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# Speed vs. Safety

*March 21 [Updated with more accurate estimate/figure after fixing an excel bug]* How fast should we drive? From a social cost perspective, faster speeds save time, which has a value, but faster speeds cost lives, which also have a value. To illustrate the trade-off I did some back of the envelope calculations, imagining, like a macro-economist, a single road represents the whole t

Speed vs. Safety (updated)

ransport system. Annually there are about 30-40,000 people killed in the US, there are an annual Vehicle Miles Traveled of 3,208,517,000,000. The average speed of travel isn't known directly, but if we assume the average person travels in a car 60 minutes per day (the 1 hour travel time budget) this implies, at approximately 30 miles of travel per day per traveler, about 30 MPH, which seems about right (including 1/4 of travel on freeways at higher speeds and 3/4 on surface streets and roads at lower speeds, and including traffic signals). As the saying goes, Your Mileage May Vary, and this is intended to be indicative -- not a universal answer. Some additional assumptions:

We take the Value of Life to be $10,000,000, and assume fatalities are the only cost associated with crashes (they are about 78 % of total crash costs according to our analyses, so we should inflate this number to get total crash costs) [US DOT says $9.6 M]

We take the Value of Time to be $15/hour [US DOT gives a lot of ranges, but this number is high for all surface travel excluding freight]

We assume the number of deaths drops linearly with speed, to zero at zero MPH. The improvement is likely non-linear, as reductions in speeds from high speeds are more valuable than from low speeds.

We assume the value of travel time savings is constant, independent of the amount of time saved.

To be clear, these are huge assumptions. Examining the figure we see the lines cross at about 75 MPH, which is the minimum total cost. So why don't we set the speed limit to 75MPH? *Note that:*

A Political Economy of Access: Infrastructure, Networks, Cities, and Institutions by David M. Levinson and David A. King

Travel time savings are, while still speculative in terms of their valuation, both private and real,

The statistical value of life is far more abstract. The value of my life to me is infinite. The value of your life to me is, sadly, not. Yet, I am willing to take risks that increase the probability of my dying in order to save time or earn more money. These are the kinds of factors that allow an estimate of value of a statistical life.

Death and crashes are probabilistic affairs, while the time lost is deterministic. People are gamblers.

There are some other benefits to faster travel not accounted for, such as more or longer trips (to better destinations, or the ability to get better real estate at the same price), which increase consumer surplus. The analysis here does not consider user response to lower speeds, which would be to travel less (or higher speeds and travel more). There are also issues like travel time reliability.

Since 1988 The Statistical Value of Life has risen 6-fold in US DOT estimates, the value of time has little more than doubled. (If we cut the value of life to $3M, (effectively holding the tradeoff more similar to 1988 levels), the tradeoff is

*much higher*.)Speed limits reflect what travelers will travel at, not what we wish they would travel at.

If you dislike these number, you can roll your own analysis on individual roads. The difficulty is not measuring the speed of those roads, but measuring their safety. There is a Highway Safety Manual for such purposes, but crashes are highly random events.

**UPDATE 2**: Axel Waleczek made an interactive Tableau, so you can test your own scenarios.

**Additional Readings**

Hauer, E. (1994) CAN ONE ESTIMATE THE VALUE OF LIFE OR IS IT BETTER TO BE DEAD THAN STUCK IN TRAFFIC?

*Transportation Research A*. 28(2).