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Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity

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Abstract

This paper develops necessary and sufficient conditions for monotone comparative statics predictions in several general classes of stochastic optimization problems. There are two main results, where the first pertains to single crossing properties (of marginal returns, incremental returns, and indifference curves) in stochastic problems with a single random variable, and the second class involves log-supermodularity of functions with multiple random variables (where log-supermodularity of a density corresponds to the property affiliation from auction theory).

Suggested Citation

  • Athey, S, 1996. "Comparative Statics under Uncertainty : Single Crossing Properties and Log-Supermodularity," Working papers 96-22, Massachusetts Institute of Technology (MIT), Department of Economics.
    • Handle: RePEc:mit:worpap:96-22
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    Citations

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    Cited by:

    1. Lones Smith, 2000. "Private Information and Trade Timing," American Economic Review, American Economic Association, vol. 90(4), pages 1012-1018, September.
    2. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    3. Mathias Dewatripont & Patrick Legros & Steven A. Matthews, 2003. "Moral Hazard and Capital Structure Dynamics," Journal of the European Economic Association, MIT Press, vol. 1(4), pages 890-930, June.
    4. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
    5. Susan Athey & Scott Stern, 1998. "An Empirical Framework for Testing Theories About Complimentarity in Organizational Design," NBER Working Papers 6600, National Bureau of Economic Research, Inc.
    6. Szkup, Michal, 2017. "Preventing Self-fulfilling debt crises," MPRA Paper 82754, University Library of Munich, Germany.
    7. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    8. Arthur Snow, 2000. "LeChatelier Effects for the Competitive Firm under Price Uncertainty," Southern Economic Journal, John Wiley & Sons, vol. 66(3), pages 715-728, January.
    9. Michal Szkup, 2015. "Preventing Self-Fulfilling Crises," 2015 Meeting Papers 1144, Society for Economic Dynamics.
    10. Ghossoub, Mario, 2010. "Supplement to "Belief heterogeneity in the Arrow-Borch-Raviv insurance model"," MPRA Paper 37717, University Library of Munich, Germany, revised 22 Mar 2012.
    11. Hennessy, David A., 1997. "The short- and long-run comparative statics of uncertainty," Economics Letters, Elsevier, vol. 55(3), pages 347-353, September.
    12. Michal Szkup, 2022. "Preventing Self-Fulfilling Debt Crises: A Global Games Approach," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 22-55, January.
    13. Troyan, Peter, 2017. "Collusion and signaling in auctions with interdependent values," Journal of Economic Theory, Elsevier, vol. 170(C), pages 319-345.
    14. Jorge Ibarra-Salazar, 2005. "The Newsboy Model: Changes in Risk and Price," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 30(1), pages 99-109, June.
    15. Athey, Susan. & Stern, Scott, 1969-, 1998. "An empirical framework for testing theories about complementarity in orgaziational design," Working papers WP 4022-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    16. Saak, Alexander E. & Hennessy, David A., 2001. "Location, Land Quality, And Rental Volatility," 2001 Annual meeting, August 5-8, Chicago, IL 20747, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. McAdams, David, 2002. "Isotone Equilibrium in Games of Incomplete Information," Working papers 4248-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    18. Steven Matthews, 2002. "Moral Hazard and Capital Structure Dynamics (joint with Mathias Dewatripont and Patrick Legros) Note the special time," Theory workshop papers 357966000000000095, UCLA Department of Economics.

    More about this item

    Keywords

    STATISTICS ; DECISION MAKING ; RISK ; UNCERTAINTY;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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