IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v138y2008i1p21-50.html
   My bibliography  Save this article

The demand for information: More heat than light

Author

Listed:
  • Keppo, Jussi
  • Moscarini, Giuseppe
  • Smith, Lones

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Keppo, Jussi & Moscarini, Giuseppe & Smith, Lones, 2008. "The demand for information: More heat than light," Journal of Economic Theory, Elsevier, vol. 138(1), pages 21-50, January.
    • Handle: RePEc:eee:jetheo:v:138:y:2008:i:1:p:21-50
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(07)00059-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-1733, November.
    2. Giuseppe Moscarini & Lones Smith, 2001. "The Optimal Level of Experimentation," Econometrica, Econometric Society, vol. 69(6), pages 1629-1644, November.
    3. Giuseppe Moscarini & Lones Smith, 2002. "The Law of Large Demand for Information," Econometrica, Econometric Society, vol. 70(6), pages 2351-2366, November.
    4. 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.
    5. 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.
    6. 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.
    7. 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 637-654, May-June.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessandra Fogli & Laura Veldkamp, 2007. "Nature or nurture? learning and female labor force dynamics," Staff Report 386, Federal Reserve Bank of Minneapolis.
    2. Jae Wook Kim & Jin Hwa Rhee & Chul Hung Park, 2024. "How Does Digital Transformation Improve Supply Chain Performance: A Manufacturer’s Perspective," Sustainability, MDPI, vol. 16(7), pages 1-16, April.
    3. Azevedo, Eduardo M. & Mao, David & Montiel Olea, José Luis & Velez, Amilcar, 2023. "The A/B testing problem with Gaussian priors," Journal of Economic Theory, Elsevier, vol. 210(C).
    4. Michael Jong Kim, 2020. "Variance Regularization in Sequential Bayesian Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 966-992, August.
    5. Dai, Min & Huang, Shan & Keppo, Jussi, 2019. "Opaque bank assets and optimal equity capital," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 369-394.
    6. Hoffmann, Florian & Inderst, Roman & Turlo, Sergey, 2018. "Regulating Cancellation Rights with Consumer Experimentation," EconStor Preprints 253659, ZBW - Leibniz Information Centre for Economics.
    7. Jeffrey L. Hoopes & Daniel H. Reck & Joel Slemrod, 2015. "Taxpayer Search for Information: Implications for Rational Attention," American Economic Journal: Economic Policy, American Economic Association, vol. 7(3), pages 177-208, August.
    8. Axel Anderson & Lones Smith, 2013. "Dynamic Deception," American Economic Review, American Economic Association, vol. 103(7), pages 2811-2847, December.
    9. 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.
    10. Heyen, Daniel & Goeschl, Timo & Wiesenfarth , Boris, 2015. "Risk Assessment under Ambiguity: Precautionary Learning vs. Research Pessimism," Working Papers 0605, University of Heidelberg, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    2. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Papers (Old Series) 9201, Federal Reserve Bank of Cleveland.
    3. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, February.
    4. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    5. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    6. repec:uts:finphd:40 is not listed on IDEAS
    7. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    8. A Craig Burnside & Jeremy J Graveline, 2020. "On the Asset Market View of Exchange Rates," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 239-260.
    9. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    10. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    11. Elyès Jouini & Clotilde Napp, 1998. "Contiuous Time Equilibrium Pricing of Nonredundant Assets," Working Papers 98-30, Center for Research in Economics and Statistics.
    12. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    13. Bibinger, Markus & Mykland, Per A., 2013. "Inference for multi-dimensional high-frequency data: Equivalence of methods, central limit theorems, and an application to conditional independence testing," SFB 649 Discussion Papers 2013-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    15. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    16. Melenberg, B. & Werker, B.J.M., 1996. "On the Pricing of Options in Incomplete Markets," Discussion Paper 1996-19, Tilburg University, Center for Economic Research.
    17. El-Khatib, Youssef & Goutte, Stephane & Makumbe, Zororo S. & Vives, Josep, 2023. "A hybrid stochastic volatility model in a Lévy market," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 220-235.
    18. Wilhelm, Jochen, 2000. "Das Gaußsche Zinsstrukturmodell: Eine Analyse auf der Basis von Wahrscheinlichkeitsverteilungen," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 6, University of Passau, Faculty of Business and Economics.
    19. Brisset, Nicolas, 2017. "On Performativity: Option Theory And The Resistance Of Financial Phenomena," Journal of the History of Economic Thought, Cambridge University Press, vol. 39(4), pages 549-569, December.
    20. N. S. Gonchar, 2020. "Derivatives Pricing in Non-Arbitrage Market," Papers 2010.13630, arXiv.org.
    21. Jouini, Elyes & Kallal, Hedi & Napp, Clotilde, 2001. "Arbitrage and viability in securities markets with fixed trading costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 197-221, April.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:138:y:2008:i:1:p:21-50. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.