category: literaturenote citekey: taymarginaleffectincreasingageing2008 title: Marginal effect of increasing ageing drivers on injury crashes authors: "Tay, Richard" year: 2008 date: 2008-00-00 2008 doi: 10.1016/j.aap.2008.07.012 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2008.07.012" zotero_key: 3SAGSNPW zotero_storage: KJ84TTZA collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Tay, Richard"

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Accident Analysis and Prevention

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Short communication

Marginal effect of increasing ageing drivers on injury crashes

Richard Tay^∗

Department of Civil Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4

article info

Article history: Received 14 October 2007 Received in revised form 6 June 2008 Accepted 14 July 2008

Keywords: Marginal effects Ageing drivers Injury crashes Licensing

abstract

The safety effects of the ageing driving population have been a topic of research interests in health and transportation economics in recent years due to the ageing of the baby boomers. This study adds to the current knowledge by examining the marginal effects of changing the driver mix on injury crashes using data from the Canadian Province of Alberta between 1990 and 2004. Results from a Poisson regression model reveal that increasing the number of young and ageing drivers will result in an increase in the number of injury crashes whereas increasing the number of middle-aged drivers will result in a reduction. These results are in contrast to those obtained in a previous study on the marginal effects of changing the driver mix on fatal crashes in the Australian State of Queensland and some possible explanations for the differing results are provided.

1. Introduction

Like many countries around the world, the population of Canada is ageing. The number of mature drivers, defined as drivers who are 65 years of age or older, increased by 1.8 times the general population between 1988 and 1998 (Transport Canada, 2001). More importantly, although total casualty collisions had decreased over that decade, collisions involving mature drivers had increased. In 1988, 10.5 and 8.1% of fatal and injury collisions involved at least one mature driver but these percentages increased to 15.5 and 11.5%, respectively, in 1998 (Transport Canada, 2001). It should be noted that the ageing drivers' share of total driving population has increased by amuch larger amount than the corresponding increase in their share of the total crashes. The marginal effect of increasing the number of ageing drivers is therefore uncertain.

Moreover, the above statistics provide only a partial view of the effects of increasing the number of ageing drivers on road safety because they ignore the interactive effects due to the changing driver mix on the roads (Tay, 2006). Any significant increase in one segment of the driving population will change the traffic flow, highway design requirements and social norms, resulting in a change in the average crash risks of all drivers. For example, in anticipation of an increase in the number of aging drivers, many jurisdictions including the Province of Alberta have developed new highway design and operational guidelines to accommodate these drivers (Zein et al., 2006) which are adapted from similar guidelines published in the United States (FHWA, 1998, 2001, 2004).

Taking these effects into consideration, Tay (2006) found that increasing the number of ageing drivers did not have a significant effect on the total number of fatal crashes in the Australian State of Queensland. However, the four years of monthly data in Tay (2006) did not exhibit substantial variations in the number of licensed ageing drivers. Furthermore, since many ageing drivers self-regulate to compensate for their decrease in driving abilities, their impact on the most severe type of crashes (fatal crashes) is therefore not expected to be significant whereas their effects on less severe crashes may be more pronounced (Raitanen et al., 2003; Hakamies-Blomqvist and Peters, 2000; Hakamies-Blomqvist et al., 2002; Owsley et al., 2003). In particular, since many aging drivers drive slower than the average traffic, the severity of any crashes they may be involved in is expected to lower.

Therefore, this study will instead examine the relationship between changing the number of ageing drivers and the number of injury crashes using data from the Province of Alberta in Canada. In Alberta, the total number of drivers aged 65 and above increased from 119,369 to 217,372 between 1990 and 2004 which represented an increase of 82.1%. Therefore, there is a relatively larger variation in the number and share of ageing drivers on the roads compared to the data used by Tay (2006). In addition, this study will examine the effect of increasing the number of ageing drivers on injury crashes instead of fatal crashes.

2. Data

Annual data on licensing were provided by Alberta Infrastructure and Transportation for the years 1990–2004. Annual data on crashes were obtained from the annual reports for the corresponding years published by Alberta Infrastructure and Transportation.

^∗ Tel.: +1 403 220 4725; fax: +1 403 282 7026. E-mail address: rtay@ucalgary.ca.

For simplicity, the licensing data were grouped into three categories: young drivers (25 years old and below), middle-aged drivers (26–65 years old), and ageing drivers (above 65 years old). Preliminary analyses using both 65 and 75 as the threshold ages found the results to be very robust with respect to this minor change in the definition of the ageing driver (Tay, 2007).

The Alberta collision data were reported by three severity categories: fatal crash, injury and total crashes. The annual report, however, does not provide information on the number of crashes by age or gender. Although it would be insightful to analyze both the total number of crashes and the number of crashes involving ageing drivers, this limitation is not significant. As argued by Tay (2006), changing the driver mix on the road would have a significant effect on crashes involving all age groups due to the change in the traffic system mentioned above.

3. Trend and correlation

The relationship between the number of aging drivers (aged 65 and above) and the total number of fatal crashes per year and is shown in Fig. 1. It is clear from Fig. 1a that there is no relationship between the number of aging drivers and the number of fatal crashes per year. This result is consistent with those obtained by Tay (2006) and shows that the marginal effect of increasing the number of aging drivers on the number of fatal crashes is negligible. More importantly, our results are in contrast with the findings that ageing drivers have higher fatal crash risks and thus increasing the number of aging drivers will lead to an increase in the number of fatal crashes.

It is also clear from Fig. 1b that the overall shape of the relationship between the number of aging drivers and number of injury shows a linear relationship, especially in the middle, although there may be some non-linearity at the ends. In fact, the correlation was estimated at 0.904 (p < 0.01). At the lower levels during the period analyzed, the total number of injury crashes does not appear to be dependent on the number of drivers aged 65 and above. However, as the number of drivers increases beyond some critical threshold,

Fig. 1. (a) Relationship between ageing drivers (>65) and fatal crashes and (b) effects of ageing drivers (>65) on injury crashes.

the total number injury crashes appears to be strongly and positively related to the number of ageing drivers. Conversely, beyond the second threshold, the relationship changes to a negative association between the number of ageing drivers and the total number of injury crashes. It should be noted that since the number of data points at both ends are quite small, we can not rule out the possibility that there is no threshold or turning point but simply random chance that produces the slight non-linearity at the ends.

4. Poisson regression model

All else held constant, the number of injury crashes per year, y, was assumed to be dependent on the number of drivers in each of the following age categories: young (under 25), mid-age (25–65 years old) and ageing (above 65 years old). The number of injury crashes was used for several reasons. First, fatal crashes are relatively rare events and therefore using only fatal crashes, will ignore a large part of the social cost associated with road crashes (Tay, 2002, 2006). Second, although property damage only crashes make up a large portion of the total crashes, the reliability of data is quite low and the under-reporting rate may be non random (Giles, 2001). Therefore, including property damage only crashes may create unexpected biases in the estimates.

One of the main determinants of the number of motor vehicle crashes is exposure, which is often captured by proxy variables such as vehicle kilometres travelled, driving population, vehicle population or gasoline consumption. Since the number of drivers and the number of vehicles are highly correlated with the main independent variables (number of licensed drivers by age groups), the amount of gasoline sold will be used to capture the effects of traffic and economic activities. Finally, a Trend term is included in the model to capture any longer term trend that may arise due to gradual changes in road environment or vehicle improvement over time (Joksch, 1984; Tay, 2003, 2005a,b,c).

The choice of estimation method in any statistical analysis is a combination of both art and science because the statistical properties of different models may vary depending on the validity of their underlying assumptions (Noland and Karlaftis, 2005; Tay, 2005a). Although the most widely used method of estimation is the standard regression or the ordinary least squares method, there are some concerns that the number of injury crashes per time period may not have a Normal distribution but instead follow a Poisson distribution (Michener and Tighe, 1992; Nicholson and Wong, 1993; Tay, 2001). Therefore, a Poisson regression model will be used in this analysis.

$$P(Y = y) = \frac{e^{-\lambda} \lambda^y}{y!}, \quad y = 0, 1, 2, 3...$$ (1)

$$ln(\lambda) = \beta_0 + \beta_1 Trend + \beta_2 Gas + \beta_3 Young + \beta_4 MidAge + \beta_5 Ageing$$ (2)

where is the mean of the distribution.

The above model is estimated using the software Limdep v8.0. One common concern on using the Poisson regression model is the possibility of over-dispersion. However, the Cameron and Trivedi (1990) test found no conclusive evidence of over-dispersion.

5. Estimation results

The estimation results are reported in Table 1. Overall, the model fitted the data very well, with a very high Chi-square statistic and extremely small p-value, a very high pseudo-R-square, and all the estimates are highly significant and have expected signs. There is a decreasing long term trend in the number of injury crashes per year that can be attributed to longer term improvements in road infrastructure and vehicle safety. As expected, increases in travel demand,

Table 1 Estimation results

Number of observations	15
Log-likelihood function	−240.9
Restricted log-likelihood	−2874.3
Chi-squared	5266.8
p-Value	<0.0001
Pseudo-R-square	0.944

Variables	Coefficients	p-Values
Constant	6.4075	<0.01
Trend		<0.01
Gas sales	−0.2036	<0.01
Under 25 years old	0.2156E−06	<0.01
25–65 years old	0.7978E−05 −0.3995E−05	<0.01

as captured by gasoline consumption, are positively related to the increases in the number of injury crashes.

The results in Table 1 also show that the effects of changing the driver mix on Albertan roads on the number of injury crashes are similar to those expected in conventional wisdom. An increase in the number of young or ageing drivers are associated with an increase in the number of injury crashes whereas an increase in the number of middle-aged drivers is associated with a decrease in the number of injury crashes per year.

6. Discussion

The safety effects of the ageing driving population have been a topic of research interests in health and transportation economics in recent years due to the ageing of the baby boomers (Tay, 2006; Morrisey and Grabowski, 2005; Grabowski et al., 2004; Levy et al., 1995). This study adds to the current knowledge by examining the marginal effects of changing the driver mix on injury crashes using data from the Canadian Province of Alberta between 1990 and 2004. During the period analyzed, the ratio between the smallest and largest number of licensed ageing drivers in Alberta is almost double. This drastic increase in the number of ageing drivers has raised some concerns among researchers and policy makers because ageing drivers often experience higher average fatalities rates. However, no study has yet been done on analyzing the marginal effects of increasing the number of ageing driving on the number of motor vehicle crashes in Alberta. As suggested by Tay (2006), using the average crash rates for drivers from different age groups to project the likely effects on crash outcomes may result in erroneous conclusions.

Simple analyses of the trends and correlations indicated that the number of licensed ageing drivers appear not to be related the number of fatal crashes but strongly and positively correlated with the number of injury crashes. Hence, a Poisson regression model of the effects of changing the number of young, middle-aged and ageing drivers on the number of injury crashes were estimated. The regression results show that increasing the number of young and ageing drivers are expected to increase the number of injury crashes whereas increasing the number of middle-aged drivers is expected to have the reverse effect.

The regression results are consistent with the conventional wisdom that rely on the average crash rates of the three groups of drivers (Evans, 2004) but in contrast to the results obtained by Tay (2006). One possible reason for the significant relationship found in Alberta, in contrast to the insignificant association found in Australia is the difference in the performance indicator selected. Tay (2006) used the number of fatal crashes per month whereas our analysis used the number of injury crashes per year. As shown in Fig. 1a, similar results would be obtained in Alberta if fatal crashes were used as a performance indicator. Instead, this study analyzed the marginal effect of increasing the number of aging drivers on injury crashes and was able to find a significant effect.

Since many ageing drivers are expected to self-regulate and compensate for their reduced driving abilities by driving at a slower speed, minimizing their exposure at night, wearing a seat belt, not drinking and driving, driving in familiar environment, etc., which will reduce both their likelihood and severity of crashes, the marginal effect of increasing the number of ageing drivers may be more significant in terms of injury crashes than fatal crashes (Raitanen et al., 2003; Hakamies-Blomqvist and Peters, 2000; Hakamies-Blomqvist et al., 2002; Owsley et al., 2003).

It should be noted that one of the self regulations and risk compensations adopted by many ageing drivers is a reduction in exposure which will result in a reduction in the number of crashes even if the average crash risk per distance travelled remains the same. This effect may partly explain the finding that the contribution of ageing drivers to traffic fatalities is the lowest among the three age groups. This result is found in many jurisdictions as well (Evans, 2004).

Another possible contributing factor for the difference between our results and Tay (2006) is the larger range in the number of licensed ageing drivers in Alberta (almost doubled during the period as compared to 1.2 times in the Australian study) and the relative share of ageing drivers (6.4–9.2% in our study as compared to 7.1–7.8% in the previous study). Since these studies rely on correlation analyses, larger variations in the explanatory variables are more likely to reveal any underlying relationship between the variables.

Moreover, it is possible that the relativemagnitudes of the different effects on the characteristics of the traffic systems are different between the groups of drivers in the two countries. The relative shares of the different driver groups in both countries are quite different as well as the relative trends in their growth over time. Therefore, even though the analytical model developed by Tay (2006) may still be applicable, the results obtained using data from a different location and time may produce a different net outcome. These results serve to remind us that although theoretical models can be transferred as long as the underlying assumptions are satisfied, empirical results can only be generalized after repeated studies have produced similar results.

Acknowledgements

Financial support from the Alberta Motor Association and the Social Science and Humanities Research Council of Canada are gratefully acknowledged but the views expressed by the author do not necessarily reflect those of the sponsors.

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