Journal of Safety Research 53 (2015) 17–21
Contents lists available at ScienceDirect
Journal of Safety Research journal homepage: www.elsevier.com/locate/jsr
What affects annual changes in traffic safety? A macroscopic perspective in Virginia Young-Jun Kweon ⁎ Virginia Center for Transportation Innovation and Research, Virginia Department of Transportation, Charlottesville, VA, USA
a r t i c l e
i n f o
Article history: Received 1 August 2014 Received in revised form 14 November 2014 Accepted 9 March 2015 Available online 21 March 2015 Keywords: Traffic safety Crash analysis Economic indicator Crash exposure
a b s t r a c t Introduction: Virginia saw a 20% reduction in traffic fatalities in 2008, an unprecedented annual reduction since 1950, and safety stakeholders in Virginia were intrigued about what caused such large a reduction and more generally what affects traffic safety from a macroscopic perspective. Method: This study attempted to find factors associated with such a reduction using historical data of Virginia. Specifically, the study related 18 factors to seven traffic safety measures. Results: In terms of annual changes, the study found that typical crash exposures were not generally associated with the seven measures, while two economic indicators (unemployment rate and U.S. Consumer Price Index [CPI]) were strongly associated with most of them. Conclusions: Annual changes in the CPI and unemployment rate account for about half of the annual changes in total and fatal crash counts, respectively. On average, a 1 point increase in CPI and a 1% increase in the unemployment rate are associated with about 2,500 fewer traffic crashes and about 40 fewer fatal crashes annually in Virginia, respectively. © 2015 National Safety Council and Elsevier Ltd. All rights reserved.
1. Introduction Many factors are associated with traffic safety including environmental, geometric, behavioral, vehicular, and socioeconomic factors. Examples of such factors are driving activities (e.g., vehicle miles traveled [VMT], speed, and fuel consumption); demographic characteristics (e.g., population and age distribution); economic conditions (e.g., sales, disposable income, and unemployment); and others (e.g., alcohol consumption; Hakim, Shefer, Hakkert, & Hocherman, 1991). Based on a review of studies using macro-level datasets, driving activities and demographic and economic factors are typically used to explain traffic crash consequences such as the number of fatalities in a region. For example, Partyka (1984) used population, labor force, and unemployment to predict traffic fatalities. Hedlund et al. (1984) found that economic factors appeared to contribute the most to the national fatality reduction in 1982, followed by alcohol and demographic factors. Hoxie, Skinner, and Wang (1984) used gasoline sales, gas price, unemployment, population, labor force size, and the production index as economic factors to explain the reduction in 1982. Wagenaar (1984) found that an unemployment rate was associated with traffic crashes yet its impact on reduction in traffic crashes was small. Joksch (1984) reported a nearly linear relationship between changes in the industrial production indices and traffic fatalities using national data from 1950 through 1972. Kopits and Cropper (2005) linked per capita income to traffic fatalities. Fowles and Loeb (1995)
⁎ VCTIR, 530 Edgemont Rd., Charlottesville, VA 22911, USA. Tel.: +1 434 293 1949. E-mail address: [email protected].
http://dx.doi.org/10.1016/j.jsr.2015.03.003 0022-4375/© 2015 National Safety Council and Elsevier Ltd. All rights reserved.
included unemployment rate, real disposable personal income, and alcohol consumption as control factors, and Loeb (1987) examined various socioeconomic factors and identified beer consumption as one of influential factors in predicting fatality rate changes. However, in Kweon's (2008) examination of the validity of using crash/victim rates to measure traffic safety performance of Virginia, among 20 candidate crash/victim rates, only the injury rate per million drivers was found to be valid for a long-term comparison purpose in Virginia while the other 19 rates were invalid. According to the survey by Hakim et al. (1991), the unemployment rate appears to be the most commonly used factor in explaining traffic crash consequence measures from macro perspective and it is negatively associated with traffic crashes. In 2008, all U.S. states except for four (Delaware, New Hampshire, Vermont, and Wyoming) saw a reduction in traffic fatalities, ranging from 1% in Colorado to 24% in Alaska (NHTSA, 2009). A 9.7% reduction (about 4,000 fewer fatalities) was recorded in the United States, and a 20% reduction (203 fewer fatalities) was recorded in Virginia. There was a 5.8% reduction in traffic injuries and a 3.5% reduction in total traffic crashes in the United States (NHTSA, 2009). Such reductions led to the question: What factors were associated with them? This study attempted to answer this question using historical annual data. The study attempted to find factors associated with changes in seven traffic safety measures (e.g., numbers of fatalities and of fatal crashes). The study related 18 factors including several economic indicators to the seven crash/victim annual counts in terms of annual changes. Annual time-series data were collected on the 18 factors, and annual changes instead of annual raw values were used in a regression analysis with autocorrelation treatment in case serial correlations were present.
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Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
2. Data
3.1. Data aggregation period
Empirical data were collected in Virginia and the United States on the 18 potential factors identified by a literature review. For some of the factors, data were aggregated for different intervals. For example, for Gross Value-weighted Industrial Production (GVIP), two-interval data, quarterly and yearly, were available. For consistent data analysis across all factors, a common data interval was recommended. Among the three typically found intervals (month, quarter, and year), the year interval was selected for this study mainly because annual data were available for all 18 factors. Table 1 describes the study data, including a variable description, available data period, and source. Seven traffic safety measures (crash/victim counts) that are often used to describe traffic safety conditions were collected for 40 years or more. The 18 potential relevant factors cover various aspects relevant to traffic safety ranging from aspects directly reflecting traffic crash exposures (e.g., VMT) to aspects indirectly or distantly reflecting transportation activities (e.g., U.S. Consumer Price Index [CPI]). Four traffic crash exposure measures typically used to calculate crash/victim rates, such as fatality rate per million population, were included: VMT, population, number of drivers, and number of registered vehicles. Many economic and financial indicators were also included such as unemployment rate and CPI. Some of the 18 factors, such as CPI and Producer Price Index (PPI), were not available at the state level. Thus, such data were collected at the national level.
Granger (1969) was initially considered after a review of Hoxie et al. (1984). However, it was discovered that the test would be inappropriate if data were aggregated over a period longer than a lag period of a cause–effect phenomenon (Hoxie et al., 1984). For example, if an effect was realized 1 month after a cause occurred, data should not be aggregated over a period longer than 1 month. Using data aggregated over a period longer than the lag period would lead to failure to discover a cause–effect relationship among the data if such relationship existed. Other studies (Gulasekaran & Abeysinghe, 2002; Maminggi, 1996) have warned about distortion of test results when data aggregation is involved. Because the study data were prepared on an annual basis, any cause–effect relationship that might exist with a lag period less than 1 year would probably not be uncovered regardless of statistical analysis techniques. It was conjectured that if a change in values of any of the explanatory variables in Table 1 caused a change, for example, in the number of total crashes, the effect attributable to the cause would probably be realized in a period shorter than the aggregation interval (1 year). For example, if an increase in unemployment rate in a certain month were to result in a decrease in total crashes in the next month, the cause–effect relationship could not be found by Granger's causality test using the yearly aggregated unemployment rate and crash count data because the aggregation period (1 year) is longer than the cause– effect lag period (1 month).
3. Analysis method
3.2. Serial correlation
A regression analysis was selected to analyze yearly data mainly because it can relate a traffic safety measure to multiple relevant factors. In a regression analysis, there are various types of regression models available ranging from a classical linear regression to non-linear crosssectional time-series regression. Since the data collected for this study were multivariate time-series data mostly for Virginia, cross-sectional time-series (also known as panel) regression models were not applicable. Fig. 1 is a flowchart showing how an appropriate regression model was chosen for the study.
Since the data were time-series in nature, a serial correlation might well exist; if it did, it would interfere with a statistical significance of the relationship. Thus, a statistical test for serial correlations should be performed to detect the presence of such correlations. If serial correlations were found, a regression model that corrects for the correlations embedded in time-series data should be used. Serial correlations were found in all the variables listed in Table 1 based on the Durbin–Watson test. Thus, a regression model with correction for serial correlations was employed in the study.
Table 1 List of variables of annual data used. Variable Traffic safety measures
Potential relevant factors
Fatality Fatal crash Injury Injury crash Fatality + injury (FI) Fatal + injury (FI) Crash Crash Beer CUI U.S. CPI Driver Employment U.S. gas price Gas Production GVIP Income IPI Labor force Population U.S. PPI Sales Unemployment Unemployment rate Vehicle VMT
Description
Period
Source
Number of fatalities Number of fatal crashes Number of injuries Number of injury crashes Sum of fatalities and Injuries Sum of fatal crash and injury crash Number of total crashes Per capita beer consumption (gallons) Manufacturing Capacity Utilization Index: Base 2002 U.S. Consumer Price Index (all urban consumers) Number of registered drivers Number of employed persons U.S. gas price (cents) Gasoline through company outlets volume by refiners (thousand gallons per day) Gross value-weighted industrial production: Base 2000 Per capital disposable personal income Industrial Production Index in manufacturing: Base 2000 Number of persons in labor force Population U.S. Producer Price Index (commodity) Taxable sales Number of unemployed persons Unemployment rate (=unemployment/labor force) Number of registered vehicles Vehicle miles traveled
1951–2008 1969–2008 1951–2008 1969–2008 1951–2008 1969–2008 1951–2008 1994–2008 1967–2008 1976–2008 1971–2008 1976–2008 1990–2008 1985–2008
Virginia Department of Motor Vehicles
1972–2008 1958–2008 1951–2008 1976–2008 1968–2008 1976–2008 1985–2008 1976–2008 1976–2008 1951–2008 1951–2008
Beer Institute Board of Governors of the Federal Reserve System U.S. Bureau of Labor Statistics Virginia Department of Motor Vehicles U.S. Bureau of Labor Statistics U.S. Energy Information Administration
Board of Governors of the Federal Reserve System U.S. Bureau of Economic Analysis Board of Governors of the Federal Reserve System U.S. Bureau of Labor Statistics U.S. Census Bureau U.S. Bureau of Labor Statistics Weldon Cooper Center for Public Service U.S. Bureau of Labor Statistics Virginia Department of Motor Vehicles
Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
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Fig. 1. Flowchart used to select an appropriate regression model for the study.
3.3. Normality Normality should also be checked for a dependent variable. When the distribution of the variable is found to depart severely from a normal distribution, a model designed for a non-normally distributed dependent variable should be employed. For count time-series data, an Integer-valued Auto-Regressive model has become the most common application in recent years. The seven traffic safety measures shown in Table 1 (and their annual changes) were found to be normally distributed based on the Shapiro–Wilk test that is deemed robust for a sample size less than 2,000. Thus, a typical time-series model assuming the normal distribution was employed. 3.4. Non-stationarity and differencing In applying a typical time-series model, it is assumed that variables are stationary (mean and variance are constant over time). When the variables are non-stationary (especially for the mean over time), differencing generally removes non-stationarity from the series. Non-stationarity (non-constant mean over years) was found for all the dependent variables and most of the explanatory variables based on the Phillips–Perron unit root test. Thus, first differencing was applied to convert the non-stationary variables to stationary variables. Moreover, using a year-to-year change in raw numbers is considered to be more appropriate than using the raw numbers, especially to find relevant factors explaining changes in traffic safety measures in a time-series setting. This study was interested in determining if annual changes in values of the explanatory variables were related to changes in the number of crashes and the number of victims. In other words, the study attempted to examine the relationship between the dependent and explanatory variables in terms of fluctuations, not trends. Thus, annual changes rather than annual raw values were examined, meaning the first differencing was performed on the annually aggregated data before a regression analysis was applied. 3.5. Autoregressive error model An autoregressive error model is a regression model with a serial correlation treated by including autoregressive error terms to the regression model. The model has been successfully employed in traffic safety research (Kweon, 2006, 2007; Oppe, 1989; Raeside, 2004) and
was employed in this study. The model in the first differenced format is written as follows:
ΔY t ¼ α þ β 1 ΔX 1;t þ β 2 ΔX 2;t þ ⋯ þ νt
and ν t ¼ ϕ1 vt−1 þ ϕ2 vt−2 þ ⋯ þ εt
ð1Þ where Δ a year-to-year difference operator, ΔYt = Yt − Yt − 1 Yt a traffic safety measure in year t X1,t, X2,t,… relevant factors in year t α, β1, β2,… parameters to be estimated vt an correlated error term related to year t ϕ1, ϕ2,… autoregressive parameters εt a random error, εt ~ IN(0, σ 2). The Durbin–Watson test was performed on regression residuals to find any remaining serial correlations that might temper statistical significance of the slope parameter estimates. For the models for fatality and total crash counts, autoregressive error terms were not included because the first differencing removed not only non-stationarity but also the serial correlations buried in fatality and fatal crash counts. 4. Results and discussions All data manipulation and statistical analyses were performed using SAS 9.1.3. 4.1. Relevant Factors One potential relevant factor was entered into a regression model at a time to find all factors relevant to the seven crash/victim counts. A potential factor that was statistically significant at the 0.1 level was determined to be relevant for this study. Table 2 reports relevant factors for each of the seven crash/victim counts in terms of annual changes; most of the relevant factors were statistically significant at the 0.05 level. The four most popular crash exposures used as a denominator in calculating crash rates (e.g., fatality rate per million VMT) did not explain most of the seven crash/victim counts in terms of annual changes; VMT, population, number of registered drivers, and number of registered vehicles. Annual changes in VMT and population failed to explain annual changes in all seven counts, and changes in the number of registered vehicles and the number of registered drivers explained changes in one and two of the seven, respectively. Three factors were
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Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
Table 2 Association of factors with traffic safety measures in terms of annual changes.
2 ΔInjuryt ¼ −420:296−2; 391 ΔUnemploymentRatet −0:368ν t−2 R ¼ 0:16 :
ð4Þ
Association with ΔFatality ΔFatal ΔInjury ΔInjury ΔFI ΔFI ΔTotal crash crash crash crash ΔBeer ΔCUI ΔU.S. CPI ΔDriver ΔEmployment ΔU.S. gas price ΔGas production ΔGVIP ΔIncome ΔIPI ΔLabor force ΔPopulation ΔU.S. PPI ΔSales ΔUnemployment ΔUnemployment rate ΔVehicle ΔVMT
× × × × ○ × × ○ × ○ × × × × ○ ○ × ×
× × ○ × × × × ○ × ○ × × × ○ ○ ○ ○ ×
× × ○ × × × × × × × × × ○ × ○ ○ × ×
× × ○ ○ × × × × × × × × × × × ○ × ×
× × ○ × × × × × × × × × ○ × ○ ○ × ×
× × ○ ○ × × × × × × × × × × × ○ × ×
× × ○ × × × × ○ × ○ × × ○ × ○ ○ × ×
2 R ¼ 0:26 : ð5Þ
2 Δ FIt ¼ 411:172−2; 442 ΔUnemploymentRatet −0:370 ν t−2 R ¼ 0:17 :
ð6Þ ΔFICrasht ¼ 2; 057−454:240 ΔUS:CPI t þ 0:00809 ΔDrivert −0:340 ν t−1 ΔCrasht ¼ 12; 354−2; 459 ΔUS:CPI t
Note: FI = fatal and injury; Δ is a difference operator (for example, ΔVMT = VMT in year t − VMT in year t-1); ○ indicates statistical significance at the 0.1 level; × = not statistically significant.
found to explain changes in most of the seven crash/victim counts: changes in CPI, unemployment number, and unemployment rate. Interestingly, all three are economic indicators. Annual changes in only the unemployment rate were found to be associated with annual changes in all seven counts. The unemployment rate is calculated by dividing the total number of unemployed workers by the total labor force. Although labor force did not explain any of the counts and the unemployment number did not explain two of the seven counts in terms of annual changes, combining these two factors as a rate (unemployment/ labor force) better explained crash/victim counts in that the unemployment rate explained all seven counts in terms of annual changes. 4.2. Best models Table 2 presented the results of one-factor models. However, it is possible to improve the explanatory power (for example, R2) of the regression models by adding other factors. However, adding factors that are highly correlated to the factor already in the model is likely to cause biased estimates of slope parameters and/or standard errors. Only factors found to be relevant (shown in Table 2) and not highly correlated to the factor already in the model were added to the one-factor model. For some models, such as the model for annual changes in injuries, none of additional relevant factors turned out to be statistically significant (at the 0.1 level) after being added. Thus, the one-factor model producing the highest R2 value was determined to be the best. For the model for fatalities, the model with the unemployment rate produced the highest R2value yet the other relevant factors (for example, GVIP and IPI) was highly correlated with the unemployment rate in terms of annual changes. Thus, none of the other relevant factors could be added, making the model with the unemployment rate the best model for fatalities. The best model determined for each of the seven crash/ victim counts is listed here along with its R2 value. ΔFatalityt ¼ −9:443−55:513 ΔUnemploymentRatet
ΔInjuryCrasht ¼ −2; 037−447:059 ΔUS:CPI t þ 0:00791 ΔDriver−0:326νt−1
2 R ¼ 0:23 : ð2Þ
ΔFatalCrasht ¼ −38:469−39:992 ΔUnemploymentRatet 2 R ¼ 0:45 : þ0:000227 ΔVehiclet þ 0:558ν t−1 ð3Þ
2 R ¼ 0:26 : ð7Þ
2 R ¼ 0:46 :
ð8Þ
Regarding R2, two R2 values were calculated in SAS (regression R2 and total R2); the regression R2 was reported here. The total R2 measures the prediction performance of the entire model including the structural part and the autoregressive error part, and the regression R2 measures an estimation performance of the structural part after transforming for the autocorrelation (SAS Institute Inc., 2009). Since this study was interested in how well potential factors explained the seven traffic safety measures (in other words, how well a relationship between factors and each of the safety measures fits the data), the regression R2 was deemed appropriate. Across the seven models listed, the model for total crashes displayed the highest explanatory power in terms of the R2 value, followed by the model for fatal crashes. The R2 value of 0.46 of the model for total crashes means that annual changes in CPI explain 46% of yearly variations in annual changes in total crash counts. The unemployment rate appears to be a good indicator for fatalities, fatal crashes, injuries, and FI; CPI appears to be a good indicator for injury crashes, FI crashes, and total crashes in terms of annual changes. The negative signs were found on the slope parameter estimates of changes in the unemployment rate and CPI. As for the unemployment rate, the negative slopes mean as the unemployment rate increases from the previous year, the numbers of fatalities, fatal crashes, and injuries are expected to decrease. More specifically, a 1% increase in the annual unemployment rate in Virginia is associated with about 56 fewer fatalities and about 40 fewer fatal crashes annually in Virginia on average. As for annual CPI, a 1 point increase in CPI is associated with about 2,500 fewer traffic crashes and 450 fewer injury crashes in Virginia in 1 year on average. Applying the models for fatal crash and total crash to actual data in 2008, a 1% increase in the unemployment rate recorded in Virginia predicted 78 fewer fatal crashes (43%) compared to 180 actual fatal crash reductions and an 8-point increase in CPI predicted 7,222 fewer total crashes (71%) compared to 10,123 actual total crash reductions. The unemployment rate and CPI are economic indicators reflecting different aspects of economic activities. Economic activities are believed to influence transportation activities including movements of people and goods that are in turn related to traffic safety exposures. In addition, conditions in economies are believed to influence how people use the transportation system, not only the amount but also the manner of using the system. For example, in an economic downturn, a driver is less likely to speed for various reasons such as avoiding tickets for speeding and improving gas mileage, which might in turn put the driver and occupants and occupants in other vehicles in safer conditions on highways. Interestingly, changes in crash counts (e.g., fatal crashes) are better explained than changes in victim counts (e.g., fatalities) by the relevant factors. This implies that for forecasting traffic safety measures, using crash counts is likely to offer a more accurate forecast than using victim counts probably because victim counts are largely influenced by occupancy rates that may vary over years due to various factors
Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
(e.g., economies and policies). This might have an implication in setting future safety targets for highway safety plans or policies since setting safety targets for future years probably requires forecasting traffic safety pictures in terms of some of the seven crash/victim counts and crash counts are likely to be more robustly forecast than victim counts based on relevant factors. Annual changes in injury and injury crash counts appear to be explained the least by the relevant factors found in this study.
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Acknowledgments The author thanks Cheryl Lynn (retired) of the Virginia Center for Transportation Innovation and Research (VCTIR) for her contribution to the original study, Linda Evans of VCTIR for her excellent editorial help, and the Virginia Department of Transportation (VDOT)for sponsoring this and the original study. Any views or opinions presented in this paper are solely those of the author and do not necessarily represent the views of VDOT.
5. Conclusions References This study attempted to link annual changes in seven crash/victim counts (fatality, fatal crash, injury, injury crash, fatality + injury [FI], FI crash, and total crash) in Virginia to annual changes in the 18 potential relevant factors using Virginia-specific and national time-series data and regression models with treatment for serial correlations. Annual changes instead of annual raw values were used to find factors that could explain annual fluctuations in the seven crash/victim counts. Annual changes in typical traffic crash exposure measures (VMT, population, number of vehicles, and number of drivers) were generally not associated with annual changes in the crash/victim counts; changes in number of vehicles and number of drivers were associated with changes in one and two of the seven counts, respectively, whereas changes in VMT and population were not associated with changes in any of the seven counts. Annual changes in economic indicators (unemployment rate and CPI) were strongly associated with annual changes in most of the seven crash/victim counts; especially, annual changes in the unemployment rate were associated with annual changes in all seven counts. The unemployment rate and CPI both are economic indicators reflecting different aspects of economic activities. Economic activities are believed to influence transportation activities in terms of the amount and manner of using the transportation system, which is likely to influence traffic safety. The best model was determined for each of the seven crash/victim counts based on the R2 value. Among the best models for the seven counts, the models for total crash and fatal crash had the two highest R2 values, 0.46 and 0.45, respectively. According to these models, annual changes in CPI and the unemployment rate in Virginia explained about one half of annual changes in total crash counts and fatal crash counts in Virginia, respectively. On average, a 1 point increase in CPI and a 1% increase in the unemployment rate of Virginia were associated with about 2,500 fewer traffic crashes and about 40 fewer fatal crashes annually in Virginia. In applying the models to 2008 actual data, a 1% increase in the unemployment rate recorded in Virginia predicted 43% of 180 actual reductions in fatal crashes and a 6-point increase in CPI predicted 71% of 10,123 actual reductions in total crashes. Changes in crash counts (e.g., fatal crashes) are better explained than changes in victim counts (e.g., fatalities) by relevant factors, which might be because victim counts are influenced by occupancy rates possibly varying over years. This has an implication in setting traffic safety targets for highway safety plans or policy, probably requiring forecasting future traffic safety pictures in terms of some of the seven crash/victim counts.
Fowles, R., & Loeb, P. D. (1995). Effects of policy-related variables on traffic fatalities: An extreme bounds analysis using time-series data. Southern Economic Journal, 62(2), 359–366. Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37, 424–438. Gulasekaran, R., & Abeysinghe, T. (2002). The distortionary effects of temporal aggregation on granger causality. Working Paper No. 0204, National University of Singapore, Department of Economics (www.fas.nus.edu.sg/ecs/pub/wp/wp0204.pdf). Hakim, S., Shefer, D., Hakkert, A. S., & Hocherman, I. (1991). A critical review of macro models for road accidents. Accident Analysis and Prevention, 23(5), 379–400. Hedlund, J., Arnold, R., Cerrelli, E., Partyka, S., Hoxie, P., & Skinner, D. (1984). An assessment of the 1982 traffic fatality decrease. Accident Analysis and Prevention, 16(4), 247–261. Hoxie, P., Skinner, D., & Wang, G. H. (1984). Socio-economic influences on highway fatalities: An empirical investigation. Publication DOT-HS-806-525. Washington, DC: US Department of Transportation. Joksch, H. C. (1984). The relation between motor vehicle accident deaths and economic activity. Accident Analysis and Prevention, 16(3), 207–210. Kopits, E., & Cropper, M. (2005). Traffic fatalities and economic growth. Accident Analysis and Prevention, 37, 169–178. Kweon, Y. -J. (2006). Evaluation of a proposal to set a goal for the Virginia strategic highway safety plan of a forty percent reduction in traffic fatalities and injuries by 2010. Publication VTRC 06-R34. Charlottesville, Virginia: Virginia Center for Transportation Innovation and Research. Kweon, Y. -J. (2007). Forecasting traffic safety in Virginia with a primary seat belt law. CD-ROM of ITE 2007 Annual Meeting and Exhibit Compendium of Technical Papers Pittsburg, Pennsylvania. Kweon, Y. -J. (2008). Examination of macro-level annual safety performance measures for Virginia. Transportation Research Record, 2083, 9–15. Loeb, P. D. (1987). The determinants of automobile fatalities: With special consideration to policy variables. Journal of Transport Economics and Policy, 21, 279–287. Maminggi, N. (1996). Aggregation over time, error correction models and granger causality: A Monte Carlo investigation. Economics Letters, 52(1), 7–14. National Highway Traffic Safety Administration (NHTSA) (2009). Traffic safety facts: Crash stats. Publication DOT-HS-811-172. Washington, DC: US Department of Transportation. Oppe, S. (1989). Macroscopic models for traffic and traffic safety. Accident Analysis and Prevention, 21(3), 225–232. Partyka, S. C. (1984). Simple models of fatality trends using employment and population data. Accident Analysis and Prevention, 16(3), 211–222. Raeside, R. (2004). Predicting and monitoring casualty numbers in Great Britain. Journal of Transportation and Statistics, 7(1), 61–68. SAS Institute Inc. (2009). SAS/ETS(R) 9.2 user's guide. Cary, North Carolina. Wagenaar, A. C. (1984). Effects of macroeconomic conditions on the incidence of motor vehicle accidents. Accident Analysis and Prevention, 16(3), 191–205. Young-Jun Kweon, Ph.D., P.E., is a senior research scientist at the Virginia Center for Transportation, Innovation and Research, the research arm of the Virginia Department of Transportation. He has more than 15 years of experience in highway safety, ranging from behavior and policy to operations and design aspects; statistics; and transportation research and data analysis. In recent years, he has been working on the development and deployment of safety performance functions for Virginia.
Contents lists available at ScienceDirect
Journal of Safety Research journal homepage: www.elsevier.com/locate/jsr
What affects annual changes in traffic safety? A macroscopic perspective in Virginia Young-Jun Kweon ⁎ Virginia Center for Transportation Innovation and Research, Virginia Department of Transportation, Charlottesville, VA, USA
a r t i c l e
i n f o
Article history: Received 1 August 2014 Received in revised form 14 November 2014 Accepted 9 March 2015 Available online 21 March 2015 Keywords: Traffic safety Crash analysis Economic indicator Crash exposure
a b s t r a c t Introduction: Virginia saw a 20% reduction in traffic fatalities in 2008, an unprecedented annual reduction since 1950, and safety stakeholders in Virginia were intrigued about what caused such large a reduction and more generally what affects traffic safety from a macroscopic perspective. Method: This study attempted to find factors associated with such a reduction using historical data of Virginia. Specifically, the study related 18 factors to seven traffic safety measures. Results: In terms of annual changes, the study found that typical crash exposures were not generally associated with the seven measures, while two economic indicators (unemployment rate and U.S. Consumer Price Index [CPI]) were strongly associated with most of them. Conclusions: Annual changes in the CPI and unemployment rate account for about half of the annual changes in total and fatal crash counts, respectively. On average, a 1 point increase in CPI and a 1% increase in the unemployment rate are associated with about 2,500 fewer traffic crashes and about 40 fewer fatal crashes annually in Virginia, respectively. © 2015 National Safety Council and Elsevier Ltd. All rights reserved.
1. Introduction Many factors are associated with traffic safety including environmental, geometric, behavioral, vehicular, and socioeconomic factors. Examples of such factors are driving activities (e.g., vehicle miles traveled [VMT], speed, and fuel consumption); demographic characteristics (e.g., population and age distribution); economic conditions (e.g., sales, disposable income, and unemployment); and others (e.g., alcohol consumption; Hakim, Shefer, Hakkert, & Hocherman, 1991). Based on a review of studies using macro-level datasets, driving activities and demographic and economic factors are typically used to explain traffic crash consequences such as the number of fatalities in a region. For example, Partyka (1984) used population, labor force, and unemployment to predict traffic fatalities. Hedlund et al. (1984) found that economic factors appeared to contribute the most to the national fatality reduction in 1982, followed by alcohol and demographic factors. Hoxie, Skinner, and Wang (1984) used gasoline sales, gas price, unemployment, population, labor force size, and the production index as economic factors to explain the reduction in 1982. Wagenaar (1984) found that an unemployment rate was associated with traffic crashes yet its impact on reduction in traffic crashes was small. Joksch (1984) reported a nearly linear relationship between changes in the industrial production indices and traffic fatalities using national data from 1950 through 1972. Kopits and Cropper (2005) linked per capita income to traffic fatalities. Fowles and Loeb (1995)
⁎ VCTIR, 530 Edgemont Rd., Charlottesville, VA 22911, USA. Tel.: +1 434 293 1949. E-mail address: [email protected].
http://dx.doi.org/10.1016/j.jsr.2015.03.003 0022-4375/© 2015 National Safety Council and Elsevier Ltd. All rights reserved.
included unemployment rate, real disposable personal income, and alcohol consumption as control factors, and Loeb (1987) examined various socioeconomic factors and identified beer consumption as one of influential factors in predicting fatality rate changes. However, in Kweon's (2008) examination of the validity of using crash/victim rates to measure traffic safety performance of Virginia, among 20 candidate crash/victim rates, only the injury rate per million drivers was found to be valid for a long-term comparison purpose in Virginia while the other 19 rates were invalid. According to the survey by Hakim et al. (1991), the unemployment rate appears to be the most commonly used factor in explaining traffic crash consequence measures from macro perspective and it is negatively associated with traffic crashes. In 2008, all U.S. states except for four (Delaware, New Hampshire, Vermont, and Wyoming) saw a reduction in traffic fatalities, ranging from 1% in Colorado to 24% in Alaska (NHTSA, 2009). A 9.7% reduction (about 4,000 fewer fatalities) was recorded in the United States, and a 20% reduction (203 fewer fatalities) was recorded in Virginia. There was a 5.8% reduction in traffic injuries and a 3.5% reduction in total traffic crashes in the United States (NHTSA, 2009). Such reductions led to the question: What factors were associated with them? This study attempted to answer this question using historical annual data. The study attempted to find factors associated with changes in seven traffic safety measures (e.g., numbers of fatalities and of fatal crashes). The study related 18 factors including several economic indicators to the seven crash/victim annual counts in terms of annual changes. Annual time-series data were collected on the 18 factors, and annual changes instead of annual raw values were used in a regression analysis with autocorrelation treatment in case serial correlations were present.
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Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
2. Data
3.1. Data aggregation period
Empirical data were collected in Virginia and the United States on the 18 potential factors identified by a literature review. For some of the factors, data were aggregated for different intervals. For example, for Gross Value-weighted Industrial Production (GVIP), two-interval data, quarterly and yearly, were available. For consistent data analysis across all factors, a common data interval was recommended. Among the three typically found intervals (month, quarter, and year), the year interval was selected for this study mainly because annual data were available for all 18 factors. Table 1 describes the study data, including a variable description, available data period, and source. Seven traffic safety measures (crash/victim counts) that are often used to describe traffic safety conditions were collected for 40 years or more. The 18 potential relevant factors cover various aspects relevant to traffic safety ranging from aspects directly reflecting traffic crash exposures (e.g., VMT) to aspects indirectly or distantly reflecting transportation activities (e.g., U.S. Consumer Price Index [CPI]). Four traffic crash exposure measures typically used to calculate crash/victim rates, such as fatality rate per million population, were included: VMT, population, number of drivers, and number of registered vehicles. Many economic and financial indicators were also included such as unemployment rate and CPI. Some of the 18 factors, such as CPI and Producer Price Index (PPI), were not available at the state level. Thus, such data were collected at the national level.
Granger (1969) was initially considered after a review of Hoxie et al. (1984). However, it was discovered that the test would be inappropriate if data were aggregated over a period longer than a lag period of a cause–effect phenomenon (Hoxie et al., 1984). For example, if an effect was realized 1 month after a cause occurred, data should not be aggregated over a period longer than 1 month. Using data aggregated over a period longer than the lag period would lead to failure to discover a cause–effect relationship among the data if such relationship existed. Other studies (Gulasekaran & Abeysinghe, 2002; Maminggi, 1996) have warned about distortion of test results when data aggregation is involved. Because the study data were prepared on an annual basis, any cause–effect relationship that might exist with a lag period less than 1 year would probably not be uncovered regardless of statistical analysis techniques. It was conjectured that if a change in values of any of the explanatory variables in Table 1 caused a change, for example, in the number of total crashes, the effect attributable to the cause would probably be realized in a period shorter than the aggregation interval (1 year). For example, if an increase in unemployment rate in a certain month were to result in a decrease in total crashes in the next month, the cause–effect relationship could not be found by Granger's causality test using the yearly aggregated unemployment rate and crash count data because the aggregation period (1 year) is longer than the cause– effect lag period (1 month).
3. Analysis method
3.2. Serial correlation
A regression analysis was selected to analyze yearly data mainly because it can relate a traffic safety measure to multiple relevant factors. In a regression analysis, there are various types of regression models available ranging from a classical linear regression to non-linear crosssectional time-series regression. Since the data collected for this study were multivariate time-series data mostly for Virginia, cross-sectional time-series (also known as panel) regression models were not applicable. Fig. 1 is a flowchart showing how an appropriate regression model was chosen for the study.
Since the data were time-series in nature, a serial correlation might well exist; if it did, it would interfere with a statistical significance of the relationship. Thus, a statistical test for serial correlations should be performed to detect the presence of such correlations. If serial correlations were found, a regression model that corrects for the correlations embedded in time-series data should be used. Serial correlations were found in all the variables listed in Table 1 based on the Durbin–Watson test. Thus, a regression model with correction for serial correlations was employed in the study.
Table 1 List of variables of annual data used. Variable Traffic safety measures
Potential relevant factors
Fatality Fatal crash Injury Injury crash Fatality + injury (FI) Fatal + injury (FI) Crash Crash Beer CUI U.S. CPI Driver Employment U.S. gas price Gas Production GVIP Income IPI Labor force Population U.S. PPI Sales Unemployment Unemployment rate Vehicle VMT
Description
Period
Source
Number of fatalities Number of fatal crashes Number of injuries Number of injury crashes Sum of fatalities and Injuries Sum of fatal crash and injury crash Number of total crashes Per capita beer consumption (gallons) Manufacturing Capacity Utilization Index: Base 2002 U.S. Consumer Price Index (all urban consumers) Number of registered drivers Number of employed persons U.S. gas price (cents) Gasoline through company outlets volume by refiners (thousand gallons per day) Gross value-weighted industrial production: Base 2000 Per capital disposable personal income Industrial Production Index in manufacturing: Base 2000 Number of persons in labor force Population U.S. Producer Price Index (commodity) Taxable sales Number of unemployed persons Unemployment rate (=unemployment/labor force) Number of registered vehicles Vehicle miles traveled
1951–2008 1969–2008 1951–2008 1969–2008 1951–2008 1969–2008 1951–2008 1994–2008 1967–2008 1976–2008 1971–2008 1976–2008 1990–2008 1985–2008
Virginia Department of Motor Vehicles
1972–2008 1958–2008 1951–2008 1976–2008 1968–2008 1976–2008 1985–2008 1976–2008 1976–2008 1951–2008 1951–2008
Beer Institute Board of Governors of the Federal Reserve System U.S. Bureau of Labor Statistics Virginia Department of Motor Vehicles U.S. Bureau of Labor Statistics U.S. Energy Information Administration
Board of Governors of the Federal Reserve System U.S. Bureau of Economic Analysis Board of Governors of the Federal Reserve System U.S. Bureau of Labor Statistics U.S. Census Bureau U.S. Bureau of Labor Statistics Weldon Cooper Center for Public Service U.S. Bureau of Labor Statistics Virginia Department of Motor Vehicles
Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
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Fig. 1. Flowchart used to select an appropriate regression model for the study.
3.3. Normality Normality should also be checked for a dependent variable. When the distribution of the variable is found to depart severely from a normal distribution, a model designed for a non-normally distributed dependent variable should be employed. For count time-series data, an Integer-valued Auto-Regressive model has become the most common application in recent years. The seven traffic safety measures shown in Table 1 (and their annual changes) were found to be normally distributed based on the Shapiro–Wilk test that is deemed robust for a sample size less than 2,000. Thus, a typical time-series model assuming the normal distribution was employed. 3.4. Non-stationarity and differencing In applying a typical time-series model, it is assumed that variables are stationary (mean and variance are constant over time). When the variables are non-stationary (especially for the mean over time), differencing generally removes non-stationarity from the series. Non-stationarity (non-constant mean over years) was found for all the dependent variables and most of the explanatory variables based on the Phillips–Perron unit root test. Thus, first differencing was applied to convert the non-stationary variables to stationary variables. Moreover, using a year-to-year change in raw numbers is considered to be more appropriate than using the raw numbers, especially to find relevant factors explaining changes in traffic safety measures in a time-series setting. This study was interested in determining if annual changes in values of the explanatory variables were related to changes in the number of crashes and the number of victims. In other words, the study attempted to examine the relationship between the dependent and explanatory variables in terms of fluctuations, not trends. Thus, annual changes rather than annual raw values were examined, meaning the first differencing was performed on the annually aggregated data before a regression analysis was applied. 3.5. Autoregressive error model An autoregressive error model is a regression model with a serial correlation treated by including autoregressive error terms to the regression model. The model has been successfully employed in traffic safety research (Kweon, 2006, 2007; Oppe, 1989; Raeside, 2004) and
was employed in this study. The model in the first differenced format is written as follows:
ΔY t ¼ α þ β 1 ΔX 1;t þ β 2 ΔX 2;t þ ⋯ þ νt
and ν t ¼ ϕ1 vt−1 þ ϕ2 vt−2 þ ⋯ þ εt
ð1Þ where Δ a year-to-year difference operator, ΔYt = Yt − Yt − 1 Yt a traffic safety measure in year t X1,t, X2,t,… relevant factors in year t α, β1, β2,… parameters to be estimated vt an correlated error term related to year t ϕ1, ϕ2,… autoregressive parameters εt a random error, εt ~ IN(0, σ 2). The Durbin–Watson test was performed on regression residuals to find any remaining serial correlations that might temper statistical significance of the slope parameter estimates. For the models for fatality and total crash counts, autoregressive error terms were not included because the first differencing removed not only non-stationarity but also the serial correlations buried in fatality and fatal crash counts. 4. Results and discussions All data manipulation and statistical analyses were performed using SAS 9.1.3. 4.1. Relevant Factors One potential relevant factor was entered into a regression model at a time to find all factors relevant to the seven crash/victim counts. A potential factor that was statistically significant at the 0.1 level was determined to be relevant for this study. Table 2 reports relevant factors for each of the seven crash/victim counts in terms of annual changes; most of the relevant factors were statistically significant at the 0.05 level. The four most popular crash exposures used as a denominator in calculating crash rates (e.g., fatality rate per million VMT) did not explain most of the seven crash/victim counts in terms of annual changes; VMT, population, number of registered drivers, and number of registered vehicles. Annual changes in VMT and population failed to explain annual changes in all seven counts, and changes in the number of registered vehicles and the number of registered drivers explained changes in one and two of the seven, respectively. Three factors were
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Y.-J. Kweon / Journal of Safety Research 53 (2015) 17–21
Table 2 Association of factors with traffic safety measures in terms of annual changes.
2 ΔInjuryt ¼ −420:296−2; 391 ΔUnemploymentRatet −0:368ν t−2 R ¼ 0:16 :
ð4Þ
Association with ΔFatality ΔFatal ΔInjury ΔInjury ΔFI ΔFI ΔTotal crash crash crash crash ΔBeer ΔCUI ΔU.S. CPI ΔDriver ΔEmployment ΔU.S. gas price ΔGas production ΔGVIP ΔIncome ΔIPI ΔLabor force ΔPopulation ΔU.S. PPI ΔSales ΔUnemployment ΔUnemployment rate ΔVehicle ΔVMT
× × × × ○ × × ○ × ○ × × × × ○ ○ × ×
× × ○ × × × × ○ × ○ × × × ○ ○ ○ ○ ×
× × ○ × × × × × × × × × ○ × ○ ○ × ×
× × ○ ○ × × × × × × × × × × × ○ × ×
× × ○ × × × × × × × × × ○ × ○ ○ × ×
× × ○ ○ × × × × × × × × × × × ○ × ×
× × ○ × × × × ○ × ○ × × ○ × ○ ○ × ×
2 R ¼ 0:26 : ð5Þ
2 Δ FIt ¼ 411:172−2; 442 ΔUnemploymentRatet −0:370 ν t−2 R ¼ 0:17 :
ð6Þ ΔFICrasht ¼ 2; 057−454:240 ΔUS:CPI t þ 0:00809 ΔDrivert −0:340 ν t−1 ΔCrasht ¼ 12; 354−2; 459 ΔUS:CPI t
Note: FI = fatal and injury; Δ is a difference operator (for example, ΔVMT = VMT in year t − VMT in year t-1); ○ indicates statistical significance at the 0.1 level; × = not statistically significant.
found to explain changes in most of the seven crash/victim counts: changes in CPI, unemployment number, and unemployment rate. Interestingly, all three are economic indicators. Annual changes in only the unemployment rate were found to be associated with annual changes in all seven counts. The unemployment rate is calculated by dividing the total number of unemployed workers by the total labor force. Although labor force did not explain any of the counts and the unemployment number did not explain two of the seven counts in terms of annual changes, combining these two factors as a rate (unemployment/ labor force) better explained crash/victim counts in that the unemployment rate explained all seven counts in terms of annual changes. 4.2. Best models Table 2 presented the results of one-factor models. However, it is possible to improve the explanatory power (for example, R2) of the regression models by adding other factors. However, adding factors that are highly correlated to the factor already in the model is likely to cause biased estimates of slope parameters and/or standard errors. Only factors found to be relevant (shown in Table 2) and not highly correlated to the factor already in the model were added to the one-factor model. For some models, such as the model for annual changes in injuries, none of additional relevant factors turned out to be statistically significant (at the 0.1 level) after being added. Thus, the one-factor model producing the highest R2 value was determined to be the best. For the model for fatalities, the model with the unemployment rate produced the highest R2value yet the other relevant factors (for example, GVIP and IPI) was highly correlated with the unemployment rate in terms of annual changes. Thus, none of the other relevant factors could be added, making the model with the unemployment rate the best model for fatalities. The best model determined for each of the seven crash/ victim counts is listed here along with its R2 value. ΔFatalityt ¼ −9:443−55:513 ΔUnemploymentRatet
ΔInjuryCrasht ¼ −2; 037−447:059 ΔUS:CPI t þ 0:00791 ΔDriver−0:326νt−1
2 R ¼ 0:23 : ð2Þ
ΔFatalCrasht ¼ −38:469−39:992 ΔUnemploymentRatet 2 R ¼ 0:45 : þ0:000227 ΔVehiclet þ 0:558ν t−1 ð3Þ
2 R ¼ 0:26 : ð7Þ
2 R ¼ 0:46 :
ð8Þ
Regarding R2, two R2 values were calculated in SAS (regression R2 and total R2); the regression R2 was reported here. The total R2 measures the prediction performance of the entire model including the structural part and the autoregressive error part, and the regression R2 measures an estimation performance of the structural part after transforming for the autocorrelation (SAS Institute Inc., 2009). Since this study was interested in how well potential factors explained the seven traffic safety measures (in other words, how well a relationship between factors and each of the safety measures fits the data), the regression R2 was deemed appropriate. Across the seven models listed, the model for total crashes displayed the highest explanatory power in terms of the R2 value, followed by the model for fatal crashes. The R2 value of 0.46 of the model for total crashes means that annual changes in CPI explain 46% of yearly variations in annual changes in total crash counts. The unemployment rate appears to be a good indicator for fatalities, fatal crashes, injuries, and FI; CPI appears to be a good indicator for injury crashes, FI crashes, and total crashes in terms of annual changes. The negative signs were found on the slope parameter estimates of changes in the unemployment rate and CPI. As for the unemployment rate, the negative slopes mean as the unemployment rate increases from the previous year, the numbers of fatalities, fatal crashes, and injuries are expected to decrease. More specifically, a 1% increase in the annual unemployment rate in Virginia is associated with about 56 fewer fatalities and about 40 fewer fatal crashes annually in Virginia on average. As for annual CPI, a 1 point increase in CPI is associated with about 2,500 fewer traffic crashes and 450 fewer injury crashes in Virginia in 1 year on average. Applying the models for fatal crash and total crash to actual data in 2008, a 1% increase in the unemployment rate recorded in Virginia predicted 78 fewer fatal crashes (43%) compared to 180 actual fatal crash reductions and an 8-point increase in CPI predicted 7,222 fewer total crashes (71%) compared to 10,123 actual total crash reductions. The unemployment rate and CPI are economic indicators reflecting different aspects of economic activities. Economic activities are believed to influence transportation activities including movements of people and goods that are in turn related to traffic safety exposures. In addition, conditions in economies are believed to influence how people use the transportation system, not only the amount but also the manner of using the system. For example, in an economic downturn, a driver is less likely to speed for various reasons such as avoiding tickets for speeding and improving gas mileage, which might in turn put the driver and occupants and occupants in other vehicles in safer conditions on highways. Interestingly, changes in crash counts (e.g., fatal crashes) are better explained than changes in victim counts (e.g., fatalities) by the relevant factors. This implies that for forecasting traffic safety measures, using crash counts is likely to offer a more accurate forecast than using victim counts probably because victim counts are largely influenced by occupancy rates that may vary over years due to various factors
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(e.g., economies and policies). This might have an implication in setting future safety targets for highway safety plans or policies since setting safety targets for future years probably requires forecasting traffic safety pictures in terms of some of the seven crash/victim counts and crash counts are likely to be more robustly forecast than victim counts based on relevant factors. Annual changes in injury and injury crash counts appear to be explained the least by the relevant factors found in this study.
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Acknowledgments The author thanks Cheryl Lynn (retired) of the Virginia Center for Transportation Innovation and Research (VCTIR) for her contribution to the original study, Linda Evans of VCTIR for her excellent editorial help, and the Virginia Department of Transportation (VDOT)for sponsoring this and the original study. Any views or opinions presented in this paper are solely those of the author and do not necessarily represent the views of VDOT.
5. Conclusions References This study attempted to link annual changes in seven crash/victim counts (fatality, fatal crash, injury, injury crash, fatality + injury [FI], FI crash, and total crash) in Virginia to annual changes in the 18 potential relevant factors using Virginia-specific and national time-series data and regression models with treatment for serial correlations. Annual changes instead of annual raw values were used to find factors that could explain annual fluctuations in the seven crash/victim counts. Annual changes in typical traffic crash exposure measures (VMT, population, number of vehicles, and number of drivers) were generally not associated with annual changes in the crash/victim counts; changes in number of vehicles and number of drivers were associated with changes in one and two of the seven counts, respectively, whereas changes in VMT and population were not associated with changes in any of the seven counts. Annual changes in economic indicators (unemployment rate and CPI) were strongly associated with annual changes in most of the seven crash/victim counts; especially, annual changes in the unemployment rate were associated with annual changes in all seven counts. The unemployment rate and CPI both are economic indicators reflecting different aspects of economic activities. Economic activities are believed to influence transportation activities in terms of the amount and manner of using the transportation system, which is likely to influence traffic safety. The best model was determined for each of the seven crash/victim counts based on the R2 value. Among the best models for the seven counts, the models for total crash and fatal crash had the two highest R2 values, 0.46 and 0.45, respectively. According to these models, annual changes in CPI and the unemployment rate in Virginia explained about one half of annual changes in total crash counts and fatal crash counts in Virginia, respectively. On average, a 1 point increase in CPI and a 1% increase in the unemployment rate of Virginia were associated with about 2,500 fewer traffic crashes and about 40 fewer fatal crashes annually in Virginia. In applying the models to 2008 actual data, a 1% increase in the unemployment rate recorded in Virginia predicted 43% of 180 actual reductions in fatal crashes and a 6-point increase in CPI predicted 71% of 10,123 actual reductions in total crashes. Changes in crash counts (e.g., fatal crashes) are better explained than changes in victim counts (e.g., fatalities) by relevant factors, which might be because victim counts are influenced by occupancy rates possibly varying over years. This has an implication in setting traffic safety targets for highway safety plans or policy, probably requiring forecasting future traffic safety pictures in terms of some of the seven crash/victim counts.
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