Estimating Crowding Costs in Public Transport€¦ · Estimating Crowding Costs in Public Transport Luke Haywood ∗Martin Koning † December 2012 Work in progress Abstract Preferences

Estimating Crowding Costsin Public Transport

Luke Haywood ∗Martin Koning †

December 2012Work in progress

Abstract

Preferences for transport activities are often considered only interms of time and money. Whilst congestion in automobile trafficincreases costs by raising trip durations, the same is less obvious inpublic transport (PT), especially rail-based. This has lead many eco-nomic analyses to conclude that there exists a free lunch by reducingthe attractiveness of automobile transport (most efficiently, via roadpricing) at no or little cost for public transport users.

This article argues that congestion in public transport - crowding- is also costly. We estimate the degree to which users value comfortin terms of lower density of public transport users. Using a contin-gent valuation method we describe marginal willingness to pay overdifferent parts of the distribution of in-vehicle crowding and considermoderating factors. The data used originates from the Parisian metro,a PT system subject to considerable, but variable, congestion that isnot at a point of saturation.

We apply our results to the cost-benefit analysis of a recent invest-ment in public transport in Paris and consider broader implications fortransport policy.

Keywords: Travel comfort, crowding costs, contingent valuation method,time multipliers, Paris subway

∗DIW Berlin, [email protected].†IFSTTAR-SPLOTT, [email protected].

1

Crowding in Public Transport

1 Introduction

From an economic perspective, good urban transport policy makes efficientuse of the scarce ressources time and space, subject to public budget con-straints. It has become to be accepted that past policies have led, in mostwestern countries, to inefficiently high automobile usage that has various neg-ative effects (Newman and Kenworthy (1989), Parry et al. (2007)). Ratherthan increase costs of mobility overall in order to reduce demand for trans-port, transport policies have typically focused on modal shift strategies: in-creasing the patronage of public transport systems, especially with the useof congestion or environmental tolls for cars or subsidies for public transport(Lindsey (2006), Tsekeris and Voss (2009)1). Nevertheless, not always weresuch policies accompanied by increased PT supply. Where supply elasticityof PT is low - as is the case for most rail-based PT systems - density ofpassangers in PT systems will consequently increase.

The traditional view assumes that transport users’ utility depends ontime and money only (Small and Verhoef (2007)). Under this perspective,as long as the saturation point of PT is not reached (Kraus and Yoshida(2002)), increasing PT usage should almost always lead to a societal gain. Infact, with more individuals sharing the fixed costs of PT provision (Tabuchi(1993)), there will be economies of scale provide higher frequency of vehiclesin the PT network (Mohring (1972), Proost and Dender (2008)) and reducedroad congestion decreases costs of automobile transits, as environmental re-lated externalities (Parry et al. (2007), Malibac et al. (2008)). However,this ignores comfort costs of PT congestion occurring well before the net-work reaches a bottleneck. Considering that the individuals care about theamount of space in vehicles, i.e. the inverse of passanger density, crowdedtravel conditions may decrease their utilities even if travel time is kept con-stant. Therefore, there is no free lunch by decreasing the attractiveness ofautomobile transport without improving the supply of PT.

This article examines the utility costs of PT congestion using contingentvaluation methodology (CVM, see Haab and McConnel (2003) or Mitchelland Carson (1989)) on a survey collected late 2010 in the Paris subway2. We

1Alternative non-motorised modes of transport such as bicycles, walking etc. have alsobeen encouraged but have rarely been the main focus of the discussion.

2This study was carried out without private or public funding. Survey design and datacollection were made possible thanks to many volunteers. Among the main contributors,we would like to thank Mélanie Babès for survey design and data collection, Cécile Peillon

1 Luke Haywood & Martin Koning


use declared preferences on hypothetical states of nature in order to estimatethe marginal willingness to pay for less crowded travelling conditions, whichwe find to be a first-order urban externality.

While numerous academic papers have been interested in estimating roadcongestion costs (Small and Verhoef (2007)), academic work on crowding ofPT systems is rare. Studies on urban transport policies generally attribute aninsignificant value to the crowding effect3. This asymetry between road andPT congestion contradicts the theoretical formulation of PT usage cost ini-tiated by Kraus (1991), and complexified thereafter (de Palma et al. (2011),Jara-Diaz and Gschwender (2003)). Empirical evidence on PT crowding hasmainly been assessed in technical (and unpublished) studies conducted byBritish and Australian consulting firms (Li and Hensher (2011), Wardmanand Whelan (2011)).

The Paris area is a good case in point to investigate the PT crowdingcosts. Over the last ten years, the city centre has seen a reallocation ofroad space from cars to cleaner transport modes (buses, streetcars, bikes,see Prud’homme and Kopp (2008)).

As a consequence of this popular policy of quantity regulation, as op-posed to the price regulation put forward in London or Stockholm, averagecar speeds in Paris have decreased by 10% between 2000 and 2007 (Obser-vatoire de la mobilité de la ville de Paris (2007)). Following the rise of travelcosts for cars, the individual motorised traffic with Paris as destination ororigin has been reduced by 24% (in passanger-km, pkm, see Kopp (2011)).Whilst usage of motorbikes and bicycles has increased, the majority of themodal switch seems to have occured towards the PT network.

As illustrated in table (1), PT patronage in the Paris subway increasedby 22% between 2000 and 20094. However, subway supply could not keepup with the increased demand. Note that there is no indication that theParis subway is at a bottleneck5, where demand negatively affects regular-ity. Rather, the main effect appears to have been a reduction in comfort:

for the design of the showcard, Jérémy Boccanfuso and Cindy Balmat. M. Locknar fromthe subway operator was also of assistance.

3For example, Proost and Dender (2008), de Palma and Lindsey (2006) or de Lapparent(2005) do not consider crowding costs in their models. Parry and Small (2009) integratethis dimension but with an insignificant value.

4In 2009, the subway system (including the regional trains) accounted for 60% of trans-port with Paris as origin or destination.

5Note that this refers only to the subway system in the centre of Paris (métro), notthe regional system (RER).



Table 1: Evolution of the PT newtork’s usage in the Paris area

Demand Supply Density Regularity(M pass-km) (M train-km) (pass/m2) (%)

Paris subway2000 6,011 42 1.0 982009 7,353 48 1.1 98

Source: Syndicat des Transports de la Région Ile-de-France (2009) and Observatoire de la mobilité de la ville deParis (2000). For the density indicator we assume that a train has 557 places, 139 m2. The regularity indicatoris defined as the share of travellers who wait less than 3 minutes during the peak periods.

in-vehicle passenger density grew by 10% between 2000 and 2009, whilst theregularity indicator remained constant. Thus we restrict our analysis here tothe comfort costs of PT crowding. Combined with growing road congestion(Prud’homme and Kopp (2008)), the deterioration of PT travel conditionshas been quoted as an important factor affecting job quality in the greaterParis region (Technologia (2010), ORSTIF (2010)). Commuters’ complaintsalso figured prominently in municipal and regional elections in 2008 and 2010.

The rest of the paper is organized as follows. Section (2) presents thetheoretical framework used to value PT crowding costs, based on the methodof contingent valuation and reviews previous findings in this area. Section(3) focuses on the survey collected on the platforms of lines 1 and 4 of theParis subway. Section (4) presents the empirical strategy and results, show-ing how increasing density causes crowding costs to rise. Using the estimatedvalues of PT crowding costs, section (5) highlights policy implications. Weapply our findings for an economic appraisal of an increase in the supplyof a section of the Parisian subway by using driverless trains. Section (6)concludes.

2 Valuing Crowding Costs using Contingent Valu-ation

2.1 In vehicle travel time and comfort

In order to assess the welfare costs of PT crowding, we write the utilityof PT user i at congestion level j as Ui,j , a function of in-vehicle traveltime ti, monetary expenditures pi and comfort cj . The two first arguments,money and time, are standard. We propose to integrate comfort as a factor



moderating the influence of trip duration. This is in line with the idea ofcomfort as a factor moderating flow utility, not a fixed utility cost. Individualcharacteristics Xi may also influence utility.

Ui,j = α+ θ pi +

J∑j=0

βj cj ti + δ Xi + εi (1)

In the simplest case, in-vehicle crowding is just characterized by twostates of nature (j = 0 for peak periods in which transport users must standand j = 1 for off-peak periods in which PT users are seated), the welfaredifference due to travel comfort is linked to the marginal disutilities of invehicle time (βj < 0). In fact:

Ui,1 − Ui,0 = (β1 − β0) ti > 0 (2)⇒ 0 > β1 > β0 (3)

This formulation is consistent with a wide range of reasons for preferringless congested PT. Data on satisfaction in transport is lower when individu-als lack space in vehicles (Cantwell et al. (2009)) and low density is quoted asone of the main qualitative attributes desired by PT users (Litman (2008)).Crowding on PT networks reduces the probability that passangers find aseat in carriages. Crowding prevents individuals from using time in trans-port for other activities (polychronic use of time) and may induce securityfears, increase noise levels and reduce hygiene. All these effects increase per-sonal stress, with effects found on mortality and productivity losses at theworkplace (Wener et al. (2005), Evans and Wener (2007), Cox et al. (2006)).These costs are not fixed per trip but rather they continue throughout thetrip - thus they modify the cost of time: each minute spent in j = 0 is morepainful for travellers than the same minute consumed in j = 16.

2.2 Finding the equivalent variation

Comfortable PT conditions constitute a non-market good which is not di-rectly priced, especially since public transport is subsidized. To recover thewelfare cost of PT crowding, two strategies can be taken: the first is basedon observed behaviors (revealed preferences7) whilst the second uses stated

6We abstract from the fact that users’ perceptions of trip duration may also be modifiedby passenger density, see Li (2003).

7Among them, the hedonic price and transport costs methods, see Haab and McConnel(2003).



preferences in response to hypothetical scenarios. The CVM belongs to thelatter approach (Haab and McConnel (2003), Mitchell and Carson (1989)).The basic idea is to find the equivalent variation in monetary terms whichmakes individuals indifferent between states with different levels of the non-market good (Ui,1 = Ui,0). CVM has previously been used in the valuationof transport externalities and to evaluate the subjective cost of travel time(Wardman (2004), Wardman (2001)). Interviewers propose surveyed trans-port users monetary bids to approximate the equivalent variation, i.e. thefinancial equivalent that will render individuals indifferent between differentlevels of PT service quality. For reasons outlined below (see section (3.1))our survey proposes scenarios in terms of longer commuting time (ratherthan financial cost) in exchange for less congested PT.

Starting from the indifference condition, the proposed trade-off betweentravel time and comfort then allows us to study two types of equivalentvariation. First, willingness to pay (WTP ) is the additional travel time inthe less congested state which would leave individuals indifferent with themore congested state.

Ui,1 = Ui,0

β0 ti = β1 (ti +WTP ) (4)

WTP = ti(β0 − β1)

β1(5)

The equivalent variation can also be expressed as a change in the marginaldisutility of travel time βj , a time multiplier Tm (see Wardman and Whelan(2011)):

Ui,1 = Ui,0 ⇒ β0 ti = β1 ti Tm (6)

Tm =β0β1

> 1 (7)

The time multiplier (Tm) is the marginal rate of substitution of traveltime between peak and off-peak comfort levels8. In fact, it corresponds tothe ratio of the marginal disutilities between congested and non-congestedstates.

8In the empirical part we distinguish several levels of congestion, going beyond thebinary rush-hour phenomenon.



2.3 Crowding costs in the literature

Other studies have used contingent valuation to study PT crowding costs,however work has mainly focussed on the UK and Australia and not beenpublished. Surveys by Li and Hensher (2011) and Wardman and Whelan(2011) have made findings more accessible for economists. According tothe meta-analysis of Wardman and Whelan (2011), conducted on 17 Britishstudies, the average Tm ranges from 1.60 to 2.00 for load factors comprisedbetween 100% and 200%9. Concerning the Australian PT network (Li andHensher (2011), Douglas and Karpouzis (2006)), the marginal rates of sub-stitution is, on the average, of 1.34-2.00. For the monetary equivalents, Liand Hensher (2011) proposed a WTP equal to 0.43-2.43 AUS dollars/trip,i.e. a majoration of time opportunity cost by 0.97-11.27 AUS dollars/hour.PT crowding costs are also reported to be influenced by in-vehicle traveltime and trip motives (with higher valuations for non-commuting).

The Boiteux report (Ministère de l’Equipement (2005), CommissariatGénéral du Plan (2001)) provides the reference values used for cost-benefitanalysis of transport policies in France. Without empirical foundation, itadvises to increase the opportunity cost of travel duration by a factor of 1.5when travellers cannot be seated during their trip. The only other study weare aware of for France, Debrincat et al. (2006), considers the welfare im-pact of trains’ reliability in the Greater Paris region. Their survey combineddifferent wating times, levels of information for users and comfort situations(seat, stand, stand in crowded conditions). Debrincat et al. (2006) find thatthe discomfort generated by standing during the trip corresponds to aWTPof 5-20 minutes, depending on the trains’ load factor. This result is similarto a Tm ranging from 1.30-1.9010.

Using an earlier and simpler survey design, Haywood and Koning (2012)consider crowding costs in the Parisian subway. They find crowding costsare of e 1.01-1.46/trip, or around twice the average fare currently paid bythe Parisian PT network’s users.

9The load factor is defined as the ratio of transport users over seating in public trans-port. As transport design is rather different, we prefer to focus on user density by space(not seats).

10Using these values, Leurent and Liu (2009) estimate a 15% increase in travel timefor individuals changing their route choices, accross the Parisian and the regional PTnetworks, in order to benefit from more reliable and comfortable trips.



3 Survey Design and Data

Data were collected between November 2010 and January 2011 on Parisiansubway lines 1 and 4. Interviews were carried out on the platforms of 11representative stations11.

Crossing Paris East-West, line 1 is the most frequented service of theParis network (with 750,000 users per day). In fact, it connects the PTusers to most of the strategic centers (economic, tourism) of Paris. CrossingParis North-South, line 4 faces a smaller patronage than line 1 (670,000 usersper day). It is nevertheless the second most frequented line of Paris subwaynetwork. Taken jointly, the two lines give access to the most important res-idential, touristic and business amenities of Paris, but also include some ofthe poorest neighbourhoods of the city, generating a diverse sample of 1,000PT users. Data were collected during extended morning and evening rushhours (50% between 7.30-10.00 and 50% between 17.00-19.30). Integratingthe evening peaks may be interesting: individuals asked during their morn-ing trips may be more prone to reject the trade off between travel time andcomfort because of the induced delays and the existence of scheduling costs(Arnott et al. (1990), de Palma et al. (2011)).

3.1 Temporal congestion reduction scenarios

To describe the level of passanger density in public transport, we use show-cards. First, users were asked to determine their expectation of passengerdensity during peaks (corresponding to 0, 1, 2, 2.5, 3, 4 or 6 passengersper square metre see figure (1)), providing a reference point with respect towhich the hypothetical change can be evaluated.

A hypothetical density reduction in density from this reference level wasthen proposed (the density reduction was drawn from a uniform distribu-tion). We then randomly proposed a first temporal bid (3, 6, 9, 12, 15, 18minutes)12.

11Line 1, morning peak: Gare de Lyon, Hôtel de Ville and Champs-Elysées; Line 4,morning peak: Denfert-Rochereau, Montparnasse and Odéon; Line 1, evening peak: Es-planade de la Défense, Argentine, Georges 5 ; Line 4, evening peak: Les Halles, Odéonand Saint-Sulpice.

12Whilst open questions or payment cards could provide more precise values, the binarychoice with discrete choices is said to better mimic individuals’ everyday decisions(Haaband McConnel (2003), Mitchell and Carson (1989)).



The second bid was then increased or decreased by 25% for individualswho accepted the first bid (double bounded model).

In the context of PT comfort valuation, Wardman and Whelan (2011)note the advantages of not propose monetary bids but rather phrase bids intemporal terms: users are asked how much they would increase their traveltime to compensate for differences in comfort levels. This valuation strategypresents at two advantages:

1. First, it reduces the risk that individuals freerise on others’ contri-butions by under or overreporting (strategic bias). In our case thisis particularly relevant as monetary costs are highly subsidised bothpublicly and by employers.

2. It also makes it easier for individuals to envisage the proposed scenario(reducing the so-called hypothetical bias): travellers confronted withovercrowded vehicles sometimes let a train pass before taking a spaceon the next one 13.

3.2 Double-bounded bid model

We use two rounds of bids in order to reduce the range of possible valuesproposed in the first round, with increasing or decreasing sequences depend-ing on the first answer. Using two rounds of bids has been suggested toincrease precision of the estimates of β∗j,k("double-bounded" models, Haaband McConnel (2003)). As studies using contingent valuation have becomestandard in the field of pricing non-market commodities, so have method-ological contributions highlighting certain psychological factors that may in-fluence individuals’ responses. Thus, it might be the case in double-boundedmodels that the second decision depends on the first one and that estimatesfrom the second round are not necessarly better in presence of "first bidbiases"(Herriges and Shogre (1996), Haab and McConnel (2003), Flachaireand Hollard (2007)). To check for these inconsistencies, we can use a bivari-ate probit model allowing for a correlation between the error terms of bothanswers and correcting the estimates for this effect14.

13Commuters may equally adjust their departure/arrival times in order to avoid con-gested trains (de Palma et al. (2011)), or adjust their routes accordingly (Leurent and Liu(2009)).

14The analysis of "first bid biases" generally relies on the direct estimation of theWTP .The different biases ("anchor, shift and framing") linked to the existence of a first offer



Figure 1: Showcard used during the field survey

Finally, we use information on the objective trip conditions. The PToperator only provided us with information on average density for selectedsections of lines 1 and 4 for 2008. In addition of being too old compared tothe field survey (2010), these data are for entire vehicles whilst we are mainlyinterested in the carriages’ central area as described on the showcard. There-fore we manually counted passenger density in January and February 2011 inover 80 trains. We also measured travel times necessary to connect differentpairs of stations on lines 1 and 4. These statistics will help us to reconstructprecisely individuals’ objective trip characteristics.

can easily enter the WTP specification (see Flachaire and Hollard (2007)). However, notethat assuming that Prob(Accept) = Prob(UP

i,j > UAi,j) is equivalent to Prob(Accept) =

Prob(WTPi,j > bi).



3.3 Descriptive statistics

The response rate of PT users for the core component of the survey wasaround 60% 15. Complete data were available for 688 individuals.

Table 2: Individual characteristics

Total Line 1 Line 4 Morning EveningAge (years) 35 36 34 36 35Female (%) 50% 51% 49% 50% 50%Central Paris (%) 57% 53% 62% 56% 58%Greater Paris area (%) 94% 94% 95% 92% 96%Car ownership (%) 38% 42% 33% 38% 37%Income (e/month) 2,245 2,790 2,100 2,570 2,320Time opportunity cost (e/min) 0.20 0.23 0.17 0.21 0.19

Table (2) shows that the average interviewee is aged 35 years, with equalnumbers of women and men. 57% of the individuals live in the centre ofParis (62% of line 4 users and 53% in line 1), 94% in the greater Paris area.Only 38% of our sample owns a car. Average monthly income is e 2,245, withwealthier individuals in line 1 (e 2,790)16 Using this information, it was pos-sible to calculate an individualised opportunity cost of time17 with a meanvalue of e 0.20 per minute in 2010 (e 12/h), close to the value implied by theBoiteux report (e 10.7/h in 2010, see Commissariat Général du Plan (2001)).

Table (3) shows that most trips are between home and the workplace(69% overall, higher in line 1 - 78% - and in the morning - 76%). Mosttrips were taken daily (64%) which should help individuals to evaluate sce-narios of congestion, reported door-to-door travel time was on average 45minutes, in-vehicle trip duration (10 minutes, 11.5 in line 1 and 7.9 in line4) on average only repesents 28% of total travel duration18. Once trans-

15Interviewers were instructed to report estimated values for age and gender of individ-uals refusing to take part in the survey. Older individuals tend to participate less often,with no obvious gender differentials.

16In order to entice individuals to truthfully reveal their income in a public space, weused a card representing 8 income categories, each with a different colour.

17Following D4E (2004), we calculate the time opportunity cost (wi) from individualincomes (yi) by considering 135 worked hours per month: wi = (2/3) ∗ yi/135.

18The time spent in lines 1 or 4 allow to travel 7.2 and 6.4 inter-stations respectively.The average inter-station distance strongly differs between lines 1 and 4 (0.7 km/station



Table 3: Descriptive statistics of trips

Total Line 1 Line 4 Morning EveningHome-Workplace / Workplace-Home(%) 69% 78% 62% 76% 64%Line daily usage (%) 64% 66% 62% 63% 64%Door-to-door travel time (minutes) 46 47 45 51 41Number of inter-stations 6.8 7.2 6.4 6.7 6.9In-vehicle travel time (minutes) 9.7 11.5 7.9 9.4 10.0Distance travelled (kilometers) 3.8 5.0 2.6 3.7 3.9

formed in a monetary equivalent, the in-vehicle time budget corresponds to1.9 eu/trip19. This average amount equals, at least, three times the singlefare paid by Parisian PT users. Because of higher time opportunity costand travel time, the time component is larger for line 1 (e 2.6/trip versuse 1.34/trip on line 4).

Table 4: Expected density

Expected density (pass/m2) 0 1 2 2.5 3 4 6Total 0.0% 2.3% 16.7% 27.8% 24.3% 20.2% 8.7%Line 1 0.0% 1.2% 8.7% 20.8% 26.6% 28.0% 14.7%Line 4 0.0% 3.5% 24.8% 34.8% 21.9% 12.3% 2.6%Morning 0.0% 3.2% 22.0% 29.2% 22.0% 17.3% 6.4%Evening 0.0% 1.5% 11.4% 26.3% 26.6% 23.1% 11.1%

Table (4) presents the distribution of the expected density in lines 1 and4 - this is the density that users expect to face in the train they are aboutto take. Recall this information corresponds to the reference point for laterscenarios of reduced congestion. Only 2% think they will find an empty seat(the threshold being 1 pass/m2 on the showcard), with no single person ex-pecting an empty train. At the other extreme, less than 10% of the sampleexpect to face the worst travel conditions (6 pass/m2). This proportion isfive times higher for line 1 (15%) than for line 4 (3%). As illustrated in table(5), average expected density is 3.1 pass/m2, with important variations be-tween lines 1 and 4 (3.5 pass/m2 versus 2.7 pass/m2) and between morningsand evenings (2.9 pass/m2 versus 3.3 pass/m2). These figures are highly

and 0.4 km/station).19Concerning door-to-door travel time, we find e 9.2/trip.



correlated with the objective passanger density faced, in average, by usersduring their trips: 2.4 pass/m2 considering the count data; 1.7 pass/m2 withthe 2008 agregated data from the PT operator.

Table 5: Density indicators

Total Line 1 Line 4 Morning EveningExpected density (pass/m2) 3.1 3.5 2.7 2.9 3.3Count density (pass/m2) 2.4 3.2 1.5 2.4 2.3Ratp density (pass/m2) 1.7 2.2 1.3 1.6 1.9Count density at departure (pass/m2) 2.2 2.7 1.7 2.0 2.5Ratp density at departure (pass/m2) 1.8 2.1 1.4 1.5 2.0Count density at arrival (pass/m2) 2.1 2.9 1.5 2.2 2.2Ratp density at arrival (pass/m2) 1.4 1.9 1.0 1.3 1.6

Exploratory estimates conducted with an ordered logit (see table (14) inthe appendix), confirm that reference points are significantly influenced byobjective levels of density (manual count data and official data). In line withthis information, the expected density appears to be higher for line 1 usersand for individuals interviewed during evening peaks. The only individualcharacteristics affecting perception of density is monthly income and door-to-door travel time 20.

3.4 Hypothetical scenarios

Before presenting our empirical strategy, we provide some descriptive statis-tics on the hypothetical scenarios presented to travellers. We propose ran-dom bids and random reductions in passanger density (see the distributionsin the appendix). On average, passangers are offered a reduction in densityof 1.8 pass/m2, corresponding to 60% of baseline density. The average valueof the first bid proposed to interviewees amounts to 8.7 minutes. Using thetime opportunity cost, the temporal bid is equivalent to e 1.8 per trip, closeto the valuation of current in vehicle travel time.

20The in vehicle travel time does not present any significant effect on the expecteddensity. This result is useful for the empirical study of declared preferences since it meansthat cj and ti in equation (1) are orthogonal.



Table 6: Descriptive statistics on hypothetical scenarios (1)

Total Line 1 Line 4 Morning EveningExpected density (pass/m2) 3.1 3.5 2.7 2.9 3.3Hypothetical density (pass/m2) 1.3 1.5 1.1 1.1 1.4Bid 1 (minutes) 8.7 8.5 8.9 8.9 8.5Bid 1 (e) 1.8 2.0 1.5 1.9 1.6Answer 1 positive (%) 42% 49% 35% 37% 47%Bid 2 (minutes) 8.0 8.1 7.9 7.9 8.1Bid 2 (e) 1.6 1.9 1.4 1.7 1.5Answer 2 positive (%) 42% 44% 40% 40% 44%

The acceptance rate for the first bid is 42% (49% in line 1 and 35% inline 4; 47% in the evening and 37% in the morning rush hour). These resultsare consistent with the data on objective congestion, but also with the ideathat scheduling costs may be higher in the morning, reducing the ability ofworkers to increase their trip duration at this margin. Because less than50% of the sample accepted the first hypothetical scenario, the second bid isslightly lower than the first (8 minutes). We observe that the rate of positiveanswers is stable accross rounds (42%)21.

4 Empirical Study of the Stated Preferences

4.1 Econometric strategy

Our econometric strategy focuses on the parameters of the utility function,which also allows us to compute the time multipliers22. Following the linearspecification proposed in section (2), we discretize transport time ti and levelof comfort ckj such that individuals i have a choice over situations k (k = Afor actual situation and k = P for the hypothetical situation):

Uki,j = αk + θ pi +J∑j=0

βkj ckj (ti + bki ) + δ Xi + εki (8)

21Appendix (7.1) considers an alternative decomposition of descriptive statistics bysequences of responses to bids.

22An alternative would be to estimate the marginal willingness to pay for all pairs ofreference and hypothetical density pairs on the basis of equation (4). However, samplesizes for pairs would be too small.



where j indicates the levels of comfort given by showcards (the referencepoint when k = A or the hypothetical level of comfort when k = P ), bi isthe bid that varies across individuals and which decreases or increases ac-cording to the reaction to the first bid.

This formulation implies that if an individual accepts a bid, i.e. prefersUPi over UAi , we have that:

Prob(Accept) = Prob(UPi,j > UAi,j) (9)

= Φ

α∗ +J∑j=0

β∗j,k(TPi,j − TAi,j

) (10)

where T ki,j ≡ (ti + bki ), ρ the variance of the differenced error term ε∗ =εj,P−εj,A and Φ the cumulative density function of ε∗. We normalize the dif-ferenced parameter α∗ = αP−αA

ρ and the time marginal disutility β∗j,k =βj,kρ .

In this framework, the value of comfort in situation j is described bythe coefficient β∗j,k. The marginal rate of substitution between one minuteof transport with comfort level j and one minute with the reference comfortlevel (j = 0) is then given by the ratio of any two coefficients β∗j,k and β∗0 , k.This ratio corresponds to the Tm presented in section (2).

4.2 Results

Table (7) presents the effects of different levels of passenger density on thedisutility of trip duration. All levels of passenger density greater than 1 pas-senger per square metre significantly decrease individual utility (at the 1%level). This suggests that whilst PT users prefer having some people aroundthem rather than facing empty vehicles, the utility cost of the travel timeincreases in crowded situations. Furthermore, users’ answers to the first andsecond bids are not independent: the correlation of error terms (ρ) is signif-icantly different from zero thus we focus on the bivariate probit results.

Are answers from the two rounds constant with each other? The esti-mated disutilities estimated from the second bids lie within the confidenceintervals of those obtained from the first round bids (see figure (3)). In fact,confidence intervals are always connected, suggesting that the estimates are



Table 7: Bivariate Probit estimates

Biv. probit Biv. probit Biv. probit Biv. probitAnswer 1 Answer 2 Answer 1 Answer 2

Time marginal disutility at:0 pass/m2 -0.118 -0.140 -0.116 -0.139

(0.013) (0.014) (0.014) (0.014)1 pass/m2 -0.112 -0.150 -0.111 -0.150

(0.013) (0.015) (0.014) (0.015)2 pass/m2 -0.125 -0.154 -0.126 -0.155

(0.013) (0.015) (0.014) (0.015)2.5 pass/m2 -0.139 -0.171 -0.138 -0.170

(0.014) (0.016) (0.015) (0.016)3 pass/m2 -0.155 -0.180 -0.151 -0.179

(0.017) (0.017) (0.017) (0.017)4 pass/m2 -0.173 -0.200 -0.165 -0.199

(0.019) (0.020) (0.020) (0.020)6 pass/m2 -0.191 -0.226 -0.179 -0.224

(0.022) (0.022) (0.022) (0.023)Constant 0.541 0.728 0.724 0.808

(0.115) (0.115) (0.205) (0.192)Controls No No Yes Yes

ρ 0.613 0.622(0.062) (0.062)

Log pseudo -787.8 -770.1Observations 688 688 688 688



Figure 2: Travel time marginal disutilities



close over the range of crowding costs23. Whilst this result calls for futurework, we suggest that this consistency arises from the degree of habits to thehypothetical scenarios: individuals are more prone to imagine longer, butmore comfortable trips, than oil spills near their place of residence.

Figure 3: Confidence intervals of marginal disutilities

The restriction that congestion costs do not depend on individual indi-vidual characteristics (δ = δA = δP in equation (12)) is testable: We canintroduce interaction terms of individual characteristics and trip durationand test their significance. Assuming that the (dummy) variable Zi affects

23As noted in the presentation of our bidding design (section (3.2)), the literature inenvironmental economics has been concerned with “first bid biases”. Our results indicatethat whilst such a bias may exist, it does not significantly influence estimated values of βhere.



the individual taste for crowded travel conditions, we can write:

Prob(Accept) = Prob(UPi,j > UAi,j) (11)

= Φ

α∗ +

J∑j=0

β∗j,k(TPi,j − TAi,j

)+ λ∗Zi +

J∑j=0

γ∗j,k(TPi,j − TAi,j

)Zi

(12)

where γ∗ = γP−γAρ and λ∗ = λP−λA

ρ . In that framework, the travel timemarginal disutility at crowded level j is equal to β∗j,k + γ∗j,k for individualspresenting the characteristic Zi. The γ∗j,k parameter may be considered as asensitivity premium.

To test this restriction we thus introduced interactions with various vari-ables of individual characteristics (age, gender, reason for trip, place of resi-dency, line, time of day, car ownership, line daily usage, income, door-to-doortravel time).

We find significant effects, during both rounds, only for the time of daydummy (see table (18) in the appendix) congestion appears to be more costlyduring morning peaks than during evening peaks. This may explain whytravellers are more prone to reject the hypothetical scenarios. Figure (4)contrasts the marginal disutility of crowding in the morning and eveningpeaks.

Table 8: Observed and predicted probabilities

Yes-Yes Yes-No No-Yes No-NoObserved (%) 25 17 17 41Biprobit (%) 30 13 13 44Biprobit and controls (%) 30 12 14 44Biprobit and morning (%) 30 13 13 44

To conclude this econometric study of the stated preferences, we cancompare the predicted probabilities of answering to the hypothetical sce-narios with those observed in the sample. As indicated in table (8), thedifferent tested models do not succeed in predicting perfectly the outcomes.Thus, they tend to over-estimate the probabilities of "Yes-Yes" and "No-No" answers, whilst under-estimating the intermediate sequences ("Yes-No"



Figure 4: Marginal disutility of trip duration during morning rush-hour tran-sit



and "No-Yes"). However, the gap between the observed and the predictedprobabilities is not that large (3-5%). Moreover, the different specificationsdo not radically differ in predicting the answers’ sequences.

4.3 The "time multipliers"

With these results, we can now calculate the "time multpliers" depending onthe level of comfort. In order to compute the Tm, one first has to choose areference level of congestion. We could use the empty subway as benchmark(with j = 0 pass/m2). However, calculating PT crowding costs with respectto empty subways appears inconsistent with the social utility of infrastruc-ture24. Therefore we use the 1 pass/m2 situation, with 2 seats (on 8) stillavailable on the showcard 25.

Table 9: Time multipliers

Probit Probit Biprobit BiprobitDensity Tm1 Tm2 Tm1 Tm20 pass/m2 1.05 0.91 1.05 0.931 pass/m2 1.00 1.00 1.00 1.002 pass/m2 1.12 1.06 1.12 1.032.5 pass/m2 1.24 1.18 1.24 1.143 pass/m2 1.38 1.24 1.38 1.204 pass/m2 1.54 1.40 1.54 1.336 pass/m2 1.69 1.66 1.71 1.51

In table (9), we find that the value of Tm ranges from 1.12 (for crowdingof 2 pass/m2) to 1.69 (6 pass/m2) when using the first answers. It meansthat travellers would be indifferent between spending 1 minute in worst travelconditions and seating 1.7 minute. Considering the results from the secondbids, biprobit estimates provide lower crowding valuations than those ob-tained with a simple probit: the maximum Tm becomes 1.51 for 6 pass/m2

and the minimum Tm 1.03 at 2 pass/m2. In spite of these important dif-ferences, as confirmed on Figure (5), it should be clear that the Tm is anincreasing function of the in vehicle passanger density

We can use the model estimated with the interaction terms to look at how24The same is true for road congestion, where analyses often calculate congestion costs

starting from an empty road.25Note also that the estimates from the first round suggest that PT users prefer this

situation over the situation with no other passengers.



Figure 5: Time multipliers



the value of Tm change between the morning and evening peaks (see table(19) in the appendix). Whilst the valuations seem to be robust when focusingon the evening peaks’ trips (the maximum Tm are of 1.78-1.64), the same isless obvious for the morning rush hours. Because the interaction term is notsignificant for the 6 pass/m2 situation, the Tm thus drops to 1.13-1.08, closeto the value associated with the 2 pass/m2 situation. The most interestingresult from this model is probably linked to the marginal rate of substitutionbetween one minute during morning and evening peaks. The latter rangesfrom 1.41 to 1.92 when using the first answers. This morning-peak-remiummay be seen as a proxy for the scheduling costs linked to late arrivals atwork and earlier departures from home (Arnott et al. (1990); de Palma et al.(2011)).

These overall Tm valuations appear to be consistent with the literaturepresented in section (2), even if the maximum values are somewhat lowerthan those of Debrincat et al. (2006) or Whelan and Crockett (2009). It isalso noticeable that the rule of thumb used in France to take into accountpublic transport congestion is remarkably close to these results (Commis-sariat Général du Plan (2001), Ministère de l’Equipement (2005)). Aboveall, these results stress that ignoring the crowding effect during the peakperiods may significantly alter the analyses of PT usage costs.

An influential way of presenting congestion costs on roads (used to es-timate speed-flow density relationships) expresses the time multiplier Tmas a function of in-vehicle passanger density. Ideally, this information couldbe used to design pricing and supply schedules in a public transport network.

In line with Whelan and Crockett (2009), we test a simple linear form.We also normalize the data to have the point (cj=1 pass/m2, Tm=1) infigure () as origin. Using the values from the first round (without controls):

Tm(cj) = 1 + 0.14 cj (13)

for cj > 1pass/m2 (R2 = 92.1)

5 Policy Implications

5.1 The Generalized Cost of Public Transport

We now add crowding costs tot he traditional presentation of generalizedpublic transport costs (GC(cj)) in terms of money and time. Defining w as



the opportunity cost of trip duration, we apply the time multipliers Tm(cj)taking into account crowindg costs and in-vehicle travel time (ti),

GC(cj) = pi + w ti Tm(cj). (14)

The figures in table (10) have been calculated with the average values ofin-vehicle travel times, the expected density and the time opportunity cost.We also assumed that pi = 0.5e/trip which approximately corresponds tothe average private cost incurred by passengers taking into account pub-lic and employer subsidisation. For the Tm(cj), we rely on equation (13).According to these results, the generalized cost of Paris subway usage dur-ing peak periods rises to e 3.28/trip compared to e 2.44/trip when seatingin trains is available. Neglecting PT crowding costs would lead to a 35%under-estimation of welfare costs of transport activities during rush hours.

Table 10: Generalized costs, time multipliers and willingness to pay

Total Line 1 Line 4 Morning EveningGC(peaks) (e/pass) 3.28 4.44 2.35 3.28 3.28GC(seat) (e/pass) 2.44 3.14 1.84 2.47 2.40Tm 1.43 1.49 1.38 1.40 1.46WTP (min/pass) 4.2 5.6 3.0 3.8 4.6WTP (e/pass) 0.84 1.28 0.51 0.80 0.87

Whilst the GC(cj) strongly differs between lines 1 and 4 (because oflonger trips’ duration and a higher time opportunity cost on the former), wedo not observe any difference between morning and evening peaks. Moreover,the average Tm ranges from 1.38 (on line 4) to 1.49 (on line 1), with a meanvalue of 1.43. This corresponds to an increase in time value by e 0.09/min,i.e. e 5.16/h.

One way of estimate crowding costs applies Tm to the in-vehicle traveltime spent in the congested state (Jara-Diaz and Gschwender (2003), Feifei(2011), see section (5)). Monetary equivalents of crowding costs (per trip orper minute) can be imputed using time valuations.

WTP = ti (Tm− 1) (15)

Alternately, it is possible to study PT crowding costs by focusing onthe willingness to accept a reduction in travel time in exchange for worse



travel conditions. Using equation (15), the average WTP is equal to 4.2min/trip26, i.e. e 0.84/trip once transformed into a monetary equivalent.This represents the amount individuals would be willing to pay in order toenjoy a seat during their rush hours’ trips.

Estimates of the generalized costs are lower when using the objectivedensity (count data) indicators (see table (5)). However, the difference isnot as important as one might expect: GC(peaks)=e 3.09/trip with thecount data and GC(peaks)=e 2.90/trip with the objective data from thePT operator. The same conclusion applies when considering the Tm-densityrelationship estimated from second answers. With the expected density, wefind a corresponding GC(peaks)=e 3.10/trip. Using the count or the Ratpdata provides e 2.95 /trip and e 2.80/trip respectively. Compared to thebenchmark situation, this still implies a 15-27% increase in the generalizedcost of PT usage.

Using the estimates of WTP , we can estimate the welfare gains inducedby a policy which would offer a seat to all passengers during peak periods.Assuming that 50% of the 750,000 trips daily performed in line 1 occur dur-ing peaks, we apply the monetarizedWTP (e 1.28/trip). On the basis of 300days per year of commuting, we find a potential welfare benefit of e 144m.The same calculation for line 4 (with WTP=e 0.51/trip and 670,000 dailyusers) gives a figure of e 51m. Extending the analysis to the whole networkwith 1,479m transport users (739,5m during peak periods) applying an av-erage WTP of e 0.84 per trip results in crowding costs of e 621,2m for 2009.

We can also use the Tm-density relationship to estimate the evolution ofthe crowding costs in the Paris subway. According to the statistics providedin table (1), the passanger density in the Paris subway network grew by 10%over 2000-2009 (considering peak and off-peak periods). Using equation (14),average densities in table (5) and assuming that the travel time and the timeopportunity cost from our sample are representative for the whole Paris net-work, we find a GC(cj) difference of e 0.30/trip. Applying the latter resultto 1,479m trips performed in 2009 (Syndicat des Transports de la Région Ile-de-France (2009)), we get a rise of e 444m rise in the GC(cj) paid by Parissubway users27. This growing congestion in trains appears more expensive

26A simple calculation from descriptive statistics on hypothetical scenarios (see tables(3) and (10)) would give a WTP equal to 4.1 min/trip, i.e. 9.7×0.42.

27If we restrict calculations to individuals who were already subway users in 2000, theadditionnal congestion costs are of e 369m.



than the times losses induced by the municipal policy of road space narrow-ing. Thus, the increase in time costs over 2000-2009 may be estimated ate 294 m for individuals still driving cars in Paris 28. However essential modalshift policies are for the environment and to preserve the attractiveness ofcity centres, this clearly illustrates that there is no free lunch in modal shiftpolicies.

5.2 The subway crowding externality

Once we have recognized that the GC(cj) is significantly influenced by PTcrowding, the existence of a congestion externality should be explicited. Infact, this non-market interaction generates an external cost (MC(cj)) andcalls for public interventions minimising the social cost of subway usage(SC(cj)). Following a Pigouvian framework, largely used to study roadcongestion (Quinet and Vickerman (2004), Small and Verhoef (2007)), wecan write:

SC(cj) = GC(cj) +MC(cj) = GC(cj) +∂GC(cj)

∂cjcj (16)

Using our estimates of the relationship between the time multiplier andpassenger density, we can distinguish the marginal cost of subway congestionaccording to the levels of comfort in trains. Table (11) shows that the averageexternal cost in the Paris subway is e 0.81/pass (using the average expecteddensity of 3 pass/m2). In addition, we observe that the social cost of PTusage becomes quite large for very crowded conditions. Thus, the SC(cj)reaches e 5.70/pass when 6 pass/m2 are found in the trains, for a GC(cj)equal to e 4.07/pass. This should be compared to the benchmark situation,i.e. e 2.44/trip. Even if the MC(cj) represents only 30% of the SC(cj) inworst travel conditions, these figures underline that ignoring the externalityof subway congestion would hide an important feature of urban transportsystems.

We can compare the valuation of the crowding externality to other non-market interactions linked to urban transportation (road congestion, acci-

28Based on updated figures from 2007, around 4,900m pkm were driven in Paris in 2009(Observatoire de la mobilité de la ville de Paris (2009), Kopp (2011)). Over 2000-2009, theaverage car speed in Paris decreased by 10% (17.4 km/h and 15.6 km/h, Observatoire dela mobilité de la ville de Paris (2009)), which means an additional 0.3 minute to perform 1kilometer. Assuming that car users have the same time opportunity cost as subway userswe find e 0.06/km. This yields e 294m in additional congestion costs.



Table 11: Generalized, external and social costs of Paris subway usage

Density GC(cj) MC(cj) SC(cj) MC/SC(e/pass) (e/pass) (e/pass) (%)

0 pass/m2 2.44 0 2.44 01 pass/m2 2.44 0 2.44 02 pass/m2 2.98 0.54 3.52 152.5 pass/m2 3.12 0.68 3.80 183 pass/m2 3.25 0.81 4.06 204 pass/m2 3.53 1.09 4.62 246 pass/m2 4.07 1.63 5.70 29

dents, noise, local pollutants, GHG). Since the values provided by the Hand-book on estimation of external costs in the transport sector (Malibac et al.(2008)) or by Leurent et al. (2009) are kilometric ones, we have to divide themarginal cost found previously for subways (e 0.81/pass at 3 pass/m2) bythe average distance of a trip performed in the Paris network (3.8 kilometresin our sample, see table (3)). Thus, we obtain a kilometric cost of e 0.21.As indicated in table (12), the marginal cost of subway congestion is half thecorresponding value for road congestion in Paris (e 0.43/km using Leurentet al. (2009)) - but exceeds estimates of the costs of other externalities.

Table 12: Urban transport marginal costs

Subway Road Cars Local Cars GHGcongestion congestion accidents pollutants noise emissions

MC (eu/km) 0.21 0.43 0.07 0.02 0.01 0.01

The relevance of the crowding externality could be underlined by con-ducting costs-benefits analyses of transport investments, such as pro-bikes,buses or streetcars policies. Taking into consideration the benefits of subwaydecongestion may significantly alter the Net Present Values and the InternalRates of Return of new projects. Note also that the MC(cj) figures in table(11) could be used as proxies for an hypothetical taxation aiming at inter-nalizing the social cost of subway usage29. Whereas fares do not vary bytime of day in Paris, the fares in London underground network are increased

29It should be noted that our cost estimates are not equivalent to the optimal tax level,which would cover the - lower - level of crowding costs at the optimal level of PT usage.



by 30-70% during rush hours. To conclude this analysis, we rather producea simple economic appraisal of the recent line 1 automation.

5.3 Investment in capacities

Since late 2012, line 1 of the Parisian subway has been automated, i.e. itnow runs without drivers. By launching this new system, the operator seeksto improve reliability and service quality. The new system allows the op-erator to finetune the supply of line 1 in response to a varying demand.Does the initial investment of e 629m - e 479m for the new rolling stock and150m for installations in platforms (automatic gates essentially, see RégieAutonome des Transports Parisiens (2011)) - correspond to a socially desir-able policy?

We identify three main effects of the Line 1 automation on the well-being ofsubway users:

1. The average commercial speed of line 1 will increase by 10% (RégieAutonome des Transports Parisiens (2011)), during both peak andnon-peak periods. Considering our 11.5 minutes figure for rush hours(see table (3)), in-vehicle travel time will drop to 10 minutes.

2. During peaks, line 1 automation will allow a 20% growth of trains’ fre-quency: from intervals of 1 minute 45 secondes currently to 85 secondes(Régie Autonome des Transports Parisiens (2011)), i.e. 10 secondessaved on waiting time30.

3. Assuming a constant peak demand for line 1, trains’ higher frequencyimplies that the (reduced) in vehicle time is consumed with more com-fortable travel conditions. Thus, the average expected density (3.5pass/m2) will face a 20% decrease and fall to 2.9 pass/m2.

We can use our results to compute the corresponding welfare changes.

The value of the saved waiting times on platforms is doubles vis-à-visin-vehicle values - as recommanded by the Boiteux report (CommissariatGénéral du Plan (2001)) - reduced waiting times then generate a gain ofe 8.6m for line 1 commuters (accounting 375,000 trips during peaks and 300

30Assuming a uniform distribution of arrivals on platforms, mean waiting times willdrop from 53 secondes to 43 seconds.



days per year). Automation also leads to a reduction by e 79.6m per year ingeneralized costs due to improved speed and comfort during peaks. Assum-ing that the in vehicle travel time does not vary accross peak and off-peakperiods, non commuters are finally e 38.8m better-off. Taken jointly, theannual benefit for Line 1 users induced by the automation reaches e 127 m.

In order to calculate the Net Present Value of the investment, we comparethe sum of future discounted benefits (using a 4% discount rate, as officialyrecommended in France, Commissariat Général du Plan (2005)) to the initialcost of e 629m. Given the social cost of raising public funds by taxation,French guidelines suggests augmenting costs by a factor of 1.3 (Ministèrede l’Equipement (2005)). As illustrated in table (13), the net present valueof line 1 automation is e 1,035m over a 20 year horizon. This correspondsto the discounted value of the time resources saved by the project, net ofthe financial costs. The Internal Rate of Return is 5.8%, well above the 4%threshold. Therefore, the automation of subway lines seems to be a goodinitiative to improve travel comfort.

The cost-benefit analysis cannot take into account all impacts. In partic-ular, these simple calculations assume constant demand for line 1 travel31.

In fact, the subway usage in Central Paris has been increasing for 10years. Faster and more comfortable travel conditions in line 1 may attractusers to the line. A close substitute on part of the line is the regional trainservice RER A. Transporting 1 million passengers per day, it serves 5 sta-tions in common with line 1 in central Paris32 and provides different trip’scaracteristics. Connecting one of the pairs of stations takes around 15% less(in vehicle) time with the RER A (9.3 minutes considering the average tripin our sample) but is associated with a 30% higher passanger density (anaverage expected density equal to 4.6 pass/m2)33.

31Other improvements in the CBA would include the variation of operational costs andcommercial receipts due to Line 1 automation, the reliability of service’s gains and thevariations of in vehicle comfort related to the renewal of the rolling stocks. Nevertheless,the latter effect appears to be small: according to commercial sources, the new carriagesin Line 1 offer the same numer of places than old ones (720 places per train). Moreover,these old carriages have been moved on Line 4 (whose former train counted 700 places,i.e. a 3% increase in Line 4 supply, keeping trains’ frequency constant)

32Nation, Gare de Lyon, Chatelet, Charles de Gaulle, La Défense.33The 15% difference in travel time has been calculated by comparing durations in

RER A (from Ratp website) with those in line 1 clocked during our counting work, forthe different possible pairs of stations. The 30% difference in passanger density is a roughapproximation deduced from the difference in daily patronage between RER A and line 1.



Table 13: Net Present Value of Line 1 automation

Constant demand Report fromin Line 1 RER A

Line 1, before:Waiting time (secondes) 53 53Peak density (pass/m2) 3.5 3.5Travel time (minutes) 11.5 11.5Line 1, after:Waiting time (secondes) 43 43Peak density (pass/m2) 2.9 3.1Travel time (minutes) 10.0 10.0RER A, before:Peak density (pass/m2) 4.6 4.6Travel time (minutes) 9.3 9.3RER A, after:Peak density (pass/m2) 4.6 4.4Travel time (minutes) 9.3 9.3Annual benefits:Peak waiting time gains Line 1 (em) 8.6 8.6Off-peak time gains Line 1 (em) 38.8 38.8Peak time and comfort gains Line 1 (em) 79.6 72.0Peak comfort gains for switchers (em) − 1.7Peak comfort gains RER A (em) − 4.3Total (em) 127.0 125.4Net Present Value (em) 1,035 1,012Internal Rate of Return (%) 5.8 5.8



Assuming that 5% of the daily 500,000 commuters in RER A can switchtowards Line 1, the average density in that service will reach 3.1 pass/m2 af-ter the automation (-10% compared to the ex ante situation). For the formerline 1 users, time and comfort gains are thus slightly smaller: 72 millions eu-ros per year34. For the 25,000 individuals who switched, we can hypothesizea 1.7 million euros reduction in the generalized costs of transit. Finally, weshould add the gains for those commuters, (say, 95%) who continue to usethe RER A (475,000 passengers per day) and now face a reduced passangerdensity (4.4 pass/m2) during their 9.3 minutes trip in Paris. Calculationsprovide a figure of e 4.3m. Under this scenario, the overall annual benefitsinduced by the line 1 automation are now of e 125.4m. As illustrated intable (15), the net present value of the project is still favorable (e 1,012mover 20 years), as is the internal rate of return (5.8%).

Despite obvious limitations, our economic appraisal shows that subwayautomation may be an example of a good PT investment to relieve congestionin the Parisian PT network. Even if the improved service quality may attractPT users from other services, reduced density in other PT systems maycompensate for reduced comfort gains in the new infrastructure.

6 Conclusion

Using new data from a survey of Paris subway users we find that crowdingin PT systems is a non-negligible factor affecting individuals’ utility of tripsand crowding constitutes a first-order urban externality.

Whereas the typical private monetary cost of a trip was e 0.50, we founda monetized total trip cost including congestion costs of e 2.40 for a seatedpassengers and around e 4.10 under the most congested conditions. Ourempirical results also allowed to approximate the marginal cost of subwaycrowding (e 0.80 per trip), and to calculate the opportunity cost of trans-port time as a function of in-vehicle density (making the time multiplier afunction of crowding). The value of travel time has to be increased by 40%in order to account for crowding during peaks.

These figures have been calculated using a contingent valuation approach34We assume that the waiting times on platforms and the time gains for non commuters

in line 1 are not affected by the train report.



that proposed a trade-off between (increased) travel time and (decreased)passanger density. Individuals’ stated preferences appeared to be quite ro-bust and consistent. The field survey we collected in lines 1 and 4 offers arich empirical material calling for future research.

Whilst most models used to evaluate transport policies recognise the ex-istence of public transport crowding, typically the calibrations used do notgiven significant weight to this factor. First, the design of public transportnetworks needs to focus not only on the duration of trips, but also take intoaccount crowding. Second, policies aimed at incentivising modal shift shouldfully factor in the effect of increased public transport usage on current usersof public transport. This underlines the necessity of accompanying modalshift policies focussing on restrictions for road transport with increased in-vestment in public transport infrastructure. We provide evidence on theadditional costs of restrictive road policies and the additional benefits ofpublic transport infrastructure for the Parisian case.



7 Appendix

7.1 Descriptive statistics by sequence of bidding answers

Table (17) shows that 25% of subway users accepted both time bids ("Yes-Yes"). This proportion is higher for line 1 users (59% of the "yes-Yes"respondents) and for evening trips (57%). At the other extrem, we observethat 41% of the sample rejected twice the trade-off between travel time andcomfort ("No-No"). This category is over-represented in line 4 (56%) andduring morning peaks (54%). Whilst this information is consistent with thevariations of in vehicle comfort accross lines and periods, it may also be ex-plained by the hypothetical extra travel time proposed to users: the first bidproposed to those who rejected the hypothetical scenario was twice the onefaced by individuals accepting it (5.3 minutes and 10.9 minutes respectively).



Table 14: Ordered logit estimates of the comfort "reference point"

1 2 3 4 5Count density 0.70*** 0.49*** 0.50*** 0.50*** 0.50***

(0.07) (0.11) (0.11) (0.11) (0.12)Morning -0.75*** -0.80*** -0.80*** -0.84***

(0.14) (0.14) (0.14) (0.14)Line 1 0.65*** 0.64*** 0.56** 0.58**

(0.23) (0.24) (0.24) (0.25)In vehicule travel time -0.00 -0.00

(0.01) (0.01)"Door-to-door" travel time 0.00** 0.00**

(0.00) (0.00)Home-Work 0.09 0.01

(0.16) (0.17)Line daily usage 0.17 0ă.20

(0.16) (0.16)Age -0.01 -0.01

(0.07) (0.07)Male 0.05 0.07

(0.14) (0.14)Parisian -0.08 0.03

(0.15) (0.16)Income 0.08** 0.08**

(0.04) (0.04)Car ownership -0.08 -0.11

(0.16) (0.16)Observations 686 686 686 686 686Pseudo R2 0.05 0.07 0.07 0.07 0.07

Table 15: Distribution of the first time bid

3 min. 6 min. 9 min. 12 min. 15 min. 18 min.Distribution 21.5% 27.8% 16.0% 14.7% 14.0% 6.0%



Table 16: Hypothetical levels of comfort

Expected density (pass/m2) 1 2 2.5 3 4 6Hypothetical density0 pass/m2 100% 51.3% 29.5% 26.4% 19.4% 16.7%1 pass/m2 48.7% 31.4% 21.6% 20.9% 8.3%2 pass/m2 38.6% 31.1% 21.6% 16.7%2.5 pass/m2 21% 20.1% 18.3%3 pass/m2 18,00% 13.3%4 pass/m2 26.7%

Table 17: Descriptive statistics on hypothetical scenarios (2)

Yes-Yes Yes-No No-Yes No-NoTotal (%) 25 17 17 41Line 1 (%) 59 59 43 44Morning (%) 43 47 54 54Expected density (pass/m2) 3.3 3.3 3.0 3.0Hypothetical density (pass/m2) 1.2 1.3 1.1 1.3Bid 1 (min) 5.3 8.6 8.5 10.9Bid 2 (min) 6.9 10.9 6.2 8.3



Table 18: Interactions with the morning peaks

Biprobit BiprobitAnswer 1 Answer 2

Time marginal disutility at:0 pass/m2 -0.086 -0.110

(0.018) (0.017)1 pass/m2 -0.091 -0.125

(0.018) (0.018)2 pass/m2 -0.110 -0.132

(0.018) (0.019)2.5 pass/m2 -0.113 -0.145

(0.018) (0.021)3 pass/m2 -0.133 -0.158

(0.021) (0.022)4 pass/m2 -0.125 -0.160

(0.022) (0.024)6 pass/m2 -0.160 -0.205

(0.028) (0.029)Morning 0.126ns 0.311ns

(0.23) (0.221)Interaction with Morning:

0 pass/m2 -0.069 -0.073(0.027) (0.025)

1 pass/m2 -0.051 -0.064(0.028) (0.027)

2 pass/m2 -0.054 -0.061(0.028) (0.028)

2.5 pass/m2 -0.067 -0.071(0.030) (0.030)

3 pass/m2 -0.073 -0.062(0.036) (0.033)

4 pass/m2 -0.117 -0.108(0.044) (0.04)

6 pass/m2 -0.070ns -0.055ns

(0.045) (0.044)Constant 0.493 0.606

(0.16) (0.153)Rhô 0.595

(0.065)Log pseudo -774.6Observations 68835 Luke Haywood & Martin Koning


Table 19: Time multipliers with the "Morning" interaction

BiProb BiProb BiProb BiProb Biprobit BiProbDensity Tm1 Tm2 Tm1 Tm2 Tm1 Tm2

Morning Morning Evening Evening Morn./even. Morn./even.0 pass/m2 1.10 0.96 0.96 0.88 1.80 1.651 pass/m2 1.00 1.00 1.00 1.00 1.57 1.512 pass/m2 1.11 1.02 1.13 1.06 1.41 1.462.5 pass/m2 1.26 1.14 1.23 1.16 1.46 1.483 pass/m2 1.38 1.16 1.36 1.26 1.59 1.394 pass/m2 1.72 1.43 1.39 1.28 1.92 2.476 pass/m2 1.13 1.08 1.78 1.64 1.00 1.00



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Estimating Crowding Costs in Public Transport€¦ · Estimating Crowding Costs in Public Transport Luke Haywood ∗Martin Koning † December 2012 Work in progress Abstract Preferences