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Goodness-of-fit and utility estimation: what's possible and what's not

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  • Joshua Lanier
  • John K. -H. Quah

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.

Suggested Citation

  • Joshua Lanier & John K. -H. Quah, 2024. "Goodness-of-fit and utility estimation: what's possible and what's not," Papers 2405.08464, arXiv.org.
  • Handle: RePEc:arx:papers:2405.08464
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    References listed on IDEAS

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