Statistical Decisions under Ambiguity: An Axiomatic Analysis

Consider a decision maker who faces a number of possible models of the world. Every model generates objective probabilities, but no probabilities of models are given. Applications of this framework include statistical decision making with model uncertainty, e.g. due to concerns for misspecification, or Robust Bayesian decision analysis. I characterize a number of decision rules including Bayesianism, maximin expected utility, minimax expected regret, and the Hurwicz criterion. The main contributions are the unified axiomatization of many rules in a framework tailored to statistical decision making, an axiomatic system that relaxes transitivity as well as menu-independence of preferences, and the introduction of several new decision criteria. JEL classification codes: C44, D81. ∗I am greatly indebted to Peter Klibanoff and Chuck Manski for their comments, suggestions, and corrections. I am also grateful to Kim Border and Itai Sher for helpful discussions. Of course, all errors are mine. Financial support through the Robert Eisner Memorial Fellowship, Department of Economics, Northwestern University, as well as a Dissertation Year Fellowship, The Graduate School, Northwestern University, is gratefully acknowledged. Address: Jörg Stoye, Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208-2600, [email protected].