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Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets

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  • Donald J. Brown
  • Chris Shannon

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.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 68 (2000)
Issue (Month): 6 (November)
Pages: 1529-1540
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Handle: RePEc:ecm:emetrp:v:68:y:2000:i:6:p:1529-1540

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References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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 687-91, May.
  3. 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.
  4. 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.
  5. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
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Cited by:
  1. Nobibon, Fabrice T. & Cherchye, Laurens & De Rock, Bram & Sabbe, Jeroen & Spieksma, Frits C.R., 2008. "Heuristics for deciding collectively rational consumption behavior," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/198271, Katholieke Universiteit Leuven.
  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. Laurens CHERCHYE & Bram DE ROCK & Frederic VERMEULEN, 2007. "The revealed preference approach to collective consumption behavior: testing, recovery and welfare analysis," Center for Economic Studies - Discussion papers ces0724, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  4. P.A. Chiappori & I. Ekeland & F. Kubler & H.M. Polemarchakis, 2002. "Testable Implications of General Equilibrium Theory: a differentiable approach," Working Papers 2002-10, Brown University, Department of Economics.
  5. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2011. "Revealed preference tests for weak separability: an integer programming approach," Center for Economic Studies - Discussion papers ces11.25, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  6. 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.
  7. Anat Bracha & Donald J Brown, 2007. "Affective Decision Making: a Behavioral Theory of Choice," Levine's Bibliography 122247000000001676, UCLA Department of Economics.
  8. 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.
  9. Anat Bracha & Donald J. Brown, 2007. "Affective Decision Making: A Behavioral Theory of Choice," Cowles Foundation Discussion Papers 1633, Cowles Foundation for Research in Economics, Yale University.
  10. 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.

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