Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets
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 tâtonnement. 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 tâtonnement. 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 tâtonnement, equilibrium prices are locally unique and equilibrium comparative statics are locally monotone are not refutable with a ﬁnite data set.
Brown, Donald J. and Shannon, Chris, "Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets" (1998). Cowles Foundation Discussion Papers. 1418.