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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 t�tonnement. 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 t�tonnement. 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 t�tonnement, equilibrium prices are locally unique and equilibrium comparative statics are locally monotone are not refutable with a finite data set.

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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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  1. 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.
  2. John K.-H. Quah, 2000. "The Monotonicity of Individual and Market Demand," Econometrica, Econometric Society, vol. 68(4), pages 911-930, July.
  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. Kirman, A P & Koch, K J, 1986. "Market Excess Demand in Exchange Economies with Identical Preferences and Collinear Endowments," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 457-63, July.
  5. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  6. 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.
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Cited by:
  1. 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.
  2. 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.
  3. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2008. "An Afriat Theorem for the collective model of household consumption," Center for Economic Studies - Discussion papers ces0825, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  4. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jeroen Sabbe & Frits C.R. Spieksma, 2008. "Heuristics for deciding collectively rational consumption behavior," Center for Economic Studies - Discussion papers ces0824, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  5. Donald J. Brown, 2012. "Notes on Computational Complexity of GE Inequalities," Cowles Foundation Discussion Papers 1865, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Anat Bracha & Donald J Brown, 2007. "Affective Decision Making: a Behavioral Theory of Choice," Levine's Bibliography 122247000000001676, UCLA Department of Economics.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Donald J. Brown & Ravi Kannan, 2006. "Two Algorithms for Solving the Walrasian Equilibrium Inequalities," Working Papers 945, Economic Growth Center, Yale University.

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