Identification and Statistical Decision Theory
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Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis aims to place an informative upper bound on what may be learned about population parameters of interest with specified sample data. Statistical decision theory has studied decision making with sample data without reference to identification. This paper asks if and how identification analysis is useful to statistical decision theory. I show that the answer is positive and simple when the relevant parameter (true state of nature) is point identified. However, a subtlety arises when the true state is partially identified, and a decision must be made under ambiguity. Then the performance of some criteria, particularly minimax regret, is enhanced by permitting randomized choice of an action, which essentially requires availability of sample data. I show that an informative upper bound on the performance of decision making holds when the knowledge assumed in identification analysis is combined with sample data enabling randomized choice. I emphasize that using sample data to randomize choice is conceptually distinct from its traditional econometric use to infer population parameters.
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