The second page contains a succinct summary of theoretical reasons why this is true. The rest of the paper goes over empirical findings: http://www.acsu.buffalo.edu/~keechung/MGF743/Readings/G2%20D...

Since then, we have additional data points from the decimalized US equity markets. See http://www.sec.gov/rules/other/2014/34-72460.pdf for a bibliography. The weight of the evidence points towards thinner books. Incidentally, the SEC is looking to increase the tick size for illiquid small-cap stocks for this very reason.