Necessary Speed Limits?

In How to Think Like an Economist, Roger Arnold mentions that in the absence of speed limits we should expect more crashes and deaths than with the current regulations. I disagree.

In the absence of a speed limit every driver has an incentive to drive faster. However every single driver also realizes that everyone else is driving faster and that in such conditions any casualties might be fatal. Because of this each individual driver has an incentive to pay a lot more attention when driving than when speed limits exist. The final result is that people might be driving faster but will also be a lot more careful when driving. Therefore, the occurrence of more crashes and deaths does not necessarily follow.

Whether driving without speed limits is more dangerous is an empirical questions that cannot be answered a priori. My guess is that the number of crashes with and without speed limits in highways might be similar in either case otherwise the famous Autobahns in Germany would have a speed limit regulation.

If I were to be a social planner I would probably choose to eliminate any speed limits in highways and save on enforcing costs. However, I would still enforce speed limits in urban areas to reduce the number of pedestrians that are hit by cars.