Forecasting Road Fatalities by the Use of Kinked Experience Curve

Transcription

1 Forecasting Road Fatalities by the Use of Kinked Experience Curve Yu-Sang Chang KDI School of Public Policy and Management 87 Heogiro, Dongdaemun-gu Seoul , Korea Jinsoo Lee KDI School of Public Policy and Management 87 Heogiro, Dongdaemun-gu Seoul , Korea January 2011 * We are happy to acknowledge competent research support provided by our graduate research assistant, Yun-seok Jung. We are also grateful to the KDI School of Public Policy and Management for providing financial support and to International Road Transport (IRT) for providing valuable data. 1 Electronic copy available at:

2 Forecasting Road Fatalities by the Use of Kinked Experience Curve Abstract According to the World Health Organization, more than one million road traffic deaths occur every year throughout the world. In order to cope with this challenge, many countries have established quantified road safety targets backed up with comprehensive safety strategies. Road safety targets need to be based on reliable forecasting methods. Following the pioneering work by Elvik (2010), this paper attempts to develop such forecasting models for 13 OECD countries based on the data available from 1970 to Deploying the methodology of both classical and kinked experience curves, we obtained the averaged experience slope of 55% from the kinked experience curve in contrast to 68.6% from the classical experience curve. The averaged standard deviation and R 2 calculated also show better fit to the data from the use of the kinked over the classical analysis. For the two simulated forecasting periods, we, then, calculate mean absolute percentage error (MAPE) to measure forecasting accuracy. In comparing the MAPEs calculated from the kinked versus the classical models, we find that forecasting accuracy for the kinked models is again significantly higher. Finally, we use our kinked models to forecast the road fatalities for 13 countries through JEL classification: R41; R48 Keywords: Road Fatalities; Kinked Experience Curve 2 Electronic copy available at:

3 1. Introduction According to the World Health Organization, more than one million road traffic deaths occur every year throughout the world. In order to cope with this challenge, many countries have established quantified road safety targets backed up with comprehensive safety strategies. Road safety targets need to be based on reliable forecasting methods. Following the pioneering work by Elvik (2010), this paper attempts to develop such forecasting models for 13 OECD countries based on the data available from 1970 to Deploying the methodology of both classical and kinked experience curves, we obtained the averaged experience slope of 55% from the kinked experience curve in contrast to 68.6% from the classical experience curve. The averaged standard deviation and R 2 calculated also show better fit to the data from the use of the kinked over the classical analysis. For the two simulated forecasting periods, we, then, calculate mean absolute percentage error (MAPE) to measure forecasting accuracy. In comparing the MAPEs calculated from the kinked versus the classical models, we find that forecasting accuracy for the kinked models is again significantly higher. Finally, we use our kinked models to forecast the road fatalities for 13 countries through In his pioneering work, Elvik developed both simple and complex forecasting models for eight OECD countries for the period of In his simple time trend model, he selected the best fitting model from five different functions ranging from linear, logarithmic, exponential, geometric, and polynomial. His complex model of negative binomial regression model analyzed countries, year, GDP per capita, and road safety target as the independent variables. And then, he tested the stability of long-term trends by adopting five alternative time periods for simulated forecasting. For example, one of the simulated forecasting used trend lines fitted to the data for to forecast the road fatality rates for About the results from the simple trend models, Elvik concludes that even trend lines that fit past trends very closely are usually worthless for predictive purpose. 1 As for the results from the complex models, Elvik concludes that although a multivariate model may fit historical data better than a simple tend line, it may not provide a better basis for prediction. To apply a multivariate model for prediction all explanatory variables need to be predicted. It is very unlikely that a meaningful basis for such prediction could be developed. 2 1 Elvik (2010), p Elvik (2010), p Electronic copy available at:

4 In spite of these pessimistic conclusions reached by Elvik, we believe that a simple learning or experience curve which is widely used in the health care, manufacturing and energy sectors with a great deal of success may provide more accurate forecast in road fatalities. This paper is made up of the following six parts. It begins with a brief literature review on the application of learning and experience curve to analyze read fatalities. Special attention will focus on the use of the so-called kinked experience curve. Second, historical data available on thirteen OECD countries will be analyzed by the use of both the classical and the kinked experience curve. Third, forecast of road fatalities will be made for the two simulated time periods of 1990 to 2007 as well as 2000 to Fourth section of this paper will calculate and compare the MAPEs resulting from the use of two alternative forecasting models. Fifth, by the use of the kinked experience models, we will forecast the road fatalities of 13 countries for the year of Finally, we will end with the discussion of our results and conclusions. 2. A brief literature survey Beginning with the study of the man-hour required for manufacturing Boeing aircrafts by Wright (1936), learning or experience curve models have been applied widely in industrial sectors. (Day 1977, Day and Montgomery 1983, Dutton and Thomas 1984, Liberman 1984, Stern and Deimlev 2006). More recently, the experience curve analysis has attracted renewed interest, especially in new technology areas in health care, alternative energy, climate control and others (Braham 2008, Chabous and Johntson 2000, Ethana and Clara 2002, Grantcharov et al. 2003, Hopper et al. 2007, Horowita and Salzhauer 2006, Nemet 2006, Weiss, et al. 2010, Yeh et al. 2005). In a recent review article on the application of experience curve, Weiss, et al. (2010B) identifies 124 cases of applications in manufacturing industry and 207 cases of applications in energy industry, totaling 331 application cases reported in the literature. In general, improvement patterns of performance measures such as unit prices, unit costs, fatality rates, or other physical efficiency metrics as dependent variable are to be explained by the cumulative volume or experience as an independent variable. More specifically, the relationship between the two variables is linear when both variables are expressed as a logarithmic function. Therefore, a given percentage change in cumulative volume or experience will generate a constant percentage improvement in performance measure. In spite of widespread applications in many other areas, we are not aware of any previous reported study of road fatality rates explicitly using the methodology of the experience curve. However, Minter (1987) has been the first to suggest that the learning curve model may provide a 4

5 fundamental explanation for the improvement pattern of road fatalities. He has also pointed out that the well-known Smeed s Law (Smeed, 1949, Adams, 1985) may be analogous to the learning curve model. Extending on the applicability of the learning curve, Oppe (1989) mentioned that improvement patterns of road fatalities had been interpreted as the learning curve for the society and that the decrease is supposed to result from the combination of all efforts made to improve traffic system, such as the improvement of the road system, vehicle design, crash measures, legislation, education, and individual learning (SNOV 1986). The traffic density as such may also have had a direct effect on the decrease of fatality rare. 3 In other words, all such efforts made to improve traffic safety ranging from better road, vehicle, crash prevention, legislation, education, enforcement, individual driving, etc. in combination will be represented in the past experience factor which is measured as the cumulative distance of road travelled. Thus, the logic of experience curve analysis is that the greater is the combination of these efforts made for the country in the past, the less will be the number of road fatalities. Broughton(1999) has made another major contribution when he observed an accelerated decline of fatality and all killed or seriously injured (KSI) rate from about 1983 in his Great Britain study which covered the period of 1949 to Even more important is the fact that he built an alternate forecasting model incorporating these accelerated rate reduction alter conducting elaborate statistical analysis. However, he was unable to explain the precise cause for the new trend by suggesting that this could well be the result progressive rather than immediate of major changes that occurred in the fast half of the decade 4 Changes in improvement or learning rates over time have also been observed by Boston Consulting Group (1968) when they suggested the kinked experience price slope as a function of the product life cycle. Some energy modeling groups also used kinked (piece-wise linear) learning curves, with successively lower learning rates at more mature development stages (McDonald and Schrattenhilzer, 2001; Konarritakis et al., 2002; Nakicaoric et al., 1995). More recently, Van Sark, (2008) has summarized the three empirical kinked price slopes which show higher, not lower, learning rates during the later stages in photovoltaic, ethanol and wind technologies. The kinked experience curve analysis where the output measure can be represented as the physical performance measures is more relevant to the study of road fatalities. Weiss et al., (2010A) reported the kinked experience curve analysis on the energy consumption rate of five major home appliances in two successive time period, before and after, the introduction of an energy policy in the Netherlands. The results show significantly higher learning slopes for the later time period. For 3 Oppe (1989), p Broughton (1999), p.359 5

6 example, the learning slope of 17% for refrigerators during the first time period of 1964 to 1994 had increased to 49% during the second period of 1995 to More recently, two other articles (Chang and Lee 2010, Chang, et al. 2011) have documented a large number of kinked experience patterns from the cases of suicide rates as well as survival rates of organ transplantations. Although the case of more than one kinked curve is theoretically possible, we are unaware of any reported empirical cases of multiple kinked curves. Unless the history of road fatality data to be studied displays a multiple kinked pattern, we will limit our analysis to a single kinked curve analysis. 3. Historical Experience Curve for Highway Fatalities in 13 OECD Countries Now we are ready to specify an experience curve of two types, classical and kinked, to be used in this study as follows: For classical experience curve: y(x t ) = y (x 1 )x t -b (1) where t = 1, 2, 3,., T x t = cumulative distance travelled in billion km through year t b = experience slope y(x t ) = fatality rate per billion km at cumulative distance travelled in billion km through year t y(x 1 ) = fatality rate per billion km at cumulative distance travelled in billion km through year 1 For kinked experience curve: y(x t ) = y(x 1 -b1 )x t (2) for the time period from the first year through one year before the kinked year where t = 1, 2, 3,., k-1 b 1 = experience slope for equation (2) 6

7 -b2 y(x t ) = y(x k )x t (3) for the time period from the kinked year through 2007 where t = k, k+1,., T b 2 = experience slope for equation (3) y(x k ) = fatality rate per billion km at cumulative distance travelled in billion km through year k The kinked year will vary by country. However, it is important that x 2, cumulative distance travelled, be counted from 1970, the beginning year of our study period. Annual data on the number of fatalities and the distance travelled for 13 OECD countries have been specially provided to us by International Road Transport (IRT). Figure 1 presents the result of our analysis on Great Britain by the use of both the classical experience curve and the kinked experience curve. As shown in Figure 1, the kinked year observed is 1980, and the slope during the kinked time period of is 55.36%. In contrast, the experience slope from the classical experience curve for the entire period of 1970 to 2007 is 68.4%. R 2 of 0.98 from the kinked curve is larger than 0.89 from the classical experience curve. Standard deviation of 0.06 from the kinked curve is much smaller than 0.20 from the classical curve. The summary of our analysis on 13 countries by the use of both classical and kinked experience equations are shown in Table 1. Figure 2 through 9 present the historical patterns of road fatalities by the use of both classical and kinked experience curve. Historical patterns in Figure 3, 5, 7 and 9 show that each of the 13 countries has clear-cut kinked pattern without exception. A close examination of the individual experience equation confirms the existence of kinked pattern for each country. For example for each country, the second slope from the kinked experience curve is significantly steeper than the slope from the classical experience curve. The averaged second slope of the kinked curve for 13 countries is 55.03% in comparison with 68.56% calculated as the averaged slope of the classical curves. Standard deviation associated with respective slope for each country is also smaller from the second kinked slope than standard deviation calculated from the classical slopes. The averaged standard deviation from the second slopes of the kinked curve is 0.09 in comparison with 0.20 calculated average of standard deviation of classical slope. Newey-West t test shows that difference between the second to the first slope in the kinked model is statistically significant at p value of less than for each of the 13 countries, as well. The averaged R 2 for the kinked equations is in contract to as the average of R 2 for the classical equations. Notice also that the kinked year has been observed to have occurred in 1980 for 9 out of 13 countries, while 3 countries had 1985 as their kinked years. Only one country, Finland, had 1976 as her kinked year. 7

8 In summary, it is remarkable that clear-cut kinked pattern does exist for each of these 13 countries. Furthermore, the second kinked experience curves have generated significantly steeper slopes which fit much better with the available data. 4. Simulated Forecasting Models For the purpose of simulating forecasting in our study, we have selected the two periods. For the classical experience curve analysis, we have a long simulated forecasting period covering 1990 to 2007, with the estimation period of , and the shorter period covering 2000 to 2007, with the estimation period of 1970 to We will name them long blind and short blind model respectively. As for the use of kinked experience curve, our estimation years will begin with the kinked year through 1989 for the long period and the kinked year through 1999 for the short-period. Forecasting periods by the kinked experience curve will be identical to those in the classical curve analysis. We will name them long intelligent and short intelligent model. These four forecasting models are displayed in table 2. Since cumulative distance travelled during the simulated forecast periods are assumed to be unknown, we had to forecast cumulative billion KM travelled for the long forecast period (1990 to 2007) and for the short forecast period (2000 to 2007). After testing several models, we have chosen to use a simple linear trend model. For the distance travelled data during the estimation periods, we have again used data we have obtained from IRT, covering the period of 1970 through 1989 and also through For example, we have developed the simple linear regression forecasting model for Great Britain as shown in figures 2A and 2B. y = 0.014X Long forecasting model (R 2 = 0.955) y = 0.013X Short forecasting model (R 2 = 0.977) Table 3 lists two separate forecasting equations of distance travelled we have estimated for each of 13 countries together with the respective values of R 2. Adding actual distances travelled from 1970 through 1989 in the long model and through 1999 in the short model will generate the cumulative actual distance travelled. Then, we have added forecasted annual distance travelled during the forecasting period to the actual cumulative distance travelled to generate forecasted cumulative distances travelled for each year during the forecast period. This was repeated for each country. 8

9 Now we are ready to develop four forecasting models for road fatality rate. We conducted our regression analysis with the classical experience curve and the second part of the kinked experience curve with data from the respective estimation periods. Figures 3A, 3B, 3C, and 3D show the respective new slopes estimated for each of the four forecasting equations for the Great Britain. They are: Long blind model = 79.82% Short blind model = 71.01% Long intelligent model = 60.33% Short intelligent model = 53.07% Notice that these slopes for forecasting models are different from those slopes shown in Table 1. We have repeated the same steps for estimating the four types of experience curve equations for each of the remaining countries. These results are shown in Table 4. Table 4 summaries complete results of our analysis showing details of the four forecasting equations for the of long blind, the short blind, the long intelligent, and the short intelligent models for each country. Each experience equation has its slope as well as standard deviation and R 2 estimated. Now, we are ready to forecast fatality rate per billion KM travelled for each year during the two simulated forecasting periods of and A graphic example for the Great Britain is again shown in Figures 3A through 3D. As shown in Figures 3A, 3B, 3C, and 3D for the Great Britain, we plot these estimated cumulative distance travelled as squares to generate road fatality rates for each year during the forecasting periods. In contrast, actual yearly road fatality rates during the same time periods are plotted as circles. We have numerically repeated the same steps for each of the remaining countries as well to generated yearly forecasted fatality rates during these two simulated forecasting periods. 5. Analysis of the Forecasting Errors Now the question can be raised as to how accurate are our simulated forecasts in comparison to the actual suicide rates. To measure forecasting accuracy, we have used Mean Absolute Deviation (MAD) and Mean Percentage Prediction Error (MAPE) which are defined as follows: MAD = 9

10 MAPE = / The results of our calculated MADs and MPPEs for each country are shown in Table 5. As expected, nearly all the MAPEs from the intelligent model show significant reduction from their counterpart from the blind model. The largest reduction occurs in the case of Denmark s long forecasting models where the blind model s MAPE of 68.12% decreased to just 6% from the intelligent model. The MAPE of 51.98% from the short blind model is reduced to 9.04% for the short intelligent model. Austria displays another major reduction of the MAPE from long blind model of % to just 15.28% from the long intelligent model and 59.12% from the short blind model to 6.44% from the short intelligent model. The only exception occurs in Finland where the long blind s MAPE of 37.78% actually increases to 38.9% from the intelligent model. Overall, the averaged MAPEs from the short intelligent model is 15.48% in comparison with 46.75% from the short blind model. Similarly, the averaged MAPEs from the long intelligent model is 26.92% in contrast to 67.31% from the long blind model. In other words, the short model generates the value of MAPE which is only 36% of the counterpart from the short blind model. The averaged MAPEs from the long intelligent model also generates only 43% of its counterpart from the long blind model. These results clearly indicate the superiority of the intelligent models over the blind models. 6. Forecasts of Road Fatalities for the future Now we are ready to forecast the road fatalities for the years of 2010, 2020, and We have used our second kinked experience equations we had estimated earlier and shown in Table 1. In addition, we need the cumulative distance travelled from 1970 through the years of 2010, 2020, and Therefore, we have estimated new linear equations to forecast annual distance travelled for each of the 13 countries as shown in Table 7. Using these equations, we have projected yearly forecasted distance travelled from 2008 through These yearly forecasts are added to generate cumulative distance travelled for each country. For example, the cumulative distance travelled for Finland is estimated to be billion kilometers by 2020, and billion kilometers by Using these cumulative distance travelled it is now possible to forecast road fatality rate per billion kilometer for each country. Again 10

11 in the case of Finland, the 2030 fatality rate is forecasted to be 4.55 persons per billion kilometer as follows: Y=1072.8X. which is the second kinked experience equation from Table 1. With the cumulative distance travelled, X, of , we calculated the fatality rate, Y, of 4.55 persons per one billion kilometer. Y = x = 4.55 We have repeated the same process to generate the road fatality rates for each of 13 countries. By multiplying the forecasted fatality rate to annual distance travelled for the respective year has generated the number of fatalities for the years of 2010, 2020, and 2030 for each country. Both fatality rates and the number of fatalities are summarized in Table 8. According to these forecasts, all the countries will experience a considerable reduction in their road fatality rates without exception. For example, Slovenia s fatality rate of in 2010 will decrease to 5.12 by Similarly, the number of fatalities in Slovenia will decline to 136 persons by 2030 from 249 in Therefore, Slovenia is projected to realize the maximum percentage of reduction in both the fatality rate and the number of fatalities. There are several other notable examples of radical reduction of fatality rate predicted. For example, 2010 fatality rates of Belgium (10.47), Austria (8.05), Denmark (6.49), and Switzerland (6.56) are projected to be almost halved by 2030 with Belgium (6.20), Austria (3.99), Denmark (3.56), and Switzerland (3.83). However, there are some countries where the actual number of fatalities is projected to decline only slightly. For example, United States will have her number of fatalities going from 39,185 in 2010 to only 36,271 by 2030 due to an increasing distance travelled forecasted. Similarly, Finland and Israel also may have relatively small decline in their number of fatalities by For the group of 13 countries, as a whole, the averaged fatality rate of 7.94 in 2010 is projected to decline to 5.83 in 2020 and 4.54 in Summary and Conclusions The most important finding of this study is the fact that each of the 13 countries show 11

12 remarkably similar single kinked pattern without exception. Although these kinked experience equations are derived empirically, there is little doubt that they have generated significantly more accurate forecast than the classical experience equation. Our simulated forecasts have generated significantly smaller averaged mean percentage prediction errors which is 36% to 43% of those from the classical equations. Although multiple kinked experience equation is theoretically possible, we have not observed any multiple kinked pattern from any these countries. On the other hand, if such multiple pattern were to occur, kinked experience equation can accommodate such variation. Another interesting finding is that the kinked years occurred in the year of 1980 for the majority of 9 countries. That means that time period after the respective kinked year ranged from 22 to 32 years, a long enough period to generate statistically meaningful data. In other words, the kinked experience equations are derived from large number of historical data. What may account for these observed kinked patterns? We can begin with the concept of learning curve for the society where the combination of all the safety improvement efforts from better road, vehicle, crash prevention, legislation, etc. will improve road safety for a nation (Minter 1987, Oppe 1989). And then, we proposed to add the concept of shared learning and cooperation among the countries involved. We recognize that each country has a vast pool of expertise and knowhow of reducing road fatalities which have accumulated over many years of safety promotion efforts. By sharing these valuable knowledge among interested countries, several comprehensive road safety strategy frameworks have been formulated to develop objective-related cost-effective, and practical measures to target achievement (Elvik,1993; Allsop,2000,2009; ETSC,2001,2003; OECD Scientific Expert Group,1994,2008). When many OECD countries have established national road safety targets (Wong, et al. 2006, Wong and Sze 2010), exchange of safety expertise would have been greatly facilitated for mutual benefit. We suggest that the cumulative effect of mutual sharing and cooperation among countries are likely to have caused in kinked patterns among these 13 countries to have begun around In other words, shared learning and cooperation among countries is much more likely to develop when these countries are working on the common interest public-sector issues such as road fatalities. As a matter of fact, gaining a momentum from shared learning and cooperation may have generated a tipping point phenomenon when a majority of countries begin to show a faster fatality reduction around the year of Overall, we are encouraged by the fact that our intelligent forecasting model which incorporates kinked experience curve appears to be a reliable forecasting tool for these countries studied. And perhaps, other countries may also benefit from the use of this methodology in the future. Following many successful applications in industry, health care and energy sector, the 12

13 experience curve analysis, in general, and the kinked experience curve, in particular, deserve to be used as another effective forecasting tool for traffic accident analysis as well. We also plan to further test the concept of kinked experience curve application to other socially critical areas as suicide, organ transplant, and alternative energy technologies where the similar effects from the shared learning and experience from the countries involved may be expected. 13

14 Reference Adams, J. G. U. (1985), Smeed s law, seat belts and the emperor s new clothes, In L. Evans and R. Schwing (eds.) Human Behaviour and Traffic Safety, New York: Plenum Press Allsop, R.E. (2000), Strategies and targets for reducing death and injury in road traffic accidents. In: Reading in Injury Prevention and Control, 3rd National Conference on Injury Prevention and Control, 6 9 Allsop, R.E. (2009), Britain s 11-year road safety strategy beyond midterm and in a European context, International Journal of Sustainable Transportation, 3, Boston Consulting Group (1968), Perspectives on experience, Boston Consulting Group Brahmi, Sondes Kahouli (2008), Technological learning in energy environment economy modelling: A survey, Energy Policy, 36, Broughton, J. (1991), Forecasting Road Accident Casualties in Great Britain, Accident and Analysis and Prevention, 23(5), Chambers, S. and Johnston, R. (2000), Experience curves in services: macro and micro level approaches, International Journal of Operations & Production Management, 20(7), Chang, Y.S. and Lee, J.S. (2010), Is Forecasting Future Suicide Rate Possible? Application of Experience Curve, KDI School of Public Policy & Management Paper No , Working Paper Series, Available at SSRN: Chang, Y.S. et al. (2011), The Speed and Impact of a New Technology Diffusion in Organ Transplantation; A Case Study Approach, Forthcoming KDI School of Public & Management Working Paper Series 14

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18 Table 1. Classical and Kinked Experience Exquations for 13 Countries (1970~2007) Country Kinked year Time Period Experience Curve Newy-West t statistic Equation Slope(%) SD R 2 b 2 -b 1 t-value p-value Finland 1970 ~ 2007 ( Total ) Y = X ~ 1975 ( 1st ) Y = X < ~ 2007 ( 2nd ) Y = 1, X Israel 1970 ~ 2007 ( Total ) Y = X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = X Belgium 1970 ~ 2007 ( Total ) Y = 1, X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 9, X USA 1970 ~ 2007 ( Total ) Y = X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 3, X Norway 1970 ~ 2007 ( Total ) Y = X ~ 1984 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 1, X Sweden 1970 ~ 2007 ( Total ) Y = X ~ 1984 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 6, X Austria 1970 ~ 2007 ( Total ) Y = 2, X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 37, X Great Britian 1970 ~ 2007 ( Total ) Y = 1, X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 20, X France 1970 ~ 2007 ( Total ) Y = 3, X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 99, X Ireland 1970 ~ 2007 ( Total ) Y = X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 1, X Denmark 1970 ~ 2007 ( Total ) Y = X ~ 1984 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 18, X Switzerland 1970 ~ 2007 ( Total ) Y = X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 15, X Slovenia 1970 ~ 2007 ( Total ) Y = X ~ 1979 ( 1st ) Y = X ~ 2007 ( 2nd ) Y = 24, X Average of Total Period Average of 1st Period Average of 2nd Period < < < < < < < < < < < <

19 Table 2. Structure of Simulated Forecasting Models Name Estimation Period Forecasting Period Long "Blind" 1st : ( 1970 ~ 1989 ) ( 1990 ~ 2007 ) Long "Intelligent" 1st : ( Kinked year ~ 1989 ) ( 1990 ~ 2007 ) Short "Blind" 2nd : ( 1970 ~ 1999 ) ( 2000 ~ 2007 ) Short "Intelligent" 2nd : ( Kinked year ~ 1999 ) ( 2000 ~ 2007 ) 19

20 Table 3. Simulated Forecasting Equations for Distance travelled No Country Period Estimation Forecasting Forecasting Equation R 2 1 Finland 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Israel 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Belgium 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x USA 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Norway 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Sweden 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Austria 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x GB 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x France 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Ireland 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Denmark 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Switzerland 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x Slovenia 1970 ~ ~ 2007 Y = x ~ ~ 2007 Y = x

21 Table 4. Experience Curve Equations for Simulated Forecasting Country Model Exp. Curve Name Estimation Peiod Forecasting Period Equation Slope(%) SD R 2 Finland Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1976 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1976 ~ 1999 ) 2000 ~ 2007 Y = X Israel Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X Belgium Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X USA Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X Norway Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1985 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1985 ~ 1999 ) 2000 ~ 2007 Y = X Sweden Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1985 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1985 ~ 1999 ) 2000 ~ 2007 Y = X Austria Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X Great Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Britain Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X France Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X Ireland Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X Denmark Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1985 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1985 ~ 1999 ) 2000 ~ 2007 Y = X Switzerland Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X Slovenia Long "Blind" ( 1st : 1970 ~ 1989 ) 1990 ~ 2007 Y = X Long "Intelligent" ( 1st : 1980 ~ 1989 ) 1990 ~ 2007 Y = X Short "Blind" ( 2nd : 1970 ~ 1999 ) 2000 ~ 2007 Y = X Short "Intelligent" ( 2nd : 1980 ~ 1999 ) 2000 ~ 2007 Y = X

22 Table 5. Comparison of MAD and MAPE of Simulated Forecasting Models Country Model MAD MAPE % % Finland Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Israel Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Belgium Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % USA Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Norway Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Sweden Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Austria Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Great Britain Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % France Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % 22

23 Ireland Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Denmark Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Switzerland Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Slovenia Long "Blind" ( 1st ) % % Long "Intelligent" ( 1st ) % % Short "Blind" ( 2nd ) % % Short "Intelligent" ( 2nd ) % % Average of Long "Blind" % % Average of Long "Intelligent" % % Average of Short "Blind" % % Average of Short "Intelligent" % % 23

24 Table 6. Forecasting Equations for Annual Distance Travelled Country Equation R 2 Finland Y = X Israel Y = X Belgium Y = X USA Y = X Norway Y = X Sweden Y = X Austria Y = X GB Y = X France Y = X Ireland Y = X Denmark Y = X Switzerland Y = X Slovenia Y = X * Forecasting equations are estimated from historical early distance travelled from 1970 to

25 TABLE 7. FORECAST OF ROAD FATALITIES, THE NUMBER OF FATALITIES THROUGHT 2030 Country Year A B C A B C A B C Finland Israel Belgium , USA , , , Norway Sweden Austria Great Britain , , , France , , , Ireland Demark Switzerland Slovenia Average Legend A : Cumulative distance travelled in billion kilometer B : Number of Fatality C : Fatality rate per billion kilometer travelled 25

26 Figure 1. Historical Experiecne Curve for Highway fatalities in Great Britain Kinked year: 1980 Total Period: 1970~2007 y = x Slope= 68.40% SD= 0.20 R² = Fatality rate per billion kiliometer traveled stPeriod: 1970~1979 y = x 0.18 Slope= 88.27% SD= 0.04 R² = nd Period: 1980~2007 y = 20164x Slope= 55.36% SD= 0.06 R² = Cumulative distance traveled in billion kilometer beginning

27 Figure 2. Classical Experience Curves for Road Fatalities of USA, GB and France 100 *Country: Equation, (Slope, SD, R 2 ) USA: y=581.73x 0.35, (78.3, 0.11, 0.919) GB: y=1346.6x 0.55, (68.4, 0.20, 0.89) France: y=3728.1x 0.59, (66.62, 0.23, 0.89) 50 Fatality rate per billion kilometer Cumulative distance traveled in billion kilometer beginning 1970 USA GB France USA GB France Figure 3. Kinked Experience Curves for Road Fatalities of USA, GB and France 100 *Country: Equation, (Slope, SD, R 2 ) USA: (1)y=118.12x 0.18, (88.33, 0.05, 0.886), (2)y=3783.8x 0.52, (69.64, 0.04, 0.973) GB: (1)y=104.52x 0.18, (88.27, 0.04, 0.992), (2)y=20164x 0.85 (55.36, ) France: (1)y=510.51x 0.30, (81.06, 0.10, 0.885), (2)y=99323x 0.95 (51.69, 0.11, 0.951) Fatality rate per billion kilometer traveled Cumulative distance traveled in billion kilometer beginning 1970 USA(1) USA(2) GB(1) GB(2) France(1) France(2) USA GB France 27

28 Figure 4. Classical Experience Curves for Road Fatalities of Austria, Denmark and Israel 120 Fatality rate per billion kilometer traveled *Country: Equation, (Slope, SD, R 2 ) Austria: y=2462.2x 0.7, (61.69, 0.26, 0.891) Denmark: y=469.14x 0.54, (68.97, 0.20, 0.873) Israel: y=482.9x 0.56, (67.88, 0.19, 0.93) Cumulative distance traveled in billion kilometer beginning 1970 Austria Denmark Israel Austria Denmark Israel Figure 5. Kinked Experience Curves for Road Fatalities of Austria, Denmark and Israel 120 Fatality rate per billion kilometer traveled *Country: Equation, (Slope, SD, R 2 ) Austria: (1)y=302.6x 0.27, (83.10, 0.11, 0.811), (2)y=37683x 1.1, (46.81, ) Denmark: (1)y=153.51x 0.31, (80.5, 0.08, 0.926), (2)y=18748x 1.09 (47.04, 0.07, 0.973) Israel : (1)y=143.52x 0.19, (87.54, 0.10, 0.748), (2)y=758.7x 0.64 (64.08, ) Cumulative distance traveled in billion kilometer beginning 1970 Austria(1) Austria(2) Denmark(1) Denmark(2) Israel(1) Israel(2) Austria Denmark Israel 28

29 Figure 6. Classical Experience Curves for Road Fatalities of Belgium, Sweden, Finland and Norway 150 Fatality rate per billion kilometer traveled *Country: Equation, (Slope, SD, R 2 ) Belgium: y=1409.4x 0.59, (66.48, 0.18, 0.929) Sweden: y=334.85x 0.49, (71.1, 0.16, 0.905) Finland: y=539.98x 0.58, (66.85, 0.16, 0.941) Norway: y=268.06x 0.51, (70.08, 0.15, 0.912) Cumulative distance traveled in billion kilometer beginning 1970 Belgium Sweden Finland Norway Belgium Sweden Finland Norway Figure 7. Kinked Experience Curves for Road Fatalities of Belgium, Sweden, Finland and Norway ` 150 Fatality rate per billion kilometer traveled *Country: Equation, (Slope, SD, R 2 ) Belgium: (1)y=346.18x 0.31, (80.5, 0.09, 0.907), (2)y=9685.2x 0.86, (55.06, ) Sweden: (1)y=138.68x 0.33, (79.44, 0.12, 0.86), (2)y=6142.7x 0.90 (53.66, 0.06, 0.958) Finland: (1)y=138.27x 0.25, (83.91, 0.07, 0.892), (2)y=1072.8x 0.69 (62.03, ) Norway: (1)y=115.95x 0.32, (80.11, 0.13, 0.827), (2)y=1273x 0.76 (58.93, ) Cumulative distance traveled in billion kilometer beginning 1970 Belgium(1) Belgium(2) Sweden(1) Sweden(2) Finland(1) Finland(2) Norway(1) Norway(2) Belgium Sweden Finland Norway 29