The authors address this in a few places. The gist is that arbitrage became much faster but not more efficient. Here’s a summary from page 6:
> The usual economic intuition about obvious arbitrage opportunities is that once discovered, competitive forces eliminate the inefficiency. But that is not what we find here. Over the time period of our data, 2005–2011, we find that the duration of ES-SPY arbitrage opportunities declines dramatically, from a median of 97 milliseconds in 2005 to a median of 7 milliseconds in 2011. This reflects the substantial investments by HFT firms in speed during this time period. But we also find that the profitability of ES-SPY arbitrage opportunities is remarkably constant throughout this period, at a median of about 0.08 index points per unit traded. The frequency of arbitrage opportunities varies considerably over time, but its variation is driven almost entirely by variation in market volatility. These findings suggest that while there is an arms race in speed, the arms race does not actually affect the size of the arbitrage prize; rather, it just continually raises the bar for how fast one has to be to capture a piece of the prize.
> The usual economic intuition about obvious arbitrage opportunities is that once discovered, competitive forces eliminate the inefficiency. But that is not what we find here. Over the time period of our data, 2005–2011, we find that the duration of ES-SPY arbitrage opportunities declines dramatically, from a median of 97 milliseconds in 2005 to a median of 7 milliseconds in 2011. This reflects the substantial investments by HFT firms in speed during this time period. But we also find that the profitability of ES-SPY arbitrage opportunities is remarkably constant throughout this period, at a median of about 0.08 index points per unit traded. The frequency of arbitrage opportunities varies considerably over time, but its variation is driven almost entirely by variation in market volatility. These findings suggest that while there is an arms race in speed, the arms race does not actually affect the size of the arbitrage prize; rather, it just continually raises the bar for how fast one has to be to capture a piece of the prize.