How do the lengths of the lead lag time between stocks evolve? Tick-by-tick level measurements across two decades

There has been an extraordinary decrease in order execution time on stock exchanges in the past two decades. A related question is whether there has been a similar reduction in orders of magnitude for the lengths of the lead lag time between stocks. If the answer is affirmative, and the lengths of the lead lag time have long fallen below the human reaction time, algorithms have taken over information diffusion from one stock to another. Otherwise, humans continue to be in authority. In this study, the lengths of the lead lag time within pairs of stocks of large US companies are estimated using the Hayashi-Yoshida estimator, for each year from 2000 to 2022. We first construct stock pairs, with each pair containing two stocks from the same industrial sector. The median length of the lead lag time for each year shows a general trend of decline over time. From 2000 to 2005, the median lengths are a few seconds. By 2021 and 2022, they are less than 10 milliseconds. We also study a second construct in which stock pairs are randomly formed, but each pair contains stocks from two different sectors. The median length of the lead lag time for each year shows a decline over time, similar to the first construct. Overall, the lengths of the lead lag time in the second construct are not remarkably longer than those in the first construct. This shows that being in the same sector, at the tick-by-tick level, is not an important factor in determining the length of the lead lag time between stocks.