Reconsidering the impossibility of informationally efficient markets

Abstract

This article reconsiders Grossman and Stiglitz's (1980) analysis and delivers a comparative static result which the original exhibition misses. In detail, an increase of the payoff of the risk-free security is reported to affect the informativeness of the rational expectations equilibrium adversely. Furthermore, contrary to Grossman and Stiglitz (1980) both the noisy rational expectations equilibrium and the equilibrium in the market for information are characterized explicitly as functions of the underlying economy's parameters. The incompatibility of a fully revealing rational expectations equilibrium and costly acquisition of private information is obtained by means of an argument borrowed from linear regression theory.

Notes

¹ Technically, in Grossman's (1976) analysis the equilibrium price of the security is a sufficient statistic for private information.

² Grossman and Stiglitz's (1980) proof of the Theorem 2 applies the χ² distribution. Cf. Grossman and Stiglitz (1980, p. 406).

³ Cf. Grossman and Stiglitz (1980, Theorem 1).

⁴ Technically, the risky security's equilibrium price is not a sufficient statistic for the informed investors’ private information. That is both and . cf. Equations (A5–A8) in the Appendix.

⁵ Proposition 2 focuses on the explicit characterization of interior equilibria in the market for information that is on equilibria such that the fraction of informed investors meets 0 < λ < 1. Obviously, λ = 0 and λ = 1 characterize equilibria in the market for information if being uninformed or being informed dominates the other alternative, respectively.

⁶ Cf. Grossman and Stiglitz (1980, p. 406). In Equation (A18) the risk-free security's payoff is lost whereas it is still present in Equation (A15).

⁷ Note that the informed investors’ conditional variance of the risky security's payoff is independent of the risk-free security's payoff (cf. Equation A6).