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Index-wise comparative statics

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  • Koch, Caleb M.

Abstract

This paper identifies a necessary and sufficient condition for index-wise comparative statics, which can: (i) establish comparative statics of a single decision without solving the entire model and (ii) enable analysis in settings where substitutability among variables otherwise precludes the use of current comparative statics methods. We prove this result with an extended version of lattice theory. By means of an example, we highlight the advantages as well as disadvantages offered by index-wise comparative statics.

Suggested Citation

  • Koch, Caleb M., 2019. "Index-wise comparative statics," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 35-41.
  • Handle: RePEc:eee:matsoc:v:102:y:2019:i:c:p:35-41
    DOI: 10.1016/j.mathsocsci.2019.09.004
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    1. Natalia Lazzati & John K.-H. Quah & Koji Shirai, 2018. "Nonparametric analysis of monotone choice," Discussion Paper Series 184, School of Economics, Kwansei Gakuin University.
    2. Kelvin Lancaster, 1962. "The Scope of Qualitative Economics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 99-123.
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    4. John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
    5. Michael Kremer, 1993. "The O-Ring Theory of Economic Development," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 551-575.
    6. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 209-227, March.
    7. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    9. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    10. Robert Shimer & Lones Smith, 2000. "Assortative Matching and Search," Econometrica, Econometric Society, vol. 68(2), pages 343-370, March.
    11. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    12. 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.
    13. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    14. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
    15. Natalia Lazzati, 2015. "Treatment response with social interactions: Partial identification via monotone comparative statics," Quantitative Economics, Econometric Society, vol. 6(1), pages 49-83, March.
    16. Christian Gollier, 2011. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1329-1344.
    17. Quirk, James, 1997. "Qualitative comparative statics," Journal of Mathematical Economics, Elsevier, vol. 28(2), pages 127-154, September.
    18. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 439-454.
    19. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    20. , A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
    21. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    22. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    23. Koji Shirai, 2013. "Welfare variations and the comparative statics of demand," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 315-333, June.
    24. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    25. Qingmin Liu & George J. Mailath & Andrew Postlewaite & Larry Samuelson, 2014. "Stable Matching With Incomplete Information," Econometrica, Econometric Society, vol. 82(2), pages 541-587, March.
    26. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    27. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    28. Koji Shirai, 2009. "A generalization of monotone comparative statics: Correction," Economics Bulletin, AccessEcon, vol. 29(1), pages 116-121.
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