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Testing the Validity of a Demand Model: An Operations Perspective

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
obesbes{at}wharton.upenn.edu
robert.phillips{at}nomissolutions.com
assaf{at}gsb.columbia.edu

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.

Key Words: pricing; parametric and nonparametric estimation; model misspecification; hypothesis testing; goodness-of-fit test; asymptotic analysis; performance analysis
History: Received: June 4, 2008; accepted: February 27, 2009.