Aggregation, Determinacy, and Informational Efficiency for a Class of Economies with Asymmetric Information☆

Abstract We identify and analyze a class of economies with asymmetric information that we call quasi-complete. For quasi-complete economies we determine equilibrium trades, show that the set of fully informative equilibria is a singleton, and give necessary and sufficient conditions for the existence of partially informative equilibria. Besides unifying some familiar settings, such as those of Grossman (1976) and Milgrom and Stokey (1982), the following new results are proved: (a) The same restrictions that deliver Gorman aggregation under symmetric information are sufficient for Gorman aggregation under asymmetric information, even under partially informative prices; (b) the traditional assumptions of quadratic utilities and endowment spanning that result in the CAPM under symmetric information deliver a conditional CAPM under asymmetric information with prices that need not be fully informative; (c) the linear equilibrium in Grossman's (1976) model is the only equilibrium (linear or not), while minor changes in the normality assumptions result in indeterminacy and partially informative equilibria; and (d) if there is no aggregate endowment risk, asymmetrically informed agents with common priors sell the risky part of their endowment in every equilibrium. Journal of Economic Literature Classification Numbers: D82; G14; C62.

[1]  Lawrence M. Ausubel.  Partially-Revealing Rational Expectations Equi-librium in a Competitive Economy , 1990 .

[2]  F. Milne.  Consumer Preferences, Linear Demand Functions and Aggregation in Competitive Asset Markets , 1979 .

[3]  Roy Radner,et al.  Rational expectations in microeconomic models: An overview , 1982 .

[4]  Younes Yves,et al.  On the theory of incomplete markets , 1987 .

[5]  Nicholas C. Yannelis,et al.  Efficiency and incentive compatibility in differential information economies , 1997 .

[6]  Robert A. Pollak,et al.  Additive Utility Functions and Linear Engel Curves , 1971 .

[7]  Beth E Allen,et al.  The Existence of Rational Expectations Equilibrium: A Retrospective: Essays in Economic Analysis, A Tribute to Roy Radn , 1998 .

[8]  Stephen A. Ross,et al.  Mutual fund separation in financial theory—The separating distributions , 1978 .

[9]  J. Tobin.  Liquidity Preference as Behavior towards Risk , 1958 .

[10]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[11]  Jonathan B. Berk,et al.  Necessary Conditions for the CAPM , 1997 .

[12]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[13]  J. L. Kellogg.  On the uniqueness of fully informative rational expectations equilibria w , 1998 .

[14]  Lars Tyge Nielsen.  Common knowledge: The case of linear regression , 1996 .

[15]  Sanford J. Grossman.  ON THE EFFICIENCY OF COMPETITIVE STOCK MARKETS WHERE TRADES HAVE DIVERSE INFORMATION , 1976 .

[16]  Necessary Conditions for Aggregation in Securities Markets , 1978 .

[17]  Nancy L. Stokey,et al.  Information, Trade, and Common Knowledge , 1982 .

[18]  David M. Kreps.  A note on "fulfilled expectations" equilibria , 1977 .

[19]  R. Radner.  Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices , 1979 .

[20]  Mark Rubinstein,et al.  An aggregation theorem for securities markets , 1974 .

[21]  W. M. Gorman.  Community Preference Fields , 1953 .

[22]  H. Polemarchakis,et al.  Asset markets and the information revealed by prices , 1993 .

[23]  Joseph E. Stiglitz,et al.  The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds , 1970 .

[24]  G. Constantinides,et al.  Financial markets and incomplete information , 1989 .

[25]  R. Myerson,et al.  Efficient and Durable Decision Rules with Incomplete Information , 1983 .

[26]  J. Ingersoll.  Theory of Financial Decision Making , 1987 .

[27]  B. Allen.  The existence of fully rational expectations approximate equilibria with noisy price observations , 1985 .

[28]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[29]  Hugo Sonnenschein,et al.  On the existence of rational expectations equilibrium , 1982 .

[30]  Sanford J. Grossman.  Further results on the informational efficiency of competitive stock markets , 1978 .

[31]  Peter M. DeMarzo,et al.  On the uniqueness of fully informative rational expectations equilibria , 1999 .

[32]  V. Madrigal,et al.  On Fully Revealing Prices When Markets Are Incomplete , 1995 .

[33]  Stephen Morris,et al.  The Revelation of Information and Self-Fulfilling Beliefs , 1997 .