Statisticians' Equilibrium: Trading with High-Dimensional Data

Abstract

This paper uses a one period model to establish a connection between the complexity of informational environment, market efficiency, and volume. Introducing a high-dimensional estimation problem into a typical trading game, we show why agents may not condition on price in their demand curve submissions, and come to possess heterogeneous models. We define a new equilibrium concept, the “rational statisticians’ equilibrium,” wherein each agent uses only a ridge regression estimator on her own data to forecast the fundamental’s distribution. We derive quantitative properties of price informativeness and volume in these equilibria, introducing the notion of a “regularization externality” in price formation and accounting for volume spikes around earnings.