Estimating Travel Choice Probability of Link-Based Congestion Charging Scheme for Car Commuter Trips in Jakarta

Abstract

The likely effects on car commuters of enforcing congestion charging using the link-based corridor method include that they may shift to public transport, divert their route of travel, or decide not to travel to the related area. However, most recent research has focused mainly on the choice of modes. This paper examined the travel choices of private car commuters resulting from the congestion charging scheme set to be implemented in Jakarta, Indonesia. The scheme is intended to replace the current odd-even strategy. It is imperative to study all possible mutually exclusive alternatives faced by car commuters. A web-based e-survey was used for data collection, employing the stated preference method. The discrete choice multinomial logit model was chosen to analyze the data. A total of 401 of the 2125 respondents to the e-survey questionnaire link, evenly distributed to all areas of Greater Jakarta, were sampled in this study. The sample respondents who traveled by car, passing through the eight designated corridors, were analyzed. NLOGIT6 software was used to analyze the parameter of attributes, the probability of alternatives chosen, and the marginal effects of congestion charging on such corridors, employing the multinomial logit model (MNLM). One surprising finding was that the load factor and taxi fares were not significant, indicating that the level of in-vehicle overcrowding is not a concern of respondents, and taxi services are not a substitute for car travel. Another surprising finding was that income variables and job type do not significantly influence travel behavior. In terms of the probability of commuters to continue to travel by car when link-based congestion charging is imposed, only around half of the car travelers were willing to pay the congestion levy and pass through congestion charging corridors. The probability of car travelers diverting onto alternative roads is high, i.e., around 16.82% to 22.88%, while the probability of car travelers shifting to mass transportation is 17.69%. When interpreting direct marginal effects, there is a change in the probability of all travelers choosing to use private cars through the congestion charging corridor of −0.0338, or a decrease of −3.38% for every IDR 1000 increase in the congestion charging levy rate, ceteris paribus.

1. Introduction

In recent years, Jakarta has been suffering from severe traffic congestion. Data show that the average speed of traffic in the morning was 16.7 km/h, during the day, it was 15.4 km/h, and in the evening, it was 15.0 km/h [1]. In terms of the level of service, during the morning rush hour, 36% of roads were at service level C, 16% at service level D, 23% at service level E, and 12% at service level F [2]. The economic losses from this inefficient transportation system reached IDR 100 trillion annually, or around 4% of the Greater Jakarta GRDP, consisting of IDR 40 trillion in lost vehicle operating costs and IDR 60 trillion in lost travel time costs. This amount is equivalent to the cost of building two to three MRT lines in Jabodetabek. This amount is also equivalent to a loss of IDR 3 million per year for each Jabodetabek resident [1]. Through Regional Regulation No. 5 of 2014 [3], the Jakarta government intended to increase the traffic on Jakarta’s road network to 35 km/h by changing the odd-even scheme to a link-based congestion charging strategy.

Over the past three decades, there have been many studies on the implementation of congestion charging, but these focused only on certain responses from travelers. A study focusing on the effect of congestion charging on modal shifting, for example, was carried out by Agarwal and Koo [4] in Singapore with an intervention to increase ERP rates at several central business district (CBD) entry points using a quasi-experimental difference-in-differences design. Meanwhile, Nanang and Tamin [5] used a dual-model trip distribution and modal split, which is a choice model. Belgiawan et al. [6] used a random regret minimization model, while Ilahi et al. [7] used a logit model with a latent variable to examine the effects of congestion charging on modal shifting in Jakarta. In 2016, Rizki et al. [8] examined three link-based trial ERP corridors in Jakarta to understand the route diverting behavior. Meanwhile, the effect of congestion charging on WFA or teleworking/telecommuting was carried out by Dissanayake [9] in Bangkok using the nested logit model. Of the above studies on congestion charging, all of them partially examine the effect of congestion charging. Due to the effects of the implementation of congestion charging, including transportation mode shifting and route diversions, as well as choosing not to travel, but to work from anywhere (WFA) instead, research focusing on the simultaneous effects of congestion charging on modes, routes, and WFA is needed.

2. Literatures Review

2.1. The Idea of Congestion Charging

According to Lindsey [10], the idea of imposing congestion charging was first proposed by Arthur Pigou in 1920 and Knight in 1924. However, much earlier, Adam Smith proposed the idea of charging in his book The Wealth of Nations in 1776 [11], regarding both road financing and the equity of using it. Dupuit [12] argued that even if the road is a public facility, the government will need a budget to finance its operation. Many economists argue that this Pigouvian tax principle is the first best method for financing transportation [13,14,15]. The Pigouvian tax principle as a tax of negative externalities, including traffic congestion, is determined based on the level of road traffic congestion [16,17]. This is equal to the external cost of congestion, and also known as a marginal cost pricing [18]. The implementation of congestion charging is the most efficient way to reduce traffic congestion because it employs a price mechanism, along with all its advantages, such as clarity, universality, and efficiency [18,19]. Vickrey [20,21], promoted the introduction of congestion charges, both theoretically and practically. He proposed the employing the cost of using the road to influence the choice of route and mode of transportation, depending on the level of congestion, or varying according to time, location, and type of vehicle. Then, according to Lindsey and Verhoef [17], congestion charging is appropriate because people tend to make efficient choices when they are faced with all the social benefits and costs of their activities, including travel.

2.2. Discrete Choice Models

According to Moshe Ben-Akiva and Steven R. Lerman [22], McFadden [23], and Meyer [24,25], discrete choice models, such as multinomial logit (MLM) and nested logit models (NLM), are widely used. These models are used based on the concept of utility, which assumes that each traveler values the utility of each choice of transportation mode. McFadden [23] suggests that if it is assumed that each individual traveling is a rational economic consumer, then in the face of mutually exclusive alternatives, he or she will maximize its utility depending on individual budget constraints. This model directly measures the response and choice of each individual concerning the performance of the transportation system. Consumers try to maximize the commodities’ utility according to the attributes they consume. Commodity desirability or individual preferences will be determined by the commodity’s attributes. An important implication of this theory in the analysis of travel demand is that preferences do not depend on the alternative travel options available, but on what the consumer wants (desirability). Hensher, 2005, in the Applied Choice Analysis [26] further states that humans are born to be voters (sellers, traders). Individual preferences depend on the attributes and socio-demographic characteristics of the traveler. The challenge in the choice model analysis is how to maximize variability that can be measured or observed (observed heterogeneity) while minimizing variability that cannot be measured or observed (unobserved heterogeneity). The alternatives that can be chosen by each individual are limited to choosing one of the alternatives that are designed (mutually exclusive) and are as complete as possible (collectively exhaustive). In this case, each individual chooses only one alternative from a series of choice alternatives. Train [27] states that in choosing several alternatives, or so-called choice sets, in addition to mutually exclusive and collectively exhaustive characteristics, the number of alternatives must also have a limit or a finite number). The first and second characteristics do not always have to be fulfilled. For example, choices can be a combination of the first and second choices (not mutually exclusive), and some people may not choose either of these alternatives (not collectively exhausted). However, there must be a certain limit for the third characteristic that must be fulfilled in order for the number of choices to be finite.

2.3. Recent Studies

The effect of congestion charging on modal shifting was studied by Agarwal and Koo in Singapore using the difference-in-differences method with the intervention of increasing ERP rates at several entry points of the central business district (CBD). The results of the study showed that there was a significant increase in public transportation passengers [4], Nanang and Tamin simulated all possible TDM technique types in Jakarta, such as the use of busways, school buses, activity time staggering, three-in-one, odd-even, and road pricing [5]. Yudhistira et al., 2017 [28], conducted a study on the public perception of traffic jams. Yudhistira used a non-probabilistic survey of 400 respondents in Jakarta regarding the Sudirman Thamrin corridor and found that 53.4% of the respondents chose a mode of transportation based on travel time, 19% for safety reasons, and 17% based on travel costs. Belgiawan et al. [6] researched the effect of congestion charging on the mode of transportation shiftingby using the random regret minimization model from stated preference data. Then, Ilahi et al.’s research tried to include modes of transportation-on-demand services in Jakarta. He included the anti-car and pro-public transport latent variables in the multinomial logit (MNL) and mixed logit (MXL) models in the modal selection analysis. Motorcycles are the main choice of travelers in Jakarta. Ilahi et al. [7] examine the response of the people of Jakarta to congestion charging.

There are four congestion charging methods, namely cordon based, area based, link based, and road network based methods [29]. The majority of European and Asian countries implement congestion charging on a cordon or area basis, while link based pricing is used in North America, using the characteristics of a concentric road network. Elena et al. [30] and Li et al. [31] examined the social benefits of the two methods for imposing road pricing. Yudhistira [32] researched the application of cordon-based road pricing in traffic restriction areas (cordon-based pricing) using the spatial general equilibrium (SGE) model method. In Jakarta, if the ERP replaces the odd-even scheme, link-based pricing will be implemented. Such a scheme will enable travelers to choose alternative routes that are not subject to congestion charging. Regarding the weakness of this link-based pricing, Rizki et al. [8], researched three ERP trial corridors in Jakarta, investigating the possibility of commuter trips choosing alternative routes (route selection behavior), based on the length of the commuter trip.

Working from home, telecommuting, or teleworking, as well as flexible work arrangements, have been practiced since 1975 [33]. Initially, these methods were implemented due to the demand for lower housing costs and the need for a balance between work life and family interests, to help those with disabilities, and to reduce traffic congestion [34]. This trend is reinforced by the rapid improvement of information and communication technology [33], including the possibility for virtual work. Initially, in some countries, teleworking was carried out by contract workers, or those working on an output basis. However, teleworking and similar work models, such as flexible work arrangements, are now utilized by many types of workers and companies, for various reasons. Recently, transportation issues, including time wasted during travel, the challenge of living far from the workplace, and stress during the trip, have become one of the main considerations for working from home. The choice of urban [9] workers to telecommute can reduce the volume of traffic, hence easing traffic congestion. In Indonesia, there is no well-structured academic research on telecommuting. Research linking teleworking with ERP was conducted by Dissanayake [9] in Bangkok using the nested logit model.

In the context of modeling the response of travelers to congestion charging, this research provides novelty in that it examines the response of commuter travelers using the multinomial logit model, including not only modes of transportation, but also route diversions and options not to travel, or WFA. In this study, commuters making trips by private vehicles in urban areas are considered choice riders because they can choose not to commute due to the fact that they can carry out their activities anywhere, at home or in co-working spaces around their neighborhoods.

3. Methods

3.1. Models

Considering the need to find out the car commuter responses to link-based congestion charging, the model chosen in this study is the probability choice model, specifically the logit model, as proposed by McFadden [35], which calculates the probability of the n traveler choosing alternative i:

Pni = Prob (Uni + εni > Unj + εnj ∀ j ≠ i)

(1)

Pni = Prob (εnj < εni + Uni − Unj ∀ j ≠ i)

(2)

If ε_ni is given, then

F(${\epsilon }_{nj}$) = exp(−exp(${\epsilon }_{ni}+U_{ni}-U_{nj}$))

After going through complex algebraic calculations, then

$$P_{ni}=\frac{1}{\sum _j{e}^{-\left(U_{ni}-U_{nj}\right)}}$$

(3)

$$P_{ni}=\frac{e^{U_{ni}}}{\sum _j{e}^{U_{nj}}}$$

(4)

where P_ni is between 0 and 1 and never has a value of exactly 0 or 1.

Ten mutually exclusive alternatives are developed. The utility functions of the alternatives are as follows:

U(Cal) = acal + btt TT + bsdc SDC + ε_cal

(5)

U(Cat) = acat + btt TT + btol Toll + bsdc SDC + ε_cat

(6)

U(Cac) = acac+ btt TT + bcc CC + bsdc SDC + ε_cac.

(7)

U(Mal) = amal + btt TT + bsdc SDC + ε_mal

(8)

U(Mcc) = amcc + btt TT + bcc CC + bsdc SDC + ε_mcc

(9)

U(Tjc) = atjc + btt TT + bfpub Fpub + blf LF + bsdc SDC + ε_tjc

(10)

U(Trc) = atrc + btt TT + bfpub Fpub + blf LF + bsdc SDC + ε_trc

(11)

U(Txc) = atxc + btt TT + bcc CC + bftx Ftx + bsdc SDC + ε_txc

(12)

U(Ojc) = aojc + btt TT + bcc CC + bftx Ftx + bsdc SDC + ε_ojc.

(13)

U(WFA) = awfa + + bsdc SDC + ε_wfa.

(14)

where:

U(Cal): private vehicle via alternative roads

U(Cat): private vehicle via toll roads

U(Cac): private vehicle via congestion charging corridor

U(Mal): motorcycle via alternative roads

U(Mcc): motorcycle via congestion charging corridor

U(Tjc): TransJakarta Busway

U(Trc): railway (Commuterline, MRT, LRT)

U(Txc): taxi/online taxi via congestion charging corridor

U(Ojc): online motorcycle taxi via congestion charging corridor

U(WFA): WFH/WFA (no choice option)

SDC: socio-demographic characteristics, income level (Inc), car ownership (COwn), and dummy job type (d_JT)

In the model formulation, there is one generic variable, namely travel time (TT), which is the sum of the time in the vehicle and the waiting time. Travel time is considered generic for all alternatives. Then, the characteristics of congestion charging rates for the alternatives of choosing private cars passing through the congestion charging corridors (Cac) and taxis (Txc) are considered the same. Likewise, the characteristics of congestion charging rates for the alternatives of using motorcycles passing through the congestion charging corridor (Mcc) and online motorcycle taxis/ojek (Ojc) are considered the same. The characteristics of transportation fares for the alternatives of choosing the TansJakarta Busway (Tjc) or the train (Trc) are considered the same, as well as taxi/online taxi fares (Txc) and fares for the alternatives of using online motorcycle taxis/ojek (Ojc). As a result, there are six observed attribute coefficients (btt = travel time coefficient; btol = toll levy coefficient; bcc = congestion charging rate coefficient; bfpub = public transport fare coefficient; bftx = taxi fare coefficient; and blf = public transport load factor coefficient), nine ASC constants (acal, acat, acac, amal, amcc, atjc, atrc, atxc, awfa), and one SDC coefficient (binc = income coefficient; or bjt = job type dummy variable coefficient).

3.2. Stated Preference Scenarios Development

There are several ways to design scenarios, including orthogonal or factorial designs, fractional factorial designs, and efficient designs. According to Hess [36], in the last decade, research on discrete choice using the stated preference (SP) experimental design method in generating choice sets has shifted from orthogonality principles to efficient-design principles or techniques. According to Rose and Bliemer [37] some researchers questioned the suitability of orthogonal design, especially its practicality, because it requires too many situations of choice. Bliemer stated that researchers are switching to using efficient designs, even if this means that one or several attributes will appear unbalanced. In this case, the number of choice situations must exceed the estimated degrees of freedom of the coefficients. The efficient design not only tries to minimize the correlation between attributes, but also strives to make the standard error of the estimated parameters as small as possible.

In this study, scenarios were generated using Software Choice Metrics Ngene with efficient design. The Ngene Software makes it possible to create blocking or subset questions for each respondent so that it is not necessary to answer all the questions in that choice set or scenario, but rather only one block of questions. There are 40 different situations to choose from (exceeding the estimated coefficient of 16). The 40 sets of questions were divided into 10 blocks. Therefore, each respondent only answered 4 scenarios, with each choice set consisting of 10 alternatives. The respondents chose 1 out of 10 blocks based on the last digit of their cell phone number.

3.3. Survey and Sample Selection Procedures

The research objects were car travelers who passed through eight congestion charging corridors, which is the odd-even scheme, as shown in Figure 1.

The sampling method used purposive sampling by distributing questionnaire links through various social media sites of the Transportation Research Agency (website, Istagram, Facebook, Twitter, and WhatsApp) within a certain time to obtain the number of samples, according to the minimum target. The stated preference survey was conducted online and disseminated via social media and the internet. The survey was carried out for 30 days, from October to November 2021. The number of respondents was proportionally distributed in each study area. Respondents who did not meet the criterion, i.e., not usually passing through the odd-even corridors, did not continue to complete the questions about choice preferences in the choice sets. Meanwhile, private car travelers who usually drove through the congestion charging corridor continued to complete the questionnaire.

The e-survey method was selected due to a very high internet penetration rate at 2020, which is around 93.24% in Jakarta, 82.18% in West Java, and 84.07% in Banten [38]. The selection of an online survey also allows all those connected to the internet to have the same opportunity to fill out the questionnaire.

3.4. Sample Size

Following the methods of Jatnika et al. [39] the calculation of the minimum sample size for simple random sampling can be performed using the following formula:

N = (N × P × Q)/((N − 1) × D + P × Q)

(15)

N = population size;

B = bound of error (highest sampling error);

P = Q = moderate proportion estimate (0.5);

D = calculated based on B and the level of confidence.

Based on the formula, the sample can be calculated using the average daily number of travelers who usually passes through eight odd-even corridors, which will be converted into congestion charging corridors. This number is 304,213 private cars per day, or 456,319 people per day.

N_car = 456.319

B = 5%

P = Q = 0.5

D = B2/4 = 0.000625

$n_{\mathrm{c}\mathrm{a}\mathrm{r}}=\frac{\left(456.319\right)\left(0.5\right)\left(0.5\right)}{\left(456.319-1\right)\left(0.000625\right)+\left(0.5\right)\left(0.5\right)}=$ 399.65 = 400 car commuter sample

3.5. Attribute Levels

In the model formulation, there is one generic variable, namely travel time (TT), which is the sum of the time in the vehicle and the waiting time. Travel time is considered generic for all alternatives. Then, characteristics of congestion charging rates for the alternatives of choosing private cars passing through the congestion charging corridors (Cac) and taxis (Txc) are considered the same. Likewise, the characteristics of the congestion charging rates for the alternatives of using motorcycles passing through the congestion charging corridor (Mcc) and online motorcycle taxis/ojek (Ojc) are considered the same. The characteristics of transportation fares for the alternatives of choosing the TansJakarta Busway (Tjc) or the train (Trc) are considered the same, as well as taxi/online taxi fares (Txc) and fares for the alternatives of using online motorcycle taxis/ojek (Ojc). As a result, there are six observed attribute coefficients (btt, btol, bcc, bfpub, bftx, blf), nine alternative specific constants (acal, acat, acac, amal, amcc, atjc, atrc, atxc, awfa), and one SDC coefficient (binc, cown, or bjt).

By including only the main transportation impedances as vector attributes, the respondents can easily understand the choice sets in the stated preference questionnaire, even though in this study, there were ten alternatives in one choice set. Setting 40 choice sets is also challenging. However, the scenarios or choice sets can be divided into several blocks. To distribute the block of choice sets to be completed by the respondent, the last digit of the respondent’s cell phone can be used as block group of choice sets, because they are relatively evenly distributed in the ten blocks. The design alternatives can be multifaced, and they relate to all possible alternatives, but they are finite. A modal shifting alternative may be combined with route choices, as well as an alternative of not traveling. The alternative of not traveling is considered as a no choice option; therefore, it requires no attributes.

The attribute values of travel time, toll fees, and public transport fares, as well as the initial settings for congestion charging values based on the previous value of time survey, are used as initial setting values, which are then increased and decreased by 20–25% (pivoting). These values are shown in

Table 1. Alternatives, attributes, and levels.

No.	Alternative		Attributes
			Travel Time (min)	CC/Toll (IDR‘000)	Fare (IDR‘000)	LF (Percent)
1	Private vehicles via alternative road	Cal	45, 60, 75
2	Private vehicles via toll road	Cat	22, 30, 38	10, 13, 16
3	Private vehicles via congestion charging corridors	Cac	15, 20, 25	12, 16, 20
4	Motorcycles via alternative roads	Mal	45, 60, 75
5	Motorcycles via congestion charging corridors	Mcc	15, 20, 25	6, 7.5, 9
6	TransJakarta bus	Tjc	15, 20, 25		3.5, 5, 6.5	50, 100, 150
7	Trains (Commuterline, MRT, LRT)	Trc	10, 20, 30		3.5, 10	50, 100, 150
8	Online taxi/taxi via congestion charging corridors	Txc	15, 20, 25	12, 16, 20	40, 50, 60
9	Online motorcycle taxis via congestion charging corridors	Ojc	15, 20, 25	6, 7.5, 9	25, 35, 45
10	WFA	WFA

:

3.6. Data Cleaning

Data cleaning was performed by excluding the data that showed non-trading behaviors and inconsistency. Non-trading behavior is shown by always choosing the same option, regardless of the value of the attribute. Using non-trading behavior data will affect the estimated coefficients [40]. Of 2125 respondents, 1509 traveled to the center of Jakarta. A total of 447 respondents traveled to Jakarta by private car, which usually went through the eight corridors. A total of 46 respondents showed non-trader and inconsistent characteristics, resulting in 401 respondents included in the parameter estimates. Of the 401 respondents, the number of data points was 1608.

4. Results and Discussion

4.1. Socio-Demographic Data

The socio-economic characteristics of the respondents are shown in

Table 2. Socio-demographic characteristics.

No.	Socio-Demographic Characteristics	Respondent
		Sample	Percent
	Income Group
1	<IDR 3 million	14	3.49%
2	IDR 4–7 million	80	19.95%
3	IDR 8–13 million	98	24.44%
4	IDR 14–20 million	97	24.19%
5	IDR 21–30 million	57	14.21%
6	>IDR 31 million	55	13.72%
	Car Ownership
1	0 vehicles	17	4.24%
2	1 vehicle	242	60.35%
3	2 vehicles	111	27.68%
4	>2 vehicles	31	7.73%
	Job Type
1	mandatory	367	91.52%
2	discretionary	34	8.48%

:

4.2. Estimating Parameters of the Models and Determining Goodness of Fit of the Models

4.2.1. Parameter Attributes Estimation

In the discrete choice model, the parameters of the models were estimated using the method of maximum likelihood estimation (MLE). For the MNL model, the maximum likelihood function that the probability of individual i choosing an alternative j can be expressed as:

$${\prod }_j\left({P_{ij})}^{y_{ij}}\right)$$

(16)

where y^ij = 1 if individual i chooses j and zero if he or she chooses the another option.

By assuming that each individual decision is independent, the probability that each individual in the sample chooses an alternative is:

$$L\left(\beta \right)=\left({\prod }_{i=1}^n{\prod }_j\left({P_{ij})}^{y_{ij}}\right)\right)$$

(17)

where n is a sample of individuals making a decision, and β is the parameter vector in the model.

Then log likelihood function becomes:

$$LL\left(\beta \right)={\sum }_{i=1}^n{\sum }_j{y}_{ij}{\mathrm{l}\mathrm{n}(P}_j)$$

(18)

NLOGIT6 econometric software estimates the value of β that maximizes the LL(β) function.

The results of the estimation of the parameters of the models are presented in

Table 3. Comparison of parameters and goodness of fit of Models 1, 1a, 2, 3, and 4.

Constants and Coefficients	Model 1. Alternative Specific Constants and Variables		Model 1a. (Modified Model 1) Alternative Specific Constants and Variables		Model 2. Alternative Specific Constants, Variables, and Income		Model 3. Alternative Specific Constants, Variables, and Car Ownership		Model 4. Alternative Specific Constants, Variables, and Dummy Job Type
	Coefficient	Standard Error	Coefficient	Standard Error	Coefficient	Standard Error	Coefficient	Standard Error	Coefficient	Standard Error
Constants (alpha)
acal	4.11112 ***	0.27144	4.08239 ***	0.26314	4.28864 ***	0.35622	3.44977 ***	0.39585	3.53986 ***	0.44330
acat	5.43918 ***	0.55379	5.40774 ***	0.54930	5.61304 ***	0.59903	4.77833 ***	0.62295	4.86432 ***	0.65544
acac	5.64952 ***	0.33238	5.60874 ***	0.32818	5.81549 ***	0.40699	4.97487 ***	0.44234	5.06437 ***	0.48592
amal	2.52555 ***	0.27774	2.49974 ***	0.27108	2.70611 ***	0.36221	1.86688 ***	0.40123	1.95741 ***	0.44794
amcc	1.84162 ***	0.26515	1.81714 ***	0.26258	2.02369 ***	0.35604	1.18381 ***	0.39580	1.27393 ***	0.44346
atjc	3.23920 ***	0.47295	3.20394 ***	0.33217	3.41018 ***	0.40986	2.57112 ***	0.44478	2.66195 ***	0.48713
atrc	3.82483 ***	0.55363	3.78049 ***	0.39422	3.98670 ***	0.46158	3.14778 ***	0.49277	3.23866 ***	0.53127
atxc	4.95097 ***	1.80544	2.30513 ***	0.44133	2.51172 ***	0.50261	1.67157 ***	0.53166	1.76085 ***	0.56844
awfa	−0.95098 ***	0.28557	−0.95098 ***	0.28557	−0.74454 **	0.37323	−1.58395 ***	0.41117	−1.49310 ***	0.45671
Coefficients (beta)
btt	−0.03559 ***	0.00386	−0.03509 ***	0.00367	−0.03509 ***	0.00367	−0.03510 ***	0.00367	−0.03509 ***	0.00367
bcc	−0.13745 ***	0.01640	−0.13550 ***	0.01629	−0.13552 ***	0.01629	−0.13544 ***	0.01629	−0.13537 ***	0.01629
btol	−0.13341 ***	0.03730	−0.13215 ***	0.03720	−0.13205 ***	0.03720	−0.13240 ***	0.03720	−0.13213 ***	0.03720
bfpub	−0.14584 ***	0.04495	−0.14408 ***	0.04202	−0.14406 ***	0.04202	−0.14408 ***	0.04202	−0.14414 ***	0.04202
blf	−0.00674	0.21217
bftx	−0.05112	0.03472
Coefficients SDC
Inc					−0.01163	0.01300
Cown							0.49347 **	0.24906
d_JT									0.61832	0.42222
Goodness of Fits
N	1608		1608		1608		1608		1608
K	15		13		14		14		14
LL(β)	−2428.4968		−2429.5812		−2429.1934		−2427.4536		−2428.6403
LL(0)	−3702.5568		−3702.5568		−3702.5568		−3702.5568		−3702.5568
LL(C)	−2495.256		−2495.2560		−2495.2560		−2495.2560		−2495.2560
Pseudo R2 wrt LL(0)	0.3441		0.3438		0.3439		0.3444		0.3441
Pseudo R2 wrt LL(C)	0.0268		0.0268		0.0265		0.0272		0.0267
χ2 wrt LL(0)	2548.12008		2545.95118		2546.72678		2550.20632		2547.83304
χ2 wrt LL(C)	133.51855		131.34965		618.8744		622.35394		619.98066
Prob [χ2 > value ]	0		0		0		0		0
χ2 Table at α = 0.05 CI 95%	24.996		22.362		23.685		23.685		23.685

***, **==> significance at the 1%, 5% level.

.

4.2.2. Significance of Parameter Estimates

From the modeling results, the coefficients of travel time, congestion charging levy, toll rates, mass public transport fares, taxi fares, and load factors showed negative results, which indicates that the attribute is the main impedance of urban travel. Travel time, congestion charging levy rates, toll rates, and mass public transport fares significantly determine the utility of alternatives. However, the level of overcrowded onboard the transport modes (load factor) and taxi fares are not statistically significant. These findings indicate that the level of overcrowding in public transportation is not a variable that influences the choice of mode of travel in an urbanized area. Likewise, taxi fares are not significant, indicating that taxis are not the preferred mode of substitution, and taxi fares are not an attribute that determines the choice of the mode of transportation for commuters with private cars.

In Model 1, of the 15 parameters estimated, 13 were significant at α = 0.01 or 99% confidence level. Two parameter attributes are not significant, namely blf (load factor attribute or public transport occupancy rate coefficient) and bftx (online taxi and motorcycle taxi fare coefficient). The Wald statistics $=z=\frac{{\beta }_i}{{standard error}_i}$ for blf and bftx are −0.03 and −1.47, respectively. Testing the significance of those two attributes, the Wald statistic is smaller than the critical value of 1.96; thus, the hypothesis that the estimated parameter is equal to zero is accepted, and the variables are concluded to be statistically insignificant. That is also the case when evaluating the p-value by setting the 95% confidence interval at the value α = 0.05. If the p-value is less than α = 0.05, then the estimated parameters are statistically not equal to zero, and the attribute is statistically significant. If the p-value exceeds α = 0.05, the estimated parameter is statistically equal to zero, and the variable is statistically insignificant. The Wald statistic and p-value at the same level of confidence will yield the same result. The p-value of blf and bftx with p-value are 0.9747 and 0.1409, respectively, greater than α = 0.05. Therefore, the hypothesis that the estimated parameter is equal to zero is acceptable, and the variable is statistically insignificant. When blf and bftx are excluded in Model 1a, all estimated parameters (9 ASC and 4 observed attributes) show significance at the 99% confidence interval at a value of α = 0.01.

Adding the Income variable and Job Type as dummy variables, the coefficient estimates in Models 2 and 4 do not show significance. The Wald statistic is −0.8946 for binc and 1.4644 for bjt, with p-values of 0.3710 for binc and 0.1431 for bjt. In this case, it can be stated that binc = 0 and bjt = 0, and we cannot reject the Ho hypothesis: βi = 0 because the absolute value of the Wald statistic is smaller than the critical value of 1.96, and the p-value is greater than α = 0.05. In other words, the hypothesis that the estimated parameters equal zero is accepted, and the variable is statistically insignificant.

Whereas for Model 3, by adding the Car Ownership (COwn) attribute, it shows significance at α = 0.05, with the Wald statistic of COwn as 1.98 and α = 0.0476. In other words, the hypothesis that the estimated parameters are equal to zero is rejected, and the variable (Car Ownership) is statistically significant.

4.3. Determining Goodness of Fit of the Models

4.3.1. Log Likelihood

The significance of the model was determined by comparing the log-likelihood function of the estimated model to the base model. Following the methods of McFadden [35], the base model used in this study was the log-likelihood at zero coefficient (LL at Zero) or (LL0). To measure the improvement of the goodness of fit model, if the estimated log-likelihood of the model is close to zero, the model is improving [26].

The value of LL0 is calculated by the formula:

$$LL0=N\mathrm{l}\mathrm{n}\left(\frac{1}{{NAlt}_t}\right)$$

(19)

where N is the number of observations (1608 data points), and N_Alt = 10, then LL0 = −3702.5568. The LL function of Model 1a. is −2429.58121, greater than LL0 = −3702.5568, and is close to zero. Therefore, Model 1a. is better than the model without the coefficients.

4.3.2. Log Likelihood Ratio Test

• Comparing Model 1 and Model 1.a

The −2LL ratio obtained from the output model was then checked using the log-likelihood ratio formula to obtain the Chi-square model. The Chi-square result was then compared with the Chi-square table at α = 0.05 or the 95% confidence level.

$$\begin{gathered} -2LLratio=-2\left({LL}_{base model}-{LL}_{estimated model}\right)\sim \\ {\chi }_{\left(number of new parameters estimated in the estimated model\right)}^2 \end{gathered}$$

(20)

In Model 1.a., the number of parameters estimated is k = 13, with k = 9 constants (ASC) and k = 4 variable coefficients. The log-likelihood of Model 1a regarding the convergent function estimated by the log-likelihood in the basic model log-likelihood is zero, the Chi-square (χ²) is 2545.95118, greater than the critical Chi-square result according to the table at a degree of freedom 13, which is 22.362. The p statistical value of χ² is also 0.0000, which is lower than the value of α = 0.05 at the 95% confidence level. According to the −2LL ratio criterion, hypothesis H₀ that the estimated model is not better than the base model is rejected. It can be concluded that Model 1a is statistically significant.

2.

Comparing Model 1.a, Model 2, Model 3, and Model 4

In Models 2, 3, and 4, the estimated coefficients are 14 each, higher than those in Model 1a, which is 13. According to Koppelman [41] and Hensher [26], selecting the best model can be achieved by comparing the −2LL in the same way, but not against the basic model. Model 2 was compared to Model 1a, while Model 3 was compared to Model 1a. In this case, the largest LL was subtracted from the smallest LL.

The −2LL test was formulated as −2LL ratio = −2(largest LL—smallest LL) ∼χ² (the difference in the number of parameters estimated from the two models). The Pseudo R is

$$R^2=1-\frac{{LL}_{estimate dmodel}}{{LL}_{base model}}$$

(21)

The

Table 4. Comparison of the goodness of fit of Models 2 and 3 to Model 1a.

	Model 1a (Base Model)	Model 2	Model 3	Model 4
Difference in the degree of freedom (Δk)	13	1	1	1
Log-likelihood function	−2429.58121	−2429.19341	−2427.45360	−2428.64028
Pseudo R square	0.3438	0.000159616	0.000875711	0.000387281
Chi-squared	131.34965	0.7756	4.2552	1.10626
Chi-squared table	22.362	3.841	3.841	3.841

shows that the log-likelihood ratio of Model 2 was estimated by using base Model 1a, resulting in the Chi-square (χ²) of 0.7756, which was smaller than the critical Chi-squared result for the degree of freedom 1, namely 3.841. Meanwhile, the log-likelihood ratio of Model 3, gives a Chi-squared value of 4.25514, greater than the Chi-squared table at df 1, which is 3.841. Therefore, the hypothesis H₀ that the estimated model is not better than the basic model (Model 1.a), is unacceptable, and it can be concluded that Model 3 is statistically significant. The log-likelihood ratio test for Model 4 to Model 1a is 1.10626, which is smaller than the critical Chi-squared value according to the table for the degree of freedom 1. Therefore, the hypothesis H₀ that the estimated model is not better than the basic model (Model 1a), can be accepted. It can be concluded that Models 2 and 3 are not statistically significant. As a result, based on the goodness of fit criterion, only Model 1a and Model 3 are significant, while Models 2 and 4 are statistically insignificant.

For further analysis, Model 1a was used because it is better evaluated in terms of the measure of the goodness of fit and the significance of its parameter estimates.

4.4. Estimating Probability in Each Congestion Charging Corridor

The number of alternatives varies across the eight congestion charging corridors studied. This is because corridors 1, 2, 3, 4, 7, and 8 are not parallel to the toll road. Likewise, not all railway lines are parallel to the congestion charging corridors, i.e., corridors 4, 5, 6, and 8. Therefore, the alternative probability for each corridor is not the same.

Estimating of probability for each alternative is carried out by entering the initial setting values of the attributes, as depicted in Table 1, into the model. In this case, the initial setting of the congestion charging levy for cars is IDR16,000. On congestion-charging corridors where there are no toll roads, the probability of choosing a private car via congestion-charging (Cac) is around 49.05% and 53.48%. Around half of the car travelers were willing to pay the congestion levy and passed through congestion charging corridors. However, for corridors that are parallel to toll roads, the proportion of travelers who chose to pass through toll roads was around 36.06%. That is to say, if congestion charging is applied to corridors 5 and 6, then only 36.06% of travelers were willing to pay and used the congestion charging corridors.

Table 5. Probability of each alternative mode and route for each corridor.

Mode/ Route	Probability (Percent)
	Corridor 1	Corridor 2	Corridor 3	Corridor 4	Corridor 5	Corridor 6	Corridor 7	Corridor 8
Cac	49.05	49.05	49.05	53.48	36.06	36.06	49.05	53.48
Cat	No Toll				32.58	32.58	No Toll
Cal	22.88	22.88	22.88	24.94	16.82	16.82	22.88	24.94
Mal	4.69	4.69	4.69	5.11	3.44	3.44	4.69	5.11
Mcc	3.50	3.50	3.50	3.82	2.57	2.57	3.50	3.82
Tjc	9.40	9.40	9.40	10.25	6.91	6.91	9.40	10.25
Trc	8.29	8.29	8.29	No Train			8.29	No Train
Txc	0.93	0.93	0.93	1.01	0.68	0.68	0.93	1.01
Ojc	0.05	0.05	0.05	0.05	0.03	0.03	0.05	0.05
WFA	1.23	1.23	1.23	1.34	0.90	0.90	1.23	1.34
	100.00	100.00	100.00	100.00	100.00	100.00	100.00	100.00

depicts the probability of car travelers diverting into alternative roads (Cal) accounts for a high probability, that is 16.82% to 22.88%. Link-based congestion charging opened the possibility of car travelers diverting their routes to alternative non-congestion charging routes. In terms of shifting to public transportation, 17.69% of car travelers would choose mass transportation. Those who shifted to TransJakarta busways (Tjc) and trains (Trc) were 9.40% and 8.29%, respectively, far higher than those using taxis/online taxis and online motorcycle taxis/ojek, at 0.93% and 0.05%, respectively. Meanwhile, on corridors that are not parallel to the railway lines, travelers with private cars will not automatically move to the TransJakarta busway, but are proportionally distributed to other alternatives. Car commuters shift their mode to motorcycles when passing through congestion charging with a probability of 3.50% (Mcc) and 4.69% for choosing alternative roads (Mal). The probability of those who chose not to travel and carried out their activities anywhere (WFA, working from anywhere) was still greater than the probability of choosing online taxis/taxi and online motorcycle taxis/ojek, at 1.23%. These were travelers with discretionary job types, or types of work that do not require them to be present in the office to work, but who telework instead. Of course, the probability of choosing an alternative depends on the congestion charging levy rate. The probability that car travelers will choose to pay the congestion levy and pass through the congestion charging corridor will be higher if the congestion levy is cheaper, and vice versa.

As hypothesized, congestion charging greatly affects urban travel behavior in Jakarta. From a model of a private car, the tendency for route diversions is very high, higher than that for switching modes to public transport. Therefore, choosing a corridor-based congestion charging scheme, even though the main road network is relatively concentric, still allows for diversions to alternative roads, which can reduce the effectiveness of traffic control. Although the results may not exactly reflect the distribution of traffic all over road networks; however, the estimated probabilities indicate the conditions under which this is likely to happen. Traffic assignment will dynamically change over time, redistributing depending on the generalized costs. Traffic may be redistributed from alternative roads to congestion charging corridors if severe traffic congestion occurs on alternative roads until equilibrium conditions are reached.

Understanding the value of time for travelers is also important for further analysis of traffic assignments. The model estimated value of time for car travelers is IDR 15,540 per hour.

4.5. Marginal Effects

The direct marginal effects, the change in the probability of the alternative Pi to the change in the attribute of the alternative Xi, is obtained by the differentiation of Pi to Xik at the k attribute level of alternative i, ceteris paribus. Meanwhile, the cross marginal effect expresses changes as a result of unit changes in a competing alternative variable, where the variable is not an attribute of the alternative, ceteris paribus, it is formulated where bjk is an attribute of k, Pi is the probability of alternative i, and Pj is the probability of alternative j.

Table 6. Marginal effects of CC on Cac.

Alternatives		Marginal Effects CC on Cac
Private vehicles via congestion charging corridors	Cac	−0.0338
Private vehicles via alternative road	Cal	0.0172
Motorcycles via alternative roads	Mal	0.0036
Motorcycles via congestion charging corridors	Mcc	0.0026
TransJakarta bus	Tjc	0.0063
Trains (Commuterline, MRT, LRT)	Trc	0.0000
Online taxi/taxi via congestion charging corridors	Txc	0.0007
Online motorcycle taxis via congestion charging corridors	Ojc	0.0024
WFA	WFA	0.0009

shows the marginal effects of congestion charging (CC) on private vehicle choosing congestion corridors (Cac). In terms of direct marginal effects, it can be interpreted that there is a change in the probability of all travelers choosing private vehicles through the congestion charging (Cac) corridor of −0.0338 or decreasing by −3.38% for every IDR 1000 increase in the congestion charging levy rate (CC) on Cac, assuming the other attributes do not change, ceteris paribus.

The summation of probability increases for all alternatives, as shown in the table, corresponding to the marginal effects of Cac, i.e., 3.38%. Every IDR 1000 increase in the congestion charging levy rate will result a 2.08% increase in route diversions, a 0.94% increase in the shift to public transportation, a 0.26% increase in the change of mode to motorcycles passing through the CC corridor, and a 0.09% increase in those not traveling and telecommuting instead.

The marginal effect is an important estimate to predict the likely effects of levy rate changes. The marginal effects reflect the sensitivity changes regarding the probability of the alternatives.

5. Conclusions

The findings are not surprising, due to the fact that the link-based system is not a closed system. There are still alternative roads for car travelers to choose from. When the congestion charging levy is set at IDR 16,000, around a half of the car travelers will choose to travel by car, being willing to pay the levy and pass through congestion charging corridors. However, that is not the case when there is a toll road parallel to the congestion charging route, in which case, the probability of choosing congestion charging is lower. In the same way, when there is an increase in congestion charging rates, according to the marginal effect, travelers with private cars are more likely to choose alternative routes. It is estimated that the marginal effects of increasing IDR 1000, ceteris paribus, will be a reduction in the probability by 3.38%, and vice versa. Surprisingly, car travelers prefer to divert their routes rather than switching to public transport. Other findings show that the load factor as a proxy of the overcrowded rate of public transport and taxi fares are not significant attributes for car travelers.

These findings on corridor-basis congestion charging may provide insights for policy makers and regulators, as well as road planners, network designers, and traffic management officers. Policy makers and regulators should consider integrating transportation demand policy measures by simultaneously employing push and pull policies, especially in improving public transport services and parking policies. Due to the probability that a high proportion of car travelers on link-based congestion charging schemes would divert their routes, it is imperative for policy makers and regulators to consider area-based or cordon-based congestion charging rather than link-based methods. For local transport management officials, it is essential to anticipate the controlling of traffic on alternative roads, as well as to guarantee a high service level regarding mass public transportation.

Those who interested in this subject might continue the study of congestion charging in Jakarta, including the use of cordon- or area-based schemes. These studies may include the sampling of car travelers passing through other alternative routes to account for the probability of them choosing congestion charging schemes.