Sub-penny and queue-jumping

We develop a model where a public limit order book (PLB) competes with a Sub-Penny Venue, which allows Sub-Penny Trading (SPT). SPT occurs when a trader undercuts orders in the PLB by less than one penny, a practice we call queue-jumping (QJ). QJ is higher for NASDAQ than for NYSE stocks. We confirm the model's predictions that QJ increases in liquidity and in the tick-to-price ratio. We also find that QJ is associated with improved PLB market quality, especially for large capitalization stocks. Finally, we show that High Frequency Trading is negatively related to QJ