Measurement of the Congestion Externality in Rail Commuting in the Tokyo Metropolitan Area *
February 2006
Fukuju YAMAZAKI Faculty of Economics, SOPHIA UNIVERSITY 7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554 Phone & Fax 81-3-3238-3208/E-Mail
[email protected]
Yoshihisa ASADA Faculty of Real Estate Science, Department of Real Estate, MEIKAI UNIVERSITY
* We are grateful for valuable comments from Kikuo Iwata, Yoshitsugu Kanemoto, Tatsuo
Hatta, Se-il Mun, Yoko Moriizumi and Takako Idee. Science Technology Development and the Ministry of Education financially supported our research.
1
Abstract We developed an econometric model for estimating congestion costs in rail travel. Congestion charges have been estimated by using data obtained from the rent functions for the railways in the Tokyo metropolitan area. Paying attention to the rent gradient, in which the external effects of congestion should be reflected, we included the congestion rate as an explanatory variable in the estimation equation for the rent differential. We found that congestion rates have a significant and positive effect on differences in rents. By using the estimated coefficient, we found that congestion charges are between 2.05 and 9.59 times the fares. Keywords: congestion charges, Rail commuting, rent function, congestion externality, Tokyo Metropolitan area, commuting cost.
JEL Classification Code: R41, R13, H23.
2
Measurement of the Congestion Externality in Rail Commuting in the Tokyo Metropolitan Area
1. Introduction Many urban problems relate to externalities. Above all, almost all major cities in the world suffer from congestion. It is well known that congestion tolls are required to solve peak-load problems. The introduction of optimal congestion tolls requires the estimation of congestion externalities in money terms. Many papers have addressed congestion pricing on urban traffic highways. One issue is the actual measurement of congestion costs. Small [18] and Calfee and Winston [3] estimated commuters’ time costs over time. Using a sample of car commuters in the San Francisco Bay area, Small found that the travel-time cost of congestion is higher than the time cost (spent in the office) incurred in arriving early. Measurement is important for determining the time-varying congestion tolls that optimize road use.1 Hayashiyama and Sakashita [9] and Yamauchi [21] have studied road congestion in Japan. They converted time costs due to congestion into money terms, as many authors
1 Mohring [［14］, p. 214] states, “Little is known about what travelers are willing to pay to save travel time”.
3
have tried to estimate the marginal costs of road congestion.2 They, reasonably, multiplied the opportunity cost of time by the additional time wasted due to road congestion. The purpose of this paper is to estimate congestion externalities in commuter rail in Tokyo. Although congestion on the roads in Japan is a serious problem, rail congestion in the Tokyo metropolitan area is appalling. Almost all commuters in the Tokyo metropolitan area commute to the Central Business District (CBD) by rail rather than by car. They reluctantly commute to the CBD on weekdays at peak hour. Over 60% of commuters spend over two hours and over 20% spend more than three hours commuting on weekdays on congested railways.3 Rail congestion differs from road congestion in two ways. First, the negative externalities of physical discomfort and mental stress associated with rail congestion do not include the waste of time that is associated with road congestion. This is because a crowded train does not take longer to travel its route. For this reason, the negative externalities of congested trains cannot be measured in monetary term of wasted time.4 Second, whereas road congestion involves static and dynamic externalities, rail congestion involves mainly static externalities. Mun [15] recently extended the model of
2 See Mohring [14]. 3 See National Land Agency [19]. 4 Mohring [13] and recently Kraus and Yoshida [12] incorporates the waiting time at the stations in the model of the optimal congestion pricing of urban mass transit. We can, however, ignore the commuter waiting cost at the station, because each train runs so frequently that the average time spent for the commuters on the platform is less than 5 minutes at the peak period.
4
Arnott et al. [1] to examine how optimal congestion tolls vary over time on roads with bottlenecks. He showed that road congestion involves both static and dynamic externalities. While an additional driver on the road increases the travel time of other drivers leaving at the same time (the static externality), it also lengthens the queue to induce dynamic delays for other drivers starting their journeys later. However, with rail congestion, while additional passengers negatively affect other passengers on the same train, they have no effect on passengers on later trains. This is the reason that time delays due to rail congestion are negligible. Shida et al. [17], Hatta [6], and Hatta and Yamaga [8] estimated congestion costs in rail in Japan.5 Shida et al. [17] estimated the time spent by rail users avoiding congestion by starting journeys earlier or later and by using off-peak trains. Hatta [6] assumed that time is needed to overcome the fatigue induced by commuting, and estimated non-pecuniary commuting costs by using a Cobb–Douglas utility function. Hatta and Yamaga [8] extended Hatta’s model by using a CES utility function to estimate congestion costs. In this paper, we suggest that negative externalities are reflected in housing rents, and estimate externalities directly. The negative slope of the rent function implies not only additional commuting time, but also additional discomforts. Congestion increases the 5 To our knowledge, there is no econometric research on rail congestion in countries other than Japan. This is perhaps because other countries depend more on commuting by car and because office workers in other countries spend much less time commuting by rail than do those in Japan. Most office workers in Tokyo spend three hours a day commuting
5
marginal disutility of time spent on the train to yield a steeper rent function. Rather than convert negative externalities (physical discomfort and mental stress) into time costs, we estimate pecuniary congestion costs without making specific assumptions about the utility function.6 Assuming constant traffic capacity, the external effect of congestion increases substantially as the number of passengers increases. An additional passenger has negative external effects (physical discomfort, mental stress and fatigue) on other passengers using the service at the same time. Since passengers on a congested train adversely affect each other, congestion represents a public bad. Thus, passengers should pay a congestion charge, which is equal to the marginal damage caused by an additional passenger. Introducing such charges for rail travel would reduce congestion and improve the efficiency of resource allocation. However, to implement such a system of congestion tolls, it is necessary to estimate the damage caused by an additional user to other passengers using the service at the same time. This paper aims to construct an econometric model of rail congestion in the Tokyo metropolitan area, and estimate congestion tolls for rail. The paper is organized as follows. In Section 2, we develop a simple econometric model of the rail system and the housing from the suburbs by train. 6 In a model of closed community, Arnott and Mackinnon [2] showed that the shadow land rent is not necessarily higher than the market rent when there is road congestion. However, since our model assumes a small open
6
market. In Section 3, we explain the estimation method and discuss the estimation results for congestion charges. In Section 4, we present our conclusions.
2. A Model of the Rail System with Congestion Figure 1 shows that the congestion rate on the railways in the metropolitan area decreased gradually as transportation capacity increased due to the construction of new lines. The increase may also have been due to the adoption of flexitime by firms. The average congestion rate at peak hour among 31 main rail routes in the metropolitan area decreased continuously between 1990 and 1999. However, in 1999, the congestion rate remained high at about 180% for most of the 31 main routes. On ten of the 31 main routes, the congestion rate exceeded 200%. 7 Further reductions in rail congestion in the Tokyo metropolitan area are needed.
Figure 1. Average congestion rates at peak hour, 1975 to 1999
community, we depart from their assumption of a constant population. 7 See Institutution for Transport Policy Studies [11].
7
congestion rate(％)(a)
transportation capacity(b) passenger(1975=100)
230
180 170
221
220
214
213
210
152
157
156
155
157
159
157
160 150
144 143 203 143
200
139
136
190
135
133
133
140
133
130
124 121
180
136
192
131
183 180 176
175
congestion rate transportation capacity passengers
170 100
120 173
171
110 100
160 1975
1980
1985
1990
1995
1998
1999
2000
2001
2002
2003
year
(a) Indices of transportation capacity and the number of passengers are both 100 in 1975.
(b) The congestion rate is defined as the ratio of the average number of passengers to transportation capacity (%) at
peak hour on 31 rail routes into the CBD.
Source: The National Land Agency [2003] White Paper on the Metropolitan Area.
Transportation capacity has increased considerably, as Figure 1 shows. However, given that congestion is itself an external effect, users should pay congestion costs to internalize congestion externalities. The congestion tax could also be used to finance capacity increases.8 First, we clarify the relationship between congestion costs and housing rents by using 8 The possibility of self-financing by congestion tolls depends on the well-known conditions relating to homogeneity
8
a standard urban economic model that incorporates certain assumptions.9 Figure 2 shows a rail system that expands radially from the CBD to suburbs in the Tokyo metropolitan area. Consider a representative individual who commutes to the CBD from a residential area served by the railway. The individual is assumed to be homogeneous and is assumed to derive utility from consumer goods z and housing size s, which are both produced competitively. Moreover, we assume that the individual is able to move house freely at no cost.
Figure 2. A railway model ｒ０ Suburban area
CBD x
Under these assumptions, the individual’s utility function is:
in the production function for transportation services. See Mohring [13] and Henderson [11 ]. 9 For details of standard urban models, see Fujita [4].
9
U = U ( z, s ) .
(1)
The individual maximizes utility subject to the following budget constraint:
Y = z + Rs + T (r ) ,
(2)
where Y is income, R is housing rent and T is commuting cost. Prices are measured relative to the price of the consumer good, which is the numeraire. The total commuting cost T(r), which incorporates physical and psychological costs, depends on the commuting distance from the center of the city, r, and is defined as follows:
T ( r ) = ∫0 c( r
N ( x) , x )dx , K
(3)
where c( ) is the cost per unit of distance. Definition of symbols r: Time distance from the CBD (in minutes) R: Housing rent s: Housing size T: Commuting costs
10
N (x): Total number of passengers commuting to the CBD from a distance greater than x K: Transportation capacity L(r): Total floor space of dwellings on the outskirts of the city r minutes from the CBD N(r): The number of passengers commuting from the station, which is r minutes from the CBD
The unit commuting cost c (e.g., unit cost per mile) incorporates the out-of-pocket fare and the discomforts due to congestion. The cost depends on the instantaneous congestion rate
N ( x) and the distance from the center of the city x. N (x) denotes the K
number of passengers on trains passing through point x (i.e., the number commuting from further away than x). K is the transportation capacity of the train. An increase in the congestion rate is assumed to raise the unit commuting cost. Physical and mental discomforts for each unit distance increase as the congestion rate increases.10 Whether the unit cost of commuting is an increasing function of x is ambiguous. The psychological burden of marginal increases in distance faced by commuting consumers could be an increasing function of the commuting distance. Alternatively, if commuting is subject to economies of scale, the unit cost may decrease as the commuting distance
10 It is unnecessary to assume that commuters actually expend the congestion costs incorporating not only the pecuniary cost but also the psychological discomforts and fatigue. See footnote 11.
11
increases. The relationship is investigated empirically below. A given utility level can be obtained by a consumer living in another community served by rail because this community’s housing market and population are assumed to be sufficiently small relative to the metropolitan area as a whole. (This is the small opencommunity assumption.) It is well known that the above utility maximization problem is equivalent to the problem of maximizing the following rent function:
φ (r ,U ) ≡ max
Y − z ( s, u ) − T ( r ) s
(4)
That is, the solution to the problem of maximizing the bid rent subject to a constant utility level is equivalent to the solution to the utility maximization problem above. Differentiating the bid rent function with respect to the distance from the center of the city, r, and use of the envelope theorem yields the following equation:
− R' ( r ) ⋅ s ( r ) = T ' ( r )
(5)
This equation implies the well-known requirement that a marginal increase in commuting 12
cost must equal the gradient of the rent function (a change in the total rent). The economic meaning is clear. The individual incurs higher commuting expenses by residing in a suburb further from the CBD. A consumer can obtain the same utility level in the market equilibrium when rents in more-distant suburbs are lower to compensate for higher commuting costs. The following equation is obtained from equation (3) and the relationship between rent and commuting cost (5):
− R' (r ) ⋅ s(r ) = c(
N (r ) , r) K
(6)
Substituting the equilibrium condition for the housing market into equation (6) yields:
− R' (r )
L(r ) N (r ) = c( , r) n(r ) K
(7)
The stress and fatigue induced by congestion on the train are incorporated into the commuting cost, along with the rail fare and the commuting-time cost. Such psychological and physical costs are not easily assessed. The component of cost that depends on congestion must be distinguished from the 13
other component of the commuting cost. The former is associated with congestion cost, whereas the latter incorporates out-of-pocket costs and time costs. The commuting cost can be determined by estimating the rent gradient, which represents the incremental commuting cost, as equation (7) shows. Novel features of our paper are estimation of the rent function and identification of the component of congestion cost that depends on the congestion rate.11
3. An Econometric Analysis of Rail Congestion Externalities We now explain the estimation of congestion cost. First, we use cross-section data to estimate the rent function and determine what factors affect rent. We require data on the rent gradient, which represents commuting cost. Second, we use the estimated coefficient on the distance from the CBD to calculate the unit cost of the right-hand-side of equation (7). The commuting cost for each unit distance is calculated from equation (7), which describes the relationship between the bid rent and commuting cost for unit distance. Third, we regress the unit-cost function on the congestion rate and other variables. We 11 Alternatively, assuming that congestion directly reduces utility yields the following maximization problem:
u = u ( z , s,
N ) K s．t． Y = z + Rs + pr
where p is the out-of-pocket fare. The solution is: ∂u - R' (r ) s ( r ) = p N ∂( ) K Thus, we obtain the problem in the text. In any case, we must identify the disutility of congestion from the rent
14
estimate cost as a function of the congestion rate and other variables.
Estimates of the rent function Figure 3 is used to explain briefly the Tokyo metropolitan area, which includes large residential areas and has a population of about 30 million. It has four prefectures (Tokyo, Kanagawa, Saitama and Chiba). The CBD of Tokyo is usually defined as four wards (Chuo, Chiyoda, Minato and Shinjuku) in the Tokyo Prefecture. Although its area (58km2) is almost the same as that of Manhattan (57km2), the population density of the CBD of Tokyo is much lower than that of New York. The low population density implies that the CBD of Tokyo is utilized less than Manhattan. Consequently, it takes longer for workers to commute to the CBD of Tokyo. The JR Yamanote Line is a belt line that surrounds the CBD of Tokyo. A convenient network of subways has many junctions with the JR Yamanote line in the CBD. Almost all those working in the CBD daily take the train and transfer to the JR Yamanote line or subway at the terminal station of the railway expanding to the suburban area.12
gradient. 12 Hatta and Ohkawara [5] provide details of the structure of the Tokyo metropolitan area.
15
Figure 3 Honkaw agoe
Fukiage Sakado
ei
Tobu-Isezaki
-K JR
Saitam a Prefecture
Sayam ashi
Kom a
hi nt
Shiki
U shiku
Him emiya
M inam iurawa
Shinm atsudo
oh ok ･T u ak as
bu -
To
Higashikurum e
u- I k e
buk u
M itaka
Tokyo
K ei o-h on ・S
Chofu
M inatoku
o
Shibuya
M egurp
JIyugaoka
Shinyurigaoka
Kanagawa Prefecture
M achida N agatsuda
Inage
Akihabara
To
Tam asenter H ashim oto
a
ara
Shinkioiwa
Chiyodaku
ok
Od
N oborito
da w
JR-Soubu
Tokyo J R-
Shim okitazaw a -O k yu
Shinjyukuku
a
oy
H achioji
ag am ih ar
Chiba Prefecture
Ichikaw a U eno
shinjyuku
u -T
Fucyum achi
ba n
Cyuouku
Shinagawa
ke
iy
Soga
o
Shinurayasu Shinkiba M aiham a
ky
Tachikaw a Tak ao
JR-C huoh
n・ J o
Ikebukuro
N akano
Kichijoji
Kokubunji
ansi
ro
Seibu-shinjyuku
Tachikaw a
ob JR -J
Kitasenju
ate
S eib
K anam achi
Akabane
jo
Jr-ya m
Hoya Kodaira
M atsudo
i
To
ak
Tokorozaw a
Tokyo Bay
Prefectu re boundary Four wards in the center of a city
Kikuna
Estimated routes JR-Yamanote line
Aikoishida
Other routes M ain station
16
While we use data on the monthly rent per unit of available floor space (m2) on fireproofed apartments in areas where it is viable to walk to a railway station, data on wooden apartments and detached rental housing are excluded. The independent variables include time distance from the CBD, floor space, walking time to the nearest station and the frequency of trains. All data used are published in Recruit [16]. The data relate to residential areas along 12 rail routes to the CBD of Tokyo and are detailed in the Appendix. In estimation of the rent function, Box–Cox transformations of time distance from the CBD and floor space are used to account for possible non-linearities. We use the maximum likelihood method to estimate the following rent function:
R = a0 + a1
r1λ − 1
λ
+ a2
sκ − 1
κ
+ a3 r2 + ⋅ ⋅ ⋅ ⋅ +ε ,
(8)
where R is the housing rent for each square meter (m2) of housing, r1 and r2 are, respectively, time distance from the CBD and walking time from the nearest station to home, s is housing size and ε is an error term.13 Commuting time to work depends on the type of train (special express, fast or local). We processed the data on time required to commute as follows. Using railway company 13 It is well known that the error term might be spatially autocorrelated because important variables affecting the spatial environment might be omitted. However, since we consider non-linearity a more serious problem, we ignore the possibility of spatial autocorrelation.
17
timetables for 2002, we determined commuting times required by each type of train during peak hours, between 6:30 a.m. and 9.00 a.m. Similarly, the frequency with which each type of train runs was calculated from the number of services involving each type of train leaving for the CBD between 6:30 a.m. and 9.00 a.m. Then, the time required by each train was weighted by frequency to generate data on time distances.14 The estimation results for each rail line are shown in Tables 1-a and 1-b.
14 We also use frequency as an inverse indicator of average waiting time at the station in the estimation.
18
Table 1-a. Coefficient estimates of the rent function JR Chuoh
JR Keiyo
JR Sobu
Tobu–Isezaki
t-value
Estimated
t-value
Estimated
t-value
Estimated
208834
52.57**
32606.8
39.01**
48195.6
34.62**
6677990
11.93**
58298.2
40.61**
16734.1
t-value 31.80**
-71.6256
-28.50**
-246.808
-13.16**
-0.30419
-4.79**
-8.45401
-7.13**
-175.693
-14.59**
-23.9873
-12.19**
-27.8797
-12.76**
-18.0439
-6.68**
-22.4966
-9.13**
-17.7669
-3.73**
-28.3867
-9.88**
-18.1761
-5.41**
-360144
-51.41**
-29352.7
-35.07**
-52190
-33.17**
-19358400
-11.93**
-65383.7
-37.66**
-9998.43
-26.65**
2.13219 -25.1969 172.675 20.7141 -110.681 434.383 261.583
2.46* -15.05** 4.41** 5.69** -2.66** 9.40** 4.80**
7.84608 -26.9409 160.068 31.3006 -90.4429
8.84** -11.18** 3.36** 6.10** -205*
14.5623 -25.3104 170.633 32.3594 -183.357
11.19** -9.96** 3.76** 8.09** -3.39**
17.0717 -31.1349 27.9725 12.9655
2.21* -7.05** 0.28 2.01*
4.72107 -22.3311 88.7761 20.3642 -46.507
3.85** -10.77** 1.76 4.42** -0.95
3.75262 -23.801 174.694 29.3907 -134.478
3.69** -7.36** 2.78** 4.59** -2.54**
248.313
8.63*
λ
r1 − 1
λ
Walking Time Floor Space
JR Keihintohoku･ Takasaki Estimated t-value
Estimated Constant Time Distance from CBD
JR Jobanshin-sen Jouban Estimated t-value
sκ −1
κ Frequency of Train Building Age Room Floor Building Story Dummy New Dwelling Dummy Kichijoji^ Dummy Kunitachi^ Dummy Kameido^ Dummy Kitaurawa^ λ κ R2 White het. test Number of observations Terminal station
0.778 13.81** -1.755 -23.12** 0.868645 104.835** 872
Shinjuku
254.529 4.22** 2.220 10.65** -1.108 -16.82** 0.82988 102.641** 413
0.129 8.98** -1.023 -11.32** 0.884407 149.573** 335
Ueno
Ueno
^ denotes particular station dummy. * indicates significant at 5% and ** indicates significant at 1%.
19
1.320 15.68** -2.900 -19.25** 0.870001 52.8709* 76
Tokyo
0.329 11.78** -1.179 -18.11** 0.873508 139.5425** 504
Tokyo
0.298 9.86** -0.641 -12.25** 0.878407 26.133 207
Asakusa
Table 1-b Coefficient estimates of the rent function Tobu–Tojo
Time Distance from CBD
λ
Walking Time Floor Space
sκ −1
κ Frequency of Train Building Age Room Floor Building Story Dummy New Dwelling Dummy Senkawa^ Dummy Meidaimae^ Dummy Gotokuji^ Dummy Shimokitazawa^ Dummy Jiyugaoka^ λ κ R2 White het. test Number of observations Terminal station
Seibu–Ikebukuro
Keio-hon･ Sagamihara Estimated t-value
Odakyu–Odawara
Tokyu–Toyoko
Estimated
t-value
Estimated
t-value
Estimated
t-value
Estimated
t-value
Estimated
26842.6
48.19**
46750.4
49.66**
80267.1
50.99**
72946.6
41.01**
238731
38.58**
534555
23.59**
-41.3425
-24.54**
-132.358
-45.25**
-51.2781
-35.03**
-208.085
-33.81**
-1527.03
-39.92**
-702.852
-32.96**
-23.3221
-9.14**
-19.2337
-7.11**
-27.4859
-11.25**
-29.9116
-10.96**
-35.8139
-12.87**
-44.8
-10.73**
-20948.7
-41.06**
-48574.9
-44.85**
-103220
-48.33**
-92294.9
-38.41**
-422367
-37.50**
-1143120
-23.32**
-0.13554 -23.7677 122.573 19.0919
-0.11 -11.67** 2.60** 4.13**
0.150826 -23.3079 188.803 19.3944 53.307
0.19 -14.72** 4.67** 4.82** 1.25
3.16935 -22.5244 125.116 16.805 111.124
2.31* -12.27** 3.20** 4.86** 2.72**
3.85841 -25.8895 148.99 26.6465 8.40149 258.38 327.661
5.40** -13.15** 3.30** 6.24** 0.16 8.48** 4.02**
4.90983 -29.6283 333.223 2.11437 103.043
5.96** -13.83** 6.97** 0.33 2.04**
0.988158 -31.1658 113.932 9.01036 219.511
0.41 -11.48** 1.69 1.14 2.40*
623.606 540.046
19.81** 10.66**
Constant
r1λ − 1
Seibu–Shinjuku
0.298 9.77** -0.641 -10.98** 0.885841 80.0354** 468
Ikebukuro
0.915 8.51** -0.85 -18.86** 0.897648 151.522** 658
0.868 20.22** -1.332 -19.61** 0.913768 154.33** 586
Shinjuku
Ikebukuro
^ denotes particular station dummy. * indicates significant at 5% and ** indicates significant at 1%.
20
0.368 9.74** -1.33 -9.25** 0.845505 177.518** 918
Shinjuku
-0.212 8.35** -1.816 -10.72** 0.864292 232.716** 968
Shinjuku
t-value
571.108 10.80** 0.081 5.35** -2.162 -12.30** 0.781368 204.893** 630
Shibuya
Almost all explanatory variables are significant, and their coefficients are consistent with theory in each equation, although dummy variables are also used. Rent decreases as the distance from the CBD increases and as walking distance increases. An increase in the frequency of trains increases the benefits and convenience of using rail because it reduces the average waiting time. Thus, it raises rent. An increase in the age of a dwelling implies a decline in housing quality, and lowers rent.15 Floor space has a positive coefficient, which suggests that scale economies affect the market for rental housing. Both the dwelling floor space and building story have positive and significant coefficients in almost all equations. These suggest that taller buildings and dwellings on higher floors are generally of higher quality.
Estimation of commuting cost Next, we estimate unit commuting costs. The rent gradient (-R') is calculated from the results in Tables 1-a and 1-b. We require data on s(r). Average floor space among families living in residential districts around the stations was obtained from the 1995 census. We used data on floor space in Tokyo, which are aggregated by towns with stations. However, these data are not available for prefectures other than Tokyo. Hence, for these
15 We use dummy variables of zero for new buildings and variables for the age of the dwelling, considering the possibility of non-linearity between the housing rent and age. In Japan, because there is little transaction volume in the secondary market for housing, a new building is valued more than an old building. See Yamazaki [23].
21
prefectures, we used average values for municipal districts. Substituting the rent gradient and the floor space into equation (7), denoted by R' and s(r), respectively, we calculate commuting costs between stations. Since data on distance from the CBD are discrete for stations rather than continuous, as in equation (7), the right-hand-side of equation (9) must be modified to incorporate the discrete term for distance, Δr, which denotes time between stations. That is:
c = − R' (r ) s(r ) ≈ −(a1r λ −1 )s(r )Δr
.
(9)
Using data obtained from equation (9) as the dependent variable, the following equation is estimated:
c = α 0 + α1 where g ≡
g μ −1
μ
N (r ) and K
δ
+ α 2 r + α 3 Δt + δ ,
(10)
is an error term.
However, there are insufficient observations for one region along one route, because the available sample size is constrained by the number of stations within a distance of one hour. There are only around 15 observations for the Seibu–Ikebukuro line. Pooling the data for each region yields a sample size of 325 from which to estimate a commuting-cost 22
function of the congestion rate g, the time distance r and the pecuniary cost (the fare per mile Δt). The congestion rate is calculated by dividing the number of commuting ticket users N(r) by the transportation capacity K in two hours at peak time.16 This marginal out-ofpocket cost of commuting is defined as the difference between the monthly commuting ticket fare from the CBD to the station and the fare to the previous station from the CBD. We used a Box–Cox transformation of the congestion rate to account for possible nonlinearity because the variable appears to have an increasing effect on the marginal disutility.17 Considering the interdependency between the congestion rate and the congestion cost, we use the instrumental variables of the highest price in commercial area around each station and the number of commuters from each station. The Hausman test rejects the hypothesis about the endogeneity of these instrumental variables at 5% significance level. Estimation results for equation (9) are reported in Table 2.
16 The number of commuters and railroad capacity are available from the Institution for Transport Policy Studies [11]. 17 We use the White test to detect heteroscedsticity. The White het test in Table 2 shows to reject a possibility of heteroscedsticity.
23
Table 2 Coefficient estimates of congestion cost Va r i a b l e s
Estimated Coefficients
t-value
Congestion rate
( α 1)
6.70497
38.28**
Distance from terminal station
( α 2)
-305.885
-2.42**
Marginal pecuniary cost
( α 3)
-0.50406
-9.58**
(μ )
1.176
18.24**
R2
.935137
White het. Test
202.371**
Number of observations
325
**indicates significant at 1%, *indicates significant at 5%.
The positive and significant estimates for α 1 and μ indicate that congestion generates negative external effects on commuters. The negative and significant coefficient on distance indicates decreasing marginal costs relating to distance, which suggests scale economies affect journeys to work. The coefficient of the commuting fare α 3 is negative and significant. This seems somewhat a surprising result, because almost all commuters are able to receive commuting allowances from firms. Furthermore, commuting costs paid by firms can be deducted from profits. 18 It implies subsidy to commuters. 19 The congestion cost is calculated from the empirical results obtained above. The congestion charge must equal the increase in the commuting costs of other passengers induced by an
18 See Hatta and Ohkawara [5]. 19 This result might show that 50% of passengers only get such implicit subsidy.
24
additional passenger. Since an increase in the number of passengers affects all passengers, we calculate the extent to which an additional passenger imposes external effects on other passengers. We determine the marginal congestion cost as follows:
Marginal Congestion Cost =
=
∂c N ∂N
(11)
∂c dg ∂c × ×N = g ∂g dN ∂g
= α 1 g μ −1 × g = α 1 g μ
Using the estimates of α 1 and μ in Table 2, we calculate estimated congestion costs between the stations on each route. These estimates are reported in Table 3. The congestion cost from the terminal station is the accumulated sum of the congestion cost to the next station evaluated from the corresponding congestion rate in each section. The congestion costs are between 2.05 and 9.59 times the regular fare, and as expected, rise with the congestion rate. A decrease in the congestion rate in a particular section reduces congestion costs in that section. The congestion costs for the JR Keiyo line and the Tobu–Isezaki line seem relatively low, while those for the Keio–Honsen , the Odakyu–Odawara and the Tokyu-
25
Toyoko lines are high. This is partly because the congestion rate for the Tobu–Isezaki line is lower than on the other lines. On the other hand, since the fare on the JR Keiyo line is higher than on the other lines, the ratio of congestion costs to fares appears lower than on other lines. Appendix shows the average fares per time and distance for each line. The Keio-honsagamihara, the Odakyu-Odawara and the Tokyu-Toyoko are cheaper and have trains run more frequently than other lines. Their price policy partly explains higher ratio of congestion cost to fares than other lines. There are problems involved in examining why congestion costs differ between rail routes. Since definitions of transportation capacity (K) differ between rail companies, so do congestion rates and congestion costs. In addition, the ratios of commuting ticket users to the total number of passengers at congested times also differ between rail routes. Therefore, we must consider these issues when comparing charges between routes.
26
Table 3 Simulation results: congestion cost (units: total cost = million yen) Congestion Congestion Congestion Congestion Time Fare (a) (b)/(a) Time Fare (a) (b)/(a) cost (b) cost (b) rate† rate† Station % Min yen yen % min yen yen JR Chuoh (Shinjyuku–Takao) total cost 317,821 Tobu–Tojo (Ikebukuro–Sakado) total cost 148,174 Ogikubo 225 10 160 142 13 160 1,158 7.24 Kamiitabashi 675 4.22 Kokubunji 194 26 380 135 36 400 2,156 5.67 Kamifukuoka 1,930 4.82 Hachioji 159 44 460 132 50 570 2,685 5.84 Sakado 2,593 4.55 Seibu–Shinjyuku (Shinjyuku–Honkawagoe) total cost 119,102 JR Jobanshin･ Joban (Ueno–Ushiku) total cost 270,701 Kitasenju 207 13 160 154 14 200 701 4.38 Saginomiya 888 4.44 Matsudo 214 23 290 136 28 260 1,452 5.01 Tanashi 1,623 6.24 Kashiwa 204 33 450 110 52 420 2,416 5.37 Sayama 2,217 5.28 Seibu–Ikebukuro (Ikebukuro–Koma) total cost 128,886 JR Keihintohoku･Takasaki (Ueno–Fukiage) total cost 173,703 Urawa 211 19 380 158 18 230 1,614 4.25 Ooizumigakuen 1,278 5.56 Oomiya 197 26 450 121 37 360 2,251 5.00 Kotesashi 1,847 5.13 Okegawa 178 41 650 112 47 450 2,584 3.98 Hannou 2,345 5.21 JR Keiyo (Tokyo–Soga) total cost 51,223 Keio-hon･sagamihara (Shinjyuku-Hachioji) total cost 246,975 Kasairinkaikoen 148 13 210 149 16 170 662 3.15 Chitosekarasuyama 1,326 7.80 Shinurayasu 160 18 290 141 31 270 1,027 3.54 Futyu 2,590 9.59 Inagekaigan 162 39 620 Keiohatiouji 115 49 350 2,149 3.47 3,176 9.07 JR-Sobu (Tokyo–Inage) total cost 193,254 Odakyu–Odawara (Shinjyuku–Aikoishida) total cost 349,023 Kameido 187 10 160 161 22 210 621 3.88 Seijogakuenmae 1,698 8.09 Nishifunabashi 170 28 290 158 38 300 1,542 5.32 Shinyurigaoka 2,804 9.35 Inage 159 46 620 139 67 480 2,333 3.76 Honatsugi 3,853 8.03 Tobu–Isezaki (Asakusa–Himemiya) total cost 103,743 Tokyu–Toyoko (Shibuya–Kikuna) total cost 69,877 Kosuge 69 17 190 165 12 150 389 2.05 Jiyugaoka 803 5.35 Takenotsuka 103 25 240 163 23 210 880 3.67 Hiyoshi 1,585 7.55 Kasukabe 109 54 500 155 29 240 1,991 3.98 Kikuna 1,896 7.90 Station
The congestion rate is a weighted average of congestion rates between stations, in which the weight is the ratio of the distance between stations to the total distance.
27
4. Conclusions In this paper, we developed an econometric model for estimating congestion costs in rail travel. Congestion charges have been estimated by using data obtained from the rent functions for the railways in the Tokyo metropolitan area. An increase in congestion generates an additional disutility that makes the rent gradient between stations steeper. Thus, some of the difference between rents indicates the disutility due to congestion on the train between stations. Paying attention to the rent gradient, in which the external effects of congestion should be reflected, we included the congestion rate as an explanatory variable in the estimation equation for the rent differential to the next station. We found that congestion rates have a significant and positive effect on differences in rents. By using the estimated coefficient of the congestion rate, we found that congestion charges are between 2.05 and 9.59 times the fares. However, we cannot treat the estimated congestion cost as the optimal charge for the following reason. We have not considered the rational reactions of consumers and firms to the proposed congestion charges. Commuters would change their journey times if they had to pay congestion charges at peak time. Some might commute to the CBD by car rather than rail. Since the demand curve for rail travel is negatively sloped, our method
28
overestimates congestion costs, unless demand for rail services is inelastic.20 However, in Japan, as Hatta and Ohkawara [5] pointed out, although commuters do not directly bear commuting costs because they receive commuting allowances from firms, they do experience time delays and fatigue when commuting. Thus, we may have neglected the possibility of having overestimated congestion costs in the short run, since we could not find the negatively sloped demand curve for commuter rail travel, as Table 2 shows. While our estimated congestion costs are optimal in short run, they are not optimal in the long run, when firms can introduce flexible working hours and relocate to reduce the commuting costs of workers. We must examine how firms might seek to avoid congestion charges. Then, we might find a negatively sloped demand curve for rail travel from which we could estimate more accurately the optimal congestion cost, with the congestion externality being equal to the congestion cost.
20 Another reason is due to the problem that the fare is not necessarily equal to the marginal cost of rail services because the fare is regulated by the authorities.
29
References ［1］Arnott, R., de Palma, A. and Lindsey, R. “Economics of a Bottleneck” Journal of Urban Economics, January 1990, vol.27, no.1, pp.111-30. ［ 2 ］ Arnott, R. J. and MacKinnon, J. G.
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on Congestion Easing” Highway and Automobile,1993. Express Highway Research Foundation of Japan, vol.36, no.10, pp. 29-38 (in Japanese). ［9］Henderson, J. V. Economic Theory and the Cities, Academic Press, 1977. New York. Institution for Transport Policy Studies [2003] Toshi Koutsu Nenpo. ［10］Kraus, M and Y. Yoshida "The Commuter's Time-of-Use Decision and Optimal Pricing and Service in Urban Mass Transit, 2002. " Journal of Urban Economics”, Vol.51, pp170-195 ［11］Mohring, H.
Transportation Economics, 1976. Ballinger Publishing Company,
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Appendix
Terminal Station JR Chuoh
Shinjyuku
Edge Station
Time
Distance
(minute)
(Km)
Fare
Number of Station
Frequency
(yen)
Fare/Distance
Fare/Time
(yen/km)
(yen/minute)
Takao
51.6
42.8
22
540
55
12.6
10.5
JR Jobanshin･ Joban Ueno
Ushiku
55.1
52.8
22
950
40
18.0
17.2
JR Keihintohoku･ Ueno Takasaki
Fukiage
57
54.2
12
950
50
17.5
16.7
JR Keiyo
Tokyo
Soga
46.3
43
17
740
25
17.2
16.0
JR Sobu
Tokyo
Soga
46.1
35.8
19
620
50
17.3
13.4
Tobu–Isezaki Asakusa
Himemiya
52.5
38.4
28
500
70
13.0
9.5
Tobu–Tojo
Ikebukuro
Sakado
50.2
40.6
26
570
55
14.0
11.4
Seibu– Shinjyuku
Shinjyuku
Honkawagoe
60.5
47.8
29
480
58
10.0
7.9
Seibu– Ikebukuro
Ikebukuro
Koma
66
48.5
28
480
43
9.9
7.3
Keio-hon ･ sagamihara Shinjyuku
Hachioji
48.8
37.9
34
350
65
9.2
7.2
Odakyu– Odawara
Shinjyuku
Aikoishida
66.2
48.5
35
520
61
10.7
7.9
Tokyu– Toyoko
Shibuya
Kikuna
28.6
18.8
16
240
55
12.8
8.4
33
