On the Possibility of Informationally Inefficient Markets Without Noise

TL;DR

This paper demonstrates that partial information revelation can occur in markets without noise traders under certain preferences, resolving the Grossman-Stiglitz paradox and showing the unique fully revealing nature of CARA preferences.

Contribution

It characterizes the conditions under which markets can be informationally efficient without noise, identifying CARA as the unique fully revealing preference class.

Findings

CARA preferences lead to exact aggregation of information in log-odds space.

Partial revelation persists even with learning from prices.

Positive value of information and trade volume are confirmed across CRRA risk aversion levels.

Abstract

Noise traders can be dispensed with entirely. Partial revelation of information through prices arises under any non-exponential expected utility preference, including CRRA, without noise traders, random endowments, supply shocks, hedging motives, or behavioral biases. The model contains zero exogenous noise. The mechanism is a mismatch between the space in which market clearing aggregates signals and the Bayesian sufficient statistic. CARA demand is linear in log-odds, so prices aggregate in log-odds space and reveal the statistic exactly. Every other preference aggregates differently; the resulting Jensen gap makes revelation partial. I prove that CARA is the unique fully revealing preference class, characterize the rational expectations equilibrium via a contour integration fixed point, and verify that partial revelation survives learning from prices. The Grossman-Stiglitz paradox is resolved: information acquisition has positive value within the rational class. Numerical solution of the rational expectations fixed point at K = 3 confirms partial revelation, positive trade volume, and positive value of information across the full range of CRRA risk aversion, vanishing only in the CARA limit.