite
@article{arxiv.2405.08464,
title = {Goodness-of-fit and utility estimation: what's possible and what's not},
author = {Yujian Chen and Joshua Lanier and John K. -H. Quah},
journal= {arXiv preprint arXiv:2405.08464},
year = {2026}
}