Vehicular mileage or amount of travel is commonly used to quantify exposure (Lloyd & Forster 2014; Naqvi, Quddus & Enoch 2020; Shen et al. 2020). WHO (2004) argues that the risk for one journey may be small but that the amount of risk accumulates with each trip. There is evidence that the risk of death from traffic injuries increases with the amount of exposure (Pulido et al. 2016). Naqvi et al. (2020) investigated the effect of fuel prices in Britain. Their study found that the number of fatal crashes decreased by 0.4% for every 1% increase in fuel prices. They concluded that fuel prices mediate fatal crashes by reducing exposure as a result of less travel and moderated driver behaviour like speed reduction. Lloyd and Forster (2014) argued that the use of vehicular mileage does not allow for disaggregation, and therefore to overcome this, they simulated both vehicle type and road types to estimate traffic flows. In order to deal with the limitation of disaggregation of travel distance, Shen et al. (2020) used the length of driving time to measure exposure, arguing that it is a more reliable measure of exposure.

The concept of exposure discussed above implies that the rate of accidents is likely to increase with the amount of travel. WHO and countries use a common globally accepted epidemiological standard where accident counts and fatalities are expressed as a function of population, for example, fatalities per 10 000 or 100 000 people. This standard helps us to compare the severity of the challenge between countries and regions. In comparing accident prevalence in districts across China, Ding et al. (2017) found that places with higher population densities recorded higher accidents per unit of population. Road accident literature normally disaggregates demographic data to determine the level of risk experienced by different groups of society. However, in this study aggregate population is used.

At a disaggregated level, the number of cars on the road has a significant impact on road traffic accidents. Ashraf et al. (2019) concluded that the rate of increase in the vehicle population in South Korea exceeded the supply of roads, leading to increased road accidents. Vehicle characteristic definitions tend to vary from country to country depending on the method of recording accidents. Torrao, Coelho and Rouphail (2012) used the make, model, wheelbase, size, weight, engine size, age of car and type of fuel the vehicle used in their road accident study in Portugal. The study found that weight differentials in accidents involving more than one vehicle played a significant role in the severity of the accident. Heavier vehicles tended to protect the occupants better than lighter ones, whose occupants were likely to suffer more severe injuries or fatalities when heavier vehicles were involved. Whereas newer vehicles tended to be safer in single-vehicle crashes, this advantage was lost when more than one vehicle was involved. Cioca and Ivascu (2017) found that the top four vehicle types that are highly likely to be involved in road accidents in Romania are cars (65%), intervention vehicles (55%), auto trailers (50%) and lorries/trucks (35%). In South Korea, passenger cars (68%) and trucks (13%) account for higher shares of road crashes (Ashraf et al. 2019).

Road quality and supply not only are critical for facilitating efficient movement but are also instrumental in the management of road safety. In Romania, 60% of road traffic accidents were caused by road alignment (Cioca & Ivascu 2017). This was further corroborated by Cristian and Lucian (2019), who concluded that road design has a significant bearing on road safety. Their study, also done in Romania, revealed that the construction of sidewalks, expanding the number of lanes in certain sections of the road and elevating pedestrian crossings reduced the occurrence of road traffic accidents. Levulytė et al. (2017) analysed pedestrian accidents in Europe too, and they identified pedestrian crossing design as a contributor to road traffic accidents. A study by Rahimi et al. (2020) found a significant influence of road engineering on single-vehicle truck crashes in Iran. Even though differences were observed between accident rates on different road types, the regression model computed by Ashraf et al. (2019) revealed that road type has little impact on road accidents. On the contrary, Štefko, Kubák and Bačík (2014) found expressways to have a significant impact on the reduction of road accidents that caused death and injury in the Slovak Republic. In South Korea, Ashraf et al. (2019) concluded that a lower rate of road surface expansion against a higher rate of vehicle population increase was a major explanator of increased road accidents.

The time of travel is normally expressed in two categories, daytime or night-time. Ashraf et al. (2019) posit that whereas road accidents occur almost equally during the night and day, more fatalities are recorded during night-time travel. John and Shaiba (2019) concluded that accident rates peak late at night, whilst during the day most accidents happen at traffic peak hours with little space between vehicles in Dubai. A study in China by Wang et al. (2019) found that accidents that occur late in the night tended to be more fatal than those occurring during the day. Closer to home, in Botswana, South Africa and Namibia, there is evidence that fatal accidents tend to happen in the night-time. This could be explained by challenges of visibility (twilight/dawn conditions are more challenging), but there is also a chance that this occurs when human policing is low (Mphela 2011), a time when reckless driving tends to be prevalent. The latter argument is further supported by Ashraf et al. (2019), who opined that night-time accident occurrence in South Korea was explained by other road use factors besides visibility challenges.

In conclusion, increased exposure leads to an increase in the risk of accidents occurring, whilst densely populated areas are likely to experience more traffic accidents than less densely populated ones. Different vehicle characteristics affect road accidents in different ways. Firstly, passenger cars are leading contributors to accident statistics, whilst heavier vehicles are likely to increase the severity of accidents if they are involved. On the other hand, increased road supply may lead to a decrease in road accidents. When it comes to the time of travel, more fatal accidents are likely to occur at night.

Road traffic accident statistics are riddled with challenges regarding the precision and availability of data (Štefko et al. 2014), owing to a lack of resources that results in under-reporting (Rolison et al. 2018) and to weaknesses in data-capturing instruments. Pulido et al. (2016) posit that there is a dire need for data on factors that measure direct exposure in many countries. Sometimes, authorities charged with recording data use different criteria for the recording of accident data. A study in Botswana by Pego (2009) found that traffic police used two different forms to record accident data, leading to inconsistencies. It is for this reason that Rolison et al. (2018) recommended a continuous review of police accident data forms. For example, a discussion with traffic police revealed that in Botswana, statistics on fatalities normally register lives lost on the accident spot. There are efforts to follow accident cases beyond this approach, so that if an eventual death is determined to be caused by the accident, then it can be recorded in the road fatality statistics. Minor crashes are likely not to be reported (Fridstrøm 1999), thereby distorting the data on accident occurrence, which technically translates to the probability of severity. It would seem that challenges with road traffic accident data are not new. Benner (1979) attributes this to the varying interests (difficult to reconcile) of different stakeholders, like the police, insurers and litigators, among others, for the same incident.

This study uses panel data retrieved from various sources. The majority came from Statistics Botswana annual reports, augmented by data from the Southern African Customs Union and the World Bank. The accident data was further corroborated with the Motor Vehicle Accident Fund Botswana statistics for purposes of consistency. Detailed data on accident characteristics could only be sourced from the annual Botswana Transport and Infrastructure Statistics Reports from 2008 to 2017. Much of this data is supplied by the Botswana Police Service traffic division to Statistics Botswana. The data summary given in Table 1 is computed from the annual Botswana Transport and Infrastructure Statistics Reports (Government of Botswana 2018b), except for variables on fuel imports.

Exposure is considered the most important variable in explaining severity (Fridstrøm 1999). Normally, this variable is measured by the vehicle mileage or amount of travel by foot for pedestrians (Hakkert & Braimaister 2002), which translate to the amount of activity on the roads. The last time Botswana attempted to measure this through traffic counts was in 2008. Consequently, the researcher used country level data on fuel imports as a proxy variable. This is not in any way a perfect measure, but it is a plausible alternative given that fuel consumption is directly proportional to vehicle kilometres, holding everything else constant. Three variables were created, one where the absolute Botswana pula (BWP) import value was used, one where this value was controlled for exchange rates and one representing the volume of imports. The latter variable was created by adjusting fuel imports for currency and price fluctuations to prevent hoarding effects. Botswana is a net importer of fuel; therefore, the United States dollar/Botswana pula (USD/BWP) exchange rate and the price per barrel in USD were used. To give context, the BWP averaged P8.37, with a minimum of P6.16 and a maximum of P11.30, to the USD over the 10 years. On the other hand, crude oil prices were as volatile, averaging $76.06, with minimum and maximum prices of $43.58 and $99.67, respectively. A lot of this behaviour followed the global economic meltdown of 2008. Data on fuel imports was retrieved from the International Merchandise Trade statistics reports from Statistics Botswana (Government of Botswana 2014, 2015, 2016, 2018a, 2019a, 2019b) and augmented with sources from the Southern African Customs Union (SACU Secretariat 2013). Statistics Botswana personnel were also consulted to fill gaps in the statistical data.

The accident count data were categorised into daylight accidents or night accidents, representing the actual occurrence of road accidents during the day or night, respectively. Botswana generally has longer days than nights, except in winter, when the shortest day lasts for just above 10 hours and 36 minutes. For purposes of this paper, daylight was from 06:00 to 18:00. Botswana, to a large extent, has a unique context in this regard because of its larger presence of roaming animals, especially along unfenced roads – increasing the chances of accidents at night. In Fridstrøm’s model, this was a dummy variable, whereas in this case, it is the actual count of accidents occurring during the two parts of the day.

Data on the road network (measured in kilometres) prior to 2011 is rather unreliable because the Transport and Infrastructure Statistics report records only the road infrastructure under central government maintenance, leaving out roads under the care of local governments. Taking the cue that the network remained constant over more than 5 years before 2011, a decision was made to equate 2009 to 2010, and only 2008 was varied because records showed an increase in 30 km from 2008 to 2009. This is likely to pose challenges regarding the variable significance.

Vehicle type in Botswana is categorised into five kinds: cars (passenger cars), light duty vehicles (LDVs), trucks, buses and tankers/horses. In the conceptual framework, these are referred to as ‘vehicle characteristics’. Tankers and horses are grouped for statistical reporting with no reasons given, despite the two being different configurations.

The study built two different aggregated models to determine the explanatory factor of a number of different variables on accident occurrence and fatalities at a macro level. Using 10-year secondary data, an econometric model was built to determine the causes of accidents and fatalities. After the data were cleaned, Statistical Package for Social Sciences (SPSS) version 26 was used to run regression curve estimates of all independent variables against fatalities and accidents as dependent variables. Only the fuel imports variable returned a significant relationship with fatalities. When the same exercise was carried out on accidents as a dependent variable, only road infrastructure did not register a significant relationship. This initial evaluation of variables is critical in visualising the singular effects of explanatory variables independent of others. Both OLS regression models were run on Gretl software (Cottrell & Lucchetti 2018), first treating all variables as explanatory variables. After every run, the least significant variable (using p-values) was manually removed and the model rerun until all the variables in the model were significant. A counter process, where eliminated variables were added back into the model, was also performed to validate the model. Further, a number of treatments/transformations were also done on the data, and different models were run to explore non-linear relationships. For example, among the transformations done were logs and percentage changes. However, these did not improve the quality of the regression models. Contrary to Conto and Ferreira’s (2011) assertion, simple OLS models provided a better fit than log-linear models using this data. Fridstrøm (1999), whose work this study is largely based on, also used logs. Therefore, the two econometric models computed in this article follow the formula given in Equation (1): yt=β1+β2xt+et t=1,2,…,T[Eqn 1]

The formula allows us to measure the temporal effects of the different factors. Therefore, we are able to determine the implications of the explanators on the dependent variables over time.

This study was primarily based on publicly available secondary data with no human subjects involved. Further, the study did not pose any harm to any person’s character, business or organisation. However, the researcher takes personal responsibility for the outcome of the results.

The accident count model is presented in Table 2a and b. Seven variables returned significant outcomes when regressed against road accident counts. The model also has a higher explanatory power, with an R² value of 0.999. Therefore, it explains 99% of the variation in the accident count. Further, an adjusted R² value of 0.998 demonstrated the strength of the model. Even with relatively few observations for a regression model, a test for normality of errors failed to reject the null hypothesis. Therefore, the errors were normally distributed, proving there is a statistically significant relationship between the dependent variable and its explanators. An alternative model to the model presented next was computed, substituting fuel imports (BWP) with fuel imports (USD). The result was a good model with the same R² value but a weaker adjusted R² value.

The variables tankers/horses (p ≤ 0.001) and night accidents (p ≤ 0.01) had a particularly significant influence on the accident counts, whereas fuel imports (BWP) (p ≤ 0.01) and fuel imports (volume) (p ≤ 0.001) had coefficients that were weak but statistically different from 0. The latter’s effect on accident count is consistent with the literature. There are three variables whose coefficients had unexpected signs. Fuel imports (BWP), trucks and tankers/horses all had negative coefficients. In terms of road accident literature, all these variables are known to grow in the same direction as accident counts. In other words, they have been known to exhibit a positive relationship with accident counts. Growth and improvement in road infrastructure have a decreasing effect on road accident counts. It is worth noting the significant impact of the night accidents variable on the accident count.

In the fatalities model in Table 3a and b, the regression model returned three fewer significant independent variables. As opposed to the accidents model, it excluded the variable night accidents, tankers/horses and trucks. The output indicated fuel imports (USD), population and cars as significant explanatory variables at a significance level of p ≤ 0.001, whereas fuel imports (volume) was significant at p ≤ 0.01. An R² value of 0.91 is testament of a very strong model, explaining 91% of the variation in the fatalities. However, population had a stronger coefficient than all the independent variables. Whereas the other three variables were significant in the model, they had minimal explanatory power on fatality counts. Added to this, the coefficient signs of cars and fuel imports (volumes) were expected to be positive instead of negative.

The model was also tested for the normality of errors using the chi-square test. The result was an insignificant p-value, which means that the hypothesis that errors were normally distributed could not be rejected. Consequently, the model proves that fatality rates are associated with the amount of activity on the national roads.

The accident count model (R² = 0.99) is more robust statistically – it has a better explanatory and forecasting power than the fatalities model (R² = 0.90). The latter has an adjusted R² value of 0.83, whereas that of the former is 0.99. This is despite the fatalities model having three fewer explanatory variables. Both the variables LDVs and buses were insignificant in both models. Findings on the buses variable are particularly inconsistent with those of Romilly (1999), whose study found increased use of buses to have a negative effect on road crashes.

The two models, however significant, present rather surprising outputs considering the expected effects of the different individual variables on dependent variables. To start with, the accident count variable is insignificant in explaining road fatalities. Logically, one expects that the number of accidents would have a bearing on fatality counts. However, Wang et al. (2019) observed a contrasting rise of accidents against declining fatalities. This could be explained by other variables like improved safety of cars, which were not accounted for in this model. Regarding accident count, Fridstrøm (1999) opines that it can be just an act of randomness, with neither particular pattern nor explanation. For example, you can record 10 accidents that lead to no single fatality but have a single accident occurrence that results in 10 fatalities, demonstrating the level of uncertainty with which fatalities can be observed.

In the fatalities model, population was the strongest determinant of fatalities, followed by fuel imports (USD), even though the latter recorded an inverse relationship. This supports the argument that the chances of road fatalities increase with population growth. On the other hand, the fuel imports (volume) variable recorded a logically positive coefficient, even though the effect was quite negligible. In both models, the fuel spend variables (fuel imports [USD] and fuel imports [BWP]) exhibited inverse relationships. The unexpected effect of these two variables might have suffered from hoarding effects of oil prices and exchange rates. Therefore, we can conclude that fuel imports (volume) is a better proxy variable for exposure.

The cars variable is the only explanator that reported different coefficient signs in each model. In the accident count model, the coefficient was positive; however, in both models the strength of the coefficients was almost the same. However, the coefficient in the accident count model is consistent with the literature, as an increase of cars on the roads increases the chances of accident occurrence. In the accident count model, the trucks variable exhibited an inverse relationship. This is contrary to the findings of Cioca and Ivascu (2017) and Ashraf et al. (2019), who found that trucks are among the leading vehicle types contributing to road accidents. However, this study did not find evidence of trucks’ contribution to accident severity. The time of day has a significant bearing on the accident count. Specifically, the night accidents variable was the largest explanator in the accident count model. This confirms the theory that more accidents are likely to occur at night (John & Shaiba 2019) because of decreased visibility and in some instances weakened policing. However, the variable was insignificant in the fatalities model, inconsistent with findings by Wang et al. (2019) and Ashraf et al. (2019). In Botswana, this resonates with the reality of roaming animals, which are notorious for causing many accidents, especially at night. The mere expansion of road infrastructure can be instrumental in reducing road crashes. In the accident count model, the road infrastructure variable displayed an inverse relationship, consistent with the findings of Štefko et al. (2014).