Testing the Validity of a Demand Model: An Operations Perspective

  • Authors:
  • Omar Besbes;Robert Phillips;Assaf Zeevi

  • Affiliations:
  • The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104;Nomis Solutions, San Bruno, California 94066, and Graduate School of Business, Columbia University, New York, New York 10027;Graduate School of Business, Columbia University, New York, New York 10027

  • Venue:
  • Manufacturing & Service Operations Management
  • Year:
  • 2010

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Abstract

The fields of statistics and econometrics have developed powerful methods for testing the validity (specification) of a model based on its fit to underlying data. Unlike statisticians, managers are typically more interested in the performance of a decision rather than the statistical validity of the underlying model. We propose a framework and a statistical test that incorporate decision performance into a measure of statistical validity. Under general conditions on the objective function, asymptotic behavior of our test admits a sharp and simple characterization. We develop our approach in a revenue management setting and apply the test to a data set used to optimize prices for consumer loans. We show that traditional model-based goodness-of-fit tests may consistently reject simple parametric models of consumer response (e.g., the ubiquitous logit model), while at the same time these models may “pass” the proposed performance-based test. Such situations arise when decisions derived from a postulated (and possibly incorrect) model generate results that cannot be distinguished statistically from the best achievable performance---i.e., when demand relationships are fully known.