This paper provides a novel approach to ordering signals based on the property that more informative signals lead to greater variability of conditional expectations. We define two nested information criteria (supermodular precision and integral precision) by combining this approach with two variability orders (dispersive and convex orders). We relate precision criteria with orderings based on the value of information to a decision maker. We then use precision to study the incentives of an auctioneer to supply private information. Using integral precision, we obtain two results: (i) a more precise signal yields a more efficient allocation; (ii) the auctioneer provides less than the efficient level of information. Supermodular precision allows us to extend the previous analysis to the case in which supplying information is costly and to obtain an additional finding; (iii) there is a complementarity between information and competition, so that both the socially efficient and the auctioneer's optimal choice of precision increase with the number of bidders.

This paper studies the intraday relationship between ultra-fast machine-driven activity (UFA) and market quality in automated equity markets. We find that higher UFA is associated with lower intraday market quality (greater quoted and effective spreads and lower depth). This effect is economically significant, and robust to different specifications, endogeneity tests, and alternative measures of UFA. Our results hold after controlling for volatility, periods of unusually high UFA (a proxy for quote stuffing), and periods where UFA is primarily driven by fleeting orders inside the spread (a proxy for spoofing and competition between liquidity providers).