Abstract We show current market practices relating to odd-lot quotes create a large “inside” market where better prices routinely exist relative to the National Best Bid or Offer. We show that odd-lot quotes play a price discovery role, and these quotes provide valuable information to traders with access to proprietary data feeds. Using a XGBoost machine learning algorithm that uses odd-lot data to predict future prices, we demonstrate a simple and profitable trading strategy. We argue the SEC’s proposed round-lot redefinition reduces—but does not eliminate—the high incidence of superior odd-lot quotes within the NBBO.

In the single-IV model, researchers commonly rely on t-ratio-based inference, even though the literature has quantified its potentially severe large-sample distortions. Building on Stock and Yogo (2005), we introduce the tF critical value function, leading to a standard error adjustment that is a smooth function of the first-stage F-statistic. For one-quarter of specifications in 61 AER papers, corrected standard errors are at least 49 and 136 percent larger than conventional 2SLS standard errors at the 5 percent and 1 percent significance levels, respectively. tF confidence intervals have shorter expected length than those of Anderson and Rubin (1949), whenever both are bounded. (JEL C13, C26)