Is vehicle weight associated with risky driving behavior? Analysis of complete national records

Abstract

A clear trend of shifting towards larger, heavier vehicles on roads fuels what has been described as an “arms race.” While larger, heavier vehicles have been shown to benefit the safety of users in the event of a car crash, it is likely that consumers’ experience of this increased safety will lead to behavioral adaptation towards more risky driving behavior. Using complete national data of the car fleet and police-issued speeding tickets over the course of an entire calendar year in Israel, we examined the association between vehicle mass and risky driving behavior in terms of speeding tickets. Controlling for consumers’ choice of car, our results indicate a positive association between vehicle mass and speeding tickets, suggesting that larger, heavier vehicles are associated with risky driving behavior.

1 Introduction

Over the last dozen years, a clear trend of shifting towards larger, heavier, and more powerful passenger vehicles has developed. Whereas car mass fell within each vehicle category (i.e., sedan, SUV, and minivan), market trends led to an increase in the average mass of new vehicles, indicating a shift in demand towards larger and heavier categories (US Environmental Protection Agency, 2021). For instance, the share of sport utility vehicles (SUVs) out of all new passenger vehicles sold in the US has tripled in the last 40 years (Winston & Yan, 2021), and is expected to account for 78% of the US market by 2025 (Voelk, 2020).

On top of pollution concerns,¹ experts and consumers argue that much more than regular size vehicles, the ever more popular large vehicles, such as crossovers, SUVs, and pickups, pose increased danger to pedestrians and cyclists (Schmitt, 2021; Zipper, 2020). Heavier vehicles are also usually higher than lighter vehicles and are, thus, likely to impact other non-motorist road users on their bodies and heads rather than their legs, thereby causing more serious injuries (White, 2004). Individual and social considerations are at play: the accentuated presence of large passenger vehicles fuels what has been described as an “arms race,” in which consumers purchase larger and heavier vehicles for comfort and self-protection (White, 2004; Wills, 2022), which, in turn, enhances preference towards these vehicles (Thomas & Walton, 2008). From a societal perspective, smaller vehicles would have been advantageous because of the lower threat posed to others in the event of a collision (Bento et al., 2017; Mu & Yamamoto, 2019; Tyndall, 2021).

Consumers might use products in risky ways. Vehicles provide a valuable and promising arena for consumer behavior research (Tomaino et al., 2020), especially in understanding how products influence behavior in safety-related contexts. Identifying the root causes of risky driving behavior is crucial for preventing or mitigating harm to drivers and their surroundings. Given the potential implications, this concern is pertinent for consumers, marketers, and policymakers alike. A critical concern stems from consumer preference for larger, heavier vehicles, which may foster a false sense of safety, potentially leading to behavioral adaptation and increased risk seeking. Consumer behavioral adaptation in the form of increased risk seeking is evident in a variety of situations. For example, climate affects mood and thus risky behavior because individuals seek arousal to repair their mood (Parker & Tavassoli, 2000). Individuals experiencing loss adapt their behavior and increase risk taking in gambling (Andrade & Iyer, 2009), and individuals experiencing safety in their location choose riskier products (Esteky, 2022).

Specifically in the realm of private vehicles, to fit their desired level of risk, individuals strive to counteract any external safety gain by adapting their behavior to compensate for the gain, in an attempt to recapture homeostasis (Wilde, 1982). As a result, behavioral adaptation of heavy vehicle drivers is likely to reduce the benefit of the vehicle’s greater objective safety for its occupants (Hedlund, 2000).

The present study aims at investigating the association between vehicle mass and risky driving behavior, taking advantage of complete national level data for the entire car fleet and police-issued speeding tickets during 1 year. We postulate that the larger and heavier the vehicle, the safer it feels, which enhances behavioral adaptation. Therefore, controlling for vehicle choice, drivers of large and heavy vehicles might be more prone to risky driving and thus pose more threat to others than might be expected.

2 Literature review

2.1 Enhanced safety and consumer behavior

The complexity of human behavior in response to enhanced safety and the way it might lead to risky behavior feeds an ongoing discussion in the literature. Iyer and Singh (2018) suggest that consumers exert less effort to reduce the probability of accidents, when they perceive the product (e.g., automobiles) as a high safety one. Bolton et al. (2006) find that products and services that mitigate risk by reducing its likelihood or severity can backfire and increase risky behavior, seriously impairing consumer welfare. For example, drugs for weight management both lowered the perceived risk of gaining weight and decreased the motivation to engage in preventive activity (Bolton et al., 2008, 2015). That is, a remedy for a risk decreases individuals’ motivation to act to prevent the potential risk. Soleymanian et al. (2019) suggest that immediate and periodic feedback on risky driving behavior can contribute to a safer driving. A meta-analysis showed that cues, such as warning labels, do indeed cause consumers to modify their behavior and promote safe usage (Purmehdi et al., 2017). However, a different meta-analysis demonstrated that in more than 20% of cases, behavior was modified in the opposite direction: cues informing that usage could be risky drove reckless behavior (Cox et al., 1997). A third meta-analysis that specifically examined the effects of threat-based messages on risky driving indicated that when driving is a source of self-esteem for drivers, death-related appeals provoked defensive responses that increased risky driving (Carey et al., 2013).

2.2 Enhanced safety in large vehicles

Several studies have shown that drivers feel safer in large vehicles. Drivers perceive larger vehicles to be safer (Thomas & Walton, 2008), and indicated that the primary reason for purchasing them was considering their own safety (Axsen & Long, 2022; Davis & Truett, 2000; Thomas & Walton, 2008). Accordingly, SUV drivers were found to have higher perceived safety compared with other car drivers (Thomas & Walton, 2007), in line with recent research indicating that an elevated viewpoint increased individuals’ risk taking primarily due to an increased sense of control (Jami, 2019).

2.3 Measuring risky driving behavior

To study risky driving, a prime measure in the literature is speeding tickets (e.g., Melman et al., 2017; Vertlib et al., 2023). An increase of the vehicle’s speed decreases the driver’s response time, increases the probability of involvement in a collision, and increases the severity of injury of the driver and other road users (Aarts & Van Schagen, 2006; Hedlund, 2000). Moreover, speeding is specifically associated with behavioral adaptation (Fuller, 2005; Smiley & Rudin-Brown, 2020). Therefore, if indeed a larger vehicle is associated with behavioral adaptation of more risky driving, speeding violations are expected to reflect this linkage.

2.4 Research context—the car market in Israel

Our research context is the private car market in Israel, with 2.98 million privately owned passenger vehicles at the end of the studied period (CBS, 2021), of which about 262,000 were newly purchased (Israel Ministry of Transport and Road Safety, 2022). Similar to other countries, the composition of the Israeli car market demonstrates a steady increase in the volume and share of SUVs and other large passenger vehicles (Steren et al., 2022), where the average mass of newly sold vehicles increased by 17.6% from 1653 kg in 2000 to 1943 kg in 2021 (Fig. 1). Fatal car crashes caused an annual average of 38.9 deaths per 1 million inhabitants in Israel, somewhat lower than Canada, higher than the UK, and similar to Germany (OECD, 2022a). The car market in Israel is different from other countries in that there are no local car manufacturers; thus, all vehicles are imported. During the studied period, the Israel Police issued 685,175 traffic violation tickets, of which 134,392 were for speeding.

Fig. 1

Average car mass of newly sold vehicles in Israel (authors’ calculations, based on Israel Ministry of Transport and Road Safety, 2022)

3 Methodology

3.1 Data

We use data of the Ministry of Transport and Road Safety in Israel, which include records of all passenger vehicles that were active in 2018. To these data, we matched all speeding tickets issued by police vehicles in 2018 obtained from Israel Police. Our data allow us to account for all vehicles with speeding violations and all those without speeding violations active during an entire calendar year. Additional advantages are that the data are a census rather than a sample, providing the strong external validity of real-world data, and that the data were collected by authorities, whereas self-report measures of mileage and violations are unreliable (af Wåhlberg & Dorn, 2015). Moreover, these real-world data reflect actual actions of drivers in their actual environment which is affected by other drivers (Jacobsen, 2013).

Each observation in our database represents a specific vehicle configuration and includes brand and model, mass, horsepower, propulsion technology, fuel type, gear type etc., and the number of speeding tickets issued in 2018 to drivers of this particular vehicle configuration. For each vehicle configuration, the number of active vehicles in 2018 functioned as weighting factors in the estimation, such that overall, we analyze the entire Israeli car fleet, which included 3095 unique configurations, representing 2,162,525 vehicles.² Whereas this data structure does not enable identifying a specific vehicle or driver conduct within vehicle configurations, it has two meaningful advantages: (1) it enables a focus on the effect of the type of vehicle and its attributes that is above and beyond any individual driver or driving characteristics and (2) it provides an aggregate level perspective that is currently limited in consumer research on risky behavior.

3.2 Modelling and estimation approach

In studying risky driving behavior, endogeneity is associated with vehicle size: riskier drivers may prefer to purchase larger vehicles. Lehmann et al. (2011) postulate that a non-complex approach, such as OLS, can be presented to “enable the reader to assess the degree to which the underlying assumptions are driving the solution” (p. 162). This is unless certain criteria are met. In the present case, the assumptions of a more complex approach are logically supported. When studying risky driving behavior, risky drivers may prefer larger vehicles. This concept is rooted in previous studies suggesting that individuals with specific characteristics tend to self-select into driving particular types of vehicles. For instance, Li (2012) discussed the consequences of drivers self-selecting into larger vehicles according to their preference to take risk. Horswill and Coster (2002) found that individuals who drive at higher speeds prefer higher-performance vehicles and Scott (2022) demonstrated that individuals exposed to car crash fatalities prefer to purchase larger, heavier vehicles. In a broader context, Winston and Yan (2021) showed that drivers who spend extended periods in traffic tend to opt for larger vehicles. These studies underscore the potential presence of endogeneity in vehicle selection and risky driving behavior.

We therefore use a two-stage least-squares (2SLS) regression model, predicting the endogenous variable using an instrumental variable in the first stage, and then using the predicted value to estimate its effect on the dependent variable in the second stage (Steren et al., 2016; Wooldridge, 2015):

$$\begin{aligned}\text{ln}&\left({m}_{i}\right)={\alpha }_{0}+{\alpha }_{1}\text{ln}\left({p}_{i}\right)+\sum\nolimits_{k=2}^{K}{\alpha }_{k}{X}_{ik-1}+\sum\nolimits_{l=K+1}^{L}{\alpha }_{l}{B}_{il-K}+{\omega }_{i} \\& {s}_{i}={\beta }_{0}+{\beta }_{1}\widehat{\text{ln}\left({m}_{i}\right)}+\sum\nolimits_{k=2}^{K}{\beta }_{k}{X}_{ik-1}+\sum\nolimits_{l=K+1}^{L}{\beta }_{l}{B}_{il-K}+{\epsilon}_{i}\end{aligned}$$

(1)

where vehicle mass, ${m}_{i}$, is a proxy for vehicle size, as vehicle size and vehicle mass are highly correlated (Whitefoot & Skerlos, 2012), and ${s}_{i}$ are observed speeding tickets for configuration $i$ divided by the number of units of this configuration (${s}_{i}$ could potentially be regarded as censored because many drivers do not commit speeding violations. The online Appendix exhibits estimation results of an IV-Tobit model, which accounts for this potential censoring). ${X}_{i}$ are control variables, including vehicle characteristics such as horsepower, gear type, fuel type, propulsion technology, number of seats, safety score, and average kilometers traveled by vehicles of this configuration, to control for the presence on the road. We also control for the location (urban or interurban) and time of day (day: 6:00–17:00; evening: 17:00–00:00; night: 00:00–6:00) of the violation to account for the road exposure of different configurations. Finally, ${B}_{i}$ are brand (manufacturer) fixed effects, accounting for features that might appeal to drivers characterized by certain levels of tendency to risky driving.

${\widehat{ln(m}}_{i})$ are the predicted natural log of vehicle mass values from the first stage. We use the weighted average price of each configuration over all model years, ${p}_{i}$, as an instrumental variable, because the assemblage of a large vehicle is more costly than that of a small vehicle (Anderson & Auffhammer, 2014). There is no direct association between vehicle price and driving behavior. Vehicle price is associated with income level, and prior literature is inconclusive regarding the association between income level and driving behavior, where high-income individuals could be less sensitive to fines, but the probability of collecting the fine is higher for high-income individuals (Garoupa, 2001), which could decrease proneness to speeding violations. Moreover, risky driving behavior can result in crashes, and high-income individuals are less likely to be involved in these (Factor et al., 2008; La et al., 2013). Finally, losing means of commuting due to vehicle seizure or license suspension is a deterrent for low-income individuals who depend on their vehicle for their livelihood (Shams et al., 2011), but, on the other hand, has a higher alternative cost for high-income individuals. For these reasons, one can predict driving behavior neither based on income level nor the value of one’s vehicle. We offer an additional instrumental variable below.

4 Results

4.1 Summary of statistics

Our sample includes 3095 unique vehicle configurations comprising 2,162,525 passenger vehicles. Table 1 provides a summary of the statistics relating to key variables. The average vehicle mass is 1743 kg and it has 121 horsepower. The average vehicle costs NIS 131,412 (~$37,800) and it travels 20,228 km annually. The average annual number of speeding tickets per vehicle is 0.06.

Table 1 Summary of statistics^a (N = 2,162,525)

4.2 Estimation results

Table 2 presents the 2SLS estimation results. The first stage estimation indicates a significant association between the instrumental variable of vehicle price and vehicle mass. The coefficient of vehicle mass in the second stage is positive, indicating that drivers in larger, heavier vehicles are more prone to speeding violations. Our results suggest that a 1% increase in vehicle mass increases the expected number of speeding tickets per vehicle by 0.024.

Table 2 Regressions results (standard errors)

4.3 Robustness

4.3.1 Robustness across enforcement methods and traffic violation types

We conducted the following robustness tests. First, in addition to speeding tickets issued by police cars, we use speeding violation data recorded by traffic enforcement cameras (column 2 in Table 3). Police cars and enforcement cameras are significantly different enforcement methods in terms of technology and usage. During 2018, these cameras issued 54,153 speeding tickets (compared with 134,392 issued by police cars). Results are robust for these two enforcement methods. We also examined the following violations as alternative dependent variables: deviation violations (e.g., lane deviation), safety violations (e.g., phone usage while driving or failure to fasten seatbelts), and disobeying traffic signals (e.g., not stopping at red light). We observe consistent results with each of these DVs (columns 3–5 in Table 3).

Table 3 Regressions results by enforcement type and violation type (standard errors)

4.3.2 Robustness across car categories

To explore potential variation in results across car categories, we segmented our data into ten distinct car categories, each representing typical usage patterns. This aligns with the notion that consumers first select the car category that suits their needs, forming a consideration set, and then choose from the available car products within this set (Giannetti & Srinivasan, 2021). We use classifications of a leading local vehicle website³: minivan, family vehicle, small family vehicle, SUV, luxury, executive, sports, commercial, supermini, and mini. Results are consistent in eight out of ten categories, suggesting that the observed effects are not confined to a general scope but rather extend to specific car categories (Table 4).

Table 4 Regressions results by vehicle category (standard errors)

In addition to car category, we segmented our data according to transmission type, with the rationale being that consumers may perceive manual transmission as enabling faster acceleration than automatic transmission. In both segments, we found a positive association between vehicle mass and speeding tickets (β = 0.139 for manual and β = 0.018 for automatic transmission, p = 0.000). We also segmented our data according to the number of car seats, as vehicles with more than five seats may belong to larger families, potentially resulting in less risky driving behavior. We found a positive association between vehicle mass and speeding tickets in cars with five or fewer car seats and in cars with more than five seats (β = 0.004 and β = 0.112 respectively, p = 0.000).

4.3.3 Alternative instrumental variable

To further demonstrate robustness, we tested a model using an alternative instrumental variable. In the absence of individual-level data on drivers, we utilized information regarding the vehicle’s towing capacity. Regulated towing capacity is correlated with larger vehicle mass, but there is no apparent theoretical relationship between towing capacity and driver behavior. Our findings remain consistent under this identification strategy (Table 5).

Table 5 Regressions results, towing capacity as IV (standard errors)

5 Discussion

We take advantage of the complete national level data of speeding tickets during a single calendar year to show that drivers of heavier vehicles are associated with a higher number of speeding tickets. Examining a single entire year means that enforcement level, economic and infrastructure conditions are consistent across all observations and potential seasonal effects are reflected in the data. After accounting for vehicle choice, the positive association between vehicle mass and speeding tickets is above and beyond any vehicle attribute, including vehicle brand. These results remain robust across markedly different enforcement methods and different traffic violations, indicating that drivers of larger, heavier vehicles tend to drive more recklessly. They support the view that behavioral adaptation occurs in response to the perceived level of risk (Iyer & Singh, 2018), potentially in an attempt to regain homeostasis (Hedlund, 2000; Wilde, 1982).

Behavioral adaptation in response to vehicle physical characteristics can emerge in several ways. For example, a nuanced version of safety perceptions could be that drivers perceive heavy vehicles as more stable, potentially leading them to speed, while those driving lighter vehicles might feel more friction as they accelerate. Additionally, other vehicle properties can influence safety perceptions. Vertlib et al. (2023) demonstrated that advanced safety systems in automobiles can provoke risky driving behavior, despite not being emphasized in the vehicle’s appearance. Furthermore, factors unrelated to physical risk can influence risk perception (Slovic, 2016). For instance, Ma et al. (2019) contended that luxury brands instill a sense of protection even without functional safety features. In the context of vehicles, this perception may arise from a sense of superiority, potentially leading individuals to disregard safety regulations. This notion aligns with Baz et al. (1999), who suggest that consumers are more inclined to take risks with stronger brand names. Some of our analyses can offer insights into these potential alternative mechanisms. For instance, violations such as phone usage, seatbelt neglect, and disobeying traffic signals are unlikely to be affected by drivers’ sense of stability or perceived friction. Yet, we find that such violations are still associated with mass. Moreover, examining brand fixed effects in our model, we find no systematic association between luxury brands and violations. For example, brands linked with speeding violations included Lexus, Audi, and BMW (all considered luxury brands on the local market), but also less luxurious brands such as Citroen, Fiat, and Kia. Similarly, brands negatively associated with speeding included Buick and Cadillac, as well as less luxurious brands such as Suzuki and Mitsubishi.

Previous studies emphasize the nuanced nature of risk perception, where cultural variations (Weber & Hsee, 1998), attitudes towards autonomy and trust in regulations (Slovic, 1993), cognitive biases and affective responses (Finucane et al., 2000; Slovic, 1993), and peer influence and societal norms (Slovic, 1999) may impact the observed association. Risky behavior is also affected by mood (Lin et al., 2006) and driving behavior can be affected by prior driving behavior and driving plans (Ben-Akiva et al., 2012). Expectations regarding one’s self-efficacy can also affect behavior in cases where one feels unsafe or threatened (Bandura, 1977, 1978). Such expectations can drive consumers’ coping behavior strategies, implemented when circumstances are challenging (Bandura, 1977; Rosenzweig & Grinstein, 2016). These entangled dimensions introduce complexity to our findings, suggesting that individual attitudes, emotions, self-efficacy, and social interactions may play roles in shaping driving behavior, inviting further exploration to unravel the complexities of these interrelated dimensions in diverse contexts.

One of the theories previously proposed as a mechanism for consumer behavior is the compensatory consumer behavior model (Mandel et al., 2017). This model suggests that self-discrepancies motivate consumers to engage in behaviors that offset or reduce the discrepancy. We propose that large cars create a different type of discrepancy—not a self-discrepancy, but rather one arising from consumers’ perception that safety in a large vehicle exceeds their usual preferences. This mismatch pushes consumers toward behaviors motivated by the need to reduce the discrepancy, thus engaging in risky driving behavior. The discrepancy still gives “rise to the motivation to engage in consumer behavior to alleviate the… discrepancy” (Mandel et al., 2017, p.137). Thus, the compensatory strategy involves an increase in risky driving. There is a notable difference between the compensatory consumer behavior model and the research context we present. In the compensatory model, consumers’ current state is perceived as negative, leading consumers to seek ways to reduce the discrepancy and alleviate the unpleasant feelings associated with it. In our case, consumers’ current state is positive—the purchase and usage of a safer product—but the resulting feeling of discrepancy remains unpleasant. Therefore, consumer behavior aims to reduce the unpleasant feelings associated with this discrepancy by increasing negative behavior.

An important proxy for risky driving behavior could be car crashes. To investigate risky driving behavior with car crashes as a key indicator, we followed Jacobsen (2013). Jacobsen proposed a method to tease out driving behavior from objective risk stemming from the vehicle’s physical characteristics. Following this methodology, we analyzed Israel Police data on fatal and severe car crashes from 2007 to 2015. Our analysis supports the notion that drivers of smaller vehicles exercise increased caution compared to those driving larger vehicles (Appendix). Still, because car crashes depend, in addition to driving behavior, on the actions of other drivers, weather conditions, road conditions, and chance, we maintain that focusing on traffic violations—rather than car crashes—enables us to study a more direct operationalization of risky behavior.

Consumers’ desire to purchase increasingly larger and heavier vehicles because these vehicles provide a sense of safety is documented in the literature. To mitigate potential inclination toward risky driving behavior, policymakers should find means of internalizing this externality, such as by restricting large and heavy vehicles from busy urban areas (Diekhoff, 2019; Zipper, 2022) or imposing high insurance rates to account for their drivers’ higher tendency of risky behavior. Some countries offer tax exemptions based on vehicle size or installed safety systems (OECD, 2022b). Considering the potential inclination toward risky driving behavior, policymakers should re-evaluate any safety-related monetary interventions across three dimensions: the safety of the vehicle’s passengers, potential harm to other road users, and the behavioral implications of driving a vehicle perceived as safe. These dimensions often conflict, making their balance complex. It would be valuable to consider interventions that remind drivers of large vehicles about their potential risky behavior. One such intervention is a technology-based nudge that alerts drivers of larger-than-average vehicles when their behavior becomes risky. Making drivers aware of potential errors, such as exceeding speed limits through visual or auditory signals, has been routinely used and found effective in mitigating undesired driving behaviors (e.g., Hussain et al., 2021; Ritchie et al., 2021). Policymakers should also find ways to educate consumers regarding a potential tendency to risky behavior in heavier vehicles. They should also engage marketers in educating consumers about safer driving in heavy vehicles that they market.

The present study has the following limitations. First, we use national records at the vehicle configuration level, because the Israel Police and the Ministry of Transportation report traffic violations at this level. This level of analysis has two meaningful advantages. (1) this level of data allows investigating the effect of vehicle’s characteristics on behavior, regardless of specific driver characteristics, thus providing a comprehensive perspective on the effect of one’s vehicle on risky driving; and (2) it provides an aggregate level perspective that is currently limited in consumer research on risky behavior. However, the aggregate nature of the data might mask individual behaviors, which could limit our conclusions’ generalizability. Driver-level data could have been instrumental in addressing unobserved heterogeneity when explaining risky driving behavior, as aggregation may obscure individual behavior. Future research could further explore the impact of mass on risky driving behavior by examining both individual and aggregate levels simultaneously. Second, our cross-sectional data cover a period of 1 year, representing a specific car fleet composition. It is possible that the effect that we assess will be different under other car-fleet compositions, with respect to the distribution of vehicle sizes, road conditions, and infrastructure in other countries.

Appendices

Appendix 1: Vehicle mass and car crash rate

We investigate the effect of vehicle mass on the probability of being involved in a fatal or severe car crash. We examine the involvement of each of five vehicle mass categories in fatal or severe car crashes, using a method that distinguishes between the objective risk that stems from the physical characteristics of the vehicle and the unobserved risk associated with driving behavior of drivers in each car category.

1.1 Methodology

We adopt Jacobsen’s (2013) methodology that distinguishes between the two risk types. As a proxy of car mass, we estimate a model of severe or fatal crashes in five engine capacity categories (0-1300, 1301-1600, 1601-1800, 1801-2000, and 2000 and higher), measured per billion kilometers traveled. Define $FS_{ij}$ as the count of fatal or severe crashes in which cars of categories i and j collided and a fatality or a severe injury occurred in the car of category i. Note that the count is asymmetric (i.e., $FS_{ij} \neq FS_{ji}$), meaning that some categories might be riskier than others.$\sum_{j=1}^j \ FS_{ij}$ is the total count of fatal or severe crashes in category I and similarly, the count of fatal or severe crashes imposed on other vehicles by cars in category I (i.e., the fatality or severe injury in a crash in which a car from category j and a car from category i) is: $\sum\limits_{j=1}^j \ FS_{ij}$.

Following Jacobsen’s (2013) model, we specify three main factors influencing risk and exposure in the context of fatal or severe crashes. The first factor is the risky driving behavior of drivers within each car category. The second factor captures the objective risk derived from a vehicle’s physical characteristics, while the third factor involves the risk associated with the presence of these vehicles on the road, quantified by the total kilometers they traveled. It is postulated that risky driving behavior, objective risk, or kilometers traveled in each category may be associated with fatal or severe crashes, $FS_{ij}$ These three risk factors are defined as follows: $\alpha_i$ represents the risky driving behavior of drivers in car category i, $\beta_{ij}$ signifies the risk per kilometer of a fatality or severe injury in car i when driven concurrently with a car from category j by an average driver, and $m_i$ denotes the number of kilometers driven by cars of category i. Risky driving behavior $(\alpha_i)$ is normalized to unity for the average driver, thereby multiplying it by the risk per kilometer driven in a certain category will increase or decrease the risk level of that category with respect to its calculated $\alpha_i$. The factors that increase $\alpha_i$ are the tendency of category i drivers to use dangerous roads, travel at risky hours, drive recklessly, or have other characteristics that increase risk per kilometer of a fatal or a severe crash.

The probability of a fatal or a severe crash in category i when colliding with category j is then modeled as the product of the objective risk, $\beta_{ij}$ and the parameters representing risky behavior of drivers in each of the categories, $\alpha_i \ \text{and} \ \alpha_j$:

$$\Pr (F{S_{ij}} \mid i,j \ {\text{driven 1 km}})={\alpha_i}{\alpha_j}{\beta_{ij}}$$

(1)

Accounting for the presence of each car category on the road, quantified by the kilometers traveled $m_i$ is an important element in the model. Specifically, $m_i$ is computed as the product of the average kilometers traveled within each category and the corresponding number of vehicles in that category. Additionally, to account for potential variations across different temporal and spatial dimensions, the sample is stratified into s bins. Each bin corresponds to specific day, evening, and night periods and different locations (inside/outside the city), such that if vehicles with lower engine capacity are more prevalent within urban settings or during nighttime, these temporal and spatial variations are accounted for.

The introduction of kilometers traveled to the equation has a multiplicative structure. In instances where the presence of a specific category on the roads, in terms of kilometers traveled, is twice that of other categories, a corresponding twofold increase in the anticipated number of crashes within that category is expected:

$$E(FS_{ijs})=m_{is}m_{js}\alpha_{is}\alpha_{js}\beta_{ij}$$

(2)

where and are observed variables, and $\alpha \ \text{and} \ \beta$ are parameters to be estimated. The separate estimation of $\alpha \ \text{and} \ \beta$, as well as the differentiation between objective risk and risky driving behavior, requires an additional equation. A potential model to isolate driver behavior from the objective risk of a crash involving two categories encompasses only single-car crashes. Assuming that overall driver risk impacts both equations, it can be identified through the following equation:

$$E(FS_{i0s})=m_{is}\alpha_{is}\lambda_{s}h_{i}$$

(3)

where $FS_{i0s}$ represents the count of fatal or severe single-car crashes in car category i, $\lambda_s$ controls the relative frequency of fatal or severe single-car crashes within each bin, and $h_i$ denotes the relative fatality risk to occupants of category i in a ‘standardized collision’. This risk is measured using the European New Car Assessment (NCAP) crash test data and reversed so that the highest score corresponds to the highest risk. To estimate the parameters of interest, we employ Maximum Likelihood estimation within a negative binomial model.

Data

2.1 Fatal and severe car crashes

We utilized Israel Police records of all fatal and severe car crashes in Israel from 2007 to 2015, which include specific vehicle characteristics(e.g., brand, model, engine-capacity, etc.), driver characteristics (e.g., age, gender, driving experience, etc.), and other specifications of each crash (e.g., date, time of day, and location). Because the data do not include information regarding vehicle mass, we used engine capacity as a proxy for vehicle mass. We filtered out crashes involving vehicles manufactured before 2000 (see details in the next section) and crashes involving more than two vehicles, as the effects of each vehicle on the other in such crashes are very complex to estimate. The final database contains 1,733 single- and 1,204 two-car crashes.

2.2 Crash test results

Euro NCAP has performed crash tests to determine the safety level of vehicles for adult passengers in a standardized method since 2000. The method estimates the severity of damage to the vehicle in five different tests: Frontal impact in offset and full overlap, side impact, pole impact and rear impact. The impact of each test is calculated and summed into a total score. The resulting Adult Occupant Protection Score (AOPS) is expressed as a percentage of the maximum achievable number of points. The higher the score – the safer the vehicle is (Euro NCAP 2024). For each of the five engine-capacity categories, we calculated the weighted average of the AOPS accounting for the share of each car model in its category.

To adjust the scores to the multiplicative form of Equation 3, we reversed the scores scale, so that a higher score represents a greater risk. For each of the five scores we calculated its proportion with respect to the sum of all scores. Then, we subtracted each result from 1 and multiplied it by 100: $\left(1-\frac{original\;score}{sum\;of\;scores}\times100\right)$. The final score appears in our model as $h_i$. The test scores represent the situation of colliding with a fixed object (e.g., trees, concrete barriers, guardrails, etc.), which is usually the case in a single-car crash. According to this data, the most dangerous engine-capacity category is 0-1300cc, with a reverse AOPS score of 84.13, and the least dangerous one is the 1601-1800cc, with a reverse AOPS score of 77.44 (Table 6).  

Table 6 Descriptive statistics by engine capacity category

2.3 Kilometers traveled

We obtained the data on kilometers traveled using the publicly available database of the Israel Central Bureau of Statistics (CBS 2007-2015). For each of the five engine-capacity categories we calculated the weighted average kilometers traveled per year:

$$\begin{array}{ccc}m_i=\frac{\displaystyle\underset{it}{\sum\left(kt_{it}\cdot n_{it}\right)/100}}9,&i=1\dots5,&t=1\dots9,\end{array}$$

where ktis the average kilometers traveled in category i at time t, n is the number of vehicles in the category, and t is the period (9 periods between 2007-2015). The calculated is an indicator of the actual presence of each engine-capacity category on the road. The most utilized category is 1301-1600cc, with an average of 22.20 billion kilometers traveled per year, and the least utilized one is 1601-1800cc, with an average of 1.51 billion kilometers traveled per year (Table 6).

Table 6, Column 1 presents fatal and severe car crashes within each engine-capacity category, while Column 2 details such crashes involving each category as the opposing car. For instance, there were 82 fatal or severe crashes involving vehicles in the 0-1300cc category with vehicles from other categories. Annual kilometers traveled are summarized in Column 3, and Column 4 presents the fatal and severe crash rate per billion kilometers for single-car crashes. Additionally, Column 5 provides the reversed NCAP crash test score calculated for each category. Notably, the arrangement of categories by the actual crash rate, from riskiest to least risky, differs from the order based on NCAP scores. This incongruence underscores that the objective risk, represented by the NCAP score under laboratory conditions, may not align with the actual risk level of a specific category, hinting at the potential influence of driving behavior.

2.4 Descriptive statistics

Table 7 presents comprehensive data on fatal or severe car crashes categorized by the defined time-location s bins. The first column presents all single and two-car crashes, while Column 2 provides the variance of crashes at the weekly level, serving as the observation unit during estimation.⁴ Column 3 indicates the share of crashes involving only one vehicle, highlighting that more than half of severe and fatal crashes are of a single vehicle. Columns 4 and 5 outline the most frequent crashes in each bin. Remarkably, single-car crashes predominantly involve vehicles with an engine capacity of 1801-2000cc, and across all bins, the most frequent two-car crash involves vehicles with an engine capacity of 1301-1600cc.

Table 7 Descriptive statistics by bins (following Jacobsen (2013))

Results

Our model estimation is presented in Table 8. The estimates of are presented in the first row, signifying the average risky behavior of drivers in each engine-capacity category, normalized such that$\frac1n{\textstyle\sum_1^i}\alpha_i=1$. Our findings reveal that drivers of vehicles with an engine-capacity of 0-1300cc exhibit the least risky driving behavior among all categories $(\alpha_i=0.72)$, with approximately two-thirds of the average risky behavior of other categories. In contrast, the 1801-2000cc category emerges as the riskiest $(\alpha_i=1.27)$ surpassing the average by about 27 percent. The $\alpha_i$ terms for the remaining categories are not significantly different from the average. The estimates of the risk of a fatal or severe crash per kilometer across all possible combinations of car categories are detailed in the subsequent rows of Table 8. We normalized the estimation of $\beta_{ij}$ to ensure that the kilometers traveled weighted sum of $\beta_{ij}$ predicts the total count of fatal or severe crashes. These findings are consistent with the prediction that light vehicle drivers drive more carefully than large vehicle drivers do.

Table 8 Estimation results