Crash responsibility, and some back of the envelope reckoning

At the same time that I was trying to get stats on the number of drivers in the .05 to .08 range who had not been involved in accidents, Canterbury's Professor of Finance Glenn Boyle was getting annoyed with the New Zealand Herald's campaigning for a 0.05 limit.

The Herald published an article noting the number of accidents involving drivers just under the legal limit, along with the usual stuff from Alcohol Healthwatch:

Statistics obtained by the Herald on Sunday under the Official Information Act show in the last four years 20 people have been killed in road accidents involving drinking drivers just below the legal limit.

Another 281 people have been seriously injured in crashes where a drink-driver was also tested and found to be just under the limit.

Alcohol Healthwatch director Rebecca Williams said the statistics clearly showed 20 people would still be alive if the Government had responded to calls for a lower alcohol limit.

Glenn was a bit miffed at the Herald's credulity here. First, banning driving above 0.08 hasn't abolished accidents involving drivers who are over the legal limit - we still do arrest lots of people for driving after having had too much to drink. So it's a bit nuts to say that 20 people would be alive if the drink driving limit were at 0.05 over those four years. Some accidents would have happened even if the driver were sober, and some of them would have happened with the driver having continued to drink. It's pretty likely that the number of accidents would be lower, but it's pretty unlikely that each and every one of those accidents would have gone away. Maybe you could make the case for it if there were substantial decreases in driving in the >0.08 range with a drop in the limit to 0.05, but I've not seen evidence on that as yet.

Glenn got in touch with the reporter and noted that I was planning on heading out with the Christchurch police over the weekend; she called and asked me about it. She'd said that she'd call back on Monday to see how things went, so I was a bit surprised to see there'd been a piece on it this past Sunday.

I'll have to clarify a couple of points.

First, I do not doubt that there is increased risk of having an accident if you are between 0.05 and 0.08 relative to a baseline of zero. I would be pretty surprised if drivers in that range were not over-represented among those having accidents. But I do not know by how much they are over-represented. You are also at increased risk of dying in an accident if you are going 100 kph than if you are going 30 kph. But we do not set the speed limit to 30 kph: the reduction in accident risk isn't worth it relative to the delays we impose. So, for example, Forester et al 1984 concluded that the 55 MPH speed limit failed cost-benefit analysis unless we put next to no value on people's time. We also do not drive cars made of nerf to protect pedestrians.

Even if we only considered increased enforcement cost as the only cost, there would still be some cut-point below which the increased risk of accident among those in the .05 to .08 range wasn't worth lowering the legal limit.

If we think that those who choose to drive in the 0.05 to 0.08 range and who do not have accidents wind up having less fun than if they were required to be below 0.05, then that reduction in fun counts for something too - it's reduced consumer surplus. That doesn't mean that it's impossible to have a fun night out while you're the designated stone-sober driver. It just means that these drivers must wind up being worse off as they see it; otherwise, they would already have voluntarily chosen to have had less to drink. That moves the cut-point for increased accident risk upwards in just the same way that increases in the opportunity cost of time increase the optimal highway speed limit.

Unless we know how many drivers who do not cause harm would be inconvenienced by a reduction in the limit to 0.05 from 0.08, we have a hard time assessing the costs of that policy move.

Here's the Herald:

National Addiction Centre director Professor Doug Sellman is convinced there is a link. He said every time someone died in an alcohol-fuelled car crash, it was a chance to point out that former Transport Minister Stephen Joyce was partly responsible.

The Government has refused to move on a lower blood-alcohol limit for drivers until it receives the results of data from the Ministry of Transport and a driver-simulation study from Waikato University.

Sellman said Government "delay tactics" were costing lives. All the information was already available to make a decision, he said. "Joyce didn't act on the international research that was there already. None of the research says we need more research. Only Stephen Joyce believed that."

Sellman said the point of a lower limit was that it would reduce the number of drivers with higher alcohol levels, too.

The Herald on Sunday has been campaigning for a lower breath-alcohol limit, and statistics last weekend showed 20 people had been killed in the past four years in road accidents involving drinking drivers who were just under the current legal limit. But even that wasn't enough to force any response from the Government.

If all that we cared about was knowing that we reduced the risk of car accidents, you could push the button tomorrow for a zero drink-driving limit. You could also push the button for a 30 kph speed limit on the highway and nerf-cars. And you could blame the Transport Minister for every death involving drivers going faster than 30 kph. But reducing accident risk isn't the only thing that matters.

If we were stuck having to do it from existing data, I'd start here. Keall et al, 2004 provide some pretty decent NZ data.

At Table 5, the report estimates of the death rate per million trips for a few BAC intervals. Among those with no alcohol, the death rate per million trips is 0.2 for both males and females. For those in the .005-.055 range, they found no accidents for women and 0.4 deaths per million trips for men. For the .055 to .105 range, which spans the legal limit of 0.08, the death rate per million trips was 1.4 for women and 1.2 for men. At Table 2, the overall excess death rate per million trips is about 1 - Table 2 controls for time of night.

Now the value of a statistical life for policy purposes in New Zealand is $3.77 million.

The excess death rate per million car trips among those in the 0.055 to .105 range is 1.2 for women and 1 for men. So we'll average that at 1.1 and stick with Table 5 results. Every million car trips taken by drivers in the 0.055 to .105 range costs $4.147 million dollars in expected VSL losses. To the extent that this includes fatalities incurred by the driver, it massively overestimates social cost. But it also doesn't count any of the costs of non-fatal accidents. Because this study only looks at fatal crashes.

So if we only count fatality costs and count all of the fatality costs falling on the driver him or herself, then it would make sense to reduce the drink driving limit from .105 to .055 if drinkers would be no more than $4.15 worse off per trip as consequence. You may see a problem here: the current drink driving limit is 0.08, not 0.105, the risk of accident is strongly increasing in BAC, and this earlier data includes the very high drink driving accident rates among 15-19 year olds, who are now subject to a zero percent limit.

I do not know whether the raw data underlying the study has actual BAC or only the bucketed BAC categories. If the former, getting access to the raw data would let me back out the portion of increased risk in the 0.05 to 0.08 category and restrict things to the over-20 cohort. But it might just be worthwhile to have a look at what MoT is currently collecting, as they're looking also at non-fatal crashes.

So here's a question then. Let's suppose that the costs of non-fatal accidents are on par with the self-imposed fatality costs incurred by drinking drivers so the $4 is ballpark ok (but note the overestimate problems as it includes people in the 0.08 to 0.105 range). Do you expect that most people enjoying a night out would be willing to accept $4 to be subject to a 0.05 rather than a 0.08 limit? Don't tell me "Oh, I would, because I never have that much anyway." This question isn't for you. This question is for those who go out for the night and either worry that they've exceeded 0.05 or know that they're in the 0.05 to 0.08 range. As you walk into the bar someone offers you $4 and says "You can have this $4 if you can guarantee that you'll stay under 0.05 tonight." If most drinkers subject to the risk take the $4, and if the $4 is ballpark correct, then moving to 0.05 makes sense. If you'd have to offer them more than $4, then it's a value-destroying proposition.

Fun fact: you can back out how much net enjoyment people get from their last few drinks - the ones that push them into the 0.05 range - from what they spend on a drink combined with their price responsiveness. When drinks at the bar range from $5 upwards, it's going to be surprising if consumer surplus from last couple of drinks is less than $4 given demand is pretty price-inelastic. In other words, it seems pretty likely that people would turn down the $4 offer. And they'd be even more likely to turn down a lower offer - and I'd be pretty surprised if the non-fatal crash costs were higher than the proportion of fatality costs falling on the drink driver.