Risk, Ambiguity, and Misspecification: Decision Theory, Robust Control, and Statistics

34 Pages Posted: 29 Nov 2022 Last revised: 22 Jun 2023

See all articles by Lars Peter Hansen

Lars Peter Hansen

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER)

Thomas J. Sargent

New York University (NYU) - Department of Economics, Leonard N. Stern School of Business; National Bureau of Economic Research (NBER)

Date Written: June 13, 2023

Abstract

What are “deep uncertainties” and how should their presence alter prudent courses of action? To help answer these questions, we bring ideas from robust control theory into statistical decision theory. Decision theory in economics has its origins in axiomatic formulations by von Neumann and Morgenstern as well as the statisticians Wald and Savage. Since Savage’s fundamental work, economists have provided alternative axioms that formalize a notion of ambiguity aversion. Meanwhile, control theorists created another way to construct decision rules that are robust to potential model misspecifications. We reinterpret axiomatic foundations of some modern decision theories to include ambiguity about a prior to put on a family of models simultaneously with concerns about misspecifications of the corresponding likelihood functions. By building on ideas from dynamic programming, our representations have recursive structures that preserve dynamic consistency.

Keywords: Variational preferences, statistical divergence, relative entropy, prior, likelihood, ambiguity, misspecification

JEL Classification: C10,C14,C18

Suggested Citation

Hansen, Lars Peter and Sargent, Thomas J., Risk, Ambiguity, and Misspecification: Decision Theory, Robust Control, and Statistics (June 13, 2023). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2022-157, Available at SSRN: https://ssrn.com/abstract=4287610 or http://dx.doi.org/10.2139/ssrn.4287610

Lars Peter Hansen (Contact Author)

University of Chicago - Department of Economics ( email )

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Thomas J. Sargent

New York University (NYU) - Department of Economics, Leonard N. Stern School of Business ( email )

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National Bureau of Economic Research (NBER)

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