Assessing the Impact of Speed Limit Increases on Fatal Interstate Crashes By Sandy Balkin, Ernst & Young LLP and J. Keith Ord, Georgetown University
Executive Summary Introduction Data Source Methodology Key Points Charts and Tables Fig 1: Trend Component for Rural Arizona Fig 2: Seasonal Component for Rural Arizona Figure 3: Irregular Component for Rural Arizona Figure 4: Significance Level of First Rural Limit Change Figure 5: Significance Level of Second Rural Limit Change Figure 6: Significance Level of Urban Limit Change Figure 7: Monthly Fatal Crashes Figure 8: Rural Seasonal Component Significance Level Figure 9: Urban Seasonal Component Significance Level Table 1: Significant Rural Changes Table 2: Significant Urban Changes Table 3: Predicted number of fatal crashes attributed to the speed limit increase on rural interstates. Table 4: Predicted number of fatal crashes attributed to the speed limit increase on urban interstates.	Introduction The purpose of this study is to investigate the relationship between speed limits and traffic-related fatalities. Specifically, we aim to answer the question: Does an increase in the speed limit result in a higher incidence of fatal crashes? Using a technique known as structural modeling, we are able to determine the impact past speed limit changes had on the number of fatal crashes on rural and urban interstates for each state based on its own, individual past experiences. This method also gives information about the seasonality, or monthly effect, of the number of fatal crashes. This introductory section continues the problem explanation by providing a historical perspective on speed limit increases and a summary of related studies. In the following sections we explain the analysis methodology used in specific detail with an example, describe the data source and present the key points from the data analysis. The relationship between speed limit and number of traffic related fatalities is a subject of great interest to insurance companies, the government at all levels and the general public. Historically, the government has taken an active role in the determination of speed limits starting with the establishment of the National Maximum Speed Limit (NMSL) by Congress in January 1974. Prior to this legislation setting the maximum speed limit to 55 mph, many states posted limits as high as 70 to 75 mph. In April 1987, Congress passed legislation allowing states to increase speed limits to 65 mph on qualifying sections of interstate highways in rural areas with less than 50,000 population. Within a few months, 38 states raised the speed limits on appropriate roads. More recently, the National Highway System (NHS) Designation Act of 1995 was signed into law on November 28, 1995. This Act ended the Federal government’s involvement in the establishment of speed limits, putting the responsibility for speed limit designation and compliance in the hands of the state governments that, in most cases, exercised their new rights and raised speed limits on rural and urban interstates. Various studies have been performed with the express purpose of determining the impact of the speed limit increases on the number of traffic-related crashes and fatalities. The following is a representative selection of such studies with references therein: Effects of the 65 mph Speed Limit Through 1990: A Report to Congress; National Highway Traffic Safety Administration; May 1992. This study looks at yearly interstate fatality data split by rural and urban roadways. The analysis is based on "expected historical trends." These projected counts were derived from statistical models based on the historical relationship between rural interstate fatalities and fatalities on other roadways. These results do not convey the impact of the speed limit increase on traffic fatalities. Rather, the study relates interstate deaths to non-interstate deaths; it also assumes a stationary, or non-changing, environment by fitting a global regression model. The authors then compare fatalities in 1986 with 1990 by computing percentage changes. This ignores historical trends and possible aberrant observations. This type of analysis may have "comparison bias." It is possible that more people chose to use interstates rather than alternative routes and that the increase in fatalities can be explained by Vehicle Miles Traveled (VMT) or actual roadway mileage. It also does not take into account the possibility that speed limits went up on several of the "other roads"—a relationship-changing event. This paper does caution that care ought to be taken when interpreting the data. The authors note that results of individual states are probably not generalizable to the entire nation. They also point out that no statistical model is capable of controlling all of the factors that affect fatalities. Farmer, Charles M., Retting, Richard A., and Lund, Adrian K.; Effect of 1996 Speed Limit Changes on Motor Vehicle Occupant Fatalities; Insurance Institute for Highway Safety; October 1997. This paper analyzes the effect of speed limit increases on interstates that occurred during and around 1996. This study employed linear regression models on trend and dummy variables to analyze the number of fatalities in states categorized by the time of their 1996 speed limit increase (early, late or none) and compare actual observed fatalities with the statistically computed, historically based trends. They first use percentage change between 1995 and 1996 to assess the impact of the 1996 legislation. They continually note that VMT may be able to explain the increase in fatalities, but the appropriate data are not available. This study continues by noting that while the national fatality toll for 1996 changed very little compared to 1995, the change in the fatality toll for individual states varied markedly between significant decreases and increases. It is also states that total Interstate fatalities increased for the 11 states that increased speed limits. The authors of this study do note that there has been an increasing trend in the portion of the fatalities that occur on roads posted 55 mph or greater and that some increase in fatalities on interstates is to be expected. Overall, this study presents a very thorough before and after comparison using percentage changes. A linear trend model, with an intervention variable, is used to compare actual 1996 fatalities with estimated 1996 fatalities based on historical trends. The combination of using annual data and non-adaptive trends limits the value of the comparisons. The Effect of Increased Speed Limits in the Post-NMSL Era: Report to Congress; National Highway Traffic Safety Administration; February 1998. This study also investigates the effect of the 1995-1996 speed limit increases on rural and urban interstates (specifically only states that had increased between December 8, 1995 and April 1, 1996 are considered). They group states into "changers" (12 count) and "non-changers" (18 count) where the latter serve as a comparison for the former. They modeled the logarithms of fatality counts for each year during 1990-1996 as functions of time and type of state. Both linear and quadratic time variables were included. The impact of the speed increase was modeled using a dummy variable equal to one in 1996 and 0 in previous years. They also included an interaction term between state group and the 1996 indicator to represent the difference between pre-1996/1996 changes for the two state types while accounting for the time trend. If this interaction term is significant, they claim that it can be concluded that the 1996 departure from the time trend among the states that increased limits is different from that of the comparison states. Again, the method may suffer from "comparison bias." The foremost problem with this type of analysis is that using such a linear and quadratic trend model is not appropriate for these series and does not perform as the authors claim it does. Including a quadratic trend may lower the residual variance for the in-sample fit, but it will damage the predictive ability of the model. By looking at the plot of Actual and Trend for rural Arizona in Figure 1, we can see that a global quadratic trend in the model does not provide a reasonable description for the length of the series. Ledolter, J. and Chan, K.S.; Evaluating the Impact of the 65 mph Maximum Speed Limit on Iowa Rural Interstates. The American Statistician; Volume 50; Number 1; February 1996. This study examines whether a significant change in the fatal and major-injury accident rates can be detected following the implementation of a higher speed limit on rural interstates in Iowa. The authors have access to quarterly data on traffic speed, traffic volume and traffic safety. To answer the posed question, they fit a time series intervention model relating number of accidents to be proportional to traffic volume and include time trend and intervention variables for the May 1987 change and quarterly seasonality. The authors find that expected numbers of fatal accidents in Iowa rose by 2 incidents per quarter on rural interstates, a statistically significant increase. BASIS FOR THE PRESENT STUDY Since the data are collected over time in regularly spaced intervals, the impact of the speed limit changes on traffic accidents may be analyzed via time series analysis and, in particular, intervention analysis. Intervention analysis is used when a change in the environment occurs at a known time and affects the phenomenon of interest (see Kendall and Ord, Chapter 13 or DeLurgio, Chapter 12 for a description). In this case, the known change is the change of speed limit. More specifically, since the change in speed limit is more or less permanent, a step intervention is most appropriate. That is, we hypothesize that the change in speed limits results in a permanent shift in the number of accidents. In this study the shift is measured as a percentage increase since we use a logarithmic transform; see the last paragraph of the next section. Next: Data Source -->