The Demand for Information: More Heat than Light
This 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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| Length: | 36 pages |
| Date of creation: | Jan 2005 |
| Publication status: | Published in Journal of Economic Theory (January 2008), 138(1): 21-50 |
| Handle: | RePEc:cwl:cwldpp:1498 |
| Note: | CFP 1258. |
| Contact details of provider: | Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA Phone: (203) 432-3702 Fax: (203) 432-6167 Web page: http://cowles.yale.edu/ More information through EDIRC
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| Order Information: | Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA |
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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