Curbside parking pricing in a city centre using a threshold

Transport Policy 52 (2016) 16–27

Contents lists available at ScienceDirect

Transport Policy journal homepage: www.elsevier.com/locate/tranpol

Curbside parking pricing in a city centre using a threshold Rong Zhang a, Lichao Zhu a,b,n a College of Transportation Engineering, Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, 4800 Cao’an Road, Jiading District, Shanghai 201804, PR China b Institute of Transport and Logistics Studies, The Business School, The University of Sydney, NSW 2006, Australia

art ic l e i nf o

a b s t r a c t

Article history: Received 19 December 2015 Received in revised form 16 June 2016 Accepted 24 June 2016

How to set reasonable pricing for curbside parking, while balancing the demand for and the supply of parking spaces, is a troublesome problem for metropolitan areas such as Shanghai. This paper addresses this problem from the perspective of choice behaviour. Our research focuses on the parking charge cut-off point, which is the minimum or maximum acceptable value that a driver sets for an attribute. A multiple linear regression model reveals that older and inexperienced drivers are more likely to ignore the charge cut-off points they themselves have set. Discrete choice models incorporating charge cut-offs are further used to analyse charge implications for parking choice behaviour. Our results show that the precision of the conventional model is improved by including a cut-off. At the same time, parking charges, the time spent searching for a parking space, and walking time after finding the parking space, all have a significantly negative influence on parking choices. Finally, a pricing scheme is put forward to reduce the occupancy rates of curbside parking to 85%. This contention is based on parking pricing models with cut-offs. We find indications that not accounting for charge cut-off points, when they are in fact present, may lead to inaccurate willingness-to-pay and upwardly biased pricing schemes. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Curbside parking Parking pricing Discrete choice Cut-off Pricing scheme

1. Introduction Curbside parking pricing has received significant attention from economic theorists (Arnott et al., 1991; Shoup, 2004; Proost, Van Dender, 2008). However, a common approach found in existing literature is to determine a curbside pricing scheme without considering garage parking pricing and the interaction between the two. If curbside and garage parking are perfect alternatives to each other, then curbside parking prices should be equal to garage parking prices, in order to achieve the goal of eliminating cruising (Shoup, 2005; Arnott and Inci, 2006). However, the two types of parking are not perfect alternatives, because of spatial differences (Arnott and Rowse, 2009). More specifically, approximately 30% of traffic is drivers cruising while looking for parking. This finding is based on a study of 11 international cities (Shoup, 2004). In addition, the average time taken to find a curbside parking space is between 3.5 and 14 min n Corresponding author at: College of Transportation Engineering, Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, 4800 Cao’an Road, Jiading District, Shanghai 201804, PR China. E-mail addresses: [email protected] (R. Zhang), [email protected] (L. Zhu).

http://dx.doi.org/10.1016/j.tranpol.2016.06.008 0967-070X/& 2016 Elsevier Ltd. All rights reserved.

(Arnott and Inci, 2006). This finding indicates that drivers prefer curbside parking over garage parking, due to curbside parking's flexibility, convenience, conservation of land and low construction and maintenance costs. However, curbside parking spaces occupy public road resources. Therefore, how to balance a road's occupancy rate and its functional goals is an important problem (Zhang et al., 2013; Zhang and Zhu, 2015). Reasonable curbside parking pricing can not only reduce vehicle cruising time and the number of cruising vehicles, but such pricing can also help to improve curb parking resource utilization. Shoup (2004) proposed that an 85% occupancy rate is appropriate for curbside parking spaces. Shoup stated that charge increases are needed when a road's occupancy rate exceeds 85%, in order to guarantee that drivers can find parking spaces any time. In other words, a city should try to optimize the use of public garages, rather than maximize the revenue of governments or companies (Pierce et al., 2015). At the very least, maximizing revenue is not the most important goal. At the same time, setting a reasonable parking price without having an adverse impact on the transportation system and other systems of a city is difficult (Simićević et al., 2013). This is especially true in cities in developing countries, due to the absence of reliable parking data. We are committed to addressing this issue in metropolitan areas

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

such as Shanghai. In what follows, we present a general introduction to the parking situation in Shanghai. Corresponding with the continuous improvement of residents' living standards, the number of private cars in Shanghai increased rapidly, from 1.5 million in 2009, to 3.2 million in 2014. This represented a 113% increase. Meanwhile, the number of parking spaces in downtown Shanghai grew from 0.77 million to just 1.13 million, an increase of only 47% (Shanghai Bureau of Statistics, 2014). The above fact indicates that the average annual growth rate of transportation facilities is lagging far behind that of the growth rate in the ownership of private cars. “Difficult to drive, difficult to park” has become one of the most important messages affecting the investment environment and socio-economic development of Shanghai. In addition, according to the 2014 Shanghai curbside parking statistics data, the ratios of parking durations of less than 1 h, between 1 and 2 h, and more than 2 h was 61.53%, 25.70%, and 12.77%, respectively, with a growing trend of average parking durations (Zhang et al., 2015). This tendency leads to an average turnover rate of only 3.09 times per day for each parking berth (Zhang et al., 2013). Based on this finding, the city's curbside parking pricing needs to be adjusted, especially in those key areas where curbside parking resources are relatively scarce. Therefore, we endeavour to propose a reasonable parking pricing scheme to influence a portion of vehicle drivers to change their main parking spots from curbside to garage parking. Our aim is to reduce the occupancy rate of curbside parking to 85% (or any other reasonable value that local government wants to achieve). At the same time, we take parking charge cut-offs into consideration to avoid a bias in price adjustments. These cut-offs represent the minimum or maximum acceptable values that a decision maker assigns to an attribute. Once the attribute value is outside the acceptable range, the driver may not choose this option (Swait, 2001; Danielis and Marcucci, 2007).

2. Related works Scholars have dedicated considerable effort to examining parking issues (Simićević et al., 2012). These scholars have used various methods, including mathematical programming (Feng and Zhu, 2008), discrete choice (Hess and Polak, 2004; Dell’Olio et al., 2009; Kobus et al., 2013), linear regression (Ottosson et al., 2013), average pricing (Cheng et al., 2012), game theory (Zong et al., 2013), and other models (Arnott and Rowse, 2009; Mei et al., 2010; Caicedo, 2012; Simićević et al., 2012). All these methods attempt to analyse parking-related issues. Their models can all be classified as choice, allocation and interaction models (Young et al., 1991). In particular, using discrete choice models (DCMs) to predict a driver's response to parking behaviour has gradually become more popular (Hess and Polak, 2004; Simićević et al., 2013). In addition, the use of DCMs in parkingrelated issues has been summarized in van der Waerden et al. (2002) and Hess and Polak (2004). Among DCMs, the multinomial logit (MNL) model (Spiess, 1996; Teknomo and Hokao, 1997; Hess, 2001; Washbrook et al., 2006; Simićević et al., 2013) and nested logit (NL) model (Bradley et al., 1993; Hunt and Teply, 1993; Hensher and King, 2001; Lu et al., 2015) have a major position in parking behaviour research. Lately, researchers have started to pay closer attention to more advanced models, such as the mixed multinomial logit (MMNL) model (Bhat and Castelar, 2002; Hess and Polak, 2004; Ibeas et al., 2014). These models reveal drivers' preferences in parking choices, with most parking choice models estimated using stated preference data (Ibeas et al., 2014). The common use of DCMs indicates that these models appear

17

to be helpful in exploring the relationship between parking charges (or other attributes) and parking behaviour, and not only because of the relative simplicity of their implementation (Albert and Mahalel, 2006; Marsden, 2006). Classic studies on the relationship between parking charges and mode choice include those conducted by Kuppam et al. (1998), Hensher and King (2001) and Washbrook et al. (2006). For example, Hensher and King (2001) applied the NL model to reveal the contribution and impact of curfew and parking rates on parking's market share. By constructing an MNL model, Washbrook et al. (2006) simulated the effect of road charges and parking charges on the probability of an individual choosing to drive alone to work. However, these scholars did not present a clear and workable curbside parking pricing adjustment scheme to governors or operators. In addition, typical researches which used the MMNL model include Hess and Polak (2004) and Ibeas et al. (2014). As far as we know, Hess and Polak’s (2004) study was the first paper to construct the MMNL model as a means to reveal drivers' taste variations for access time, search time, egress time, parking fees and expected fines. Nevertheless, these researchers ignored the impact of driver characteristics on parking choice behaviour, whereas Ibeas et al. (2014) further included driver characteristics to investigate parking behaviour in a coastal town in Spain. Ibeas's results show that variations in the age of vehicle, income and residence will significantly affect driver behaviour and willingness-to-pay (WTP). In addition, the coefficients of parking charges and the time spent looking for a space vary across the population. Both of these findings will enlighten parking governors and operators attempting to determine pricing guidelines for different districts and users. Based on the aggregation and comparison of related works, we found two deficiencies in existing literature. The first deficiency is these studies have little consideration for the diverse acceptance of different drivers in terms of parking charges. This lack of consideration caused the researchers to either overestimate or underestimate driver responsiveness to parking charge changes. The second deficiency is that the above-named studies lack the consideration of the effect of driver characteristics on their parking choice behaviour. This failure will result in biased estimators and less accurate simulation results. Therefore, it is essential to study the influence of a parking charge threshold and driver characteristics on parking choice behaviour, in order to determine a reasonable curbside parking pricing scheme with the goal of an 85% occupancy rate. In addition, our study will also help to fill in the relationship gap between the number of parking charge cut-off violations and drivers' socio-economic characteristics. The structure of this paper is as follows: Section 3 describes two different types of parking behaviour analysis models. Our survey methodology and elementary statistical analysis of data is presented in Section 4, where the relationship between the number of parking charge cut-off violations and individual characteristics is further analysed. Section 5 describes how to construct parking choice models which incorporate charge cut-offs, and in which different models are compared. Based on Section 5, a rational parking pricing scheme is proposed in Section 6. Section 7 provides the conclusions drawn from our research results, as well as avenues for further research.

3. Model specifications incorporating a cut-off 3.1. Conventional model The basic idea of DCMs is that a decision maker, i.e. a driver in this case, obtains a certain level of utility from each alternative, all

18

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

of which depends on many factors. The utility function associated with driver n choosing alternative i can be written as:

(

)

Uni = U pi ( d), d, αi, βn , εni = Vni + εni

(1)

where Vni is often called the representative utility, which is typically assumed to be linear in parameters; εni captures the factors that affect the utility but are not included in Vni , where the latter is postulated to follow the independently and identically distributed (IID) Extreme Value Type I distribution under the logit model framework; i = c , g represent curbside and garage parking, respectively; pi ( d) is the parking charge of the alternative i with parking duration d ; αi represents the other attributes that characterize the alternative i , except the charge, and βn denotes certain characteristics of the driver n. Furthermore, the driver's behaviour follows the following assumption of utility maximization:

(

Pni = P Uni > Unj, j ≠ i

)

(2)

where j = c , g . To better understand the driver's heterogeneity in this decision-making process, the MNL model and MMNL model are used to estimate parameters for comparison purposes. 3.1.1. MNL model By considering the simultaneous formulas of (Eqs. (1) and 2) and by taking into account the assumption on εni , the probability formula of the MNL model is:

Pni =

eVni 2 ∑ j = 1 eVnj

=

exp⎡⎣ θ′X ni⎤⎦ 2 ∑ j = 1 exp⎡⎣ θ′X nj⎤⎦

(3)

where θ is the parameter matrix to be estimated and X ni is the variable matrix. For simplicity, we generally assume that the observed utility is a linear combination of attributes. Since the probability has a closed form expression, the problem can be readily solved using maximum likelihood estimation (MLE). 3.1.2. MMNL model Unlike the MNL model, which assumes that decision makers' tastes are homogenous, the coefficients of some variables in the MMNL model can be defined as random and capable of accommodating heterogeneity in driver tastes. Therefore, the potential correlation structure of repeated observations of the same driver is as follows:

θnl = θl + σlvnl

(4)

where θl is the population average taste for attribute l and vnl represents individual specifics with zero mean and a standard deviation equal to one. Since there is no closed form expression for the probability of the MMNL model, the estimation of variables relies on a simulated approximation:

1 Pni = R

R

∑

exp⎡⎣ θ r ′X ni⎤⎦ 2 ∑ j = 1 exp⎡⎣ θ r ′X nj⎤⎦

given to attribute cut-offs. It is reasonable to think that an alternative with prices that have increased above a certain level will be considered unacceptable. This consideration then leads to the rejection of the alternative, regardless of how high the potential compensation from other attributes (Danielis and Marcucci, 2007). Given the potential bias that can be caused by ignoring cut-offs, such an omission may lead to overestimating the significance of the role that attributes play in particular situations, such as parking price adjustments. Several studies have sought to account for cut-offs (mainly exogenous) in the decision-making process. These studies use discrete choice frameworks, which can be divided into three categories, namely (1) dummy variable methods (Marcucci and Scaccia, 2004); (2) the MNL model, which uses piecewise linear utility functions (hereafter referred to as the MNLC model, since it incorporates cut-offs) (Swait, 2001), and (3) the CMNL (Constrained MNL) model (Martínez et al., 2009). In addition, the different types of thresholds were divided into three categories by Cantillo and Ortúzar (2006), namely (i) thresholds such as inertia, habit or reluctance to change; (ii) thresholds defined as minimum perceptible changes, and (iii) thresholds such as mechanisms of the acceptance or rejection of alternatives. In fact, Cantillo and Ortúzar (2006) have proven that the third threshold appears to be more important for improving model accuracy. However, additional evidence is needed to support this view. Since there is no clear evidence suggesting that exogenous cut-offs are superior to endogenous ones or vice versa, we herein only consider the exogenous cut-offs stated by respondents themselves for convenience (exogenous models are also estimated, but cut-off parameters in exogenous models are not statistically significant). We criticize the dummy variable method, which implies that the utility decrement which exceeds an attribute cut-off by one unit is the same as those which exceed cut-offs by two or any other amount of units. As this method cannot deal with the issue of different magnitudes of exceeding attribute cut-offs, it is abandoned here. At the same time, the latter two types of thresholds both have particular strengths and weakness. The second one features easy application and non-differentiability, and the third threshold features differentiability and the need for programming. While few applications up to this point have investigated the cut-off issue in the parking choice problem, it is meaningful to use these two models to study parking charge cut-off levels. 3.2.1. MNLC model The MNLC model incorporates cut-offs into the decision-making process by using a piecewise linear function and without fundamentally changing the nature of the DCMs. For this reason, the model has no impact on parameter estimation and software applications, compared to the conventional MNL model. The model is defined as: K

Uni =

K

K

∑ βkx nik + ∑ vk⋅κnik + ∑ wk⋅λ nik + εi k=1

k=1

k=1

(5)

U ⎤ κnik = max⎡⎣ 0, x nik − x nik ⎦, ∀ i ∈ C

where θr is the r th draw of θ ; R is the number of samples and Pni is the probability of driver n choosing mode i . Although we also applied a latent class model (LCM) to reveal driver heterogeneity from another perspective, the fact that there was no further improvement in this model's accuracy meant there was no need to detail this model.

L λ nik = max⎡⎣ 0, x nik − x nik ⎤⎦, ∀ i ∈ C

r=1

3.2. Logit model incorporating attribute cut-offs The aim of this paper is to investigate pricing thresholds. We achieve this through the use of the models mentioned below, using non-linear utility functions. Therefore, particular attention is

(6)

where i is an alternative; n is the decision maker; k is the k th attribute of the alternative (the number of attributes is K ); βk , vk and wk are parameters to be estimated; x nik is the k th attribute of L U and x nik are the alternative i faced by the decision maker n; x nik lower and upper cut-offs for x nik , respectively, and the penalty for exceeding cut-offs in the objective function is reflected via quantities vk( ≤0) and wk( ≤0). 3.2.2. CMNL model The CMNL model proposed by Martínez et al. (2009) can

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

handle both endogenous and exogenous cut-offs, having the following utility function:

∑ βkx nik k=1

1 + lnϕni + εni μ

⎛ ⎞ L U ⎟ lnϕni = ln⎜⎜ ∏ ϕnik ϕnik ⎟= ⎝ k=1 ⎠ K

L = ϕnik

K L U + lnϕnik ∑ ( lnϕnik )

k=1

1

( (

L + ρk 1 + exp wk a nk − Z nik

))

⎧ 1 if ( a nk − Z nik ) → − ∞ ⎪ ⎨ =⎪ if a nk = Z nik η ⎩ k U = ϕnik

1

( (

U − bnk + ρk 1 + exp wk Z nik

))

⎧ 1 if ( bnk − Z nik ) → ∞ ⎪ ⎨ =⎪ if bnk = Z nik η ⎩ k

(7)

L U where ϕnik and ϕnik represent the lower and upper cut-offs for the k th attribute of alternative i for the decision maker n, respectively;

ρk =

4. Survey and statistical analysis 4.1. Influence factors selection

K

Uni =

19

( )

1 ⋅ln wk

1 − ηk ηk

, in which ηk is the cut-off tolerance; β and w( ≥0)

are the parameters to be estimated; a and b are attribute values; Z is the cut-off, and definitions of the other variables are the same as in Section 3.2.1. The utility function used below is a simplified version, where ρk is omitted. 3.2.3. Difference between models To help understand the differences between the MNLC model and CMNL model, some comparisons need to be made before using these models for studying parking choice behaviour. The main difference, which is clearly shown in the two charts (Fig. 1), is in the area around the origin. For the MNLC model, there is a “kink”. Therefore, the MNLC model is more suitable in situations where the cut-off is a point, while the CMNL model is more suitable in situations where the cut-off is an interval, because of the utility's gradual change around the cut-off point. As far as we know, there is no existing research on the comparison of these two models in currently published literature. To some extent, therefore, our study can shed light on this problem.

For our survey, knowing which factor has a direct influence on parking choice was crucial, in order to conduct an in-depth analysis of parking choice behaviour. Hence, we aggregated 23 studies involving parking choice behaviour and related factors (Bradley et al., 1993; Hunt and Teply, 1993; Spiess, 1996; Teknomo and Hokao, 1997; Hensher and King, 2001; Hess, 2001; Bhat and Castelar, 2002; van der Waerden et al., 2002; Hess and Polak, 2004). Table 1 below shows that most studies considered the first two factors in their parking choice behaviour models. These two factors are (1) the egress time/walking time/walking distance and (2) the parking fee/parking charge. Approximately two-fifths of the existing studies considered capacity constraint factors, such as the occupancy rate/chance of finding free space/number of spaces. We can reasonably expect that, due to the substantial differences in study areas and research methods, scholars have not yet reached a consensus regarding the effects of the remaining factors on parking choice behaviour. Therefore, the influence factors used in DCMs are determined based on literature review, trial survey and our knowledge. Firstly, based on this historical perspective,

Table 1 Frequency of influence factors. Influence factor

Frequency (total number of occurrences)

Ratio (%)

Egress time/walking time/walking distance Parking fee/parking charge Occupancy rate/chance of finding free space/number of spaces Distance from home/travel time Type of parking Distance area entrance to parking Search time Parking time restrictions/maximum parking duration Expected fine for illegal parking Security

22/23

95.65

19/23 9/23

82.61 39.13

7/23 6/23 5/23 5/23 4/23

30.43 26.09 21.74 21.74 17.39

3/23 2/23

13.04 8.70

Note: Each factor may have other expressions as well. Here, we only list some of them for simplicity.

Fig. 1. Comparison of MNLC and CMNL models. Note: theta is the slope of the utility function in the MNLC model; beta is −1/η in the CMNL model, rho is w in the CMNL model. (a) MNLC model (b) CMNL model.

20

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

the two factors with the highest frequency, namely walking time (the time spent walking from the parking place to the destination) and parking charge (the fee paid by the driver for occupying a parking space over a period of time) were selected as the main model variables. Secondly, considering the scarcity of parking spaces in the central business district (CBD) of Shanghai, drivers are very concerned about whether or not they can park in their preferred parking lots and with a high degree of probability of finding an empty parking space (We look at the number of times drivers can find an empty parking space in ten attempts. In line with the increase in vehicle numbers, parking demand grows rapidly, leading to a lower probability of finding an empty parking space). Drivers also want short search times (the length of time a driver spends searches for a parking space) and finally, short parking operation time (the time it takes from starting to park to finishing parking). While some drivers seldom park in the parking spaces covered under our survey, making it hard to accurately describe this attribute, this situation reflects the reality of parking choice behaviour. That is, when drivers have no information regarding one attribute, they will make their parking decision based on their past experience and judgement. Moreover, the value of probability of finding an empty parking space was obtained by enquiring about the respondents choices in revealed preference (RP) scenarios. For example, a driver may answer that he believes that the probability of finding an empty parking space in a unfamiliar curbside park is 70%. In addition, the attribute's value in stated preference (SP) scenarios was set according to the actual value of the parking spaces covered under this study. If this attribute does not have any influence on driver behaviour, it is not significant and will naturally be excluded from our model. The probability of finding an empty parking space has a more dynamic impact during different hours of the day, which is very essential information in terms of establishing real time parking prices in Shanghai in the future. While the parking pricing with which we are concerned at this stage is the stable parking price throughout the day, using data collected without considering different times of the day can still meet modelling requirements. Thirdly, driver characteristics, ignored by most researchers to date, will also affect driver parking behaviour. Therefore, driver characteristics such as parking experience (always or seldom park curbside or in garage parks), sex, age, personal income and reimbursement (whether or not the employer reimburses the driver's parking fees) are further included in our models. 4.2. Questionnaire design The two alternatives of interest in our study are curbside and garage parking. Other alternatives, such as public transportation or cancelling travel are excluded, for several reasons. For example, the results obtained from a study of Greater Vancouver (Washbrook et al., 2006) show that a $1 (in July 2013, 1 US dollar was equal to 6.13RMB) increase in the parking price resulted in approximately a 4.53% reduction in the probability of individuals choosing to drive and park. A similar result was reported in Washington D. C. (Kuppam et al., 1998), where it was found that the demand for parking decreases by an average of 4.44% when the parking tax increases by $1. By converting dollars to RMBs, we can conclude that a 1RMB increase in parking charges will result in approximately a 0.72% reduction in drive and park demand. In addition, the main result of Hensher and King (2001) shows that a $1 increase in the hourly parking rates of CBDs results in approximately a 1.46% increase in the ratio of public transportation use. As expected, the results of our trial survey and formal investigation both support the view that drivers will never give up driving due to parking prices being a little higher than the status quo. All of the above facts reveal that small-scale parking price

increases do not significantly affect the probability of foregoing driving to a CBD or transferring to other travel modes. Moreover, alternatives such as public transportation and cancelling travel are excluded from our study for data collection simplicity purposes, because Hensher et al. (2005) suggested that a minimum sample size of 50 respondents for each alternative is the best sampling strategy. Our questionnaire is made up of three parts, namely (1) parking information and a charge cut-off enquiry, (2) stated preference (SP) choice and (3) detailed personal information. In particular, to reveal driver choice behavioural preferences and to avoid parameter estimation problems, our design of hypothetical scenarios used the method proposed by Dell’Olio et al. (2009). This method allows a variable value to have small fluctuations around its mean, such that the same SP scenario has a slight difference for each respondent. For example, if the search time of driver A and B are both 3 + 1.5( 2ε1−1) minutes, where the randomly generated ε1 may be different for A and B, say, 0.2 and 0.3, respectively, then the search time is 2.1 min for A and 2.4 min for B. During the previous trial survey, we found that it is hard for drivers to make decisions when the values of five variables are all different. We also found that drivers do not answer questionnaires seriously when they are presented too many SP scenarios. Therefore, the parking charge and parking operation time are determined as resident (not fixed) variables, with several attributes levels in the orthogonal experimental design rather than the other option of a non-orthogonal design. In the meantime, in order to solve the problem of too many hypothetical scenarios, one of the remaining variables (which include search time, walking time and probability of finding an empty parking space) was selected and inserted into the experimental design each time. With the exception of the parking charge having five levels, the other variables only have three levels, so we have C31 × 25 = 75 hypothetical scenarios (25 is the number of hypothetical scenarios of the orthogonal experimental design with charge, operation time and one of the remaining three attributes). Only five of these scenarios were randomly selected and presented in each questionnaire, in order to reduce respondent stress and to avoid potential data error caused by fatigue. 4.3. Data collection The study data was obtained through a face-to-face survey held in appointed car parks, after drivers had finished their parking operations. Selected locations included 10 curbside locations and six garage car parks. All of the selected parking areas are located around People's Square, and the survey was taken from 8 a.m. to 6 p.m., on July 26 and 27, 2013. Firstly, we asked questions relating to personal information and parking situations. Our questions included such items as personal income (RMB/month), sex (1 ¼female, 0 ¼ male), age (years), driving experience (years), reimbursement of parking expenses by the respondent's employer (1 ¼yes, 0 ¼ no), parking experience (1 ¼always park curbside or in garage car parks, 0 ¼seldom park curbside or in garage car parks), search time (minutes), parking operation time (minutes), walking time (minutes), parking charge (RMB) and parking duration (hours). The drivers were

Table 2 Self-selection bias check in RP/SP scenarios. The number of drivers choosing curbside parking

0

1

2

3

4

5

6

Percentage (%)

12.26 22.64 35.85 23.58 4.72 0.94 0.00

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

then asked what the highest acceptable parking charge was. Finally, the choice data related to hypothetical scenarios was collected. To verify whether or not drivers carefully considered their choices in different scenarios, checking self-selection bias is necessary. The results from Table 2 show that, at most, 12.26% of drivers never change their parking choices, but we cannot hastily say that these drivers did not answer our questions seriously. This phenomenon at least indicates that there is no serious selfselection bias. Therefore, to retain the authenticity of data, we do not artificially exclude these observations. In addition, our survey shows that garage car parks are not fully utilized. Their occupancy rates also vary significantly at different times, especially in Xinshijie, Shijibada and Hongxiang. This finding indicates that curbside parking is preferred by drivers when curbs and garage car parks both have empty parking spaces. While the number of curbside parking spaces is much less than garage car parks, and curbside parking spaces' average occupancy rates are extremely high (being up to 93.2%), garage parking spaces are also able to accommodate curb drivers in the surveyed areas. 4.4. Statistical analysis of data In all, 180 questionnaires were collected. Of these, 106 questionnaires were valid, providing 106 sets of RP data and 530 sets of SP data. Compared to garage parking, the average curbside parking duration and walking time are shorter. Although curbside parking spaces are scarce in the Shanghai city centre, finding another nearby curbside parking space is not always so difficult for drivers when their first preferred parking space is full. Therefore, the average search time for a curbside parking space is relatively low when compared to garage car parks. This fact is due to the shorter distances between curbside parking spaces. Within the survey sample, driver attitudes to parking charge thresholds are very homogenous, with only small standard deviations. As expected, and because curbside parking has advantages over garage parking (except for parking charges and the availability of vacant parking spaces), drivers stated they could afford a curbside parking charge of 16.10 RMB per hour (Table 3). That charge is significantly higher than the cost of garage parking in the same area, which is only 13.47 RMB per hour. In addition, driver characteristics such as previous parking experience, age, driving years and personal income vary substantially over the sample, whereas the percentage of female and reimbursed drivers is low, the effect of which will be discussed later. Moreover, we noticed that a number of drivers will still choose the alternative which exceeds their acceptance level in terms of parking charges, even when the parking charge of an alternative location is less than the threshold. This finding indicates that a “hard threshold” is not suitable in this case. Therefore, we only construct soft threshold models.

4.5. The relationship between individual characteristics and cut-off violations To investigate the intrinsic links between individual characteristics and the number of parking charge cut-off violations, a multiple linear regression model was estimated. This was done to determine whether or not a particular group is more sensitive to the charge cut-off points in their decision-making process, where the dependent variable is the number of parking charge cut-off violations in the SP scenarios. A backward selection regression method was used to exclude non-significant variables. Moreover, a correlation test was used to determine whether or not these variables needed to be excluded. Our results are presented in Table 4, as follows: The fact that the coefficient of age is positive shows that the more elderly drivers are more insensitive to charge cut-off points than young people. This is because older people have fewer money concerns than young people. In addition, for health reasons, the older drivers do not like walking long distances. As such, the elderly drivers would rather pay more to park in a curbside parking space which is closer to their destination. In terms of driving years, inexperienced drivers are more likely to ignore cut-off points, as these drivers are less well-informed with regard to driving and parking charge changes. In addition, drivers who have preferences regarding parking space types tend to regard enormous changes to parking charges as unacceptable. These drivers feel this way because they hate any change which can affect their stable parking preferences. Moreover, other variables such as the driver's sex, reimbursement and personal income have no impact on the number of parking charge cut-off violations. These results may help us to better understand which group or groups of drivers are more willing to break those thresholds defined by the drivers themselves. Special care must be taken regarding the constant, the significance of which means that there are more individual characteristics or other socio-demographic statistics that could be helpful in terms of the in-depth understanding of cut-off violations. In this study, only a first glimpse is provided.

5. Model construction and estimation 5.1. RP/SP data fusion Given the possible scale differences in the RP and SP datasets, it is inappropriate to mix them directly. Therefore, calculating the inclusive values of the nested logit model with degenerated branches is necessary for determining whether more complex models are required (Hensher et al., 2005). The RP/SP joint model is commonly rejected, because respondents are not able to provide any information regarding the attributes of the unchosen alternatives (Azari et al., 2013). Another reason for this rejection is that Table 4 Results of the Multiple Linear Regression Model.

Table 3 Statistical results of personal characteristics. Characteristics

Parking type

Mean

Sex (1 ¼female) Reimbursement (1 ¼yes) Parking experience (1¼ always)

Both Both Curbside parks Garage parks Both Both Both Curbside parks Garage parks

0.2254 0.2547 0.2358 0.4717 36.97 9.72 9717 16.10 13.47

Age (year) Driving years (year) Personal income (RMB/month) Parking charge cut-off (RMB/h)

21

Median

35 8 8500 15 10

Variable

Coefficient

Sex Personal income Reimbursement Age Driving years Parking experience 1 Parking experience 2 Constant R2 Adjusted R2

Excluded Excluded Excluded 0.059  0.072  0.619  0.668 2.148 0.154 0.121

Std. Dev.

t-test

0.021 0.025 0.357 0.282 0.678

2.828***  2.923***  1.736*  2.371** 3.168***

Std. Dev.

9.15 7.50 6145 3.65 2.54

22

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

information of this sort is unreliable (Hensher and King, 2001). While the number of alternatives in our research is limited to two, it was possible for respondents to provide relatively reliable information regarding the unchosen alternative. As we can see, the inclusive values of the four choice branches (including the curbside parking RP, curbside parking SP, garage parking RP and garage parking SP) are calculated. In addition, the t-tests of inclusive values are all not significant, indicating there is no big difference between the RP and SP datasets, which in turn implies that the use of the MNL model is appropriate for the mixture of the RP and SP data.

to understand the meanings of the parameter estimators. Recalling the two alternatives in this study, the utility functions of the MNL model, namely Eq. (8), the MMNL model, namely Eq. (8) (the utility function of the MMNL model is the same as that of the MNL), MMNLC model (MMNLC is the abbreviation for the MMNL model with a cut-off point), namely Eq. (9) and the CMMNL model (the combination of the CMNL and MMNL models) in Eq. (10) are as follows:

Uni = θptPTni + θstSTni + θotOTni + θwtWTni + θpfesPFESni + θcCni + θpePEni + θsexSEX ni + θageAGEni + θdyDYni + θincINCni + θafrAFR ni + θawAWni + ASCi + εni

5.2. Utility function construction Considering that people of different ages have different sensitivity to walking distances, we constructed the utility function taking this fact into account. Non-linearity in attribute variation (such as logarithmic, power series transformation or a combination of several specifications) could help to obtain more accurate WTP and policy implications. A similar study has been done in the area of urban freight transport policies (Gatta and Marcucci, 2016). The results of that study preliminarily indicate that when an attribute value only changes slightly and the model has high accuracy, the WTP bias is small (approximately less than 10%). Logarithmic and power series transformations, as well as a combination of the two, were also tested to find a better specification. However, the likelihood ratio index shows that these specifications are not significantly better or even worse than our piecewise linear specification. Besides, the variation range of attributes especially parking charges in our questionnaire was very limited, and the model assuming piecewise specification provided a relatively high model fit (see Table 5). Therefore, we believe the bias caused by our piecewise specification is within an acceptable range, even though it is not the optimum specification. In addition, another advantage of our specification is that it is more intuitive and easier

(8)

Uni = θptPTni + θstSTni + θotOTni + θwtWTni + θpfesPFESni + θcCni + θccCCni + θpePEni + θsexSEX ni + θageAGEni + θdyDYni + θincINCni + θafrAFR ni + θawAWni + ASCi + εni

(9)

Uni = θptPTni + θstSTni + θotOTni + θwtWTni + θpfesPFESni + θcCni − θcc ln( 1 + γCCni ) + θpePEni + θsexSEX ni + θageAGEni + θdyDYni + θincINCni + θafrAFR ni + θawAWni + ASCi + εni

(10)

where AW = AGE × WT is the interaction term, and the corresponding variable names for each code in (Equations (8)–10) are given in Table 5. 5.3. Parameter estimation results According to the utility functions constructed above, the MNL model with full variables was estimated. The signs of all estimators were as expected, with some variables having no significant

Table 5 Parameters estimation results of models without threshold. Variable Parking attributes Search time Walking time Probability of finding an empty parking space Charge

Code MNL

MMNL1 (T)

MMNL2 (N)

MMNL3 (U)

MMNL4 (L)

ST WT PFES

 0.06701**( 2.15)  0.09848*(  1.83) 1.45790**(2.30)

 0.07780**(  2.20)  0.10939*(  1.81) 1.52728**(2.21)

 0.08881*(  1.72)  0.10324( 1.28) 1.45775(1.38)

 0.09027**(  2.18)  0.10601(  1.56) 2.00407**(2.49)

 0.06704*(  1.69)  0.09850(  1.58) 1.45790*(1.95)

C

 0.09308***(  6.12)

 0.16862***(  5.80)

 0.33366*** (  32.35)

 0.26071*** (  10.24)

 2.37676***(  2384)

0.49013**(2.06) 0.03342***(2.63)

0.42746(1.13) 0.05755***(2.81)

0.59548**(2.10) 0.04007***(2.64)

0.42466(1.56) 0.03277**(2.19)

 0.00232**(  1.94)

 0.00217(  1.12)

 0.00263*(  1.84)

 0.00227*  1.60)

 0.16862***(  5.80)

 0.33366*** (  32.35)

 0.26071*** (  10.24)

2.37676***(  2384)

 0.58743(  1.43)

 0.10706(  0.23)

 0.58887(  0.86)

0.13082(0.25)

 0.58743(  1.20)

LL( 0)

636 8  440.8416

636 8  440.8416

636 8  440.8416

636 8  440.8416

636 8  440.8416

LL( c )

 395.9908

 395.9908

 395.9908

 395.9908

 395.9908

LL( β )

 349.7483

 340.0863

 340.3709

 334.4376

 358.0471

ρ¯2( 0)

0.1885

0.2104

0.2098

0.2232

0.1697

ρ¯2( c )

0.0966

0.1210

0.1203

0.1352

0.0756

Driver characteristics Parking experience PE 0.42465**(2.00) Age AGE 0.03246***(2.84) Interaction term Age  walking time AW  0.00244**(  2.28) Standard deviation (spread) of random parameter Charge C Constant term Constant term Model statistics Sample size Variable number

ASC

Note: T, N, U and L represent triangular, normal, uniform and lognormal distribution, respectively; the first term in  0.06701**(  2.15) is the parameter estimator, and the value in parentheses is the t-test value; ***,**,* represent that the parameter estimator is significant at 99%, 95% and 90% confidence levels, respectively; all models are estimated with Nlogit 5.0 (Econometric Software Inc, 2012); 200 Halton draws per individual were used during the maximum simulated likelihood estimation (Train, 2009).

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

influence on the drivers' parking choices. These non-influential variables included the parking operation time, sex, personal income and reimbursement, all of which were omitted for reasons of simplicity. With regard to parking operation time, the results can be explained, as there are no obvious differences parking operation time for drivers in most parking spaces. The estimator of personal income is only significant at a 0.129 significance level, which may be for the following two reasons: (1) respondents are reluctant to disclose their personal income, and (2) respondents in China have diversified income resources. As for the sex of the driver, we have reasons to believe that women are more concerned about parking charges for housekeeping considerations (0.208 significance level), but we can speculate that this result may be caused by the insufficient female sample size (see Table 3). In addition, the small sample size may also apply to the low significance level of reimbursement (0.153). These results have implications for the improvement of garage parking service quality, particularly with the objective of attracting more drivers to park in garage car parks, and especially for long parking durations. Our results show the real factors influencing driver choices. After excluding these non-significant variables, several random distributions (such as triangular, normal, uniform and lognormal distributions) are compared in the process of constructing the MMNL model (see Table 5). It is hugely important to point out the potential effects of incorrect distributional assumptions on policy implications when using the MMNL model (Hess and Polak, 2004). Because the standard error (or spread, for triangular distribution) of a distribution larger than its mean may result in behaviourally meaningless estimators (Hensher et al., 2005), a constraint, the standard error (or spread) equal to its mean, is imposed on the distribution. The accuracy of our model shows that uniform distribution is the best choice for our data. Therefore, the following analysis was performed for the MMNL model with constrained uniform distribution. LCM was also constructed to check which model is more suitable to describe driver heterogeneity for parking charges. We used this approach because the results depended on the type of heterogeneity being investigated (Marcucci and Gatta, 2012). After excluding all non-significant variables, the MLE of the best LCM assuming two classes is only 334.60961 with 11 degrees of freedom. This finding indicates that the likelihood ratio 2 of 7.6559 is less than the critical value χ0.05 ( 3) = 7.81. For this reason, we believe that the MMNL model is more appropriate in this case to describe driver heterogeneity. Based on the above comparisons, the random distribution of the MMNL models with cut-off (namely the MMNLC and CMMNL model associated with parking charges and its cut-off) was selected as a constrained uniform distribution. This means that the spread is constrained to be half of the mean here. The parameter estimation results of the models with cut-off and without cut-off are summarized in Tables 5 and 6, respectively. Based on these findings, we can consider the advantages offered by the models incorporating cut-offs. We obtain improvements in model fit when moving from the MNL to MMNL to CMMNL to MMNLC model, with high levels of taste heterogeneity for parking charge coefficients. One important thing to note is that the parameter estimators of the CMMNL model associated with charge cut-off points are not statistically significant. In addition, the MMNLC model, at a 95% confidence level, is better than the CMMNL model. As a result, the MMNLC model is chosen to determine the curbside parking pricing scheme. The comparison of penalty magnitudes with corresponding attribute weights shows that the former outweighs the latter in magnitude. For instance, the mean coefficient for parking charges is  0.17918 below the upper cut-off, whereas the penalty parameter is  0.43998. This shows the extent of drivers' aversion to parking charges that they deem, at least to some extent,

23

Table 6 Parameters estimation results of models with threshold. Variable

Code MMNLC (U)

Parking attributes Search time

ST

Walking time

WT

 0.08162** (  2.14)  0.10846* (  1.71) 1.57721**(2.14)

 0.08690** (  2.06)  0.10181* (  1.97) 1.61768*(1.86)

 0.17918*** (  3.77)  0.43998*** (  5.04)

 0.13002*** (  2.82) 1.88695(0.21)

PE AGE

0.50078*(1.93) 0.03652***(2.65)

0.62797**(2.11) 0.04449**(2.54)

AW

 0.00247* (  1.90)

 0.00297** (  1.95)

0.17918***(3.77) 0.43998***(5.04)

0.31361**(2.27) 6.83203(0.26)

 0.04607 (  0.09)

 0.02716(  0.05)

Probability of finding an empty PFES parking space Charge C Charge cut-off Driver characteristics Parking experience Age Interaction term Age  walking time

CC

Standard deviation (spread) of random parameter Charge C Charge cut-off CC Constant term Constant term ASC Penalty coefficient Penalty Model statistics Sample size Variable number

CMMNL (U)

0.00991(0.24)

γ

LL( 0)

636 9  440.8416

636 12  440.8416

LL( c )

 395.9908

 395.9908

LL( β )

 327.4246

 328.2764

ρ¯2( 0)

0.2369

0.2281

ρ¯2( c )

0.1504

0.1407

excessive. Additionally, the positive estimator of parking experiences manifests that drivers are more likely to park in their familiar parking spaces. Older people are also more willing and likely to choose curbside parking spaces which offer less walking time, particularly those older drivers who have difficulty in walking. Another interesting finding derived from the estimator ratio of age and the interaction term (age  walking time) is that drivers have a greater preference for curbside parking, as long as the walking time is less than 0.03652/0.00247 ¼15 min, ceteris paribus. This fact leads us to recommend to parking governors or operators that they should raise more in terms of parking charges by providing curbside parking spaces with shorter walking times for areas which have a greater number of aged drivers. Alternately, the governors or operators could just provide curbside parking spaces with longer walking time, in order to evacuate more aged drivers from those areas.

6. Model comparison and pricing policy implications 6.1. Comparison of model accuracy and WTP According to the Prediction Success Indices (PSI) (McFadden, 1979) summarized in Table 7, we find that the MMNL model is superior to the MNL model. We further find that the MMNLC model is the best one. A test of non-nested choice models was then applied based on the AIC (see Table 7) (Ben-Akiva and Swait, 1986). Suppose that there are Model 1 and Model 2, where the former has K1 variables and the latter has K2 variables to explain the same choice situation. Without loss of generality, suppose that

24

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

ceteris paribus. Fig. 2 shows that: (1) When parking charges are below the threshold, the utility curves of MNL and MMNLC model substantially coincide. However, the MMNL model tends to exaggerate the impact of charge on utility. (2) When parking charges exceed the threshold, the situation is reversed. That is to say, the utility curve of the MMNL model is much closer to that of the MMNLC model than the MNL model. However, the utility difference between the MMNL and MMNLC models is very large. (3) The higher a driver's parking charge threshold is, the less the utility difference between models without thresholds and the MMNLC model will be, indicating that a lesser degree of prediction error will exist. Fig. 2 intuitively shows the differences between the MNL, MMNL and MMNLC models. One point that needs to be considered is that all of the models have similar utility changing trends before reaching the parking charge cut-off point. That is, the abilities of the three models to explain and forecast driver choice behaviour are almost identical. The situation is quite different after that point. Specifically, the MNL model (the model without the cut-off point) underestimates the utility change after reaching the cut-off point. Hence, the model will overestimate the price increment needed to reach the target 85% occupancy rate. After comparing the utility differences between the MNL, MMNL and MMNLC models, we then showed the influences of driver heterogeneity and charge cut-off points on curbside parking occupancy rates caused by curbside parking price adjustments. The ratio of the curbside parking choice probability before and after the adjustment can be expressed as:

Table 7 Model accuracy comparison. Model 1

PSI

MNL MMNL(U) MMNLC(U)

0.0632 0.0825 0.0930

Model 2 MMNL (U)

MMNLC (U)

 5.5312/0.000 N. A. N. A.

 6.4555/0.0000  3.3285/0.0004 N. A.

Note: The former term of  5.5312/0.000 (namely  5.5312) is • in Φ( •) of Eq. (11); the latter term 0.000 is the corresponding Φ( •) , namely, Φ( •), the probability that Model 1 is better.

K1 ≥ K2. The probability that the pseudo ρ2 for Model 1 will be greater than that for Model 2 is asymptotically bound by the following function:

(

)

(

P ρ22 − ρ12 ≥ Z ≤ Φ − −2Z⋅LL( 0) + ( K1 − K2)

)

(11)

2

where Z is the difference in the pseudo ρ between Model 1 and Model 2, which is assumed to be larger than 0; LL( 0) equals to −N ln J in our case, where N and J are the number of observations and alternatives, respectively; Φ is the Standard Normal Cumulative Distribution Function, and the resulting probability is that Model 1 is superior to Model 2. As discussed above, we can conclude that both the MMNL (U) and MMNLC(U) models are superior to the MNL model. Furthermore, WTP and 2.5th/97.5th percentile for all variables were given in Table 8 by the model with the highest degree of accuracy, namely the MMNLC(U) model. Without any doubt, drivers' WTP for walking time is the highest, and this WTP increases when drivers get older (as the aged tend to walk less), followed by search time. As for probability of finding an empty space, when the parking charge is below a driver's threshold, they will be happy to pay an additional 10.8 RMB to increase by 10% their chances of finding an empty space. In other words, they will pay for the one time that drivers can find an empty parking space in ten times. Moreover, drivers' WTP for these attributes will increase by from 41% to 44% after parking charges exceed drivers’ thresholds. This finding indicates that drivers who tend to violate their own stated threshold may have higher WTPs. In particular, we find it interesting that the MMNL(U) with the higher degree of accuracy shows a lower bias. In greater detail, the WTPs of these attributes obtained from the MNL model are upwardly biased for at least 58% (charge o threshold) and 12% (charge Z threshold), while the MMNL(U) model produces significant WTP overestimations (at least 13% and 38% for charge o threshold and charge Z threshold, respectively). 6.2. Parking pricing simulation Based on the parameter estimators from Tables 5 and 6, the utility curves of the MNL, MMNL and MMNLC models were plotted to show how parking charge cut-off points affect these curves,

^ Pc = ^ Pca

1 R

∑n = 1 ∑r = 1

1 R

N R 1 ∑n = 1 ∑r = 1 ⎡ exp⎣ ∑ θ ′o X gn − X cn + θ ′pr Fgn − Fcna ⎤⎦

N

R

1 exp⎡⎣ ∑ θ ′o X gn − X cn + θ ′pr Fgn − Fcn ⎤⎦

(

)

(

)

(

(

)

)

=

^ Pc

( 1 − φ)P^c

(12)

^ ^ where Pc is the current probability of curbside parking; Pca means the probability of curbside parking after the rate adjustment; R is the number of samplings of the random parameter; n indicates the driver; θn is the estimator matrix of all parameters except the charge; θpr represents the r th sampling of the charge parameter estimator; X gn and X cn are the variable matrices of curbside and garage parking, respectively, except the charge; Fgn stands for the garage parking charge; Fcn indicates the curbside parking charge before the rate adjustment; Fcna denotes the curbside parking charge after the rate adjustment, Fcna = ( CHARGEcna CHARGECcna )′; CHARGE is the charge variable; CHARGEC is the charge cut-off variable, and φ is the probability that curbside parking needs to be transferred. The curbside parking price rate (in RMB/h) was gradually increased to simulate the variety of average occupancy rates and the occupancy rates during the peak daytime hours. The occupancy rates calculated by the MNL and MMNL model virtually coincide, with a slightly larger slope for the latter and closer to the MMNLC model. This finding confirms the conclusion that the accuracy of the MMNL model is higher than that of the MNL model. Compared with models without a threshold, the MMNLC model takes full

Table 8 WTP estimation results from the MMNLC(U) model. Variable

WT AW ST PFES

Unit

RMB/min RMB/(min  year) RMB/min RMB/%

Charge o threshold

Charge Z threshold

Mean increment

Mean

Median

2.5th

97.5th

Mean

Median

2.5th

97.5th

7.40 0.17 5.57 1.08

4.04 0.09 3.04 0.98

2.17 0.05 1.64 0.53

29.88 0.68 22.49 7.24

10.62 0.24 7.99 1.54

5.90 0.13 4.44 1.43

3.64 0.08 2.74 0.88

39.83 0.91 29.98 9.65

þ3.22 þ0.07 þ2.42 þ0.46

( þ 44%) ( þ 41%) ( þ 43%) ( þ 43%)

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

25

Fig. 2. Utility differences between models with and without the threshold. (a) Curb parking charge threshold (a) Garage parking charge threshold.

Fig. 3. Occupancy rate simulation under different curb parking rate Increments.(a) Average occupancy rate (a) Occupancy rate at peak hours.

driver acceptance of parking charge into account, thus showing the drivers' higher sensitivity (larger slope) to parking price adjustments. In addition, we can initially conclude that using models without thresholds to put forward parking pricing schemes will lead to a larger biased parking pricing theme from Fig. 3(a) to (b). Also, taking driver heterogeneity for parking charges into account plays a very limited role in improving the accuracy of parking pricing schemes. 6.3. Implications for curb parking pricing The average occupancy rate of curbside parking spaces is 93.20% in the surveyed area. This means that raising curbside parking charges will be necessary to reduce that occupancy rate to 85%. In the RP situation, 52.9% of all respondents chose curbside parking. Based on the parameter estimation results and choice probability obtained from the curbside parking RP data, 4.34% ( 52.9% × ( 93.2% − 85%) = 4.34% ) of curbside drivers need to be transferred to garage parking spaces. According to Eq. (12), the decrease in the curbside parking probability induced by the increased curbside parking charge is calculated in Table 9: No matter what kind of scenario we study, the fact is that the rate increment obtained from the model without charge cut-off points is almost 1.3 times that of the value obtained from models with cut-off points. This finding indicates that ignoring cut-off points will cause an upward bias. What is more, compared with the MNL model, the increment calculated by the MMNL model is slightly closer to the results of the MMNLC model. That is to say, the parking charge increments obtained from the MNL or MMNL model which could be used to reach the goal of an 85% occupancy rate are overestimated. This phenomenon is logical and easy to explain. Drivers are more inimical to the rate increment when it exceeds the threshold, which is regarded as a “watershed” of

Table 9 Curbside parking rate increment to reach the goal of an 85% occupancy rate (RMB/h). Goal

Average occupancy rate 85% Occupancy rate during peak hours - 85%

MNL

MMNL

MMNLC

Increment Potential bias

Increment Potential bias

Increment

1.809

þ 0.425 ( þ 31%)

1.759

þ0.375 ( þ 27%)

1.384

3.117

þ 0.714 ( þ 30%)

3.108

þ0.705 ( þ 29%)

2.403

decision-making behaviour. Specifically, the penalty for violating the threshold is more severe, with a larger coefficient. To cope with this issue, it is necessary to consider charge cut-off points in order to formulate a more accurate price adjustment scheme. While collecting data pertaining to drivers' thresholds for parking charges may not be permitted sometimes, a bold alternative to determine a reasonable price adjustment scheme is that the parking price increment/decrease obtained from the MNL model could be divided by 1.3. In a word, the consideration of a pricing threshold represents a warning for policy makers from the view of parking choice behaviour, WTPs, parking pricing simulation and adjustment schemes. Not accounting for charge cut-off points when present, however, may lead to biased results. 7. Conclusions This paper investigates the issue of parking choices incorporating charge cut-off points and proposes a reasonable

26

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

parking price adjustment scheme. The findings from this study, especially those related to the adjustment of curbside parking prices and the influence of price on the occupancy rates of curbside parking spaces, provide valuable insights into parking choice behaviour. Our findings could be very helpful to the governors and operators attempting to balance the demand for and functional goals of curbside parking spaces. Generally, this paper makes a contribution in the following two aspects: (1) To reveal driver acceptance of parking charges and to set a more reasonable curbside parking charge, charge cut-off points for both curbside and garage parking spaces are embedded into the MMNL model. One interesting insight from the survey is that drivers have a higher charge cut-off acceptance for curbside parking than garage parking. However, drivers tend to change parking types when confronted with exorbitant charges. This phenomenon indicates that treating the charge cut-off points of different types of parking as the same, or ignoring the effects of cut-off points on occupancy rates, are both problematic. Furthermore, a multiple regression model was undertaken to check the relationship between the number of cut-off violations stated by the drivers and those drivers' characteristics. The results provide conclusive evidence to suggest that drivers of an older age, or those with fewer driving years and less parking experience have a higher degree of tolerance with respect to parking charge cut-off points. As expected, our model estimation results show that a cut-off point does have an important influence on a driver's decision-making. In addition, significant improvement can be made by introducing cut-off variables. (2) This paper is also innovative in the way it investigates the influence of curbside parking charges on occupancy rates. We are also able to determine a reasonable charge to reach the goal of an 85% occupancy rate by establishing DCMs. Several kinds of factors which influence parking choices (especially driver characteristics) were included as a means to improve the model's accuracy. The statistically significant estimator of interaction terms (such as age  walking time) confirms the necessity of this approach, and the MMNLC model with uniform distribution incorporating cut-off points is the best model. In addition, our results show that the marginal utilities of charges are not constant over the whole range of values. Moreover, drivers are willing to pay more for reducing walking time, followed by search time. We also found that the aged drivers have a higher WTP for walking time. However, drivers' preferences for curbside parking reverse when the walking time is longer than 15 min, with all else being equal. This finding indicates that the charges for curbside parking spaces which provide a lower walking time should be higher. Simulation results also provide some implications for policy makers with regard to parking price adjustments, which may be overestimated by approximately 30% by models without cut-off points. All-in-all, this paper focuses on the impact of parking charges and those charges' thresholds on parking choices. However, at the same time, our study does not take into account other factors, such as the influence of parking information and trip purposes on parking choice. This offers a promising research topic. Besides, several kinds of heterogeneity, including the systematic and stochastic parts in utility, require further study. More efficient designs are also needed to improve parameter estimators' significance and to determine the minimum sample size in advance. In future research, further investigation of occupancy rates for different time periods could be conducted by gathering a higher volume of data with more details on both within-day and day-to-day scales. This

research should be undertaken to propose a more reasonable and flexible parking pricing scheme, which could in turn contribute to a more efficient use of parking space resources.

Acknowledgments We are grateful to the fund of the Shanghai Municipal Transport and Port Authority for its support of our investigation. We are also grateful for the insightful comments of two anonymous referees, who helped us to improve the paper. All errors are, of course, ours.

References Albert, G., Mahalel, D., 2006. Congestion tolls and parking fees: a comparison of the potential effect on travel behavior. Transp. Policy 13 (6), 496–502. http://dx.doi. org/10.1016/j.tranpol.2006.05.007. Arnott, R., Inci, E., 2006. An integrated model of downtown parking and traffic congestion. J. Urban Econ. 60 (3), 418–442. http://dx.doi.org/10.1016/j. jue.2006.04.004. Arnott, R., Rowse, J., 2009. Downtown Parking in Auto City. Reg. Sci. Urban Econ. 39 (1), 1–14. http://dx.doi.org/10.1016/j.regsciurbeco.2008.08.001. Arnott, R., De Palma, A., Lindsey, R., 1991. A temporal and spatial equilibrium analysis of commuter parking. J. Public Econ. 45 (3), 301–335. http://dx.doi.org/ 10.1016/0047–2727(91)90030-6. Azari, K.A., Arintono, S., Hamid, H., Rahmat, O.K., 2013. Modelling demand under parking and cordon pricing policy. Transp. Policy 25, 1–9. http://dx.doi.org/ 10.1016/j.tranpol.2012.10.003. Ben-Akiva, M., Swait, J., 1986. The Akaike likelihood ratio index. Transp. Sci. 20 (2), 133–136. http://dx.doi.org/10.1287/trsc.20.2.133. Bhat, C.R., Castelar, S., 2002. A unified mixed logit framework for modeling revealed and stated preferences: formulation and application to congestion pricing analysis in the San Francisco Bay area. Transp. Res. Part B: Methodol. 36 (7), 593–616. Bradley, M., Kores, E., Hinloopen, E., 1993. A joint model of mode/parking type Choice with supply-constrained application. In: Proceedings of the 21st Annual Summer PTRC Meeting on European Transport, (Highways and Planning, Manchester, England), 61–73. Caicedo, F., 2012. Charging parking by the minute: what to expect from this parking pricing policy? Transp. Policy 19 (1), 63–68. http://dx.doi.org/10.1016/j. tranpol.2011.09.006. Cantillo, V., Ortúzar, J.D., 2006. Implications of thresholds in discrete choice modelling. Transp. Rev.: A Transnatl. Transdiscipl. J. 26 (6), 667–691. http://dx.doi. org/10.1080/01441640500487275. Cheng, T.X., Wang, X., Yue, J.B., Ma, C.C., 2012. A Regional Pricing Model of Parking in the Central Commercial District of Urban. 〈http://www.paper.edu.cn/re leasepaper/content/201205–371〉. Danielis, R., Marcucci, E., 2007. Attribute cut-offs in freight service selection. Transp. Res. Part E: Logist. Transp. Rev. 43 (5), 506–515. http://dx.doi.org/10.1016/j. tre.2005.10.002. Dell’Olio, L., Ibeas, A., Moura, J.L., 2009. Paying for parking: improving stated-preference surveys. Proceedings of the ICE-Transport 162(1), 39–45. http://dx.doi. org/10.1680/tran.2009.162.1.39. Econometric Software Inc, 2012. NLOGIT version 5.0. Econometric Software Inc., New York. Feng, H.H., Zhu, C.K., 2008. Model of curb parking pricing in urban center district of China. J. Transp. Syst. Eng. Inf. Technol. 8 (5), 129–135. Gatta, V., Marcucci, E., 2016. Behavioural implications of non-linear effects on urban freight transport policies: The case of retailers and transport providers in Rome. Case Stud. Transp. Policy 4 (1), 22–28. http://dx.doi.org/10.1016/j. cstp.2015.08.001. Hensher, D.A., King, J., 2001. Parking demand and responsiveness to supply, pricing and location in the Sydney central business district. Transp. Res. Part A: Policy Pract. 35 (3), 177–196. http://dx.doi.org/10.1016/S0965-8564(99)00054-3. Hensher, D.A., Rose, J., Greene, W., 2005. Applied Choice Analysis: A primer. Cambridge University Press, Cambridge. Hess, D., 2001. Effect of Free Parking on Commuter Mode Choice: Evidence from Travel Diary Data. Transp. Res. Rec.: J. Transp. Res. Board (1753), 35–42. http: //dx.doi.org/10.3141/1753-05. Hess, S., Polak, J.W., 2004. Mixed logit estimation of parking type choice. 83rd Annual Meeting of the Transportation Research Board, Washington, DC. Hunt, J.D., Teply, S., 1993. A nested logit model of parking location choice. Transp. Res. Part B: Methodol. 27 (4), 253–265. http://dx.doi.org/10.1016/0191-2615(93) 90035-9. Ibeas, A., Dell’Olio, L., Bordagaray, M., Ortúzar, J.D., 2014. Modelling parking choices considering user heterogeneity. Transp. Res. Part A: Policy Pract. 70, 41–49. http://dx.doi.org/10.1016/j.tra.2014.10.001. Kobus, M.B., Guitierrez-Puigarnau, E., Rietveld, P., Ommeren, J., 2013. The on-street parking premium and car drivers’ choice between street and garage parking.

R. Zhang, L. Zhu / Transport Policy 52 (2016) 16–27

Reg. Sci. Urban Econ. 43 (2), 395–403. http://dx.doi.org/10.1016/j. regsciurbeco.2012.10.001. Kuppam, A., Pendyala, R., Gollakoti, M., 1998. Stated response analysis of the effectiveness of parking pricing strategies for transportation control. Transp. Res. Rec.: J. Transp. Res. Board (1649), 39–46. http://dx.doi.org/10.3141/1649-05. Lu, X.S., Liu, T.L., Huang, H.J., 2015. Pricing and mode choice based on nested logit model with trip-chain costs. Transp. Policy 44, 76–88. http://dx.doi.org/10.1016/ j.tranpol.2015.06.014. Marcucci, E., Scaccia, L., 2004. Mode choice models with attribute cutoffs analysis: the case of freight transport in the Marche Region. Eur. Transp. 25–26, 21–32. Marcucci, E., Gatta, V., 2012. Dissecting preference heterogeneity in consumer stated choices. Transp. Res. Part E: Logist. Transp. Rev. 48 (1), 331–339. http: //dx.doi.org/10.1016/j.tre.2011.08.003. Marsden, G., 2006. The evidence base for parking policies-a review. Transp. Policy 13 (6), 447–457. http://dx.doi.org/10.1016/j.tranpol.2006.05.009. Martínez, F., Aguila, F., Hurtubia, R., 2009. The constrained multinomial logit: a semi-compensatory choice model. Transp. Res. Part B: Methodol. 43 (3), 365–377. http://dx.doi.org/10.1016/j.trb.2008.06.006. McFadden, D., 1979. Quantitative methods for analyzing travel behavior of individuals: some recent developments. In: Hensher, D.A., Stopher, P. (Eds.), Behavioral Travel modeling. Croom Helm, London, pp. 279–318. Mei, Z.Y., Xiang, Y.Q., Chen, J., Wang, W., 2010. Optimizing model of curb parking pricing based on parking choice behavior. J. Transp. Syst. Eng. Inf. Technol. 10 (1), 99–104. http://dx.doi.org/10.1016/S1570-6672(09)60027-1. Ottosson, D.B., Chen, C., Wang, T., Lin, H., 2013. The Sensitivity of on-street parking demand in response to price changes: a case study in Seattle, WA. Transp. Policy 25, 222–232. http://dx.doi.org/10.1016/j.tranpol.2012.11.013. Pierce, G., Willson, H., Shoup, D.C., 2015. Optimizing the use of public garages: pricing parking by demand. Transp. Policy 44, 89–95. http://dx.doi.org/10.1016/ j.tranpol.2015.07.003. Proost, S., Van Dender, K., 2008. Optimal urban transport pricing in the presence of congestion, economies of density and costly public funds. Transp. Res. Part A: Policy Pract. 42 (9), 1220–1230. http://dx.doi.org/10.1016/j.tra.2008.03.009. Shanghai Bureau of Statistics, 2014. Statistical bulletin of the national economic and social development of Shanghai Municipality in 2014. Stat. Sci. Pract., 20–29.

27

Shoup, D.C., 2004. The ideal source of local public revenue. Reg. Sci. Urban Econ. 34 (6), 753–784. http://dx.doi.org/10.1016/j.regsciurbeco.2003.10.003. Shoup, D.C., 2005. The High Cost of Free Parking. Planners Press, Chicago. Simićević, J., Vukanović, S., Milosavljević, N., 2013. The effect of parking charges and time limit to car usage and parking behaviour. Transp. Policy 30, 125–131. http://dx.doi.org/10.1016/j.tranpol.2013.09.007. Simićević, J., Milosavljević, N., Maletić, G., Kaplanović, S., 2012. Defining parking price based on users’ attitudes. Transp. Policy 23, 70–78. http://dx.doi.org/ 10.1016/j.tranpol.2012.06.009. Spiess, H., 1996. A logit parking choice model with explicit capacities. EMME/2 Support Center, CH-2558 Aegerten. Swait, J., 2001. A non-compensatory choice model incorporating attribute cutoffs. Transp. Res. Part B: Methodol. 35 (10), 903–928. http://dx.doi.org/10.1016/ S0191–2615(00)00030-8. Teknomo, K., Hokao, K., 1997. Parking behavior in central business district-a study case of Surabaya, Indonesia. Easts J. 2 (2), 551–570. Train, K.E., 2009. Discrete Choice Methods with Simulation, second ed., Cambridge University Press, Cambridge. van der Waerden, P., Timmermans, H., Borgers, A., 2002. PAMELA: parking analysis model for predicting effects in local areas. Transp. Res. Rec.: J. Transp. Res. Board (1781), 10–18. http://dx.doi.org/10.3141/1781-02. Washbrook, K., Haider, W., Jaccard, M., 2006. Estimating commuter mode choice: a discrete choice analysis of the impact of road pricing and parking charges. Transportation 33 (6), 621–639. http://dx.doi.org/10.1007/s11116-005-5711-x. Young, W., Thompson, R.G., Taylor, M., 1991. A review of urban car parking models. Transp. Rev. 11 (1), 63–84. http://dx.doi.org/10.1080/01441649108716773. Zhang, R., Xiong, S.M., Liao, F., 2015. Colligation management mode pilot and evaluation of curb parks. Tongji Univ. Res. Report., 6–17. Zhang, R., Zhu, L.C., Lin, J.N., Zhou, J.N., 2013. Assessment of curb parking fee criterion. Tongji University Research Report, pp. 4–25. Zhang R, Zhu L.C., 2015. Curb Parking Pricing of City Center Incorporating Threshold. In: Proceedings of the 94th Annual Meeting of the Transportation Research Board, Washington, DC. Zong, F., Zhang, Y.S., Wang, Z.Z., Li, Z.Y., 2013. Parking Pricing in the Urban Central Business. J. Jilin Univ. (Eng. Technol. Ed. ) (5), 1235–1240.