Self-driving cars and the impact of Motor Accidents on Mortality

An interesting development to watch is self-driving cars which I believe will have a massive impact on many areas of our day to day lives in the near future (especially for those of us working in Personal Lines insurance). Some of the interesting recent developments in this area have been:

My interest in the subject was sparked by some of the interesting deep learning applications for self-driving cars that Andrew Ng talks about in his recent Coursera course on Convolutional Neural Networks for computer vision.

This all got me wondering what the impact on mortality would be if self-driving cars reduced or eliminated the extra deaths caused by cars every year. In particular, who would this matter the most for – the young or the old, males or females – and what impact would this have on the shape of the mortality curve. It makes sense that it would take some time for self-driving cars to begin to have a noticeable effect on mortality, but if cars on the road would be autonomous, then it would be fair to assume that the majority of deaths relating to cars that currently appear in mortality data would be avoided.

To quantify the extent of the possible impact, I recalculated a mortality curve (more formally, a lifetable) for the USA and the UK with and without the impact of car related deaths. Obviously, self-driving cars will not immediately eliminate the entire burden of car related deaths, but this number represents an upper bound on the possible beneficial impact. The rest of this post will present the data sources used, the methodology I followed and the results.

The code for this post is available on my Github here:


I used two main sources of data. Firstly the cause of death data is from the WHO Mortality database (, which compiles death counts in 5-year bands by the ICD10 classification for a large number of countries around the world.

For exposure data, I used the Human Mortality Database – the HMD –  ( which has population numbers (as well as death counts and lifetables) for countries with relatively high quality demographic data. (Notably there is now also a Human Cause of Death database, but the information was not available at the level of granularity needed for these calculations).


After experimenting a bit, I landed on using the Centre for Disease Controls classification of the ICD-10 codes to identify the deaths due to motor accidents. This classification can be found here:

Some high level reconciliations to other data sources indicate that the USA numbers are a little higher than those reported to the NHSTA ( and the UK numbers are also higher ( One would need to have significant understanding of how each of these reporting systems work (in particular, how many deaths are reported to the NHSTA versus how many go into the USA vital registration and the same for the UK), so if anyone reading the post has some input, then please let me know!


I performed the analysis in two parts. Firstly, I worked out a set of ratios indicating the percentage reduction in deaths in each five-year age band from the WHO data. Secondly, I applied these ratios to the death data at each individual age from the HMD and then calculated mortality rates using the HMD population data.

The reason two steps were needed is because I couldn’t find a comprehensive database with cause of death information in single year age bands.


The following plot shows the percentage of total deaths attributable to motor accidents.


Both the USA and UK have fewer motor deaths over time at the relatively younger ages. I wonder if this is a real effect (due perhaps to improving safety technology in cars), or something not captured completely in the coding I used. The percentage of deaths attributable to motor accidents peak at the ages around which people first begin to drive. One possible insight here is that this is also an age when deaths due to “natural” causes are low, so “extra” accidental deaths at these ages will contribute significantly to the total number of deaths, whereas at the older ages, where “natural deaths” are high, the effect is less. Something else to consider is that driving ability probably improves with time.

After stripping the motor accident deaths out of the total deaths, I produced mortality rates (qx) as shown in the following plot. To smooth these out a little, I averaged the curves over five years (note that 2017 actually consists of data from only the 2015 year):

The major effect seems to be a flattening of the so-called accident hump between 20 and 30, with more impact in the USA than the UK. The declining impact of motor accidents over time is visible in the plots for both the USA and the UK.

The impact on life expectancy at birth is as follows:

Country_Name Sex Year_centre ex ex_no_traffic Increase
UK 1 2002  76.20                 76.44         0.24
UK 1 2007  77.49                 77.71         0.22
UK 1 2012  78.94                 79.06         0.12
UK 2 2002  80.77                 80.85         0.07
UK 2 2007  81.75                 81.82         0.07
UK 2 2012  82.78                 82.82         0.04
USA 1 1997  74.13                 74.68         0.55
USA 1 2002  74.64                 75.21         0.58
USA 1 2007  75.70                 76.24         0.54
USA 1 2012  76.65                 77.08         0.43
USA 1 2017  76.62                 77.06         0.44
USA 2 1997  79.56                 79.85         0.29
USA 2 2002  79.86                 80.15         0.28
USA 2 2007  80.74                 80.98         0.25
USA 2 2012  81.45                 81.65         0.19
USA 2 2017  81.47                 81.67         0.20

Immediately noticeable is the declining impact of motor accidents on life expectancy with time, for both countries and sexes. If we take 2012 as the most robust recent estimate, then the biggest beneficiaries of eliminating motor accidents would be males in the USA.

I recently read a blog post from Bill Gardner ( who frames a change in life expectancy in a clever way, by working out the number of years of life gained or lost for the current birth cohort due to a change in life expectancy. With this idea in mind, a gain in life expectancy of 0.44 is a highly significant improvement representing about 870 000 years of life gained for the 2012 male birth cohort.


This post examined the impact of motor accident related deaths on mortality and life expectancy in the USA and the UK, to provide a view of what the maximum possible impact of introducing self-driving cars, which presumably would eliminate most of the burden of motor accident related deaths, on public health would be. Of the four groups considered, the biggest beneficiaries would be males in the USA, with about 870 000 years of life gained if motor accidents were eliminated completely.

The post did not try to quantify how much or how quickly these benefits would be realized and it seems this would be quite speculative sitting here at the beginning of 2018. The post also ignored second order effects on mortality, such as the fact that people would probably have more time to spend on pursuits other than driving when self-driving cars become a reality and the fact that the gains in life expectancy could be partially offset by other competing risks.

I found it interesting that the impact on life expectancy is lower in the UK than the USA, and it would be worthwhile to reproduce the analysis for all of the countries in the HMD.

Links – Week of 24 December

Insurance Industry News

Trov offers a combination policy (Medical + Trip Interruption + Lost Items) to passengers in Waymo self-driving cars:

LindkedIn Announcement

FT Analysis

AXA teamed up with UberEATs to provide another combination policy (A&H and Third Party Liability) to its couriers in Europe:


I blogged about sub-prime auto and increasing frequency here:

Data Vis

Design secrets behind the FT’s best charts of the year


Simply Stats with a nice summary of interesting stats/R items from 2017:

Deep Learning

This came out a few weeks ago, but it’s worth noting this new approach to  neural networks – Capsule Networks – from Hinton:






Yield Curves – Might be useful for some African countries

Approximating risk-free curves in sparse data environments

Equity Valuation

Art, Science or Craft?

Climate Change and Property Values (via the amazing Marginal Revolutions blog):

From the abstract – Homes exposed to sea level rise (SLR) sell at a 7% discount relative to observably equivalent unexposed properties equidistant from the beach. This discount has grown over time and is driven by sophisticated buyers and communities worried about global warming.


USA Personal Auto Frequency and the link to Sub-prime Loans (Speculative)

A topic receiving some attention in the USA is the deteriorating profitability in both Personal and Commercial Auto. Quite a bit has been written in industry publications, and a good summary of the situation appears in the Swiss Re Global Insurance Review for 2017.

The reasons for the increasing loss ratios (driven by increased frequency and severity) are a matter of some debate and speculation. The Swiss Re article notes increased employment, lower prices of petrol, and more drunk and distracted driving as causes of the increased frequency (I’ve also seen legalization of marijuana given as a reason) and the increased costs of repairs of newer vehicles as driving severity. However, it doesn’t seem to me that anyone has a conclusive take on the subject so here is my contribution to the topic.

It is well known that credit scores are predictive of future claims and actuaries generally include credit scores in Auto pricing models (I am making no comment on whether this is a morally unacceptable thing to do). A very good paper on the subject is Golden et al. (2016) in the NAAJ who provide some figures relating to the impact of credit score on loss ratios, frequency and severity based on a sample of data from US based P&C insurers writing Personal Lines Auto in 1998. They also provide some explanations of why credit scores are predictive. They find that credit score is a significant predictor of both frequency and severity.

It is worth wondering what has happened to the average credit score of drivers on the roads in the US. An article linked in Matt Levine’s excellent daily newsletter Money Stuff of 21 December 2017 discusses the huge increase in sub-prime auto loans made after the crisis and notes that default rates are now at the same level as in 2010. If loan underwriting was made significantly weaker over the past couple of years and many more people with lower credit scores are now on the roads compared to earlier years, then it would be fair to expect that the average credit score is worse than in previous years. Also, if credit score is still predictive of frequency and the relationship holds at the lower credit scores, then it would be fair to expect increased frequency compared to prior years.

All things being equal, this wouldn’t apply to loss ratios, since the premiums quoted for this segment would be higher than for those with better credit scores. Of course, this may not have been fully accounted for in some pricing models. However, frequency is generally calculated without reference to premiums.


Golden, L. L., Brockett, P. L., Ai, J., & Kellison, B. (2016). Empirical Evidence on the Use of Credit Scoring for Predicting Insurance Losses with Psycho-social and Biochemical Explanations. North American Actuarial Journal, 20(3), 233-251.


Links – Week of 17 December

Insurance Industry:

Horrific year for insurers

Series C funding for Lemonade = $120m

Statistical Learning:

Intro to Gaussian Processes

New research:


Free book – Visualizing Mortality Dynamics in the Lexis Diagram


Individual claims reserving: a survey

Non parametric individual claim reserving in insurance