We show that following a tick size reduction in a decimal public limit order book (PLB) market quality and welfare fall for illiquid but increase for liquid stocks. If a Sub-Penny Venue (SPV) starts competing with a penny-quoting PLB, market quality deteriorates for illiquid, low priced stocks,...

We model a public limit order book (PLB) with rational investors choosing to supply or demand liquidity. Following a reduction in the tick size the effects on PLB's market quality depend on the liquidity of the stocks. Spread improves for tick-constrained stocks and deteriorates for...

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...

This paper examines unique data on dark pool activity for a large cross-section of US stocks in 2009. Dark pool activity is concentrated in liquid stocks. Nasdaq (AMEX) stocks have significantly higher (lower) dark pool activity than NYSE stocks controlling for liquidity. For a given stock, dark...

We create proxies for constrained supply of lendable shares by combining unique data on loan fees, stock lending activity, and failures to deliver to examine how contrarian short-sale strategies are affected by constraints. Constraints affect roughly one-third of the cross- section of stocks and...