It's directly causal, algo's fighting for better position directly decrease the spread. Competition has the effect of removing unnecessary markup as the next guy who sells just a bit cheaper or offers just a bit more wins until the price is as close as possible to barely profitable. Humans are too slow to play such a tight game, computers aren't.

By a factor of 25, and it's only not more because there's a law against making them any smaller. And it's very much because of computerization; whether you consider it to be HFT is a question of whether you count the early days when computerized firms competed on price or the later ones when the aforementioned law meant they could only compete on latency.

In any case, compete they have, pushing their profits pretty close to zero. Look at the graphs in http://www.zerohedge.com/news/2013-02-13/how-getco-went-hft-... (article is terrible, it was just the easiest place to find the graphs).