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Wald Revisited: The Optimal Level of Experimentation

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Abstract

This paper revisits Wald's (1947) sequential experimentation paradigm, now assuming that an impatient decision maker can run variable-size experiments each period at some increasing and strictly convex cost before finally choosing an irreversible action. We translate this natural discrete time experimentation story into a tractable control of variance for a continuous time diffusion. Here we robustly characterize the optimal experimentation level: It is rising in the confidence about the project outcome, and for not very convex cost functions, the random process of experimentation levels has a positive drift over time. We also explore several parametric shifts unique to our framework. Among them, we discover what is arguably an 'anti-folk' result: Where the experimentation level is positive, it is often higher for a more impatient decision maker. This paper more generally suggests that a long-sought economic paradigm that delivers a sensible law of demand for information is our dynamic one namely, allowing the decision maker an eternal repurchase (resample) option.

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File URL: http://cowles.econ.yale.edu/P/cd/d11b/d1176.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1176.

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Length: 37 pages
Date of creation: May 1998
Date of revision:
Publication status: Published in Econometrica (November 2001), 69(6): 1629-1644
Handle: RePEc:cwl:cwldpp:1176

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Learning; experimentation; sequential analysis; R&D;

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  1. repec:cup:etheor:v:9:y:1993:i:3:p:431-50 is not listed on IDEAS
  2. Dutta, Prajit K., 1997. "Optimal management of an R&D budget," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 21(2-3), pages 575-602.
  3. Godfrey Keller & Sven Rady, 1998. "Optimal Experimentation in a Changing Environment," Game Theory and Information, EconWPA 9801001, EconWPA.
  4. McLennan, Andrew, 1984. "Price dispersion and incomplete learning in the long run," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 7(3), pages 331-347, September.
  5. Joseph Dimasi & Henry Grabowski & John Vernon, 1995. "R&D Costs, Innovative Output and Firm Size in the Pharmaceutical Industry," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 2(2), pages 201-219.
  6. Patrick Bolton & Christopher Harris, 1999. "Strategic Experimentation," Econometrica, Econometric Society, Econometric Society, vol. 67(2), pages 349-374, March.
  7. Cressie, Noel & Morgan, Peter B., 1993. "The VPRT: A Sequential Testing Procedure Dominating the SPRT," Econometric Theory, Cambridge University Press, vol. 9(03), pages 431-450, June.
  8. Trefler, Daniel, 1993. "The Ignorant Monopolist: Optimal Learning with Endogenous Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(3), pages 565-81, August.
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Cited by:
  1. Rauch, J E & Watson, Joel, 1999. "Starting Small in an Unfamiliar Environment," University of California at San Diego, Economics Working Paper Series qt4rp145hc, Department of Economics, UC San Diego.
  2. Hector Chade & Edward E. Schlee, 2000. "Increasing Returns in the Value of Information," Econometric Society World Congress 2000 Contributed Papers 1715, Econometric Society.
  3. Cristina Mitaritonna & Zhanar Akhmetova, 2013. "A Model of Firm Experimentation under Demand Uncertainty: an Application to Multi-Destination Exporters," Working Papers 2013-10, CEPII research center.

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