Abstract
Suppose that one has a data set consisting of prices and individual endowments for some economy. Brown and Matzkin (Econometrica 64:1249–1262, 1996) have shown that there are conditions that the data have to satisfy, if the observed prices are determined by the competitive equilibrium process, given the observed endowments, when there are no external effects in the economy’s interactions. The results here show that the same conclusion does not apply, in general, if the economy exhibits externalities. On the other hand: (i) some restrictions exist if there exist at least two commodities on which the individuals’ preferences are weakly separable; (ii) although extremely mild, restrictions exist too if one observed individual consumption for the economy that causes the external effects; and (iii) importantly, even if the previous two cases do not apply, restrictions exist when the externalities that exist are in the form of a public good.
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References
Bachmann R.: Rationalizing allocation data: a nonparametric Walrasian theory when prices are absent or Nonwalrasian. J Math Econ 40, 271–295 (2004)
Bachmann R.: Testable implications of Pareto efficiency and individual rationality. Econ Theory 29, 489–504 (2006)
Balasko Y.: The class of aggregate excess demand functions. In: Hildenbrand, W., Mas-Colell, A. (eds) Contributions to Mathematical Economics, In Honor of Gerard Debreu, pp. 47–56. North-Holland, Amsterdam (1986)
Balasko Y.: The equilibrium manifold keeps the memory of individual demand functions. Econ Theory 24, 493–501 (2004)
Balasko, Y., Tvede, M.: Individual preference rankings compatible with prices, income distributions and total resources. Econ Theory (2009, forthcoming)
Blackorby C., Primont D., Russell R.: Duality, Separability and Functional Structure: Theory and Economics Applications. North-Holland, Amsterdam (1978)
Brown D., Matzkin R.: Testable restrictions on the equilibrium manifold. Econometrica 64, 1249–1262 (1996)
Carvajal A.: Testable restrictions on the equilibrium manifold under random preferences. J Math Econ 40, 121–143 (2004a)
Carvajal, A.: Testable restrictions of game theory in games with continuous domains. RHUL Discussion Paper 04/26 (2004b)
Carvajal, A., Riascos, A.: Identification of preferences from market data. Adv Theor Econ 5, art 3 (2005)
Carvajal A., Riascos A.: Identification of individual demands from market data under uncertainty. BE J Theor Econ 8(1 Topics), 1–30 (2008)
Chambers C., Echenique F.: Supermodularity and preferences. J Econ Theory 144(3), 1004–1014 (2009)
Chiappori P.A., Ekeland I., Kübler F., Polemarchakis H.: Testable implications of general equilibrium theory: a differentiable approach. J Math Econ 40, 105–119 (2000)
Chipman J.: An empirical implication of Auspitz–Lieben–Edgeworth–Pareto complementarity. J Econ Theory 14(1), 228–231 (1977)
Debreu G.: Excess demand functions. J Math Econ 1, 15–23 (1974)
Forges F., Minelli E.: Afriat’s theorem for general budgets. J Econ Theory 144(1), 135–145 (2009)
Hansen L., Heckman J.: The empirical foundations of calibration. J Econ Perspectives 10, 87–104 (1996)
Kübler F.: Observable restrictions of general equilibrium with financial markets. J Econ Theory 110, 137–153 (2004)
Kübler, F., Schmedders, K.: Non-parametric counterfactual analysis in dynamic general equilibrium. Econ Theory (2009, forthcoming)
Kübler F., Chiappori P.-A., Ekeland I., Polemarchakis H.: The identification of preferences from equilibrium prices under uncertainty. J Econ Theory 102, 403–420 (2002)
Mantel R.: On the characterization of aggregate excess demand. J Econ Theory 7, 348–353 (1974)
Mas-Colell A.: On the equilibrium price set of an exchange economy. J Math Econ 4, 117–126 (1977)
Matzkin R.: Identification of consumers’ preferences when their choices are unobservable. Econ Theory 25, 423–443 (2005)
Matzkin R., Richter K.: Testing strictly concave rationality. J Econ Theory 58, 287–303 (1991)
Milgrom P., Shannon C.: Monotone comparative statics. Econometrica 62, 157–180 (1994)
Mishra B.: Algorithmic Algebra. Springer, Berlin (1993)
Quah J.: The comparative statics of constrained optimization problems. Econometrica 75(2), 401–431 (2007)
Rockafellar T.: Convex Analysis. Princeton University Press, Princeton (1970)
Snyder S.: Testable restrictions of Pareto optimal public good provision. J Public Econ 71, 97–119 (1999)
Sonnenschein H.: Market excess demand functions. Econometrica 40, 549–563 (1974)
Topkis D.M.: Supermodularity and Complementarity. Princeton University Press, Princeton (1998)
Varian H.: The non-parametric approach to demand analysis. Econometrica 50, 945–972 (1982)
Varian H.: Non-parametric tests of consumer behavior. Rev Econ Stud 50, 99–110 (1983)
Varian H.: The nonparametric approach to production analysis. Econometrica 52, 579–598 (1984)
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Other versions of this paper circulated under the titles “Testable restrictions of general equilibrium theory in exchange economies with externalities” and “On refutability of the Nash–Walras equilibrium hypothesis”. The paper benefited from the advise of Herakles Polemarchakis, and from discussions with Indrajit Ray, Rajiv Vohra, Susan Snyder, Moshe Buchinsky, Felix Kübler, Marcus Berliant, Chris Shannon, John Quah, Tarek Coury, Peter Neary, Jim Malcomson, Martine Quinzii and Nicholas Yannelis, and seminar audiences at several universities and conferences. The comments of two anonymous referees are also gratefully acknowledged.
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Carvajal, A. The testable implications of competitive equilibrium in economies with externalities. Econ Theory 45, 349–378 (2010). https://doi.org/10.1007/s00199-009-0474-9
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DOI: https://doi.org/10.1007/s00199-009-0474-9
Keywords
- Nash–Walras equilibrium
- Externalities
- Public goods
- Testable restrictions
- Empirical implications
- Revealed preferences