Tuesday, 20 October 2015

The optimal open road speed limit

A couple of years ago, I wrote a post about speed enforcement. However, it remains an open empirical question as to what the optimal open road speed limit is. When a driver increases their speed, the risk of an accident increases and so does the severity of the accident. That imposes a cost on the driver, and because of the non-linearity of accident damage, the marginal cost is increasing (i.e. the difference in accident severity between an accident at 110 km/hr and one at 100 km/hr is larger than the difference between an accident at 60 km/hr and one at 50 km/hr even though the speed differences are the same in absolute terms). That cost may be offset by benefits in the form lower travel times (i.e. saving the time cost of travel). Marginal benefit decreases with speed (every km/hr faster saves some time, but each km/hr saves less additional time as you go faster). The optimal speed for the driver is the speed where marginal benefit of driving faster is exactly equal to the marginal cost. At this point, driving a little bit faster entails a higher additional cost than the benefit they would receive (which is why they will drive no faster).

However, when setting a speed limit a benevolent social planner doesn't only care about the costs and benefits to drivers. Speeding drivers place additional costs on others (externalities), including risk to other drivers, pedestrians, and increased pollution and its associated health costs. So, if we wanted to know what the optimal open road speed limit is for society (not just for drivers themselves), we need to consider the additional external costs. So the optimal speed limit for society will be lower than the optimal speed limit for each individual driver (which might be one explanation for the number of drivers who consistently drive over the current limits).

Cost-benefit analyses of the speed limit are rare. Which is why I was very interested to read this paper in the Journal of Public Economics earlier this year (sorry I don't see an ungated version online) by Arthur van Benthem (Wharton School, University of Pennsylvania). In the paper, van Benthem undertakes a fairly exhaustive evaluation of the costs and benefits of a series of speed limit changes that occurred in 1987 and 1996 in the U.S. (specifically, he looks at the effects in California, Oregon and Washington states). Unlike past studies that have mostly evaluated the costs purely in terms of road accident fatalities (valued using the value of a statistical life, or VSL), this paper looks at a wider range of private and external costs, as shown in the figure below.

van Benthem first evaluates the impact of the speed limit changes on each of the variables above (fatal accidents, non-fatal accidents, infant health, etc.) by comparing roads where the speed limits were raised (mostly from 55 mph to 65 mph) with control roads where speed limits remained unchanged. He tests for and doesn't find any substitution effects, so drivers weren't induced into driving more on the roads with higher speed limits, when compared with the control roads (which is unsurprising because they are generally located in different areas).

What were the effects? In terms of the outcome variables noted in the figure above, he finds:
...that a 10 mph speed limit increase leads to a 3–4 mph increase in travel speed, 9–15% more accidents, 34–60% more fatal accidents, a shift towards more severe accidents, and elevated pollution concentrations of 14–24% (carbon monoxide), 8–15% (nitrogen oxides) and 1–11% (ozone) around the affected freeways. The increased pollution leads to a 0.07 percentage point (9%) increase in the probability of a third trimester fetal death, and a positive but small and statistically insignificant increase in the probability of infant death.
van Benthem then goes on to evaluate the costs and benefits of the speed limit changes, using common measures of the VSL (for accident-related and health-related costs), value of time (for travel time savings) and petrol prices (for increased fuel costs). He finds:
Annual net social benefits are estimated at −$189 million excluding adult health impacts, with a standard deviation of $94 million. The social costs ($345 million) exceed the benefits ($156 million) by a factor of 2.2. Using the adult health impacts from the central health impact scenario, which are admittedly uncertain, the net benefits decrease to −$390 million, with a standard deviation of $102 million... The social costs exceed the benefits 3.5 times.
In other words, the costs of increasing the speed limit outweighed the benefits by a substantial margin - the speed limit should not have been raised. And the results appear to be very robust, even when you consider a range of values for the VSL and the value of time. Of course, any cost-benefit evaluation is necessarily incomplete. It isn't possible to include every cost and benefit that might arise, and many of the costs and benefits will be fairly uncertain (as the quote above notes in the case of adult health impacts). In the paper, van Benthem notes that his analysis omits "marginal excess tax burden from changes in speeding ticket and gas tax revenues, changes in enforcement costs and increased driving pleasure at higher speeds".

So, what was the optimal speed limit? van Benthem suggests that it was not much below 55 mph. Finally, this evaluation was based on somewhat dated data. If the analysis were re-run with more up-to-date data, we might get something different - cars are now more fuel-efficient, safer to drive (even at high speeds), health care has improved (which might reduce some fatal accidents to non-fatal), and petrol prices are higher. van Benthem suggests that:
today's gap between private and social net benefits will be smaller for a 55 to 65 mph speed limit increase. For higher speed limits, the gap is likely to remain substantial because of the steeper speed-emission profile in that range and the external cost component of accidents.
Finally, the paper has a number of additional bits I found interesting:

  • The treatment effect of the speed limit changes on travel speeds increased over time - people adjusted their speeds towards the new limit, but this adjustment was not immediate. 
  • Carbon monoxide (CO) emissions triple as vehicle speeds increase from 55 mph to 65 mph!
  • van Benthem also draws a conclusion about the optimal Pigovian tax on speed, which:
would consist of a combination of a gasoline tax for climate damages, emissions taxes for local air pollutants in exhaust gas (which varywith speed), plus a speed-dependent tax to internalize accident risk imposed on others (which is also a function of traffic conditions).

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