We show that queue rationing under price controls is one driver of high-frequency trading. Uniform tick sizes constrain price competition and create rents for liquidity provision, particularly for securities with lower prices. The time priority rule allocates rents to high-frequency traders (HFTs) because of their speed advantage. An increase in relative tick size, defined as uniform tick sizes divided by security prices, increases the fraction of liquidity provided by HFTs but harms liquidity. We find that the message-to-trade ratio is a poor cross-sectional proxy for HFTs’ liquidity provision: stocks with more liquidity provided by HFTs have lower message-to-trade ratios. Received September 15, 2015; editorial decision October 7, 2017 by Editor Robin Greenwood.

Stock exchange operators compete for order flow by setting “make” fees for limit orders and “take” fees for market orders. When traders can quote continuous prices, exchange operators compete on total fee, because traders can choose prices that perfectly neutralize any fee division. The 1-cent minimum tick size, however, prevents traders from neutralizing fee division. The nonneutrality of division between make and take fees (1) allows an exchange operator to establish exchanges that differ in fee structure to engage in second-degree price discrimination and (2) destroys the Bertrand equilibrium, leads to frequent fee changes, and encourages entries of new exchanges. Received May 29, 2016; editorial decision April 19, 2018 by Editor Robin Greenwood.

The second special issue on big data in finance showcases advancements in research related to data of large size, high dimension, and complex structure since the first NBER/RFS big data conference. The papers published in this next chapter address some questions that were proposed in the initial special issue in 2021. Other papers are more directly connected to recent developments in the markets. We discuss some new research directions, following on the papers published here. They include evaluating market microstructure reforms, understanding medium-frequency trading, improving missing data imputations, and deepening data valuation. We look forward to more developments to follow.

Big data is revolutionizing the finance industry and has the potential to significantly shape future research in finance. This special issue contains papers following the 2019 NBER-RFS Conference on Big Data. In this introduction to the special issue, we define the “big data” phenomenon as a combination of three features: large size, high dimension, and complex structure. Using the papers in the special issue, we discuss how new research builds on these features to push the frontier on fundamental questions across areas in finance—including corporate finance, market microstructure, and asset pricing. Finally, we offer some thoughts for future research directions.