Friday, 1 November 2013

Police crackdowns on speeders - incentive effects?

Last Monday was Labour Day in New Zealand, meaning that we had the first holiday weekend for a few months. As you may expect, given this opportunity Kiwis take to the roads to get away for the weekend and take advantage of the break.

More cars on the roads means, almost inevitably, more motor vehicle accidents and more injuries. In most years. This year, thankfully, there was only one fatality - the lowest absolute number since records of holiday road tolls started being collected in 1956. Last year there were six deaths, 22 serious injuries and 90 minor injuries (injury statistics for 2013 aren't available as yet), and "travelling too fast for the conditions" was cited as a factor in 20 percent of the crashes.

Not surprising then, that the police want to target speeding, in order to reduce the number of fatal accidents. What is interesting though, is how the police implement this - by taking a tough line on all speeders going more than 4 km/h over the posted limit. Don't get me wrong - if you are travelling faster than the posted limit, you are breaking the law and you shouldn't complain if you are ticketed. I have never complained the few times I have been caught speeding.

There are a limited number of police cars travelling the roads, on the lookout for speeding (and other traffic offences, but let's ignore those for now). Every time a police car stops a speeder, they are effectively out of action for the time it takes to write out the ticket. In the meantime, a number of other speeding drivers are driving past, and not being stopped. I want to consider the incentive effects here. As far as I know, the police have never admitted as such, but typically the tolerance is more than 4 km/h (else why would they both highlighting that it is lower on the holiday weekend?). So, what happens when you lower the tolerance? Could doing so actually increase the number of speeding drivers?

First, let's think about the drivers' incentives. If they are rational or quasi-rational decision-makers (as I discuss with my ECON110 class), they weigh up the costs and benefits of the decision to speed. The benefits include less time wasted on the roads (an opportunity cost - you give up some time you could spend with family, friends, on the beach, whatever). The costs include the increased risk of a serious car accident, and the increased risk of a fine for speeding. For both of these costs, the cost is not absolute - it is based on risk. So, they need to consider both the probability of the event (crash or speeding ticket, respectively) occurring, and the absolute cost to them if it does. If the benefits outweigh the costs, then the driver will choose to speed.

Now let's assume for the moment that, among drivers, there is a distribution of open road driving speeds between 70 km/h and 120 km/h where 75 percent of drivers driving below 100 km/h, about 10 percent between 100 km/h and 104 km/h, about 10 percent between 105 km/h and 109 km/h, and about 5 percent at 110 km/h or above (this is similar to the unimpeded open road speed distribution from the 2012 National Speed Survey). That means that about 25 percent of all drivers are speeding, compared to the posted limit of 100 km/h.

If the police apply a tolerance of 9 km/h, they will only ticket speeding drivers going 10 km/h or more over the posted limit. This means that they are targeting the top 5 percent of drivers, and will regularly pull over a speeding driver. All of the drivers the police stop and ticket are the fastest (110+ km/h) drivers, and those drivers face some probability (let's call it P1) of being stopped and ticketed. This probability is what the rational or quasi-rational drivers take into account in deciding whether to speed or not.

Now, assume instead that the police apply a tolerance of 4 km/h. Now they are targeting the top 15 percent of drivers, and still regularly pull over speeding drivers. However, now two thirds of the drivers that are stopped are those driving between 105 and 109 km/h, and only one third are those driving 110 km/h or greater. So, now the fastest drivers face only a probability of (1/3 * P1) of being stopped and ticketed.

It is entirely possible, then, that lowering the tolerance for speeding actually reduces the disincentive (potential speeding ticket) effect of speeding. This lowers the costs of speeding for the fastest drivers and moves the cost-benefit calculation in favour of more speeding. It increases the costs of speeding for the slower drivers who now have a probability of being ticketed (which was zero before). So, overall there are likely to be the same number of fast speeding drivers on the roads, but fewer slow speeding drivers. I wish there were data available to test this hypothesised change in speeding behaviour.

Of course, the police could counteract the disincentive effect by increasing the number of police cars patrolling the open road. But, in order to completely offset the effect in our example above, they would need to triple the number of cars, and ensure that speeding drivers knew that was happening (which, of course, is exactly what the police do via the media).

Finally, having more cars on the roads naturally slows all drivers down anyway (the National Speed Survey results are based on unimpeded speeds, i.e. speeds when other cars are not slowing each other down, which is least likely on a holiday weekend). So, maybe lowering the tolerance is a good move for the police not because it lowers speeds (which would happen anyway) but because it ensures that each police car that is patrolling on holiday weekends is kept busy even though the number of speeding drivers on the roads on holiday weekends is actually lower than on non-holiday weekends. Remember that each minute spend not pulling over another driver entails an opportunity cost for the police. Food for thought.

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