Noise and aggregation of information in competitive rational expectations models ∗ Diego Garc´ ıa † Branko Uroˇ sevi´ c ‡ August 1, 2003 Abstract We study a novel set of competitive equilibria in the standard rational expectations setting (Hellwig (1980)) by taking as a parameter the size of the noise trader demand and assuming that its variance is proportional to N β , where N denotes the number of agents in the economy and β ∈ [0, 2]. We show that when agents’ information acquisition decisions are endogenous, the limiting competitive equilibrium is well-defined and leads to non-trivial information acquisition and partially revealing prices for all β ∈ [0, 2]. Three types of limiting equilibria arise as N →∞: (1) the standard case (see Verrecchia (1982)) is recovered setting β = 2, where a positive fraction of the traders becomes informed; (2) when β ∈ (0, 2), the number of informed traders grows as N β/2 , so the fraction of informed traders is negligible in the limit; (3) when β =0, the number of informed traders is independent of N . The paper provides closed-form solutions for all limiting equilibria, and discusses their different implications. JEL classification : D82, G14. Keywords : partially revealing equilibria, competitive equilibrium, rational expectations, information acquisition. ∗ We would like to thank Andrew Bernard, Peter DeMarzo, Hayne Leland, Rodolfo Prieto, Brett Trueman, and Joel Vanden for comments on an early draft, as well as participants in the Finance and Economics seminar at Dartmouth College. All remaining errors are our own. The latest version of this paper can be downloaded from http://diego-garcia.dartmouth.edu. † Correspondence information: Diego Garc´ ıa, Tuck School of Business Administration, Hanover NH 03755- 9000, US, tel: (603) 646-3615, fax: (603) 646-1308, email: diego.garcia@Dartmouth.edu. ‡ Branko Uroˇ sevi´ c, Department of Economics and Business, Universitat Pompeu Fabra, 08005, Barcelona, Spain, tel: 34 - 935422590, email: branko.urosevic@upf.edu. 1