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Causal effects between bus revenue vehicle-kilometers and bus ridership
Transportation Research Part A 130 (2019) 54–64
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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra
Causal effects between bus revenue vehicle-kilometers and bus ridership Ming-Tsung Leea, Chao-Fu Yehb, a b
T
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Department of Logistics Management, National Kaohsiung University of Science and Technology, Taiwan Department of Transportation and Logistics, Feng Chia University, Taiwan
ARTICLE INFO
ABSTRACT
Keywords: Causal effect Convergent cross mapping Revenue vehicle-kilometer Ridership Free fare bus policy Time series Taichung City
To create a sustainable urban transportation environment, transportation authorities often implement incentive strategies to attract new public transportation users. Various studies have shown that increasing bus revenue vehicle-kilometers (BK) is a key factor for increasing bus ridership (BR). In this situation, BK affects BR. However, an increase in BR may lead to an increase in BK. Then, BR affects BK. The existence and directions of causal effects between BK and BR are the research questions addressed in this study. Since 2007, the Taichung City Government has been adding and adjusting bus routes to build a dense bus network. In 2011, it implemented a free fare bus policy. BR grew from ca. 2 million per month in 2007 to 10 million per month in 2015. Moreover, BK increased by ca. 3 times during that same period. This provides an opportunity to understand the causal effects between BK and BR. Extended convergent cross mapping (ECCM) can be used to assess the causal relationship between two variables without modelling. We adopted this method to distinguish the influences of BK and BR. According to the results, increasing BK attracted more public transit passengers during the period 2007 to 2010. However, there was no effect of BR on BK. After implementation of free fare bus policy in 2011, increases in BK led to increases in BR and increases in BR drove incremental growth of BK. The result was a virtuous cycle of mutual influence between BK and BR. In conclusion, increasing BK, such as route length or number of scheduled runs, can promote the usage of public transportation. Moreover, authorities can implement free fare bus policy to attract potential users and force incremental growth of BK.
1. Introduction Excessive reliance on private motor vehicles creates negative external costs, such as air pollution, noise pollution, road congestion, traffic accidents and greenhouse effect, etc. Moreover, many of these external costs are not borne by motor vehicle users alone, but rather by the whole society (Yeh, 2013). Moving toward sustainable development of urban transportation and shifting from private motor vehicle usage to public transportation usage are development consensuses shared by many cities around the world. Increasing public transportation ridership requires the gradual building of transportation networks and elevation of service standards, to create a positive impression of public transportation among the public. According to the European Commission on Transportation Research, direct strategies for increasing public transportation ridership include improvements in service quality and quantity (Taylor et al., 2009).
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Corresponding author at: No. 100, Wenhwa Rd., Seatwen, Taichung 40724, Taiwan. E-mail address: [email protected] (C.-F. Yeh).
https://doi.org/10.1016/j.tra.2019.09.019 Received 26 January 2017; Received in revised form 7 September 2019; Accepted 16 September 2019 0965-8564/ © 2019 Published by Elsevier Ltd.
Transportation Research Part A 130 (2019) 54–64
M.-T. Lee and C.-F. Yeh
Previous studies have shown that public transportation ridership is mainly affected by transit service levels (Liu, 1993; Kohn, 2000; Kain and Liu, 1995, 1996; Gomez-Ibanez, 1996). McLeod et al. (1991) developed two multivariate time-series regression models of public transportation ridership for Honolulu, Hawaii. The results indicated that fare, number of buses and revenue miles are the factors that influence ridership. Therefore, improvements in public transportation service quality, building of dense public transportation networks, development of new type transportation systems and strengthening of transportation management are all effective and appropriate urban transportation policies (Vlek & Michon 1992; Gärling et al. 2002). De Menezes and John (1983) demonstrated that the major factor influencing the use of mass transit is network scale. Kain and Liu's (1995, 1998) econometric analyses of the determinants of transit ridership clearly showed that the service length of public transportation contributes to its success. Kohn (2000) indicated that revenue vehicle-hours and revenue vehicle-kilometers are independent variables of transit ridership in Canada. Increasing revenue vehicle-hours or vehicle-kilometers to attract ridership appears to be a straightforward strategy. In recent years, in many cities in the US, Canada, Germany, and Belgium, public transportation development strategies have included free fare policies in certain areas or along designated corridors (Bamberg and Schmidt, 2001; Heath and Gifford, 2002; Brown et al., 2003; De Witte et al., 2006; Vobora, 2008). Fare reductions are a direct and flexible strategy for influencing passenger choice behavior (Borndörfer et al., 2012). Reducing fare decreases travel cost and makes public transit more attractive. Fujii et al. (2001) demonstrated that short-term improvements in transportation system service levels, such as lowering of fares, lead to longterm changes in transportation mode preferences. Thøgersen (2006) illustrated that fare change can affect the use of transit and car ownership. Moreover, dwindling of fares to zero elicits positive perceptions of public transit (Shampanier et al., 2007). According to the results of the above-mentioned studies, low fare and dense network encourage people to choose public transit. However, low fares have not always shown a clear effect on ridership. Kain and Liu (1996) conducted econometric analyses for inducing ridership on 184 public transport systems over a period of 30 years. Their findings implied that transit agencies can increase ridership by increasing revenue miles rather than reducing fares. Taylor and Fink (2009) indicated that service coverage and service frequency are key factors that influence ridership. They demonstrated that service quantity has a stronger influence than fare or pricing. Vobora (2008) noted that free fare is not a major influencing factor for attracting transit passengers and even argued against the implementation of free fare policy. Since 2004, Taichung City has implemented a series of public bus policies, including reinforcing bus network and reducing bus fare. Bus ridership (BR) grew from ca. 2 million per month in 2007 to 3 million per month in 2011 and reached more than 10 million per month in 2015. This is one of only a few examples of continuous annual BR growth in Taiwan. This case allows an opportunity to investigate the influence between bus revenue vehicle-kilometers (BK) and BR, where BR represents bus system revenues and BK reflects service time, service areas, number of routes in a service area, and service frequency of a route. Although there may be a high level of correlation between BK and BR, it is still not possible to determine whether increases in BK truly drive incremental growth of BR or whether changes in BR stimulate adjustments in BK. Therefore, it is necessary to analyze the existence and directions of the causal relationship between BK and BR. Moreover, in 2011, Taichung City implemented the i384 8-km-free fare bus policy in which passengers using electronic ticket ride free for the first eight kilometers of each trip. The government paid that fare to bus operators, according to the electronic ticket data of each passenger. This is similar to other urban area free fare bus policies and makes bus service more attractive. The causal relationship between BR and BK in a free fare bus policy context is analyzed in this paper. 2. Literature review Empirically, the level of service supply, which is generally measured in revenue vehicle-hours or revenue vehicle-miles, is highly correlated with transit demand (Taylor et al., 2009). Improvements in the quality of service can affect public transportation ridership (Thompson and Brown, 2006; Transit Cooperative Research Program, 2005). De Menezes and John (1983) discussed the factors that influence people living in cities in the US and Europe to use public transportation. They carried out regression analyses with variables such as public transportation system usage rate (number of times each person uses public transportation per year), public transportation route network density (route length per square kilometer), population density and vehicle ownership rate. The results revealed that network scale is the most important factor that influences public transportation use in American and European cities. Kain and Liu (1995, 1998) analyzed the determinants of transit ridership and clearly showed that the service length of transit in a rapidly growing metropolitan area contributes to its success. Moreover, in another study by Kain and Liu (1999), an increase of 26% in service miles for fixed route operations in San Diego's Metropolitan Transit System (MTS) led to an 18% increase in transit ridership. Kohn (2000) conducted a study of 85 Canadian urban transit agencies with transit data from 1992 to 1998 to identify independent variables related to ridership. The findings showed that revenue vehicle-hours correlate with transit use and that revenue vehicle-hours and revenue vehicle-kilometers are both independent variables of transit ridership in Canada. Thus, increasing the quantity of transit service (frequency and coverage) improves ridership if there is latent demand. Free fare and fare subsidy bus policies have been used to stimulate ridership in recent years. Cervero (1988) studied the urban public transportation systems of 18 countries in the 1980 s and found that a 10% increase in public transportation subsidies, with a reduction in fare of 5–7%, leads to 2–3% increases in ridership. In other words, there is a relationship between fare subsidy and ridership increase. The same experience characterizes other urban regions where transit operators have used immense subsidies to augment service and lessen real fares. Such policies have been successfully implemented in Portland (Oregon), Los Angeles, and Atlanta (Liu, 1993; Kain, 1997). The impact of changes in transit fares on ridership has been theoretically evaluated using price elasticity strategies (Cervero, 1990; Baum, 1973; Lago et al., 1981; Doxsey, 1980). Holmgren (2007) indicated that fare elasticity is −0.38, which means that an increase of 2.6% in fare reduces ridership by 1%. Price elasticities and effect of price changes on demand 55
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have attracted a great deal of attention. Bamberg and Schmidt (2001) focused on student monthly bus pass offered during the school year in Giessen, Germany, which was low in price and could be used on different types of public transportation systems within 50 km. Following the implementation of this policy, student ridership on public transportation increased from 15.3% to 30.8%. Moreover, the proportion of students using private vehicles decreased from 43.6% to 30.0%. Perone (2002) focused on the effects of a short-term free fare bus policy during off-peak hours in the US cities of Trenton and Denver during the period 1978–1979. The results showed 16% and 36% increases in ridership, respectively, during the policy period. Hodge et al. (1994) also looked at free fare bus policy in these two cities and proposed that the free fare period be changed to peak hours to reduce traffic congestion. Boyd et al. (2003) studied bus ridership on the campus of the University of California at Los Angeles after implementation of leading-in free fare bus policy. Bus ridership rose more than 50%, with a decrease in automobile trips of more than 1000 each day. Cats et al. (2016) investigated trip pattern changes based on individual travel habit survey of 1500 households for one year after the implementation of free-fare public transport (FFPT) policy in Tallinn, the capital of Estonia. Public transportation usage and ridership increased by 14% and 24%, respectively. The effect of FFPT on ridership was substantially lower than that reported in previous studies due to the high levels of service provision and public transport usage and the low level of public transport fees that were already in place prior to FFPT in Tallinn. Kain and Liu (1999) found that large increases in public transport use achieved in Houston and San Diego are principally due to fare reductions and service increases. De Witte et al. (2008) demonstrated a certain margin for a further modal shift from car use towards public transport. For public transport to be more attractive to car users, the price paid by the commuter should be lowered, the quality and capacity of the public services should be improved and the mobility policy of companies should be adjusted in favor of public transport. De Witte et al. (2006) studied the implementation of free public transport policy on the public transport usage of 3162 university students in the Flemish Region of Belgium in 2003 and 2004. Among them, 51.2% benefitted from this free fare policy, while 48.8% did not. From the results of that study, public transport usage by those students who benefitted from this free public transport policy increased. Public transport usage also increased among non-benefitting students. In other words, free fare bus policy is not the only factor involved in increasing ridership. Accessibility of routes, frequency of service and on-time service are important considerations for students. Taylor and Fink (2009) focused on the internal factors influencing urban transit ridership. Frequency, coverage and reliability were shown to be more important than fare in determining ridership. Vobora (2008), director of public transit agency Lane Transit District (LTD) in Oregon, expressed that LTD cannot absorb a loss in fare revenue or respond to significantly increased demand when providing fare-free bus policy. Considering financial and operational impacts, he concluded that implementation of a free fare system should be re-examined if subsidies become crucial for maintaining and expanding bus service. Previous studies have found that BR effectively increases based on the supply of BK. In this situation, we should observe BK affecting BR. On the other hand, free fare or fare subsidy bus policy may attract new transit users and large increases in passengers may force operators to increase BK. In this case, we should observe that BR affects BK. The previous studies were mainly performed on data collected from surveys or questionnaires to summarize the relationships between independent and dependent variables. Although there may be a high level of correlation between BK and BR, it is still not possible to determine whether increases in BK truly drive incremental growth of BR or whether changes in BR stimulate adjustments in BK. Identifying the existence and directions of causal effects between BK and BR from observational data is necessary. This is important in transportation policy development for determining the driving force, as well as for evaluating whether a given policy reaches expected outcomes. 3. Methodology 3.1. Principles of cross mapping method Cross mapping method operates under state-space representation of the dynamical system. It assumes that the investigated time series X and Y are manifestations of respective dynamical systems. According to Takens’ (1981) theorem, we can approximately reconstruct the two attractor manifolds, MX and MY, from the respective X and Y using time delay embedding. Take time series X of length L, {X} = {X(1), X(2), …, X(L)}, as an example. Each point in E-dimensional space MX is denoted as a vector x(t) = < X(t), X(t − τ), X(t − 2τ), …, X(t − (E − 1)τ) > , where time lag τ and dimension E are positive integers. If the time indices of neighboring points in the historical data of manifolds MY can be used to identify the neighboring points in the manifolds MX, there is a causal effect of X influencing Y. Sugihara et al. (2012) developed convergent cross mapping (CCM) to evaluate the success of cross mapping by correlation coefficient of X(t) and X (t)|MY , denoted as r[X(t), X (t)]. Fig. 1 shows the principles of the cross mapping for X influencing Y and X not influencing Y, respectively. This estimation is calculated from a weighted mean of the X(ti) values: i=E+1
X (t ) =
wi X (ti),
(1)
i=1
where the time indices are denoted as ti = t1, …, tE+1 from closest to farthest in the manifolds MY, the weight wi = ui/∑ui, ui = exp{-d [y(t), y(ti)]/d[y(t), y(t1)]}, and d[y(t), y(ti)] is the Euclidean distance between two vectors in MY. With longer data length L on cross mapping, there are more points in MY and shorter distances among E + 1 nearest neighbors. Therefore, if X influences Y, X (t) converges to X(t) and correlation coefficient r[X(t), X (t)] increases. The higher values of r[X(t), X (t)] indicate stronger causal force for X's influence on Y. Furthermore, cross mapping of Y's influence on X can be calculated analogously. CCM can detect causality without modelling. This is an advantage when we deal with a complex system in which relationships 56
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Fig. 1. Principles of CCM (Sugihara et al., 2012).
between variables are unclear. However, it fails to distinguish between unidirectional strong coupling and bidirectional causality (Ye et al., 2015; Mønster et al., 2016). Ye et al. (2015) extended the CCM (ECCM) by considering time delays. Fig. 2 expresses the principles of ECCM for detecting X's influence on Y. The CCM is extended to a reasonable time step j at which X may influence Y. The estimation Eq. (1) is modified as i=E +1
X (t + j) =
wi X (ti + j).
(2)
i=1
If X influences Y with some time delays, the nearest neighbors of current state y(t) at MY should identify the time indices of corresponding nearest neighbors of past values x(t + j), where j is non-positive value. Rj represents the average value of r[X(t + j) X (t + j)]s calculated from respective segments of length L in a whole time series. The peaks of all Rjs located in the range of nonpositive j indicate that X causes Y. If ECCM detects a positive j from cross mapping of MY, this indicates that Y influences X but X does not influence Y. Future independent variable X influencing past dependent variable Y is unreasonable. We adopted the ECCM approach in this study. This approach can be applied to coupling variables, such as BK and BR, no matter if the coupling force is strong or weak. 3.2. ECCM demonstration by simulation The state space reconstruction is determined by two parameters, τ and E. Referring to the workable ranges of the parameters by Sugihara and May (1990) and Sugihara et al. (2012), we chose τ = 1–2 and E = 2–4 to form 6 (=2 * 3) candidate sets for time delay embedding. False nearest neighbors (FNN, Kennel et al. 1992) method was used to choose the set of τ and E for ECCM. Minimal sum of FNN ratios from respective time series X and Y was adopted: Set (τ & E) = arg. min. (FNN Ratio of X + FNN Ratio of Y). After calculating all Rjs, we used student’s t-test to examine the null hypothesis H0: Rj ≦ 0.3 for each j. |Rj| ≦ 0.3 was considered no correlation or negative correlation, which is unreasonable with ECCM. Then, we used one-way ANOVA to examine the null hypothesis H0: Rjs larger than 0.3 are all equal. If Rjs were not all equal, Fisher’s least significant difference (LSD) was used to determine the largest Rj to find the peak of the ECCM. The significance level of all statistical tests in this study was 0.05. To clearly understand the ECCM results in terms of causality direction and causality strength, we simulated 3 respective causality systems between coupled logistic difference equations, shown as Eqs. (3a)–(3c). The logistic difference equations, which play a prominent role in chaotic behavior, were also simulated by Ye et al. (2015) and Sugihara et al. (2012). The 3 causality systems represent the following situations, respectively: 57
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Fig. 2. Principles of ECCM.
(a) X influences Y while Y influences X (X(t − 1) ⇒ Y(t) while Y(t − 1) ⇒ X(t)) (b) X does not influence Y while Y influences X (X ⇏ Y while Y(t − 1) ⇒ X(t)) (c) X does not influence Y while Y does not influence X (X ⇏ Y while Y ⇏ X)
X (t ) = X (t Y (t ) = Y (t
1)[\;3.8 1)[\;3.7
1.5X (t 1.6Y (t
1) 1)
0.25Y (t 0.05X (t
1)] 1)]
X (t ) = X (t Y (t ) = Y (t
1)[\;3.8 1)[\;3.7
1.5X (t 1.6Y (t
1) 1)]
0.25Y (t
1)]
X (t ) = X (t Y (t ) = Y (t
1)[\;3.8 1)[\;3.7
1.5X (t 1.6Y (t
1)] 1)]
(3a) (3b) (3c)
Fig. 3(a–c) presents the ECCM results for causality systems of Eqs. (3a)–(3c), respectively. Diamond points denote the peaks of ECCM on t-test, ANOVA and LSD. Fig. 3(a) demonstrates a bidirectional causality system. The two respective peaks of Y cross mapping X and X cross mapping Y are both located at j = −1. Moreover, the higher value of Rj=−1 of X cross mapping Y than of Y cross mapping X indicates stronger causal force of Y on X than of X on Y. Fig. 3(b) presents a unidirectional causality system. The peak of X cross mapping Y is located at j = −2, indicating that Y causally influences X. The peak of Y cross mapping X occurs in the range of positive j and indicates that X has no effect on Y. In Fig. 3(c), all Rjs of Y cross mapping X and X cross mapping Y are near 0; indicating no causal relationship between X and Y. 4. Empirical study 4.1. Description of study site In Taichung City, with 2.7 million residents, the bus system serves as the backbone of public transit. To stimulate BR, the Taichung City Government began reforming the urban bus network in 2007 and launched a quasi-free fare bus policy in 2011. These resulted in public transport usage rate increases from 3% to 10% from 2004 to 2014 (Department of Statistics, Ministry of 58
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Fig. 3. ECCM results for causality direction and causality strength.
Transportation and Communications, 2014). From this successful experience, we have an opportunity to investigate the relationship between BK and BR under different situations. Since 2007, the Taichung City Government has been creating and adjusting bus routes to build a dense bus network. In 2009 and 2010, the government launched TTJ I & II policies to form a denser and more widespread bus network. In June 2011, the Taichung City Government implemented the i384 8-km-free fare bus policy, allowing passengers using electronic ticket to ride free for the first eight kilometers of each trip. A chronology of bus policies in Taichung City is shown in Table 1. Fig. 4 shows the data for the Taichung bus system between 2007 and 2015. With the implementation of new bus policies, BR in Taichung City grew from ca. 2 million per month in 2007 to more than 10 million per month in 2015. There were only 5 city bus operators and 42 routes in 2007. Those numbers grew to 15 operators and more than 200 routes in 2015. BK increased by ca. 3 times from 2007 to 2015. From 2007 to 2010, BR grew from 2.0 to 2.8 million passengers per month and BK increased from 1.0 to 1.8 million per month. After implementation of policies A and B, TTJ I & II, there were 7 city bus operators and 54 bus routes in 2010. We named this period the “steady growth stage”. Between February and May 2011, following the merging of Taichung City and Taichung County, some intercity bus routes became city bus routes. Many routes with stable ridership were brought into the city bus system. This led to a large growth in monthly BR and BK, but this growth was not related to bus promotional policies. From June 2011 to June 2015, in addition to increases in bus frequency and routes, the Taichung City Government implemented free fare bus policy for the first eight kilometers on all city bus routes, meaning the government subsidized bus fares for trip distances of less than 8 km. Passengers only needed to pay fare for the distance beyond 8 km. As the average trip distance is around 8 km in Taichung City, many passengers benefited from this policy. BR grew from 4.5 to 11.0 million per month and BK grew from 3.0 to 5.8 million per month. This successful experience is most remarkable in Taiwan. We named this period the “explosive growth stage”. In this study, we investigated the causal relationship between BK and BR in these two stages. The periods of these respective stages are listed in Table 2. During the period 2007 to 2015, the geometric mean of annual population growth rate in Taichung City, including ex Taichung County, was about 0.65%. BR growth was much larger than population growth. Background information on Taichung City is shown in Tables 3 and 4 in Appendix I. As shown in Fig. 4, there are low points in the data every February and August, most likely due to winter and summer school breaks. It is necessary to eliminate seasonal factors from the data to avoid their influence on identifying causal relationship. The deseasonalized BR and BK by multiplicative decomposition model are shown in Fig. 7 in Appendix II. Table 1 Chronology of bus policies in Taichung City. Item
Policy
Date
Description
A
TTJ I
B
TTJ II
18th May 2009 1st Jan. 2010
C
i3848-km-free
1st Jun. 2011
D
New trunk line
10th Mar. 2013
Seven Taichung Transit Jet (TTJ) bus routes were launched based on the concept of “on time, efficient, and new vehicles”. Passengers using electronic ticket rode free along these seven routes until Dec. 31, 2009 TTJ service range was expanded from the Taichung City center to rural districts (Dali, Taiping, Tanzi). Passengers using electronic ticket rode free along these routes until Dec. 31, 2010 Passengers using electronic ticket could ride free for the first 8 km of each trip on city bus routes. (On Jul. 8, 2015, this was expanded to the first 10 km free.) Seven high speed bus routes along freeway or expressway were launched. The buses along these routes carry identifying markings and are referred to as new trunk lines
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Fig. 4. Taichung bus system data.
Table 2 The two research stages. Research Stage
Starting and Ending Dates
Steady Growth Explosive Growth
Jan. 2007–Dec. 2010 Jun. 2011–Jun. 2015
4.2. Results of ECCM Fig. 5 shows the ECCM results for the steady growth stage. The peak of BR cross mapping BK is in the range of negative lag j (=−2 to −4), which means that BK influences BR. Both BK and BR grew by around 50% during that 4-year period. Increases in BK attracted new passengers and resulted in higher BR. For BK cross mapping BR, peaks of Rjs are at j = −6, −4, −2, 3, and 5, meaning they are spread among positive and negative lags. The result is noisy and flat, with no causal impact of BR on BK. BK incremental growth was not triggered by BR. This stage exhibited unidirectional causality for the relationship between BK and BR. Fig. 6 shows the ECCM results for the explosive growth stage, during which the first eight kilometers free fare bus policy was implemented. Peaks of BR cross mapping BK and BK cross mapping BR are located at j = −2 and 0. This means that BR and BK influence each other in a bidirectional causality system. During this 4-year period, BK and BR grew 100% and 150%, respectively. Increases in BK attracted new passengers and resulted in higher BR. Moreover, BR increases forced incremental growth of BK. Growth in new passengers, triggered by BK or quasi-free fare bus policy, forced the government or operators to increase BK, e.g., by creating new routes or increasing number of scheduled buses. A virtuous cycle of mutual influence between BK and BR was, therefore, established. 5. Conclusion and discussion The purposes of public transport development are to maintain existing passengers and to attract new passengers. Transit ridership directly represents system performance, as well as revenues. Therefore, increases and decreases in BR have come to symbolize
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Fig. 5. ECCM results for steady growth stage (τ = 2 & E = 2).
Fig. 6. ECCM results for explosive growth stage (τ = 2 & E = 2).
whether transportation policy is successful or not. BK, which reflects service time, service areas, number of routes in a service area, and service frequency of a route, denotes the supply of the transit system. There have been many studies that have focused on the correlation between BK and BR. However, it is still not possible to determine whether changes in BK truly drive changes in BR or if increases or decreases in BR stimulate adjustments to BK. Therefore, analyzing the causal relationship between BK and BR to confirm the causal direction is necessary. Such information allows city administrators to understand driving forces when drafting policy and to evaluate whether a given policy reaches expected outcomes. To assess causal relationship between BK and BR, we adopted the ECCM approach, which was developed by Sugihara et al. (2012) and revised by Ye et al. (2015). As there is no model building process in ECCM, we did not have to face the situation of building models in a complex system in which relationships between variables are unclear. We used public transit data of Taichung City from
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2007 to 2015 to investigate possible causal relationships between BK and BR. During that period, several bus policies were implemented. BR was ca. 2 million per month in 2007 and grew to more than 10 million per month in 2015. In addition, BK increased by ca. 3 times. According to the BK and BR time series, we divided this period into steady growth stage and explosive growth stage. ECCM was used to analyze the causal relationships between these two variables in these two stages. In the steady growth stage, both BK and BR grew gradually and ECCM exhibited unidirectional causality system. BK causally influenced BR, while BR did not influence BK. In this period, BK was an explanatory factor for modeling BR, consistent with the results found in the literature. BK incremental growth was not triggered by BR. In the explosive growth stage, 8-kilometer free fare bus policy was implemented. ECCM revealed that BR and BK influence each other in a bidirectional causality system. As in the steady growth stage, BK served as the explanatory variable for modeling BR. Moreover, ECCM revealed the force of BR's influence on BK. The result was a virtuous cycle for public transit development. Increases in BK attracted new passengers, resulting in higher BR, while increases in BR drove adjustments to BK. When BR growth was only caused by BK growth, BR time series exhibited gradual growth. If BR growth is only caused by free fare bus policy, BR time series should show a single increment and then stay flat. In the explosive growth stage, BR revealed explosive growth in combination with BK growth and free fare bus policy, leading to a virtuous cycle of mutual influence between BK and BR. According to the results, cities that desire to promote usage of public transit can expand their route network or increase the number of scheduled runs, accompanied by implementation of free fare bus policy. We conclude with a short discussion of a conventional analysis method, Granger causality test (1969). A variable X is “Granger cause” variable Y if the predictability of Y significantly improves when X is added as an independent variable. In other words, the predictability of Y significantly declines when X is eliminated from the model. The key requirement of this method is separability. Variable X contains unique causative information, which is not found in other variables, and can be removed by eliminating the variable from the model. If the effects of BK on BR do not exist in past BR time series, BK and BR are separable and Granger causality test is an appropriate method for detecting causal effects. However, BK and BR are not separable, but rather coupled. We did attempt the Granger causality test to identify the causal relationships of our research cases, but no causal effects could be identified. According to empirical studies, the Granger causality test is still useful for detecting causal effects between strongly coupled variables, but fails with weak to moderate coupling variables (Sugihara et al., 2012). ECCM, based on the idea of nonlinear attractor reconstruction of time series data, can be applied to coupling variables, no matter if the coupling force is strong or weak. We adopted the ECCM approach in this study and causal effects were successfully identified. Appendix I See Tables 3 and 4. Table 3 Population and motorized vehicle ownership in Taichung City. Item
Population (million) Annual growth rate of population (%) Motorized vehicle ownership (MVO, million) Annual growth rate of MVO (%)
Year 2007
2008
2009
2010
2011
2012
2013
2014
2015
2.607 0.73 2.449 2.53
2.624 0.66 2.508 2.40
2.636 0.45 2.55 1.68
2.648 0.48 2.605 2.13
2.664 0.6 2.685 3.08
2.685 0.77 2.726 1.55
2.702 0.62 2.669 −2.10
2.72 0.67 2.663 −0.23
2.74 0.9 2.693 1.15
2007
2008
2009
2010
2011
2012
2013
2014
2015
15.40 2.85
15.39 −0.08
14.40 −6.43
16.65 15.64
17.98 8.00
18.13 0.80
18.87 4.12
19.72 4.51
19.54 −0.93
Table 4 Per capita national income in Taiwan. Item
Per capita national income (PCNI, US$ 1000) Annual growth rate of PCNI (%)
Year
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Appendix II See Fig. 7.
Fig. 7. Deseasonalized monthly BR and BK in Taichung City.
Appendix B. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.tra.2019.09.019. References Bamberg, S., Schmidt, P., 2001. Theory-driven subgroup-specific evaluation of an intervention to reduce private car use. J. Appl. Soc. Psychol. 31 (6), 1300–1329. Baum, H.J., 1973. Free public transport. J. Transp. Econ. Policy 7 (1), 3–19. Borndörfer, R., Karbstein, M., Pfetsch, M.E., 2012. Models for fare planning in public transport. Discr. Appl. Math. 160, 2591–2605. Boyd, B., Chow, M., Johnson, R., Smith, A., 2003. Analysis of effects of fare-free transit program on student commuting mode shares: Bruingo at University of California at Los Angeles. Transp. Res. Rec.: J. Transp. Res. Board 1835, 101–110. Brown, B.B., Werner, C.M., Kim, N., 2003. Personal and contextual factors supporting the switch to transit use: evaluating a natural transit intervention. Anal. Social Issues Public Policy 3 (1), 139–160. Cats, O., Susilo, Y.O., Reimal, T., 2016. The prospects of fare-free public transport: evidence from Tallinn. Transportation. https://doi.org/10.1007/s11116-0169695-5. Cervero, R., 1990. Transit pricing research: a review and synthesis. Transportation 17 (2), 117–139. Cervero, R., 1988. Land-use mixing and suburban mobility. Transp. Quart. 42 (3), 429–446. De Menezes, J., John, F., 1983. Factors influencing transit use in European and U.S. cities. Transp. Res. Rec. 936, 44–47. De Witte, A., Macharis, C., Lannoy, P., Polain, C., Steenberghen, T., Van de Walle, S., 2006. The impact of ‘‘free” public transport: the case of Brussels. Transp. Res. Part A: Policy Pract. 40, 671–689. De Witte, A., Macharis, C., Mairesse, O., 2008. How persuasive is free public transport? A survey among commuters in the Brussels Capital Region. Transp. Policy 15, 216–224. Doxsey, L.B., 1980. Elasticity measures of behavioral response to off-peak fare-free transit. Transp. Res. Board N761, 7–14. Fujii, S., Gärling, T., Kitamura, R., 2001. Changes in drivers’ perceptions and use of public transport during a freeway closure: effects of temporary structural change on cooperation in a real-life social dilemma. Environ. Behav. 33, 796–808. Gärling, T., Gärling, A., Loukopoulos, P., 2002. Forecasting psychological consequences of car use reduction: a challenge to an environmental psychology of transportation. Appl. Psychol.: Int. Rev. Gomez-Ibanez, Jose A., 1996. Big-city transit, ridership, deficits and politics. J. Am. Plan. Assoc. 62 (1), 30–50. Granger, C.W.J., 1969. Investigating causal relations by econometric models and crossspectral methods. Econometrica 37, 424–438. Heath, Y., Gifford, R., 2002. Extending the theory of planned behavior: predicting the use of public transportation. J. Appl. Soc. Psychol. 32 (10), 2154–2189. Hodge, D.C., Orrell III, J.D., Strauss, T.R., 1994. Fare-free Policy: Costs, Impacts on Transit Service and Attainment of Transit System Goals. Report Number WA-RD 277.1. Washington State Department of Transportation. Holmgren, J., 2007. Meta-analysis of public transport demand. Transp. Res. Part A 41, 1021–1035. Kain, J.F., 1997. Cost-effective alternatives to Atlanta's costly rail rapid transit system. J. Transp. Econ. Policy 25–49. Kain, F., Liu, Z., 1999. Secrets of success: assessing the large increases in transit ridership achieved by Houston and San Diego transit providers. Transp. Res. Part A: Policy Pract. 33, 601–624. Kain, F., Liu, Z., 1998. An econometric analysis of the determinants of transit ridership, 1960–1990. Report prepared for the US Department of Transportation. Transport System Center, Cambridge, Massachusetts. Kain, F., Liu, Z., 1996. Econometric analysis of determinants of transit ridership: 1960–1990. Prepared for the Volpe National Transport Systems Center. U.S. Department of Transportation. Kain, F., Liu, Z., 1995. Secrets of success: how Houston and San Diego transit providers achieved large increases in transit ridership. Report prepared for Federal Transit Administration.
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Kennel, M.B., Brown, R., Abarbanel, H.D.I., 1992. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403. Kohn, Harold M., 2000. Factors affecting urban transit ridership. From the Bridging the Gaps Conference, Canadian Transportation Research Forum, Charlottetown, Prince Edward Island, Canada. Liu, Z., 1993. Determinants of Public Transit Ridership: Analysis of Post World War II Trends and Evaluation of Alternative Networks. MA Harvard University, Cambridge. Lago, A., Mayworm, P.D., McEnroe, J.M., 1981. Further evidence on aggregate and disaggregate transit fare elasticities. Transp. Res. Board N799, 42–47. McLeod, M., Flannelly, K., Flannelly, L., Behnke, R., 1991. Multivariate time-series model of transit ridership based on historical, aggregate data: the past, present, and future of Honolulu. Transp. Res. Rec. 1297, 76–84. Ministry of Transportation and Communications, 2014. Annual Statistics Report, website: http://www.motc.gov.tw/ch/home.jsp?id=54&parentpath=0,6. Mønster, D., Fusaroli, R., Tylen, K., Roepstorff, A., Sherson, J.F., 2016. Inferring causality from noisy time series data – a test of convergent cross-mapping. Conference Paper Presented at COMPLEXIS 2016, Rome, Italy. Perone Jennifer, S., 2002. Advantages and Disadvantages of Fare-free Transit Policy. Center for Urban Transportation Research, Tampa, FL. Shampanier, K., Mazar, N., Ariely, D., 2007. Zero as a special price: the true value of free products. Market. Sci. 26, 742–757. Sugihara, G., May, R.M., 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734. Sugihara, G., May, R., Ye, H., Hsieh, C.-H., Deyle, E., Fogarty, M., Munch, S., 2012. Detecting causality in complex ecosystems. Science 338, 6106. Takens, F., 1981. Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898. pp. 366–381. Taylor, B., Fink, C., 2009. The factors influencing transit ridership: a review and analysis of the ridership literature. Working Paper. Department of Urban Planning, UCLA. Taylor, B.D., Miller, D., Iseki, H., Fink, C., 2009. Nature and/or nurture? Analyzing the determinants of transit ridership across US urbanized areas. Transp. Res. Part A: Policy Pract. 43 (1), 60–77. Thøgersen, J., 2006. Understanding repetitive travel mode choices in a stable context: a panel study approach. Transp. Res. Part A: Policy Pract. 40, 621–638. Transit Cooperative Research Program: Evaluation of Recent Ridership Increases (Research Results Digest 69). Retrieved March 22, 2010, from http://www.trb.org/ news/blurb_detail.asp?id=4900. Thompson, G.L., Brown, J.R., 2006. Explaining variation in transit ridership in U.S. metropolitan areas between 1990 and 2000. Transp. Res. Rec. 1986, 172–181. Vlek, C., Michon, J., 1992. Why we should and how we could decrease the use of motor vehicles in the near future. IATTS Res. 15, 82–93. Vobora, A., 2008. Fare-Free Service at Lane Transit District: An Overview of Financial and Operational Impacts, Lane Transit District of Oregon. Retrieved November 2009. Ye, H., Deyle, E.R., Gilarranz, L.J., Sugihara, G., 2015. Distinguishing time-delayed causal interactions using convergent cross mapping. Sci. Rep. 14750 (5). Yeh, C.F., 2013. Evaluation methods for external costs road traffic based on objective territorialization in the metropolis. Cities 31, 76–84.
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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra
Causal effects between bus revenue vehicle-kilometers and bus ridership Ming-Tsung Leea, Chao-Fu Yehb, a b
T
⁎
Department of Logistics Management, National Kaohsiung University of Science and Technology, Taiwan Department of Transportation and Logistics, Feng Chia University, Taiwan
ARTICLE INFO
ABSTRACT
Keywords: Causal effect Convergent cross mapping Revenue vehicle-kilometer Ridership Free fare bus policy Time series Taichung City
To create a sustainable urban transportation environment, transportation authorities often implement incentive strategies to attract new public transportation users. Various studies have shown that increasing bus revenue vehicle-kilometers (BK) is a key factor for increasing bus ridership (BR). In this situation, BK affects BR. However, an increase in BR may lead to an increase in BK. Then, BR affects BK. The existence and directions of causal effects between BK and BR are the research questions addressed in this study. Since 2007, the Taichung City Government has been adding and adjusting bus routes to build a dense bus network. In 2011, it implemented a free fare bus policy. BR grew from ca. 2 million per month in 2007 to 10 million per month in 2015. Moreover, BK increased by ca. 3 times during that same period. This provides an opportunity to understand the causal effects between BK and BR. Extended convergent cross mapping (ECCM) can be used to assess the causal relationship between two variables without modelling. We adopted this method to distinguish the influences of BK and BR. According to the results, increasing BK attracted more public transit passengers during the period 2007 to 2010. However, there was no effect of BR on BK. After implementation of free fare bus policy in 2011, increases in BK led to increases in BR and increases in BR drove incremental growth of BK. The result was a virtuous cycle of mutual influence between BK and BR. In conclusion, increasing BK, such as route length or number of scheduled runs, can promote the usage of public transportation. Moreover, authorities can implement free fare bus policy to attract potential users and force incremental growth of BK.
1. Introduction Excessive reliance on private motor vehicles creates negative external costs, such as air pollution, noise pollution, road congestion, traffic accidents and greenhouse effect, etc. Moreover, many of these external costs are not borne by motor vehicle users alone, but rather by the whole society (Yeh, 2013). Moving toward sustainable development of urban transportation and shifting from private motor vehicle usage to public transportation usage are development consensuses shared by many cities around the world. Increasing public transportation ridership requires the gradual building of transportation networks and elevation of service standards, to create a positive impression of public transportation among the public. According to the European Commission on Transportation Research, direct strategies for increasing public transportation ridership include improvements in service quality and quantity (Taylor et al., 2009).
⁎
Corresponding author at: No. 100, Wenhwa Rd., Seatwen, Taichung 40724, Taiwan. E-mail address: [email protected] (C.-F. Yeh).
https://doi.org/10.1016/j.tra.2019.09.019 Received 26 January 2017; Received in revised form 7 September 2019; Accepted 16 September 2019 0965-8564/ © 2019 Published by Elsevier Ltd.
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Previous studies have shown that public transportation ridership is mainly affected by transit service levels (Liu, 1993; Kohn, 2000; Kain and Liu, 1995, 1996; Gomez-Ibanez, 1996). McLeod et al. (1991) developed two multivariate time-series regression models of public transportation ridership for Honolulu, Hawaii. The results indicated that fare, number of buses and revenue miles are the factors that influence ridership. Therefore, improvements in public transportation service quality, building of dense public transportation networks, development of new type transportation systems and strengthening of transportation management are all effective and appropriate urban transportation policies (Vlek & Michon 1992; Gärling et al. 2002). De Menezes and John (1983) demonstrated that the major factor influencing the use of mass transit is network scale. Kain and Liu's (1995, 1998) econometric analyses of the determinants of transit ridership clearly showed that the service length of public transportation contributes to its success. Kohn (2000) indicated that revenue vehicle-hours and revenue vehicle-kilometers are independent variables of transit ridership in Canada. Increasing revenue vehicle-hours or vehicle-kilometers to attract ridership appears to be a straightforward strategy. In recent years, in many cities in the US, Canada, Germany, and Belgium, public transportation development strategies have included free fare policies in certain areas or along designated corridors (Bamberg and Schmidt, 2001; Heath and Gifford, 2002; Brown et al., 2003; De Witte et al., 2006; Vobora, 2008). Fare reductions are a direct and flexible strategy for influencing passenger choice behavior (Borndörfer et al., 2012). Reducing fare decreases travel cost and makes public transit more attractive. Fujii et al. (2001) demonstrated that short-term improvements in transportation system service levels, such as lowering of fares, lead to longterm changes in transportation mode preferences. Thøgersen (2006) illustrated that fare change can affect the use of transit and car ownership. Moreover, dwindling of fares to zero elicits positive perceptions of public transit (Shampanier et al., 2007). According to the results of the above-mentioned studies, low fare and dense network encourage people to choose public transit. However, low fares have not always shown a clear effect on ridership. Kain and Liu (1996) conducted econometric analyses for inducing ridership on 184 public transport systems over a period of 30 years. Their findings implied that transit agencies can increase ridership by increasing revenue miles rather than reducing fares. Taylor and Fink (2009) indicated that service coverage and service frequency are key factors that influence ridership. They demonstrated that service quantity has a stronger influence than fare or pricing. Vobora (2008) noted that free fare is not a major influencing factor for attracting transit passengers and even argued against the implementation of free fare policy. Since 2004, Taichung City has implemented a series of public bus policies, including reinforcing bus network and reducing bus fare. Bus ridership (BR) grew from ca. 2 million per month in 2007 to 3 million per month in 2011 and reached more than 10 million per month in 2015. This is one of only a few examples of continuous annual BR growth in Taiwan. This case allows an opportunity to investigate the influence between bus revenue vehicle-kilometers (BK) and BR, where BR represents bus system revenues and BK reflects service time, service areas, number of routes in a service area, and service frequency of a route. Although there may be a high level of correlation between BK and BR, it is still not possible to determine whether increases in BK truly drive incremental growth of BR or whether changes in BR stimulate adjustments in BK. Therefore, it is necessary to analyze the existence and directions of the causal relationship between BK and BR. Moreover, in 2011, Taichung City implemented the i384 8-km-free fare bus policy in which passengers using electronic ticket ride free for the first eight kilometers of each trip. The government paid that fare to bus operators, according to the electronic ticket data of each passenger. This is similar to other urban area free fare bus policies and makes bus service more attractive. The causal relationship between BR and BK in a free fare bus policy context is analyzed in this paper. 2. Literature review Empirically, the level of service supply, which is generally measured in revenue vehicle-hours or revenue vehicle-miles, is highly correlated with transit demand (Taylor et al., 2009). Improvements in the quality of service can affect public transportation ridership (Thompson and Brown, 2006; Transit Cooperative Research Program, 2005). De Menezes and John (1983) discussed the factors that influence people living in cities in the US and Europe to use public transportation. They carried out regression analyses with variables such as public transportation system usage rate (number of times each person uses public transportation per year), public transportation route network density (route length per square kilometer), population density and vehicle ownership rate. The results revealed that network scale is the most important factor that influences public transportation use in American and European cities. Kain and Liu (1995, 1998) analyzed the determinants of transit ridership and clearly showed that the service length of transit in a rapidly growing metropolitan area contributes to its success. Moreover, in another study by Kain and Liu (1999), an increase of 26% in service miles for fixed route operations in San Diego's Metropolitan Transit System (MTS) led to an 18% increase in transit ridership. Kohn (2000) conducted a study of 85 Canadian urban transit agencies with transit data from 1992 to 1998 to identify independent variables related to ridership. The findings showed that revenue vehicle-hours correlate with transit use and that revenue vehicle-hours and revenue vehicle-kilometers are both independent variables of transit ridership in Canada. Thus, increasing the quantity of transit service (frequency and coverage) improves ridership if there is latent demand. Free fare and fare subsidy bus policies have been used to stimulate ridership in recent years. Cervero (1988) studied the urban public transportation systems of 18 countries in the 1980 s and found that a 10% increase in public transportation subsidies, with a reduction in fare of 5–7%, leads to 2–3% increases in ridership. In other words, there is a relationship between fare subsidy and ridership increase. The same experience characterizes other urban regions where transit operators have used immense subsidies to augment service and lessen real fares. Such policies have been successfully implemented in Portland (Oregon), Los Angeles, and Atlanta (Liu, 1993; Kain, 1997). The impact of changes in transit fares on ridership has been theoretically evaluated using price elasticity strategies (Cervero, 1990; Baum, 1973; Lago et al., 1981; Doxsey, 1980). Holmgren (2007) indicated that fare elasticity is −0.38, which means that an increase of 2.6% in fare reduces ridership by 1%. Price elasticities and effect of price changes on demand 55
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have attracted a great deal of attention. Bamberg and Schmidt (2001) focused on student monthly bus pass offered during the school year in Giessen, Germany, which was low in price and could be used on different types of public transportation systems within 50 km. Following the implementation of this policy, student ridership on public transportation increased from 15.3% to 30.8%. Moreover, the proportion of students using private vehicles decreased from 43.6% to 30.0%. Perone (2002) focused on the effects of a short-term free fare bus policy during off-peak hours in the US cities of Trenton and Denver during the period 1978–1979. The results showed 16% and 36% increases in ridership, respectively, during the policy period. Hodge et al. (1994) also looked at free fare bus policy in these two cities and proposed that the free fare period be changed to peak hours to reduce traffic congestion. Boyd et al. (2003) studied bus ridership on the campus of the University of California at Los Angeles after implementation of leading-in free fare bus policy. Bus ridership rose more than 50%, with a decrease in automobile trips of more than 1000 each day. Cats et al. (2016) investigated trip pattern changes based on individual travel habit survey of 1500 households for one year after the implementation of free-fare public transport (FFPT) policy in Tallinn, the capital of Estonia. Public transportation usage and ridership increased by 14% and 24%, respectively. The effect of FFPT on ridership was substantially lower than that reported in previous studies due to the high levels of service provision and public transport usage and the low level of public transport fees that were already in place prior to FFPT in Tallinn. Kain and Liu (1999) found that large increases in public transport use achieved in Houston and San Diego are principally due to fare reductions and service increases. De Witte et al. (2008) demonstrated a certain margin for a further modal shift from car use towards public transport. For public transport to be more attractive to car users, the price paid by the commuter should be lowered, the quality and capacity of the public services should be improved and the mobility policy of companies should be adjusted in favor of public transport. De Witte et al. (2006) studied the implementation of free public transport policy on the public transport usage of 3162 university students in the Flemish Region of Belgium in 2003 and 2004. Among them, 51.2% benefitted from this free fare policy, while 48.8% did not. From the results of that study, public transport usage by those students who benefitted from this free public transport policy increased. Public transport usage also increased among non-benefitting students. In other words, free fare bus policy is not the only factor involved in increasing ridership. Accessibility of routes, frequency of service and on-time service are important considerations for students. Taylor and Fink (2009) focused on the internal factors influencing urban transit ridership. Frequency, coverage and reliability were shown to be more important than fare in determining ridership. Vobora (2008), director of public transit agency Lane Transit District (LTD) in Oregon, expressed that LTD cannot absorb a loss in fare revenue or respond to significantly increased demand when providing fare-free bus policy. Considering financial and operational impacts, he concluded that implementation of a free fare system should be re-examined if subsidies become crucial for maintaining and expanding bus service. Previous studies have found that BR effectively increases based on the supply of BK. In this situation, we should observe BK affecting BR. On the other hand, free fare or fare subsidy bus policy may attract new transit users and large increases in passengers may force operators to increase BK. In this case, we should observe that BR affects BK. The previous studies were mainly performed on data collected from surveys or questionnaires to summarize the relationships between independent and dependent variables. Although there may be a high level of correlation between BK and BR, it is still not possible to determine whether increases in BK truly drive incremental growth of BR or whether changes in BR stimulate adjustments in BK. Identifying the existence and directions of causal effects between BK and BR from observational data is necessary. This is important in transportation policy development for determining the driving force, as well as for evaluating whether a given policy reaches expected outcomes. 3. Methodology 3.1. Principles of cross mapping method Cross mapping method operates under state-space representation of the dynamical system. It assumes that the investigated time series X and Y are manifestations of respective dynamical systems. According to Takens’ (1981) theorem, we can approximately reconstruct the two attractor manifolds, MX and MY, from the respective X and Y using time delay embedding. Take time series X of length L, {X} = {X(1), X(2), …, X(L)}, as an example. Each point in E-dimensional space MX is denoted as a vector x(t) = < X(t), X(t − τ), X(t − 2τ), …, X(t − (E − 1)τ) > , where time lag τ and dimension E are positive integers. If the time indices of neighboring points in the historical data of manifolds MY can be used to identify the neighboring points in the manifolds MX, there is a causal effect of X influencing Y. Sugihara et al. (2012) developed convergent cross mapping (CCM) to evaluate the success of cross mapping by correlation coefficient of X(t) and X (t)|MY , denoted as r[X(t), X (t)]. Fig. 1 shows the principles of the cross mapping for X influencing Y and X not influencing Y, respectively. This estimation is calculated from a weighted mean of the X(ti) values: i=E+1
X (t ) =
wi X (ti),
(1)
i=1
where the time indices are denoted as ti = t1, …, tE+1 from closest to farthest in the manifolds MY, the weight wi = ui/∑ui, ui = exp{-d [y(t), y(ti)]/d[y(t), y(t1)]}, and d[y(t), y(ti)] is the Euclidean distance between two vectors in MY. With longer data length L on cross mapping, there are more points in MY and shorter distances among E + 1 nearest neighbors. Therefore, if X influences Y, X (t) converges to X(t) and correlation coefficient r[X(t), X (t)] increases. The higher values of r[X(t), X (t)] indicate stronger causal force for X's influence on Y. Furthermore, cross mapping of Y's influence on X can be calculated analogously. CCM can detect causality without modelling. This is an advantage when we deal with a complex system in which relationships 56
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Fig. 1. Principles of CCM (Sugihara et al., 2012).
between variables are unclear. However, it fails to distinguish between unidirectional strong coupling and bidirectional causality (Ye et al., 2015; Mønster et al., 2016). Ye et al. (2015) extended the CCM (ECCM) by considering time delays. Fig. 2 expresses the principles of ECCM for detecting X's influence on Y. The CCM is extended to a reasonable time step j at which X may influence Y. The estimation Eq. (1) is modified as i=E +1
X (t + j) =
wi X (ti + j).
(2)
i=1
If X influences Y with some time delays, the nearest neighbors of current state y(t) at MY should identify the time indices of corresponding nearest neighbors of past values x(t + j), where j is non-positive value. Rj represents the average value of r[X(t + j) X (t + j)]s calculated from respective segments of length L in a whole time series. The peaks of all Rjs located in the range of nonpositive j indicate that X causes Y. If ECCM detects a positive j from cross mapping of MY, this indicates that Y influences X but X does not influence Y. Future independent variable X influencing past dependent variable Y is unreasonable. We adopted the ECCM approach in this study. This approach can be applied to coupling variables, such as BK and BR, no matter if the coupling force is strong or weak. 3.2. ECCM demonstration by simulation The state space reconstruction is determined by two parameters, τ and E. Referring to the workable ranges of the parameters by Sugihara and May (1990) and Sugihara et al. (2012), we chose τ = 1–2 and E = 2–4 to form 6 (=2 * 3) candidate sets for time delay embedding. False nearest neighbors (FNN, Kennel et al. 1992) method was used to choose the set of τ and E for ECCM. Minimal sum of FNN ratios from respective time series X and Y was adopted: Set (τ & E) = arg. min. (FNN Ratio of X + FNN Ratio of Y). After calculating all Rjs, we used student’s t-test to examine the null hypothesis H0: Rj ≦ 0.3 for each j. |Rj| ≦ 0.3 was considered no correlation or negative correlation, which is unreasonable with ECCM. Then, we used one-way ANOVA to examine the null hypothesis H0: Rjs larger than 0.3 are all equal. If Rjs were not all equal, Fisher’s least significant difference (LSD) was used to determine the largest Rj to find the peak of the ECCM. The significance level of all statistical tests in this study was 0.05. To clearly understand the ECCM results in terms of causality direction and causality strength, we simulated 3 respective causality systems between coupled logistic difference equations, shown as Eqs. (3a)–(3c). The logistic difference equations, which play a prominent role in chaotic behavior, were also simulated by Ye et al. (2015) and Sugihara et al. (2012). The 3 causality systems represent the following situations, respectively: 57
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Fig. 2. Principles of ECCM.
(a) X influences Y while Y influences X (X(t − 1) ⇒ Y(t) while Y(t − 1) ⇒ X(t)) (b) X does not influence Y while Y influences X (X ⇏ Y while Y(t − 1) ⇒ X(t)) (c) X does not influence Y while Y does not influence X (X ⇏ Y while Y ⇏ X)
X (t ) = X (t Y (t ) = Y (t
1)[\;3.8 1)[\;3.7
1.5X (t 1.6Y (t
1) 1)
0.25Y (t 0.05X (t
1)] 1)]
X (t ) = X (t Y (t ) = Y (t
1)[\;3.8 1)[\;3.7
1.5X (t 1.6Y (t
1) 1)]
0.25Y (t
1)]
X (t ) = X (t Y (t ) = Y (t
1)[\;3.8 1)[\;3.7
1.5X (t 1.6Y (t
1)] 1)]
(3a) (3b) (3c)
Fig. 3(a–c) presents the ECCM results for causality systems of Eqs. (3a)–(3c), respectively. Diamond points denote the peaks of ECCM on t-test, ANOVA and LSD. Fig. 3(a) demonstrates a bidirectional causality system. The two respective peaks of Y cross mapping X and X cross mapping Y are both located at j = −1. Moreover, the higher value of Rj=−1 of X cross mapping Y than of Y cross mapping X indicates stronger causal force of Y on X than of X on Y. Fig. 3(b) presents a unidirectional causality system. The peak of X cross mapping Y is located at j = −2, indicating that Y causally influences X. The peak of Y cross mapping X occurs in the range of positive j and indicates that X has no effect on Y. In Fig. 3(c), all Rjs of Y cross mapping X and X cross mapping Y are near 0; indicating no causal relationship between X and Y. 4. Empirical study 4.1. Description of study site In Taichung City, with 2.7 million residents, the bus system serves as the backbone of public transit. To stimulate BR, the Taichung City Government began reforming the urban bus network in 2007 and launched a quasi-free fare bus policy in 2011. These resulted in public transport usage rate increases from 3% to 10% from 2004 to 2014 (Department of Statistics, Ministry of 58
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Fig. 3. ECCM results for causality direction and causality strength.
Transportation and Communications, 2014). From this successful experience, we have an opportunity to investigate the relationship between BK and BR under different situations. Since 2007, the Taichung City Government has been creating and adjusting bus routes to build a dense bus network. In 2009 and 2010, the government launched TTJ I & II policies to form a denser and more widespread bus network. In June 2011, the Taichung City Government implemented the i384 8-km-free fare bus policy, allowing passengers using electronic ticket to ride free for the first eight kilometers of each trip. A chronology of bus policies in Taichung City is shown in Table 1. Fig. 4 shows the data for the Taichung bus system between 2007 and 2015. With the implementation of new bus policies, BR in Taichung City grew from ca. 2 million per month in 2007 to more than 10 million per month in 2015. There were only 5 city bus operators and 42 routes in 2007. Those numbers grew to 15 operators and more than 200 routes in 2015. BK increased by ca. 3 times from 2007 to 2015. From 2007 to 2010, BR grew from 2.0 to 2.8 million passengers per month and BK increased from 1.0 to 1.8 million per month. After implementation of policies A and B, TTJ I & II, there were 7 city bus operators and 54 bus routes in 2010. We named this period the “steady growth stage”. Between February and May 2011, following the merging of Taichung City and Taichung County, some intercity bus routes became city bus routes. Many routes with stable ridership were brought into the city bus system. This led to a large growth in monthly BR and BK, but this growth was not related to bus promotional policies. From June 2011 to June 2015, in addition to increases in bus frequency and routes, the Taichung City Government implemented free fare bus policy for the first eight kilometers on all city bus routes, meaning the government subsidized bus fares for trip distances of less than 8 km. Passengers only needed to pay fare for the distance beyond 8 km. As the average trip distance is around 8 km in Taichung City, many passengers benefited from this policy. BR grew from 4.5 to 11.0 million per month and BK grew from 3.0 to 5.8 million per month. This successful experience is most remarkable in Taiwan. We named this period the “explosive growth stage”. In this study, we investigated the causal relationship between BK and BR in these two stages. The periods of these respective stages are listed in Table 2. During the period 2007 to 2015, the geometric mean of annual population growth rate in Taichung City, including ex Taichung County, was about 0.65%. BR growth was much larger than population growth. Background information on Taichung City is shown in Tables 3 and 4 in Appendix I. As shown in Fig. 4, there are low points in the data every February and August, most likely due to winter and summer school breaks. It is necessary to eliminate seasonal factors from the data to avoid their influence on identifying causal relationship. The deseasonalized BR and BK by multiplicative decomposition model are shown in Fig. 7 in Appendix II. Table 1 Chronology of bus policies in Taichung City. Item
Policy
Date
Description
A
TTJ I
B
TTJ II
18th May 2009 1st Jan. 2010
C
i3848-km-free
1st Jun. 2011
D
New trunk line
10th Mar. 2013
Seven Taichung Transit Jet (TTJ) bus routes were launched based on the concept of “on time, efficient, and new vehicles”. Passengers using electronic ticket rode free along these seven routes until Dec. 31, 2009 TTJ service range was expanded from the Taichung City center to rural districts (Dali, Taiping, Tanzi). Passengers using electronic ticket rode free along these routes until Dec. 31, 2010 Passengers using electronic ticket could ride free for the first 8 km of each trip on city bus routes. (On Jul. 8, 2015, this was expanded to the first 10 km free.) Seven high speed bus routes along freeway or expressway were launched. The buses along these routes carry identifying markings and are referred to as new trunk lines
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Fig. 4. Taichung bus system data.
Table 2 The two research stages. Research Stage
Starting and Ending Dates
Steady Growth Explosive Growth
Jan. 2007–Dec. 2010 Jun. 2011–Jun. 2015
4.2. Results of ECCM Fig. 5 shows the ECCM results for the steady growth stage. The peak of BR cross mapping BK is in the range of negative lag j (=−2 to −4), which means that BK influences BR. Both BK and BR grew by around 50% during that 4-year period. Increases in BK attracted new passengers and resulted in higher BR. For BK cross mapping BR, peaks of Rjs are at j = −6, −4, −2, 3, and 5, meaning they are spread among positive and negative lags. The result is noisy and flat, with no causal impact of BR on BK. BK incremental growth was not triggered by BR. This stage exhibited unidirectional causality for the relationship between BK and BR. Fig. 6 shows the ECCM results for the explosive growth stage, during which the first eight kilometers free fare bus policy was implemented. Peaks of BR cross mapping BK and BK cross mapping BR are located at j = −2 and 0. This means that BR and BK influence each other in a bidirectional causality system. During this 4-year period, BK and BR grew 100% and 150%, respectively. Increases in BK attracted new passengers and resulted in higher BR. Moreover, BR increases forced incremental growth of BK. Growth in new passengers, triggered by BK or quasi-free fare bus policy, forced the government or operators to increase BK, e.g., by creating new routes or increasing number of scheduled buses. A virtuous cycle of mutual influence between BK and BR was, therefore, established. 5. Conclusion and discussion The purposes of public transport development are to maintain existing passengers and to attract new passengers. Transit ridership directly represents system performance, as well as revenues. Therefore, increases and decreases in BR have come to symbolize
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Fig. 5. ECCM results for steady growth stage (τ = 2 & E = 2).
Fig. 6. ECCM results for explosive growth stage (τ = 2 & E = 2).
whether transportation policy is successful or not. BK, which reflects service time, service areas, number of routes in a service area, and service frequency of a route, denotes the supply of the transit system. There have been many studies that have focused on the correlation between BK and BR. However, it is still not possible to determine whether changes in BK truly drive changes in BR or if increases or decreases in BR stimulate adjustments to BK. Therefore, analyzing the causal relationship between BK and BR to confirm the causal direction is necessary. Such information allows city administrators to understand driving forces when drafting policy and to evaluate whether a given policy reaches expected outcomes. To assess causal relationship between BK and BR, we adopted the ECCM approach, which was developed by Sugihara et al. (2012) and revised by Ye et al. (2015). As there is no model building process in ECCM, we did not have to face the situation of building models in a complex system in which relationships between variables are unclear. We used public transit data of Taichung City from
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2007 to 2015 to investigate possible causal relationships between BK and BR. During that period, several bus policies were implemented. BR was ca. 2 million per month in 2007 and grew to more than 10 million per month in 2015. In addition, BK increased by ca. 3 times. According to the BK and BR time series, we divided this period into steady growth stage and explosive growth stage. ECCM was used to analyze the causal relationships between these two variables in these two stages. In the steady growth stage, both BK and BR grew gradually and ECCM exhibited unidirectional causality system. BK causally influenced BR, while BR did not influence BK. In this period, BK was an explanatory factor for modeling BR, consistent with the results found in the literature. BK incremental growth was not triggered by BR. In the explosive growth stage, 8-kilometer free fare bus policy was implemented. ECCM revealed that BR and BK influence each other in a bidirectional causality system. As in the steady growth stage, BK served as the explanatory variable for modeling BR. Moreover, ECCM revealed the force of BR's influence on BK. The result was a virtuous cycle for public transit development. Increases in BK attracted new passengers, resulting in higher BR, while increases in BR drove adjustments to BK. When BR growth was only caused by BK growth, BR time series exhibited gradual growth. If BR growth is only caused by free fare bus policy, BR time series should show a single increment and then stay flat. In the explosive growth stage, BR revealed explosive growth in combination with BK growth and free fare bus policy, leading to a virtuous cycle of mutual influence between BK and BR. According to the results, cities that desire to promote usage of public transit can expand their route network or increase the number of scheduled runs, accompanied by implementation of free fare bus policy. We conclude with a short discussion of a conventional analysis method, Granger causality test (1969). A variable X is “Granger cause” variable Y if the predictability of Y significantly improves when X is added as an independent variable. In other words, the predictability of Y significantly declines when X is eliminated from the model. The key requirement of this method is separability. Variable X contains unique causative information, which is not found in other variables, and can be removed by eliminating the variable from the model. If the effects of BK on BR do not exist in past BR time series, BK and BR are separable and Granger causality test is an appropriate method for detecting causal effects. However, BK and BR are not separable, but rather coupled. We did attempt the Granger causality test to identify the causal relationships of our research cases, but no causal effects could be identified. According to empirical studies, the Granger causality test is still useful for detecting causal effects between strongly coupled variables, but fails with weak to moderate coupling variables (Sugihara et al., 2012). ECCM, based on the idea of nonlinear attractor reconstruction of time series data, can be applied to coupling variables, no matter if the coupling force is strong or weak. We adopted the ECCM approach in this study and causal effects were successfully identified. Appendix I See Tables 3 and 4. Table 3 Population and motorized vehicle ownership in Taichung City. Item
Population (million) Annual growth rate of population (%) Motorized vehicle ownership (MVO, million) Annual growth rate of MVO (%)
Year 2007
2008
2009
2010
2011
2012
2013
2014
2015
2.607 0.73 2.449 2.53
2.624 0.66 2.508 2.40
2.636 0.45 2.55 1.68
2.648 0.48 2.605 2.13
2.664 0.6 2.685 3.08
2.685 0.77 2.726 1.55
2.702 0.62 2.669 −2.10
2.72 0.67 2.663 −0.23
2.74 0.9 2.693 1.15
2007
2008
2009
2010
2011
2012
2013
2014
2015
15.40 2.85
15.39 −0.08
14.40 −6.43
16.65 15.64
17.98 8.00
18.13 0.80
18.87 4.12
19.72 4.51
19.54 −0.93
Table 4 Per capita national income in Taiwan. Item
Per capita national income (PCNI, US$ 1000) Annual growth rate of PCNI (%)
Year
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Appendix II See Fig. 7.
Fig. 7. Deseasonalized monthly BR and BK in Taichung City.
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