Monday, 4 November 2013


Cabinet's decided to bring forward legislation knocking the drink driving limit from 0.08 to 0.05.

In 2009, National first started talking about this move. Would it make sense? They held off pending further study. I've not seen the papers they now have on this, but here's how I'd suggested checking it back in 2010.

We'd need to start with population data on the proportion of drivers in the .05 to .08 range, adjusted by time of day. Use that in combination with standard MoT figures on the cost of crashes to estimate the excess cost imposed by drivers in the .05 to .08 range. Simply knowing the number of accidents among drivers in that range doesn't tell us the extent to which they're over or under represented in the crash data.

Then we'd need some measure of the elasticity of costs with respect to the law change. Doing it properly would require not only knowing what portion of those in the .05 to .08 range consequently avoided accidents by cutting back to .03, but also whether there were any resulting decreases in driving in the >.08 range - it's not entirely implausible that some people start making bad decisions about just having another couple at 0.07 that they'd not have made at 0.05. That wouldn't be easy to find since jurisdictions changing their BAC can accompany it with stepped-up enforcement, making it hard to disentangle effects. As a ballpark first cut, it might not be nuts to just reckon that excess accidents in the 0.05 to 0.08 range disappear. That's not all accidents: just the portion in excess of base rates.

Finally, we'd need some measure of the lost consumer surplus among those who consumed less but who would have otherwise driven home safely in the 0.05 to 0.08 range. Put a value on that, weigh it up against the accident cost savings, and see whether the policy makes sense.

So what do we know about accident rates? The latest MoT figures are for 2011. Three of 183 fatally injured drivers were in the .05-.08 range: 1.6%. That doesn't give us the proportion of crashes caused by drivers in that range, but it should be in the ballpark.

But what's the baseline? In December of last year, MoT was working on figuring that out. In early October, they sent me some of the aggregate data; I'd been holding off on doing much with it until I emerged from the grading and until they'd sent me the promised raw data, but we'll go with what we've got at this point.

Of 29,577 people tested in the MoT 2012 survey, 1.3% were between 0.05 and 0.08. If the 2011 MoT crash figures are ballpark right, and if there aren't weird things going on in the time-of-day data that I haven't yet got, then drivers in the .05 to .08 range are slightly over-represented in the aggregate crash statistics. Instead of being involved in 2.379 of the 183 fatalities, drivers in the .05 to .08 range were involved in 3. So by those figures, we might reckon on preventing one driver fatality annually by abolishing drinking among those in the .05 to .08 range.

From Brownlee's press release:
A two year review of the impact of lowering the legal blood alcohol limit by 30 milligrams suggests 3.4 lives will be saved a year and 64 injury causing crashes avoided – and save $200 million in social costs over 10 years.
“Data collected by Police over the past 22 months shows 53 drivers were involved in fatal and serious injury crashes with blood alcohol readings of between 51 and 80 milligrams per 100 millilitres of blood,” Mr Brownlee says.
I'll look forward to seeing the study on which that was based.

Note for now that if 1.3% of drivers are in the 51 to 80 range, we should really be counting only the excess accidents among that range, not all accidents. In 2011, there were 259 total crashes involving fatalities, 1717 total crashes involving serious injury, and 7828 involving minor injury. So 1976 drivers were involved in fatal and serious injury crashes in 2011. From that, we need to net out crashes involving drivers over the legal limit: the appropriate benchmark comparison would be drivers under 0.05. After minor tedium, it looks like about 251 fatality crashes and 1621 serious injury crashes involved drivers under the 0.08 limit: 1872 fatal and serious injury crashes.*

If drivers in the .05 to .08 range had accident rates proportionate to those below .05, we'd have expected them to have had 1.3% of the total number of crashes net of those crashes involving those above the .08 limit. And so that would be 3.3 fatal crashes and 21 serious injury crashes, or about 24 fatal and serious injury crashes.

In the last 22 months, according to Brownlee's press release, 53 drivers with BAC ranged 50-80 were involved in fatal or serious injury crashes. That works out to 29 per year.

If this is ballpark correct, then we had about five crashes more than expected in 2011 among those in the .05 to .08 range. Without access (yet) to the study Brownlee's citing, I don't know what part of these were fatal crashes and what part were serious injury crashes, but if they follow the aggregates, then just under one of those would have been a fatality crash and the other four would have been serious injury crashes. In 2011, 259 fatal crashes resulted in 284 fatalities; avoiding (just under) one fatality crash per year would save (just over) one life. We can't be particularly confident in this number as year-to-year variation in crash stats would affect things, and I'm using 2011 aggregate crash stats and more recent .05-.08 range crash stats.

I'm curious to see the workings on Brownlee's 3.4 figure.

But suppose Brownlee's numbers are right and we save $20m per year in social costs of crashes. That would be the benefit. There were, in 2006, on the order of 850,000 car trips per day among those commuting for work. Some will have a beer or two before driving home. And suppose further that there are only 150,000 non-work car trips to get an even million driver trips per day. 1.3% of the driving population surveyed were between .05 and .08. So we're talking about something on the order of 13,000 car trips per day involving drivers in the affected range, or about 4.7 million car trips per year undertaken by those in the .05 to .08 range. If each of those drivers would have been willing to pay $4.25 to be under the .08 rule instead of the .05 rule, then the law change has done more harm than good - about what I'd reckoned using a different back-of-the-envelope calculation last year.

* In 2011, alcohol offenders were involved in 8 fatal crashes, 533 injury crashes, and 1670 non-injury crashes - the stats here do not distinguish minor from serious injuries. But if we apportion percentages to follow national aggregates, we would expect that 18% of the injury crashes involved serious injuries: 96. Netting those from the totals, we have 251 fatality crashes not involving drink driving > 0.08 and 1621 serious injury crashes not involving drink driving > 0.08. The 2012 MoT survey had 0.8% of drivers registering BAC > 0.08 - taking them out of the denominator is within rounding error.


  1. To avoid the "no support for heavy punishment" problem in your conclusion, couldn't the penalty scale with the magnitude of the breach? Seems an easy fix. Don't we already do that with speeding? (If not, we should!)

  2. And that's what National's done in 2013 by putting a lower fine for .05-.08 driving.