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Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets

Author

Listed:
  • Donald J. Brown

    (Department of Economics, Yale University)

  • Chris Shannon

    (Department of Economics, University of California, Berkeley)

Abstract

This paper studies the extent to which qualitative features of Walrasian equilibria are refutable given a finite data set. In particular, we consider the hypothesis that the observed data are Walrasian equilibria in which each price vector is locally stable under tatonnement. Our main result shows that a finite set of observations of prices, individual incomes and aggregate consumption vectors is rationalizable in an economy with smooth characteristics if and only if it is rationalizable in an economy in which each observed price vector is locally unique and stable under tatonnement. Moreover, the equilibrium correspondence is locally monotone in a neighborhood of each observed equilibrium in these economies. Thus the hypotheses that equilibria are locally stable under tatonnement, equilibrium prices are locally unique and equilibrium comparative statics are locally monotone are not refutable with a finite data set.

Suggested Citation

  • Donald J. Brown & Chris Shannon, 1998. "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets," GE, Growth, Math methods 9802003, University Library of Munich, Germany, revised 02 Mar 1998.
  • Handle: RePEc:wpa:wuwpge:9802003
    Note: LaTex .dvi, This is an version updated Feb 1998.
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    References listed on IDEAS

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    1. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
    2. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-691, May.
    3. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
    4. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-1262, November.
    5. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.
    6. A. P. Kirman & K. J. Koch, 1986. "Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 457-463.
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    Citations

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    Cited by:

    1. Cherchye, L.J.H. & Crawford, I. & de Rock, B. & Vermeulen, F.M.P., 2011. "Aggregation without the Aggravation? Nonparametric Analysis of the Representative Consumer," Discussion Paper 2011-143, Tilburg University, Center for Economic Research.
    2. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2010. "An Afriat Theorem for the collective model of household consumption," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1142-1163, May.
    3. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    4. Laurens CHERCHYE & Bram DE ROCK & Frederic VERMEULEN, 2007. "The revealed preference approach to collective consumption behavior: testing, recovery and welfare analysis," Working Papers Department of Economics ces0724, KU Leuven, Faculty of Economics and Business, Department of Economics.
    5. Chiappori, P. -A. & Ekeland, I. & Kubler, F. & Polemarchakis, H. M., 2004. "Testable implications of general equilibrium theory: a differentiable approach," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 105-119, February.
    6. Laurens Cherchye & Ian Crawford & Bram Rock & Frederic Vermeulen, 2016. "Gorman revisited: nonparametric conditions for exact linear aggregation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(2), pages 203-220, June.
    7. Per Hjertstrand & James Swofford, 2012. "Revealed preference tests for consistency with weakly separable indirect utility," Theory and Decision, Springer, vol. 72(2), pages 245-256, February.
    8. Donald J. Brown, 2014. "Approximate Solutions of the Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income," Cowles Foundation Discussion Papers 1955R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2014.
    9. Carvajal, Andres & Polemarchakis, H.M., 2008. "Identification of Pareto-improving policies: Information as the real invisible hand," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 167-179, January.
    10. Donald J. Brown, 2014. "Approximate Solutions of Walrasian and Gorman Polar Form Equilibrium Inequalities," Cowles Foundation Discussion Papers 1955RR, Cowles Foundation for Research in Economics, Yale University, revised Jan 2015.
    11. Donald J. Brown, 2012. "Notes on Computational Complexity of GE Inequalities," Cowles Foundation Discussion Papers 1865R, Cowles Foundation for Research in Economics, Yale University, revised Aug 2012.
    12. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits Spieksma, 2011. "Heuristics for Deciding Collectively Rational Consumption Behavior," Computational Economics, Springer;Society for Computational Economics, vol. 38(2), pages 173-204, August.
    13. Carvajal, Andres & Ray, Indrajit & Snyder, Susan, 2004. "Equilibrium behavior in markets and games: testable restrictions and identification," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 1-40, February.
    14. Finn Christensen, 2016. "Comparative Statics and Heterogeneity," Working Papers 2016-01, Towson University, Department of Economics, revised Oct 2016.
    15. Donald J. Brown, 2012. "Notes on Computational Complexity of GE Inequalities," Cowles Foundation Discussion Papers 1865, Cowles Foundation for Research in Economics, Yale University.
    16. Donald J. Brown & Ravi Kannan, 2005. "Two Algorithms for Solving the Walrasian Equilibrium Inequalities," Cowles Foundation Discussion Papers 1508R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2006.
    17. Donald J. Brown, 2014. "Approximate Solutions of the Walrasian Equilibrium Inequalities with Bounded Marginal Utilities of Income," Cowles Foundation Discussion Papers 1955, Cowles Foundation for Research in Economics, Yale University.
    18. Laurens Cherchye & Ian Crawford & Bram De Rock & Frederic Vermeulen, 2015. "Revealed Preference and Aggregation," Working Papers ECARES ECARES 2015-08, ULB -- Universite Libre de Bruxelles.
    19. repec:wsi:wsbook:6875 is not listed on IDEAS
    20. Anat Bracha & Donald J. Brown, 2007. "Affective Decision Making: A Behavioral Theory of Choice," Cowles Foundation Discussion Papers 1633R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2009.
    21. Donald J. Brown & Ravi Kannan, 2005. "Decision Methods for Solving Systems of Walrasian Inequalities," Cowles Foundation Discussion Papers 1508, Cowles Foundation for Research in Economics, Yale University.
    22. Bachmann, Ruediger, 2004. "Rationalizing allocation data--a nonparametric Walrasian theory when prices are absent or non-Walrasian," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 271-295, June.
    23. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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