Making decisions under model misspecification

Excerpts

The consequences of a decision may depend on exogenous contingencies and uncertain outcomes that are outside the control of a decision maker. This uncertainty takes on many forms. Economic applications typically feature risk, where the decision maker knows the correct probabilistic model governing the contingencies but not necessarily the decision outcomes. Yet, this is a demanding assumption. As a result, statisticians and econometricians have long wrestled with how to confront ambiguity over models or unknown parameters within a model. Each model is itself a simplification or an approximation designed to guide or enhance our understanding of some underlying phenomenon of interest. Thus, the model, by its very nature, is misspecified, but in typically uncertain ways. How should a decision maker acknowledge model misspecification in a way that guides the use of purposefully simplified models sensibly? This concern has certainly been on the radar screen of statisticians and control theorists, but it has been largely absent in formal approaches to decision theory.

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The protagonist of our analysis is a decision maker who is able to formulate models – for instance a policy maker having to decide a climate policy based on existing alternative climate models – but is concerned about their misspecification and wants to use a decision criterion which accounts for that. Our axiomatic analysis, which has a normative nature, aims to derive a criterion of this kind to help the decision maker to cope with model misspecification in a principled way.

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Reference

Simone Cerreia-Vioglio, Lars Peter Hansen, Fabio Maccheroni, Massimo Marinacci “Making decisions under model misspecification” (2020) DOI: 10.48550/arXiv.2008.01071 arXiv:2008.01071

@Article{cerreia2020,
  title = {Making decisions under model misspecification},
  author = {Cerreia-Vioglio, Simone and Hansen, Lars Peter and Maccheroni, Fabio and Marinacci, Massimo},
  year = {2020},
  month = {8},
  day = {1},
  doi = {10.48550/arXiv.2008.01071},
  arxiv = {2008.01071},
  url = {https://arxiv.org/abs/2008.01071}
}