On the Utility of Models: Bridging the Theoretical and Analytical Sides of Model Selection

Abstract

Scientific inquiry often hinges on selecting models that adequately capture the phenomena under investigation, by employing different strategies and toolkits based on modeling purposes and contexts of analysis. Within this landscape, the theory of model selection has been broadly constructed around two primary focuses. On the one hand, philosophers of science emphasize the conceptual integrity of models (e.g., Grüne-Yanoff and Marchionni, 2018, Tieleman, 2022), that is how well a model’s structure aligns with theoretical frameworks or explanatory aims. On the other hand, econometricians focus on output adequacy measured through criteria such as predictive performance, hypothesis testing, and information criteria (e.g., Hotelling, 1958, Box, 1979, Myung, 2000, Spanos, 2021). Striking a balance between these perspectives remains a central challenge, with both practical and theoretical implications. In fact, while most models are usually scrutinized separately in their theoretical consistency and empirical performance, the prerequisite for enacting the latter vis a vis the former, that is the unambigous distinction among different families of models on the same phenomenon, remains unfulfilled. This paper aims at elucidating such necessary prerequisites and proposes a unified framework for model selection that leverages Utility Theory as the central criterion, integrating both conceptual and statistical evaluations into a single decision-making process. In doing so, the framework relies and enhances the analogical understanding within the field of model theory (Bartha, 2010, Knuuttila and Loettgers, 2017).

Paul Bartha. By Parallel Reasoning: The Construction and Evaluation of Analogical Arguments. Oxford University Press, New York, 2010.

George E.P. Box. Robustness in the Strategy of Scientific Model Building. In Robustness in Statistics, pages 201–236. Elsevier, 1979. doi: 10.1016/B978-0-12-438150-6.50018-2.

Till Grüne-Yanoff and Caterina Marchionni. Modeling model selection in model pluralism. Journal of Economic Methodology, 25(3):265–275, July 2018. doi: 10.1080/1350178X.2018.1488572.

Harold Hotelling. The Statistical Method and the Philosophy of Science. The American Statistician, 12(5):9–14, December 1958. doi: 10.1080/00031305.1958.10482568.

Tarja Knuuttila and Andrea Loettgers. Modelling as Indirect Representation? The Lotka–Volterra Model Revisited. The British Journal for the Philosophy of Science, 68(4):1007–1036, December 2017. doi: 10.1093/bjps/axv055.

In Jae Myung. The Importance of Complexity in Model Selection. Journal of Mathematical Psychology, 44(1):190–204, March 2000. doi: 10.1006/jmps.1999.1283.

Aris Spanos. Philosophy of Econometrics. In The Routledge Handbook of the Philosophy of Economics. Routledge, 2021.

Sebastiaan Tieleman. Model Transfer and Universal Patterns: Lessons from the Yule Process. Synthese, 200(4):267, June 2022. doi: 10.1007/s11229-022-03737-4.

Raffaello Seri

Professor of Econometrics

My research interests include statistics, numerical analysis, operations research, psychology, economics and management.