The Demand for Information: More Heat than Light
AbstractThis paper produces a comprehensive theory of the value of Bayesian information and its static demand. Our key insight is to assume 'natural units' corresponding to the sample size of conditionally i.i.d. signals -- focusing on the smooth nearby model of the precision of an observation of a Brownian motion with uncertain drift. In a two state world, this produces the heat equation from physics, and leads to a tractable theory. We derive explicit formulas that harmonize the known small and large sample properties of information, and reveal some fundamental properties of demand: (a) Value 'non-concavity': The marginal value of information is initially zero; (b) The marginal value is convex/rising, concave/peaking, then convex/falling; (c) 'Lumpiness': As prices rise, demand suddenly chokes off (drops to 0); (d) The minimum information costs on average exceed 2.5% of the payoff stakes; (e) Information demand is hill-shaped in beliefs, highest when most uncertain; (f) Information demand is initially elastic at interior beliefs; (g) Demand elasticity is globally falling in price, and approaches 0 as prices vanish; and (h) The marginal value vanishes exponentially fast in price, yielding log demand. Our results are exact for the Brownian case, and approximately true for weak discrete informative signals. We prove this with a new Bayesian approximation result.
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Bibliographic InfoPaper provided by Society for Economic Dynamics in its series 2005 Meeting Papers with number 798.
Date of creation: 2005
Date of revision:
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Postal: Society for Economic Dynamics Christian Zimmermann Economic Research Federal Reserve Bank of St. Louis PO Box 442 St. Louis MO 63166-0442 USA
Web page: http://www.EconomicDynamics.org/society.htm
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Value of information; non-concavity; heat equation; demand; Bayesian analysis;
Other versions of this item:
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-01 (All new papers)
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