Note that Uber was not the only taxi reform in NYC. A quote from the paper: "For my analysis, I use data from collisions that occurred from January 2007 through July 2013. This period includes Uber’s entrance into the New York market in May 2011, allows for a substantial pre-intervention period, and omits two potentially confounding entrances in the New York City transportation market that could influence the alcohol-related collision rate. The first entrance occurred in August 2013 as New York City introduced a new form of taxi medallion to serve only the “outer boroughs” of Brooklyn, Queens, the Bronx, Staten Island, and northern Manhattan. These “boro” taxis were painted green rather than the typical yellow medallion taxis, and banned from picking up in lower Manhattan, where most street-hail yellow taxi rides originate."

Note also that Uber in NYC is operated by TLC-licensed drivers against whom it is very easy to file a complaint for dangerous driving, which is different from many other cities. I used NYC's lovely 311 app to file a complaint against just such a driver for shouting at me after he drove at me head-on in a 2-way bike lane. I expect he'll face a significant fine.