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The Wald Problem and the Equivalence of Sequential Sampling and Static Information Costs

10 Pages Posted: 23 Jun 2017 Last revised: 15 Sep 2017

Stephen Morris

Princeton University - Department of Economics

Philipp Strack

University of California, Berkeley - Department of Economics

Date Written: September 6, 2017

Abstract

We consider the sequential sampling problem of Wald (1945). The static cost of attaining any experiment is equal to the expectation of the log likelihood ratio. This equivalence between sequential sampling generalizes to settings where the flow cost depends on the current posterior. The induced cost of any sampling strategy can be represented as a posterior separable cost function. Conversely any posterior separable cost function corresponds to some sequential sampling model with posterior dependent flow cost. As a special case we obtain that Entropy cost (Sims, 2010) corresponds to a flow cost which vanishes when the agent is close to certain about the state.

Keywords: Sequential Sampling, Entropy Cost, Information Acquisition

JEL Classification: D83, C1

Suggested Citation

Morris, Stephen and Strack, Philipp, The Wald Problem and the Equivalence of Sequential Sampling and Static Information Costs (September 6, 2017). Available at SSRN: https://ssrn.com/abstract=2991567

Stephen Edward Morris (Contact Author)

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

Philipp Strack

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

HOME PAGE: http://philippstrack.com

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