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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- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
- Giuseppe Moscarini & Lones Smith, 2002. "The Law of Large Demand for Information," Econometrica, Econometric Society, vol. 70(6), pages 2351-2366, November.
- Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991.
"Information and Timing in Repeated Partnerships,"
Econometric Society, vol. 59(6), pages 1713-33, November.
- Dilip Abreu & Paul Milgrom & David Pearce, 1997. "Information and timing in repeated partnerships," Levine's Working Paper Archive 636, David K. Levine.
- David G. Pearce & Dilip Abreu & Paul R. Milgrom, 1988. "Information and Timing in Repeated Partnerships," Cowles Foundation Discussion Papers 875, Cowles Foundation for Research in Economics, Yale University.
- Kihlstrom, Richard E, 1974. "A Bayesian Model of Demand for Information About Product Quality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 99-118, February.
- Chade, Hector & Schlee, Edward, 2002. "Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information," Journal of Economic Theory, Elsevier, vol. 107(2), pages 421-452, December.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Gryglewicz, Sebastian, 2011. "A theory of corporate financial decisions with liquidity and solvency concerns," Journal of Financial Economics, Elsevier, vol. 99(2), pages 365-384, February.
- Fogli, Alessandra & Veldkamp, Laura, 2007.
"Nature or Nurture? Learning and Female Labour Force Dynamics,"
CEPR Discussion Papers
6324, C.E.P.R. Discussion Papers.
- Laura Veldkamp & Alessandra Fogli, 2007. "Nature or Nurture? Learning and Female Labor Force Dynamics," 2007 Meeting Papers 1021, Society for Economic Dynamics.
- Alessandra Fogli & Laura Veldkamp, 2007. "Nature or nurture? learning and female labor force dynamics," Staff Report 386, Federal Reserve Bank of Minneapolis.
- Luis Cabral, 2007. "Lock in and Switch: Asymmetric Information and New Product Diffusion," Working Papers 07-11, New York University, Leonard N. Stern School of Business, Department of Economics.
- Axel Anderson & Lones Smith, 2013. "Dynamic Deception," American Economic Review, American Economic Association, vol. 103(7), pages 2811-47, December.
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