L'homme, ivre d'une ombre qui passe, porte toujours le châtiment d'avoir voulu changer de place. Charles Baudelaire, Les hiboux[1]

5. Deductions and data

If we overlook short-term fluctuations in the accident rate and other variables that influence it, we can deduce a major consequence of risk homeostasis: the annual accident loss is the consequence of the hourly risk people are willing to take times the time they spend on the road times the number of people in the population.

In other words, when we count up the total numbers of accidents across the entire road network in a jurisdiction, across the entire population, and over an extended period of time (such as one year), the total traffic accident loss (A) = the target risk (R) multiplied by the average number of hours (h) spent in traffic multiplied by the number of members in the population (N). This is the basic equation shown in Table 5.1.

The data necessary for direct testing of this equation are, unfortunately, lacking at present. While the number of people in the population (N) can be assessed with considerable reliability, and some estimates of the amount of time spent in traffic (h) are in existence, the value of the target level of risk (R) remains resistant to quantification, as has been discussed in Section 4.6. We will, therefore, have to resort to validating the main idea by testing the derivatives, the other two equations in the table.

As far as the total loss due to traffic accidents (A) is concerned, reasonably trustworthy accident data exist for fatalities only, although even these have been questioned.[2] Road accidents with property damage only, and even those with physical injury, are usually not reported in a reliable manner.[3,4] When focusing on fatal accidents, some of the available data may be inspected for their agreement with deductions that can be derived from the above equation when the terms are juggled around. This is precisely how the other two equations below were derived and you will have no difficulty in verifying that both are merely alternative versions of the one above.

The first of these deductions is cross-sectional in nature (see Equation 2 in the table). It says that the average moving speed in different road sections is inversely proportional to the accident rate per passing vehicle in those road sections. In Sections 3.1 and 3.3 we found evidence that the lower the accident rate per km driven in a given road section, the faster people will drive in that road section. The present deduction, however, is more demanding: the product of the accident rate per km driven and the average driving speed should be independent of the road section in which the driving is done.

This deduction involves a comparison, within the same time frame, of average moving speeds (in km/h) between various road sections with different accident rate records per vehicle-kilometre [A/(n x km)]. The term km/h stands for average vehicle speed in each road section, while A/(n x km) is the accident loss divided by the number of vehicles that pass a road section of a length measured in km. If findings agree with these deductions, they offer support for the notion that the accident rate is stable per time unit of exposure and independent of where the driving is done. Note that the comparison of speeds between sections is different from the study of speed differences between individual drivers at a particular location and how these are related to accident involvement.[5]

A word of warning! Please note that the cross-sectional deduction holds only to the extent that the value of the target risk level (R) is invariant across the different drivers who pass through different road sections. This may or may not be true, since it's conceivable that drivers with different target levels of risk choose different routes and are more likely to be seen in some road sections than in others. For the longitudinal deduction to bear out fully, it's necessary that the target level of risk (R) and the amount of time spent on the roads (h) remain constant over the years. This is not quite true, as we will see below, in Section 5.4, which discusses the effects of economic factors on the traffic accident rate. Finally, the amount of the accident loss (A) would have to be assessed in a constant fashion when testing either one of the deductions, and this condition is not likely to be approximated, unless one considers fatalities only.

5.1 Cross-sectional and longitudinal accident data

Another researcher did not observe the same drivers in each road section, but followed a somewhat different method of data collection. Accident rates for 40 different road sections in and around Detroit, Michigan, were gathered from police records over a two-year period. Accident severity was not considered, only accident numbers. For each road section, the number of passing vehicles was counted over a period of 48 hours, and the average driving speeds were determined over 84 hours, using a method that may have been more convenient than accurate.

From the data plotted in Figure 5.1, a correlation r = -0.57 may be calculated between the frequency of accidents per unit distance driven in various road sections, and average moving speed in these road sections. If the three outlying data points are disregarded, the correlation increases to r = -0.66.

As can be seen in this figure, the author related the accident rate (A) per million vehicle miles of each of the road sections to total travel time per road section (T), in an exponential function instead of a simple linear one (as the deduction from risk homeostasis would predict; see Equation 2 in Table 5.1). Additional calculations show, however, that the non-linear component, reflected in the curved solid line, is not statistically significant. It would seem that the data are in reasonable agreement with what the theory would expect: where the spatial accident rate is half as high, people drive twice as fast. This expectation is presented by the dotted line in Figure 5.1. In other words, the accident rate per time unit of exposure remains essentially constant from road section to road section.

Figure 5.1: Accident rates per million vehicle miles (m.v.m.) related to average total travel time per mile in various road sections of different road design (graph adapted).[6]

Figure 5.2: The traffic death rate per distance travelled, the traffic death rate per capita, and the road distance travelled per capita in the USA, 1923-1987.[8]

The product of the data points on these two curves equals the numbers of deaths per 100,000 inhabitants, and this per capita death rate shows no clear change over time. There are ups and downs in the per capita fatality rate and the causes of these will be the topic of Section 5.4. At this point we note that the ups and downs hover around an average of about 23 deaths per 100,000 residents, but, more importantly, over a period of more than 60 years, no consistent long-term upward or downward trend can be detected! Thus, there is general agreement with the longitudinal deduction: as the death rate per km drops to one-half, people drive twice as many kilometres. Consequently, the temporal accident rate--the traffic death rate per year per head of population--remains unaffected by the change in the spatial accident rate

5.2 The accident rate "per km driven" as distinct from "per head of population"

The reduction (by a factor of eight or so) in the death rate per unit distance driven between 1923 and 1987 may have been caused by interventions such as the building of more forgiving roads, the construction of more controllable and crashworthy cars, by advances in the medical treatment of accident victims, and other factors. At any rate, major progress has been made.

In contrast, the degree of traffic safety per citizen per year has not been so favourably affected. From the perspective of risk homeostasis theory, this is not surprising, because the theory expects people to change their behaviour in the face of accident countermeasures that do not alter the target level of risk, and to change it in a manner such that the temporal accident risk remains essentially the same. Accordingly, they simply "consume" the technological innovations for the purpose of maximizing their net benefit. And if their target level of accident risk is not reduced, there is no reason to expect the accident rate per citizen to go down.

As we have seen with respect to the cross-sectional deduction in Section 5.1, in those locations where the accident rate per vehicle-kilometre is low, drivers move faster and the accident rate per hour behind the wheel remains essentially unaltered. Driving at twice the speed allows people to cover a given distance in half the time, and by spending the same amount of time on the road they can double the amount of mobility. So, if more road sections that offer a low spatial accident rate are being built, people will react by adding to their mobility accordingly.

The fact that the curve describing mileage per capita shows no sign of tapering off in recent years suggests that the human desire for greater mobility is insatiable--provided faster travel is made available. In 1923, Americans travelled on average 760 miles (about 1,225 km) in motor vehicles. By 1987, this figure had risen to 7,840 miles (12,625 km). Note that these mobility rates are calculated per resident, not per licensed driver. They include everybody in the nation, regardless of age or whether they have a driver's licence.

So, when shall we call a safety measure effective? If we take the accident rate per km driven as the criterion, technological interventions can clearly be effective. They are productive from an engineering point of view, and any country's ministry of transport will be only too happy to point this out. Interventions of this kind are also productive for your own personal benefit, because they allow you to move faster per unit distance of mobility and thus to enjoy a greater distance of mobility against the same risk of death per hour on the road.

But from the point of view of public health, the story is quite different, since there is no reduction in the number of people killed on the roads. That country's ministry of health will not be equally pleased. Neither should you, because your likelihood of becoming a traffic fatality is not diminished, and it may even have increased! In fact, there have been periods in which the death rate per unit distance of mobility dropped while the traffic death rate per inhabitant showed an increase. In the years following the Second World War and including 1972, the year before the oil crisis, Ontario experienced an era of relatively steady economic growth. Data on the fatality rate per km driven are available as of 1955, hence the choice of the time period covered in Figure 5.3.

Figure 5.3: Traffic deaths per distance driven and per capita, and distance driven per capita in a period of economic growth; Ontario 1955-1972.[9]

This takes us to a remarkable inference: one and the same accident countermeasure may improve safety per kilometre driven and contribute to an increase in the accident rate per head of population! As other researchers have put it: "Making an activity safer may increase mortality."[12] The apparent paradox in this statement is due to the fact that making an activity such as driving safer per km of mobility may attract more people to it so that more people will die in that activity. Thus, the provision of more crashworthy cars and forgiving roads may lead to a reduction in the death rate per km driven, to no change in the death rate per hour of exposure to traffic, and to a higher traffic death rate per head of population.

Consider another scenario, one in the area of lifestyle-dependent health. Imagine that somebody invents a cigarette that reduces the death rate per cigarette smoked to one-half that of present-day cigarettes. Is that progress? Should the marketing of these cigarettes be hailed as a boon for public health? The answer is that it all depends. If there is no change in people's desire to be healthy, smokers might react by smoking twice as much. Their death rate would not be altered. But this is not the only potential repercussion: the very availability of the "safer" cigarette may lead fewer people to stop the smoking habit, and may seduce more non-smokers to yield to the temptation, because smoking has become less dangerous. As a result, the smoking-related death rate per capita would increase.

Once again, when shall we call a safety measure effective? The answer depends on the criterion of choice. The drop in the accident loss per unit distance of mobility may be viewed as a triumph by the ministry of transport, while the attendant rise in the traffic accident loss per capita may give rise to grave concern in the ministry of health. The latter might argue that "yes, the operation was successful, but the patient died." In other words, it would seem that engineering interventions for the purpose of greater safety can put more kilometres into people's years, but fail to add years to people's lives.

Whatever denominator one chooses for the calculation of the accident rate, it is obvious that a clear distinction should be made between the accident rate per unit distance of mobility, and the accident rate per hour of road use or per inhabitant. If the denominator of the accident rate is not clearly spelled out, the discussions about traffic safety and about theories of accident causation and the effectiveness of diverse accident countermeasures will remain muddled forever, as they have been in the past and currently still are.[13]

5.3 A historical note on what happened between 1870 and 1910

Around the turn of the century, motor-vehicle fatalities, and those associated with bicycles, including those wonderful velocipedes, became more frequent from year to year, while those associated with horses and horse-drawn vehicles--the latter not shown in the graph--dropped, and the total number of traffic fatalities showed no clear upward trend. Without a change in their total number, fatal accidents appeared to have undergone a metamorphosis: the horse was replaced by the engine as the source of power, and the carriage was replaced by the car as the vehicle of death. There was risk redistribution, but no risk reduction. Mobility increased, but no change in the overall traffic death rate is apparent in these early data. In Chapter 12 we shall see that, in a similar fashion, the overall violent death rate per capita has not changed appreciably between 1900 and 1975 in the majority of countries.

Figure 5.4: Road deaths related to various means of transport in England and Wales from 1870 to 1910. [15]

5.4 Traffic accidents and the state of the economy

As was discussed in Section 4.1, the target level of risk is assumed to depend on four classes of utility factors:

1. The benefits expected from risky behaviour alternatives.
2. The costs expected from cautious behaviour alternatives.
3. The benefits expected from cautious behaviour alternatives.
4. The costs expected from risky behaviour alternatives.

When the economy is in a recession, the benefits expected from risky behaviour are reduced, because time is worth less money. There is less to be gained from driving many km and from driving fast. There is less to be gained from driving through a red or amber light or from cutting corners in other ways. At the same time, the costs expected from risky behaviour are increased, because the costs of accidents, gasoline, insurance surcharges for having an accident, of car repairs, of vehicle wear and tear, etc., rise relative to real income. In terms of Figure 4.2 in Section 4.1, expected gain (the top curve) moves downward and the expected loss (the bottom curve) drops moresharply, with the result that the optimal level of exposure to risk (the point marked by the arrow) moves toward the left, indicating a lower level of target risk.

This is precisely why some of the complex formulae that have been developed by economists for the purpose of longitudinal prediction of accident loss have included price and income fluctuations over time, among several other variables. But the interpretation of these prediction equations has often been obscure.[16,17] In part, this was due to lack of independence between the variables that were entered into the prediction formulae. It was also due to heterogeneous criteria that were being predicted, for instance, deaths per km driven in some studies and deaths per capita in others. That these two criteria are not interchangeable as yardsticks of safety has been shown in Section 5.2. In fact, decreases in the accident loss per km driven may occur in the same time period in which the loss per head of population remains unaltered or even increases. Different criteria of safety may be as different as apples and oranges, and confusion between them turns comparative studies into lemons.

The difficulties of interpretation have been reduced by the simpler equations put forward in recent times. In a study of American trends in the annual numbers of people killed in traffic between 1960 and 1983, a set of no more than three variables produced a remarkably accurate prediction. The variables were: the annual numbers of people unemployed, the number of workers employed, and the number of people not in the labour force. When USA citizens between ages 15 and 19--whose financial prosperity is particularly sensitive to economic fluctuations, since they're the last to be hired and the first to be fired--were considered separately, the relationship between the economic juncture and the traffic death rate was found to be even more pronounced than in the population as a whole. The young don't have the financial reserves to buffer the impact. In statistical terms: the coefficient of determination was R² = 0.89 forthe citizenry as a whole and R² = 0.98 for people between 15 and 19.[18] The coefficient of determination, by the way, simply equals the square of the correlation coefficient (r).

It should be noted that, due to the growth of the American population by about 1% per year, the interpretation of the marked correlation between the predicting variables still presented a problem. Increases in the size of the population alone, when everything else remains the same, would be expected to lead to an increase in the number of people killed. Population increases alone would not, however, be expected to lead to an increase in the traffic fatality rate per 100,000 inhabitants.

This is also true for a study of British data[19] that used a slight modification of the earlier procedure and arrived at a somewhat lower coefficient of determination: R² = 0.88. Another researcher avoided the lack-of-independence problem by expressing the unemployment rate as a percentage of the work force.[20] Marked correlations were found (simple r's in the order of 0.7) between monthly unemployment statistics for younger and older males and females in British Columbia and the traffic casualty rate per 106 km driven during 84 consecutive months from 1978 through 1984. The study concluded that "some portion of [the decrease in frequency and severity of road accidents] can be attributed to increases in unemployment which appear to remove young male drivers from the driving population". It should be noted that this investigation focused on the rate of accidents per unit distance driven, not per head of population, although the latter would seem to be the criterion of greatest interest from a public health and safety perspective.

5.4.1 Additional analyses of unemployment rates

Figure 5.5: Annual variations in the unemployment rate and the traffic death rate per capita in the USA, 1948-1987.

Figure 5.6: Annual variations in the unemployment rate and the traffic death rate per capita in the Netherlands, 1968-1986.

To complicate matters further, over the years there have been changes in various countries in the proportion of young people in the population, with the young being involved more often in accidents and more likely to be laid off in bad economic times. There have also been changes in the definition of what constitutes "being unemployed" as well as changes in legislation and in agreements that offer employees greater or lesser protection from being laid off. The implication is that changes in the economic juncture may be less directly reflected in the unemployment rate of some countries than in others, and less in some time periods than in others.

5.4.2 New questions arising

Furthermore, when the road fatalities vanish during bad economic times, where do they go? Are they replaced by other forms of violent death, such as suicides and homicides?

Is the reduction in the traffic death rate offset by an increase in other forms of lifestyle-dependent death, for instance, in mortality associated with smoking, drinking, exercising too little or too much, or other health-relevant habits?

Does the reduction in the traffic fatality rate per capita during bad economic times signify a net decrease in mortality when all causes of death are considered, or do causes of death that are usually not attributed to lifetyle become commensurately more prominent?

The second question on which some data were analysed concerns the process through which an economic recession leads to a reduction in traffic fatalities per capita. Do people drive less or do they drive more safely, or both? Again, data were derived from the National Safety Council and the US Department of Labor. The mileage per capita was calculated by dividing the death rate per capita by the death rate per mile (note that km/A=(A/N)/A/km); see Table 5.1). As is suggested by Figure 5.7, both effects occur.

Reductions in mileage driven or reductions in the rate of growth in mileage driven seemed to occur in years that showed a major increase in the unemployment rate, e.g. 1954, 1958, 1974 (the year of the oil crisis), 1980 and 1982. Sudden reductions in the death rate per mile driven can also be seen in years in which unemployment surges: 1949, 1954, 1958, 1961, 1974 and 1982. Increases in employment seem to be associated with more road mobility per head of population and with more road deaths per mile driven. So, during bad economic times people reduce the distance they drive, and when they drive, they drive in a more cautious manner.

How can the remarkable patterns presented in this section be explained? It would seem absurd to suggest that the traffic death rate is responsible for the unemployment rate. Not enough employed people die on the roads to provide substantial job opportunities for those out of work. Two other possibilities remain: either the fluctuations in the unemployment rate cause the variations in the death rate, or the fluctuations in both are due to some third factor or set of factors. I think that the first of these offers the most likely explanation. For reasons mentioned at the start of this section, when the economy is depressed, so is the level of risk people are willing to take on the road. When the economy is booming, there is also more to be gained from more and faster driving. In such a period, the value of current time is increased.[30]

Figure 5.7: Annual unemployment rate, traffic death rate per mile driven and mileage driven per capita, USA, 1948-1987.[31]

5.5 Is there no counterevience?

their form, but with their substance.

First, some critics have pointed out that, over the years, there have been major reductions in the traffic accident rate per distance travelled. As you can see from Figures 5.1, 5.2 and 5.3, this is indeed an observation of fact. Facts, however, can only contradict a theory to the extent they are in conflict with what a theory predicts. RHT does not say that the accident rate per kilometre driven cannot be reduced--witness Chapters 4 and 5. If it did, the theory would be as unrealistic as this criticism is irrelevant. RHT deals with accident rates per time unit of road-user exposure, including the risk per head of population per calender year (see the beginning of this chapter and Section 5.2).

Second, some critics attack RHT because they fail to distinguish between the cross-sectional and longitudinal predictions that follow from RHT, as specified in Table 5.1 at the beginning of this chapter. Here are the facts: the traffic accident toll in the USA, expressed as the number of fatalities divided by the estimates of aggregate distance driven in motorized travel, diminished by a factor of approximately 2.5 over the years from 1943 to 1972 (see Figure 5.2). If the time spent on the road and the target level did not change in this period, and if one may overlook the comparatively small kilometrage in non-motorized road travel, then the average speed of mobility must have increased by this same factor 2.5 if RHT is correct. The critics in question[33,34] follow the same train of thought, but their reasoning derails beyond this point. They say that the average speed of motor vehicles should have increased by this factor and, as this is not the case, RHT must be wrong. However, the correct inference from RHT--which is also drawn by others[35]--is that the average speed of road mobility of the population should have increased by that factor when aggregated across all modes: on foot, by bicycle, automobile, etc. Somebody who buys her or his first car also generally purchases a greater speed of mobility.

Consider now that, in the period concerned, the number of motor vehicles per US inhabitant has risen from 0.23 to 0.58, the number of driver's licences from 0.34 to 0.56, while the network of high-speed roads has been greatly expanded and cars have been made more powerful. Consider also that the estimate of the total motor vehicle mobility divided by the number of inhabitants increased approximately fourfold, i.e., from some 1500 to 6000 miles on average per head of population. Although it may not be possible to determine from these data by how much the average speed per citizen (aggregated across all modes) in road traffic has increased, there would seem to be no evidence in clear conflict with the RHT estimate of a factor of about 2.5.

Third, the well-established fact that accidents are usually, though not always, more frequent when it is raining has been called "a good demonstration of the failure of risk homeostasis".[36] Indeed, RHT would have some explaining to do if it were true that the total accident loss (the sum of frequency of accidents times their average severity) per road user in rain is greater than in fair weather, but no such fact has been established.[37] It turns out that accidents in rain, although more numerous per kilometre of driving,[38] are less severe on average than those on dry pavement. For instance, over a seven-year period in Ontario, the ratio of recorded fatal to personal-injury accidents under dry conditions was found to be about 40% higher than under wet pavement conditions. This ratio was about the same or higher still when dry road conditions were compared with pavements covered with loose snow, slush, packed snow and ice. Moreover, the fatal plus personal-injury accidents constitute a smaller fraction of all recorded accidents when they happen in rain.[39]

A report published by a group of international experts mentions that in the city of Oslo, 15% of all accidents happened on snow and ice-covered roads, though they carried only 5-10% of all traffic, but the relative number of fatal accidents was found to be lower; there was more material damage and less personal injury.[40] Further, several studies report a reduction in both motorized and pedestrian traffic under rainy conditions.[41,42] Similarly, in Britain, thick fog has been found to reduce traffic volumes to about 70% of normal on weekdays and to about 50% on weekends.[43] On an expressway in France, heavy rain was found to cause drivers to increase the time gap between the car ahead and themselves, and to reduce average speed by as much as 36 km/h.[44]

It would seem reasonable to conclude from this that people react to inclement weather in at least two ways: they reduce the amount of travelling under these conditions and they behave in traffic in a manner such that, although more accidents happen per km driven, the average severity of the accidents is considerably less than when the weather is fine.

Suppose, nevertheless, that it had been established that the accident loss per time unit of road-user exposure is greater in rainy weather. Would that necessarily gainsay RHT? Rain and wet roads reduce both motorized and pedestrian travel and this reduction is self-selective: some people decide to stay off the roads while others decide to travel. It has been observed that under rainy conditions, there is an increase in the proportion of male highway drivers to the total number of those who are still on the road.[45] These individuals may have a higher habitual level of risk tolerance. Additionally, their risk acceptance may also be raised temporarily. Using the roads under adverse conditions is experienced as unpleasant, and this is why many refrain from it. People may attempt to reduce the duration of their trip and thus accept more accident risk than they normally would. Although drivers slow down in the rain (sometimes by little[46] and sometimes by much[47,48]) and pedestrians tend to move faster, the adaptation in speed may be less than would occur without the momentary increase in risk acceptance. Alternatively, it may be true that those who brave adverse weather are unrepresentative of the road-user population as a whole, in that they underestimate the danger of an accident under these conditions more than is true for the population in general.

Whatever the value of these interpretations, it is difficult to see clear evidence against RHT in the observation that there are more accidents in the rain.

Several other observations have been mentioned by various authors as counter-evidence to RHT. Examples are: the effects of speed limits; the effects of special road markings on drivers' speed and accidents at junctions; the effects of new occupational health legislation upon accidents in industry; the fact that there have been reductions in the occupational accident rate over several decades; the alleged safety benefit of radial versus cross-ply tires and studded tires in particular; the supposition that the obligation to wear crash helmets is beneficial to the safety of motorcyclists; and the idea that the manufacture of more crashworthy cars increases the safety of the driver. All of these objections seem relatively easy to refute,[49,50] and so is the argument that the drastic reduction in the per capita traffic accident rate that has occurred in Japan constitutes evidence against RHT (see Section 8.4).

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