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Monotone Comparative Statics Under Uncertainty

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  • Athey, Susan

Abstract

This paper analyzes monotone comparative statics predictions in several classes of stochastic optimization problems. The main results characterize necessary and sufficient conditions for comparative statics predictions to hold based on properties of primitive functions, that is, utility functions and probability distributions. The results apply when the primitives satisfy one of the following two properties: (i) a single-crossing property, which arises in applications such as portfolio investment problems and auctions, or (ii) log-supermodularity, which arises in the analysis of demand functions, affiliated random variables, stochastic orders, and orders over risk aversion.

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  • Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
    • Handle: RePEc:hrv:faseco:3372263
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    1. Leonid Kogan & Stephen A. Ross & Jiang Wang & Mark M. Westerfield, 2006. "The Price Impact and Survival of Irrational Traders," Journal of Finance, American Finance Association, vol. 61(1), pages 195-229, February.
    2. Ormiston Michael B. & Schlee Edward E., 1993. "Comparative Statics under Uncertainty for a Class of Economic Agents," Journal of Economic Theory, Elsevier, vol. 61(2), pages 412-422, December.
    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. Meyer, Jack & Ormiston, Michael B, 1989. "Deterministic Transformations of Random Variables and the Comparative Statics of Risk," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 179-188, June.
    5. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    6. Ormiston, Michael B, 1992. "First and Second Degree Transformations and Comparative Statics under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 33-44, February.
    7. B. H. Strulovici & T. A. Weber, 2008. "Monotone Comparative Statics: Geometric Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 641-673, June.
    8. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    9. Jutta Roosen & David A. Hennessy, 2003. "Tests for the Role of Risk Aversion on Input Use," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(1), pages 30-43.
    10. Robert Chambers & J. Quiggin, 2008. "Comparative statics for state-contingent technologies," Journal of Economics, Springer, vol. 93(2), pages 203-214, March.
    11. Sandmo, Agnar, 1971. "On the Theory of the Competitive Firm under Price Uncertainty," American Economic Review, American Economic Association, vol. 61(1), pages 65-73, March.
    12. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
    13. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
    14. 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.
    15. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    16. Alexander E. Saak, 2003. "Spatial and Temporal Marketing Considerations under Marketing Loan Programs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 872-887.
    17. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    18. Eeckhoudt, Louis & Gollier, Christian, 1995. "Demand for Risky Assets and the Monotone Probability Ratio Order," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 113-122, September.
    19. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    20. Ormiston, Michael B. & Schlee, Edward E., 1992. "Necessary conditions for comparative statics under uncertainty," Economics Letters, Elsevier, vol. 40(4), pages 429-434, December.
    21. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    22. Pratt, John W, 1988. "Aversion to One Risk in the Presence of Others," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 395-413, December.
    23. Landsberger, Michael & Meilijson, Isaac, 1990. "Demand for risky financial assets: A portfolio analysis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 204-213, February.
    24. 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.
    25. Ignacio Esponda, 2008. "Behavioral Equilibrium in Economies with Adverse Selection," American Economic Review, American Economic Association, vol. 98(4), pages 1269-1291, September.
    26. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
    27. Christian Gollier, 2007. "Whom should we believe? Aggregation of heterogeneous beliefs," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 107-127, October.
    28. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    29. Meyer, Jack & Ormiston, Michael B., 1983. "The comparative statics of cumulative distribution function changes for the class of risk averse agents," Journal of Economic Theory, Elsevier, vol. 31(1), pages 153-169, October.
    30. Jewitt, Ian, 1986. "A note on comparative statics and stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 249-254, June.
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