The Demand for Information: More Heat than Light

37 Pages Posted: 24 Feb 2005

See all articles by Jussi Keppo

Jussi Keppo

National University of Singapore - NUS Business School

Giuseppe Moscarini

Cowles Foundation for Research in Economics; Yale University - Department of Economics

Lones Smith

University of Wisconsin at Madison - Department of Economics

Date Written: January 2005

Abstract

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.

Keywords: Value of information, Non-concavity, Heat equation, Demand, Bayesian analysis

JEL Classification: D81, D83

Suggested Citation

Keppo, Jussi and Moscarini, Giuseppe and Smith, Lones, The Demand for Information: More Heat than Light (January 2005). Cowles Foundation Discussion Paper No. 1498. Available at SSRN: https://ssrn.com/abstract=671743

Jussi Keppo

National University of Singapore - NUS Business School ( email )

1 Business Link
Singapore, 117592
Singapore

Giuseppe Moscarini (Contact Author)

Cowles Foundation for Research in Economics ( email )

Box 208281
New Haven, CT 06520-8281
United States

HOME PAGE: http://economics.yale.edu/people/giuseppe-moscarini

Yale University - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3596 (Phone)

HOME PAGE: http://www.econ.yale.edu/~mosca/mosca.html

Lones Smith

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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