A quantitative transportation project investment evaluation approach with both equity and efficiency aspects

Research in Transportation Economics 36 (2012) 93e100

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A quantitative transportation project investment evaluation approach with both equity and efficiency aspects Jing Shi*, Nian Zhou 1 Institute of Transportation Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 19 April 2012

The motivation of this study is to develop a method for evaluating transportation investment quantitatively with consideration of both efficiency and equity. The current evaluation methods, predominantly costebenefit analysis (CBA), concentrate mainly on the economic efficiency. Lacking equity considerations, these evaluation methods may result in an inappropriate investment. China is now a typical country with such a problem. With the huge investment in transportation infrastructure flooded in eastern provinces decades ago, these areas are benefitting the high GDP growth rate which is supported by these infrastructure, while the western provinces are suffering from the poor transportation system. Developing countries tend to invest more in comparatively developed areas for a higher return rate, leaving diversity between areas become more and more huge. This study introduced equity impacts into transportation investment evaluation methods after the concepts of various types of equity have been reviewed. Four quantitative models are proposed corresponding to 4 types of equity. Hereafter, an evaluation model from both equity and efficiency aspects for highway infrastructure investment appraisement is developed based on the theory of Wilson’s entropy. The Lagrangian method is used to testify the model and to prove the result possesses optimal benefit distribution. This model takes account of the differences among different areas and social groups. Sensitivity analysis is conducted before twelve highway investment projects in China are studied with the method. The evaluation result is observably different from the one derived from the CBA. This fundamental consideration of transportation equity as well as the quantitative models may be helpful to developing countries or areas. However, further studies on transportation equity still need and the model still needs to be improved.
2012 Elsevier Ltd. All rights reserved.

Keywords: Transportation investment Equity Costebenefit analysis Wilson entropy

1. Introduction Transportation infrastructures have great impacts on both social and economic development. The investment on transportation system, like new transportation infrastructures plans, is huge. However, uncharged transportation facilities could hardly cover the construction cost. Thus sequentially spending limited financial funds on transportation projects according to their rewards is advisable. Therefore, various evaluation techniques and manuals are put forward and the longstanding most widespread method is costebenefit analysis (CBA). The CBA method is widely used in

* Corresponding author. Department of Civil Engineering, Tsinghua University, Beijing 100084, China. Tel./fax: þ86 10 62772300. E-mail address: [email protected] (J. Shi). 1 Department of Civil Engineering, Tsinghua University, Beijing 100084, China. 0739-8859/$ e see front matter
2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.retrec.2012.03.002

different countries such as UK (Vickerman, 2000), France (Quinet, 2000), USA (Lee, 2000), Japan (Morisugi, 2000), and many other developing countries (Talvitie, 2000). The CBA method is efficient in dealing with the economic efficiency of project investment. But its drawback of neglecting social equity impacts, another significant aspect of social welfare is also noticeable (Guo, 2001). Sustainable transportation and Green Transportation put forward last century also calls for transportation equity. Sustainable transportation development indicates that some groups or individuals should not benefit at the expense of others, especially the disadvantaged groups or individuals (Sanchez, Stolz, & Ma, 2003). And transportation equity is surely one big issue when considering distributing the welfare gained from economic development through the entire society fairly. Moreover, harmonious development among regions is a Chinese official policy, which takes transportation equity among regions as an important aspect. Therefore, this study aims at probing into modeling the

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J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100

transportation equity quantitatively and developing a comprehensive evaluating approach for transportation investment with consideration of both efficiency and equity aspects is significant. 2. Literature review It seems not easy for people to judge whether something is fair, not to mention the degree of fairness or justice due to the complexity of equity analysis. There are no universal definitions of equity and fairness. This well explains why few researches were conducted on social equity in the past. However, unfairness was found by a growing number of researchers in recent years. Litman (2003) stated that nearly one third of Canadian families are transportation disadvantaged, and inadequate transport sometimes leads to social exclusion. This is particularly true for people who cannot afford or drive automobiles but living in automobiledependent communities. High-income class people who own private car (only 20% in Beijing) unfairly enjoy the greatest share of benefits from transportation projects at the expense of the low quality of other transportation modes, such as transit service and facilities for walking and cycling (Zhu & Li, 2003). According to the principle of diminishing marginal utility, 100 dollars has a higher value for low-income groups than high-income ones. Thus, most people would prefer public policies promoting the economic status of the low-income class rather than the high-income class (Almeida, Haddad, & Hewings, 2004). Álvarez, Cantos, and García (2007) found that people of different income levels have different sensitivities on the transportation toll. And Rune Elvik (2009) similarly pointed out that transportation infrastructure would affect people’s safety in different regions in different degrees. John Rawls (1971) set up the widely accepted theory of justice which is called “justice as fairness.” The theory is composed of two principles of justice. The first principledprinciple of equal basic libertiesdexpresses an egalitarian concept of justice. And the second principleddifference principledstates that people who are equally talented and motivated must have equal opportunities to attain desirable positions, which means people’s lives should depend on neither their birth nor upbringing. John Rawls’s theory is used to test whether the constitution, laws, elementary social rights etc are fair. Since transportation is treated as people’s basic rights in contemporary society, John Rawls’s theory can be introduced into the transportation area. Initially, the recognition of equity is limited in the judgment of income distribution. Classical ways of judging are the Lorentz Curve and the Geordie Coefficient. With the extension of the research area, the concept of equity permeates through various disciplines and social problems. The European Union Transport Research Fourth Framework Program invokes two dimensions of equity, horizontal equity associated with the principle of equality of opportunities, and longitudinal equity associated with the comparison of conditions between present and past, for each individual citizen, and social groups. The National Cooperative Highway Research Project held in 1994 defines equity as the distribution of cost and benefit among people of different incomes (Viegas, 2001). Jones (2004) defined transportation equity as comprised of spatial equity and social equity. Raux and Souche (2004) review these issues of equity, and propose the three dimensions of territorial, horizontal and vertical equity in a study implemented in Lyon. Litman (2005) classified transportation equity into horizontal and vertical types. These concepts of equity refer to a reasonable allocation of benefits among various social groups or individuals, but do not consider the problem of distribution of opportunities. The Intermodal Surface Transportation Efficiency Act (ISTEA) of USA advocates that transportation infrastructure decisions should involve public participation. This is because the traditional planning system

merely includes experts and governors in the decision-making process and excludes the public. Shi, Yang, Huang, and Ying (2009) define transportation equity mainly in four aspects according to China’s situation: equity among diverse traffic mode users, different social groups, different regions, and different generations. When it comes to the evaluation model of transportation equity, Silva and Tatam (1996) made some modifications to the MultiCriteria Assessment models and selected the criteria to represent regional and community groups’ interests. The evaluation results can address both efficiency and equity issues, but the whole procedure is too complex and relies on a large-scale investigation of personal intent. The purpose of this study is to establish an evaluation model for transportation projects investment considering equity quantitatively. Parameters reflecting social compensation on disadvantaged groups are introduced and different kinds of equity and various equity impacts of transportation investments are considered in the model. The evaluation example in the latter part of this article could be useful reference for decision makers. 3. Classification and quantitatively measure of transportation equity In this part, four quantitative evaluation models corresponding to four kinds of equity are described. 3.1. The equity among different traffic modes users From the view of equity among different transportation mode users, one should cover the social costs he causes. One normal case of unequal is that road users like walkers have to bear the extra cost such as noise, air pollution, brought by automobile users. A model measuring the difference of the cost can be used to evaluate the equity among different traffic modes. The model can be expressed as follow:

min SV

¼

P

Z

SVi ðtÞdt ci; t  Z X X  P  ¼ CSij ðtÞ  CRij ðtÞdt  i

i

j

(1)

j

Subject to

CSij ðtÞ>0; i ¼ 1; 2; .; I

CRij ðtÞ>0 j ¼ 1; 2; .; J

where: SVi(t)dthe difference between what the users of traffic mode i should pay and what he pays indeed in a given time period t; CSij(t)dthe social cost j that the users of traffic mode i should pay in a given time period t; CRij(t)dthe personal cost j that the users of traffic mode i pays in a given time period t; Idthe number of kinds of traffic modes; Jdthe number of kinds of social cost. Payment and gain in this model can be supplemented according to the time and budget of the evaluation work. For example, tax could be considered while money directly spent is included if it is needed in certain research. If the difference between CSij(t) and CRij(t) is larger, it means other road users pay more extra costs caused by users i. Social equity would be worsen. So the smaller SV represents a fairer state.

J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100

Gidthe benefit that the project brings to group i, and Gi is normalized; aidthe weighting coefficient for social compensation; Smaxdsubject to equation (4), the maximum systemic entropy at the optimal distribution state; mdthe number of social groups.

3.2. The equity among different social groups Sustainable development of transportation requires no social groups been sacrificed for other groups’ benefits. To ensure each social group enjoys fair accessibility, transportation disadvantaged groups should be compensated by improving their travel conditions. For example, the low-income class prefers relatively inexpensive transportation modes, such as public transit. So it is important to improve the condition of public traffic modes. The aging population is another group which is thought to be transportation disadvantaged. From the view of equity, those senior citizens should enjoy the same travel opportunity as others. Hence special consideration on convenience of the transportation system is needed. All in all, transportation projects with the most comprehensive consideration on equity among different social groups are the ones should be invested most. Meanwhile, the government should compensate the disadvantage groups for not gaining equal benefits from transportation investment according to this type of transportation equity. With the development of equity, many models, mainly based on horizontal equity,2 are put forward and the optimal state is absolutely equally benefits distribution. Another problem about equity among different social groups is social compensation for transportation disadvantage people, which refers to vertical equity.3 An evaluation model based on Wilson entropy is set up (Shi, Yang, Ying, & Huang, 2008; Yang, Shi, & Lu, 2005). In thermodynamics, the systemic entropy describes the disordered extent of a system. When the systemic entropy reaches the maximum, the energy in the system becomes most evenly distributed. According to the resemblance of the thermal system and the transportation system, we use systemic entropy to describe the equilibrium degree of the benefit distribution in a region. The larger the systemic entropy of a region is, the fairer the benefit distribution in the region is. Firstly, the definition of social compensation ai will be explained. Benefited groups will be identified according to their benefit and cost brought by the project. And based on the principle of vertical equity, those transportation disadvantaged groups should get benefit compensation. ai is the weighting coefficient for social compensation, which is established from social investigations. For any group i, ai  1, the bigger ai is, the more compensation group i should get. The model can be expressed as follows:

min R ¼ 1 

S ¼

S Smax

m X Gi ðlnGi  lnai Þ i¼1

ai

8 m > > < P 1G ¼ 1 i s:t: i ¼ 1 ai > > : 0G a i i

95

According to the model, it is known that 0  R  1. The smaller the R, the bigger the S. And the bigger the S is, the larger the systemic entropy of the region is. So a smaller R means a more equable society. When R ¼ 0, the benefit distribution reaches optimal and it is the most equity status. When R ¼ 1, the society reaches a most inequity status. 3.3. The equity among different regions Based on the theory of scale economy, investment in developed regions may gain more economic benefits. If decisions are made with the monetary aspect of the investment is considered, the disparities between developed regions and undeveloped ones will increase. So the equity issue must be considered before transportation investment is allocated among different regions. The improvement of transportation infrastructure in undeveloped regions will bring more social benefit, which will decrease the disparity among different regions. In the following formula, price index P, housing expense Q , and average personal income Y are used to indicate the economic developed level of different regions. Region k is used as a reference to calculate the equity evaluating index b4 of regions. b be can be formulated as:

b¼



P Pk

ð1BÞð13 Þ 

Q Qk

Bð13 Þ 

Y Yk

3 (5)

where:

bdthe equity evaluating index of a region. The bigger b is, the more undeveloped the region is. The project should be constructed earlier; Y, Ykdthe average personal income of the region studied and that of the reference region; P, Pkdthe price index of the region studied and that of reference region; Q , Q kdthe housing expense of the region studied and that of reference region; Bdthe proportion that the housing expense takes in the family’s cost; 3 dthe level of equity that population comprehend, between 0 and 1. It can be get from investigation.

(2)

(3) In general, the more developed the region is, the bigger the value of 3 is and the smaller the value of b is. So those undeveloped regions usually get a greater b.

(4)

where: Rdthe extent of benefit equity among different social groups; Sdthe systemic entropy at one benefits distribution state;

2 Horizontal equity is concerned with the distribution of impacts among individuals and groups considered equal in ability and need. 3 Vertical equity is concerned with the distribution of impacts among individuals and groups that differ in abilities, needs, income, or social class.

3.4. The equity among different generations The impacts transportation investments and policies could bring to people in different periods and the notion of sustainable transportation attracted us to analyze the transportation equity among different generations. The concept of Sustainable Transportation is the ability to meet the needs of current society to move freely, gain access, communicate, trade, and establish relationships without compromising the ability of future generations to meet

4

The derivation of Regional Equity Coefficient b is explained in the Appendix A.

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J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100

their own needs. It mainly involves the distribution of welfare and resource among generations. The transportation infrastructure usually cost a great capital investment and has a long serving life. The main points of the equity among different generations are as follow.

C ¼

B ¼ 1. The transportation infrastructure usually needs huge amounts of land. As long as the land limited, the conflict between the provision and the need of land will exist. The over use of the land will deprive our progeny’s developing rights. 2. The transportation system consumes energy while brings out environmental pollution, such as air pollution, acid rain, noise, photochemical radiation. The pollution will impair living quality of our progeny. 3. The urban spatial structure is the reflection of the urban history and culture. Transportation facilities usually damage the traditional culture by changing the urban spatial structure in reality. The core of the equity among different generations is to ensure their surviving and developing rights, which is still unrecognized by majority. The evaluation model can be expressed as follows:

 Kn;n1 ¼

En En1

 f ðiÞ

f ðiÞ ¼ f ðM; S; LÞ

(6) (7)

where: Kn, n  1dthe index of evaluation for equity among different generations. In this research, 10 years is taken as one generation. While Kn, n  1 ¼ 1, the next two generations reaches relative equity. While Kn, n  1 < 1, it is more beneficial for the former generation. While Kn, n  1 > 1, it is more beneficial for the later generation; En, En  1dliving quality of generation n and generation n  1. It can be reflected by the evaluation indexes of resource and environment; f(i)dthe preference rate of generation n and generation n  1. It is a function on life level (M), technology level (S), environment level (L). As the increase of these levels, people are more willing to, and also more capable to increase investment on them, so as the preference rate. 4. Highway infrastructure investment evaluation model considering both equity and efficiency

T X

Cj

T X

Bj

j ¼ 1 ð1

(9)

 q0 Þj

where: jda single year in the evaluation period, j ¼ 1, 2, ., T. Tdthe total evaluation period of highway projects Cj, Bjdcosts and benefits in the year j. q0dsocial discount rate. Based on the CBA method and the principle of consumer surplus, time value, operating cost, environmental cost, and expense of accident loss are taken into account in the quantitative analysis of C, B. While C > B, usually it is not worth to invest except for some special reasons such as political reasons. While B > C, the highway facility is worth investing. If many highway facilities are waiting in the list, the value of B and the rate of B/C are considered to decide the building orders. 4.2. Equity issues impacting on highway infrastructure investment The equity impacts of highway infrastructure investment could be categorized into three aspects: public involvement and awareness of the decision-making process, regional equity with regard to the differences of economic development among areas, and vertical equity with regard to the differences of social-economic benefits distribution between advantaged and disadvantaged groups. To use the model to analyze the equity impacts, social groups should be divided according to the net benefit caused by highway infrastructure first. In general, social groups can be divided into four, road users, roadside residents, local government, and project contractor. The cost and benefit for the group i will be calculated for evaluation of highway project investment. 4.3. Evaluation model While investments in different regions are compared, regional equity index b and social compensation coefficient a should be considered together. Equity impacts among different groups and different regions are considered in the following model. m X Gi ðlnGi  lnai Þ

S ¼ bj

i¼1

In China, highway is developing very fast. However highway development is meeting several limitations, such as short of huge investment, land use limitation, adequate environmental problems, of course the balance between provide and supply.

bj ¼

4.1. Traditional evaluation method for highway investment

s:t:

The widely used traditional evaluating method is called CBA (costebenefit analysis). All the cost and benefit generated during the whole project lifecycle, which is the construction period plus 30e50 years depending on the service lifespan of the facility, are converted into the net present values (NPV). The social discount rate, such as 4% (0e40 years) in Japan and 3.5% (0e30years) in England, is used to convert all the costs and benefits into the Net Present Value (NPV). Then the benefit NPV and the cost NPV are used to decide whether it is worth to invest in a highway facility.

(8)

j j ¼ 1 ð1  q0 Þ

8 < :



bj

Pj Pk

ð1BÞð13 Þ 

m 1 P

i ¼ 1 ai

(10)

ai

Rj Rk

Bð13 Þ 

Yj Yk

3

Gi ¼ 1

0  Gi  ai

(11)

(12)

where:

bjdthe equity index of region j; mdthe number of social groups in region j. Other parameters have the same meanings as chapter 3. In this model, public participation and awareness 3 , regional equity among different areas bj, and vertical equity among different

J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100

benefit groups ai are all included. investigations.

3

is derived from social

4.4. Optimal benefit distribution The Lagrangian method is used to prove the existence of optimal state. A parameter l is introduced to help to solve the math problem.

L ¼ S þ l bj

m X 1 i¼1

vL vGi

¼

ai

! Gi  1

(13)

bj vS þl ai vGi

(14)

bj bj ðlnGi  lnai Þ þ ðl  1Þ ai ai

¼ 

The point which satisfies vL/vGi ¼ 0 is the point L gains extreme value, and the optimal benefit distribution is achieved. This model could reflect the vertical equity. Let vL/vGi ¼ 0, equation (14) can be written as:

bj bj  ðlnGi  lnai Þ þ ðl  1Þ ¼ 0 ai ai 0Gi ¼ ai eðl1Þ

(15)

With consideration of equation (12), we can get e(l  1) ¼ 1/mbj. Thus,

G0i ¼

Smax

1 ai m bj

(16)

ai 1 ln m mb bj X m j ¼ bj ai i¼1

R ¼ 1

bj

  ln mbj

!   ¼ ln mbj

(17)

1

ai

!

1  lnn  lnbj    2 ln nbj

(19)

The value of bj is determined by the relative developed level of the region j and a preset reference region. So we can choose the reference region to make bj > 1 established for each j. n is the number of social groups, and n  3 in general. So ln n > 1, ln bj > 0, 1  ln n  ln bj < 0, vR/vbj < 0. The increase of bj will lead to a decrease of R. Undeveloped areas have larger bj and smaller R. The equity evaluation result of such highway infrastructure investment for these regions is preferential and the compensation for undeveloped areas could be estimated. Equations (13)e(17) are used to calculate the potential max value of the S of a special region, so bj could be treated as a constant for region j. Consider the sensitivity of the systematic entropy in equation (20). According to equation (15), ln Gi  ln ai ¼ l  1. So:

vS vGi

bj ðlnGi  lnai þ 1Þ ai bj bj ¼  ðl  1 þ 1Þ ¼   l < 0 ai ai

¼ 

bj v2 S ¼  <0 ai Gi vG2i

(20)

(21)

Then, it is known that the increase of Gi will lead to a decrease in S. And the decreasing rate becomes larger as Gi becomes larger. That is, when ai is fixed, the increase in benefit of one social group will lead the relative decrease of others and lead to the decrease of equity. And the benefit increase of these originally benefit more whose Gi is larger will lead more imbalance among different groups. 5. Model application 5.1. Process of evaluation

m X Gi ðlnGi  lnai Þ i¼1

n X Gi ðlnGi  lnai Þ

vR ¼ vbj

97

(18)

ai

In equation (16), G0i is the optimal distribution of the benefitecost rate (BCA). We know from equation (16), 1/m is the optimal distribution without any compensation, which means the BCR of each benefit group is equal. The optimal distribution G0i is in direct proportion with ai. The larger the value of ai is, the larger the distribution of G0i is. Disadvantaged groups have to obtain a relatively higher BCR than other groups to reach the optimal status, which represents the status of equity. This result satisfies the concept of equity among different regions and different benefit groups. 4.5. Sensitivity analysis The optimal distribution G0i is inversely proportional with bj, and this can be reflected by the differential coefficient of equity index R:

Twelve highway project examples are taken to validate the availability of the new equity evaluation model. Those projects are differently located from the developed eastern district (E1 w E4), the developing middle district (M5 w M8) to the undeveloped western district (W9 w W12) of China. The benefitecost ratios (BCR) of each project are also given (Table 1). The main steps of the evaluation process are as follows. Step 1: Divide the local people mostly influenced by the project into several social groups. The influences of those projects are practically analyzed in four community groups e road users, roadside residents, the project contractor and government as showed in Fig. 1. Step 2: Calibrate the parameters a, 3 . In the model, parameters a and 3 reflect the compensation and social awareness of equity respectively. Their values depend on people’s subjective perceiving, and should be obtained from a questionnaire.

Table 1 Benefit estimation of twelve project examples. Project Location Benefitecost ratio (BCR)

E1 Beijing 2.12

E2 Liaoning 1.78

E3 Jiangsu 2.35

E4 Fujian 1.96

M5 Shanxi 2.25

M6 Henan 1.66

Project Location benefitecost ratio (BCR)

M7 Jiangxi 1.43

M8 Guangxi 1.27

W9 Gansu 1.40

W10 Tibet 1.35

W11 Xinjiang 1.36

W12 Sichuan 1.52

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J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100

Environment influence Social-economic influences of road projects

Table 3 The modified coefficient of regional equity.

Accessibility Travel time Traffic cost Safety

Road Users

Roadside residents Economic influence

Project Location

Air pollution Noise Scenery Ecological system Emergent evacuation Real estate Industry

Project contractors

Project profit Project flexibility

Local government

Road investment Maintenance cost Public service cost Utilization of road space Tax

Fig. 1. An example of benefit groups for road construction projects.

Therefore, we designed an investigation in order to get the current status of public recognition of equity problems and gain the value of parameters with statistical methods. The data are collected from specialists, officials and citizens via the web or a face-to-face interview. Step 3: Calculate b. Regional status of the project location is taken into account (Table 2) and b is calculated as showed in Table 3. Step 4: Use the evaluation model to calculate the equity index R of each project and draw a ranking according to the value of R. The smaller the value of R is, the fairer the project is.

5.2. Comparison of investment priority with different principles We make final estimation from three different viewpoints e efficiency, equity, both efficiency and equity. Principle 1: efficiency Traditional estimation methods of highway projects mainly pay attention to the efficiency of investment. CBA is used to rank the priority of those projects, and its rule is that the larger the value of BCR of a project, the higher rank the priority of this project investment gets. Table 2 Regional economic status of twelve project examples, China Statistical Yearbook (2005).

E1 E2 E3 E4 M5 M6 M7 M8 W9 W10 W11 W12

Location

Price index P

Housing expense Q

Personal income Y

Proportion of housing expense B (%)

Beijing Liaoning Jiangsu Fujian Shanxi Henan Jiangxi Guangxi Gansu Tibet Xinjiang Sichuan

100.2 101.7 101.0 100.8 101.8 101.6 100.8 101.1 101.1 100.9 100.4 101.7

4737 2291 2197 2297 1611 1388 1210 1883 1275 1753 1817 1421

10584 5159 5274 5324 2934 3129 2739 2567 2171 2825 3237 2839

8.6 10.4 10.7 11.9 11.0 11.5 11.6 13.9 9.5 5.8 9.0 10.1

Note: the housing expense R is the average selling price of houses with the unit of Yuan/square mile. The unit of personal income Y is Yuan/person/year.

b Project Location

b

E1 Beijing 1.00

E2 Liaoning 1.58

E3 Jiangsu 1.57

E4 Fujian 1.56

M5 Shanxi 2.25

M6 Henan 2.19

M7 Jiangxi 2.39

M8 Guangxi 2.46

W9 Gansu 2.71

W10 Tibet 2.25

W11 Xinjiang 2.11

W12 Sichuan 2.30

Principle 2: equity Another important object of public project investment is to improve social equity. The equity estimation of highway projects is based on the benefit incidence of various community groups and regional equity of project locations. Its rule is that the smaller the value of equity estimation index R (see Table 4) of a project, the higher rank the priority of this project investment gets. Principle 3: both efficiency and equity Only when both efficiency and equity aspects of highway projects are taken into account, a comprehensive and reasonable conclusion can be drawn. The index R ranges from 1 to 0, which is the same to BCR. To adjust the result based on BCR, we define the division of the benefitecost ratio and equity estimation index (BCR/R) as the ultimate index. A larger value of BCR/R of a project shows that the project is comparatively better when both efficiency and equity are considered. And higher priority should be given to such a project when making investment decisions. The priority ranking of those projects are listed in Table 5. 5.3. Evaluation result The estimation results under the equity principle are quite different from those gained under the efficiency principle, especially for projects W9 w W12 located in the undeveloped western regions. The most important comparison of the results is between those under the efficiency principle and under both the efficiency and the equity principle. The rank of project E1 drops from No.3 to No.5, and the rank of project E2 drops from No.5 to No.9. In contrast, the rank of project M6, M7, and W9 increases obviously. The new estimation method concerning both efficiency and equity proves to be effective to reflect the compensation for disadvantaged groups and undeveloped regions. The Fig. 2 describes the results in another form. Table 4 Standard benefit ratio and equity estimation index. Standard benefit ratio of four groups Gia

E1 E2 E3 E4 M5 M6 M7 M8 W9 W10 W11 W12

Road users

Roadside residents

Project contractor

Government

0.759 0.526 0.456 0.486 0.338 0.371 0.328 0.329 0.298 0.366 0.388 0.350

0.174 0.058 0.118 0.107 0.068 0.067 0.056 0.049 0.045 0.029 0.035 0.042

0.114 0.063 0.096 0.078 0.057 0.041 0.052 0.049 0.036 0.066 0.070 0.056

0.030 0.016 0.023 0.019 0.014 0.007 0.010 0.003 0.012 0.004 0.004 0.010

Systemic entropy S

Equity estimation index R

0.789 1.081 1.329 1.237 1.598 1.440 1.602 1.545 1.687 1.406 1.355 1.514

0.431 0.414 0.277 0.325 0.273 0.336 0.291 0.324 0.292 0.360 0.365 0.318

a The data of benefits and costs of each group are provided by China International Engineering Consulting Corporation (CIECC).

J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100 Table 5 Priority ranking of project investment. Efficiency estimation

Equity estimation

Both efficiency and equity

E3 M5 E1 E4 E2 M6 W12 M7 W9 W11 W10 M8

M5 E3 M7 W9 W12 M8 E4 M6 W10 W11 E2 E1

E3 M5 E4 M6 E1 M7 W9 W12 E2 M8 W10 W11

Jiangsu Shanxi Beijing Fujian Liaoning Henan Sichuan Jiangxi Gansu Xinjiang Tibet Guangxi

Shanxi Jiangsu Jiangxi Gansu Sichuan Guangxi Fujian Henan Tibet Xinjiang Liaoning Beijing

Jiangsu Shanxi Fujian Henan Beijing Jiangxi Gansu Sichuan Liaoning Guangxi Tibet Xinjiang

99

developing countries who need to decide which project should be invested first while considering sustainable development. This study is original when it comes to evaluate transportation equity in a quantitative way. However, further study is needed to make the model more precise and more practicable.

Acknowledgments The financial supports of the National Natural Science Foundation of China (No.70571046), and National High-Tech Research and Development Program of China (863 Program, Grant No.2007AA11Z202) are acknowledged. I also acknowledge the contribution of my graduated students: Ms. YANG Lang, Ms. WU Zhaozhang, Mr. YING Xiwen and Mr. HUANG Qian, who were the members of this study projects. Appendix A. Derivation of a regional equity coefficient b

Fig. 2. Priority ranking curve of project investment.

Both efficiency and equity curve/rank are below the efficiency curve/rank for projects located in eastern developed regions, and above the efficiency curve/rank for projects located in middle and undeveloped western regions. This conclusion verifies the equity aspect of the new estimation method again. 6. Conclusions In China, transportation infrastructure investment is huge. Construction of transportation infrastructure usually brings convenience and economic development. However, construction needs cannot be fully satisfied because of the limitation of capital and other resources. Hence, the priority evaluation of transportation infrastructure projects is very necessary. As an important aspect of sustainable transportation, transportation equity has gradually drawn researchers’ attention. However, the usual evaluation method is the BCA which ignores the impact of equity. Although some researchers have already begun theoretical studies on transportation equity, practical and quantitative evaluation methods are still in need. This paper attempted to study the transportation equity quantitatively. Four quantitative evaluating models are established to analyze four aspects of transportation equity separately. Based on these models, an entropy type model with consideration of both efficiency and equity is proposed and used for highway investment evaluation. This model evaluates different highway investment in different regions based on the result of the BCA. Hence, a comprehensive and reasonable judgment takes both efficiency and the equity aspects into account can be made. It proved that the model is sensitivity, practical and applicable. As a case study, the proposed model is applied to judge the priority of 12 highway projects in different areas of China. The evaluation result shows the differences while considering the equity issue. The case might be irradiative for authorities in

A regional coefficient b is introduced to the evaluation model, the theoretical discussion of which is well explained in the Guide for Road Projects Evaluation Part 2 Integrated Evaluation (Committee of Road Projects Evaluation, 1999). In different regions, a one-unit increase in average personal income may lead to a different amount of social welfare increase. Based on this fact, the coefficient b of region j is defined as the ratio of the social welfare increase caused by a one-unit increase in personal income of region j and that of the standard region i. Let I be the set of regions under evaluation. For j˛I, let Yj be the average personal income of region j with the utility function Vj. Then let W ¼ W(V1,., Vi,., VI) be the social welfare function. Thus, the social welfare increase of region j due to a one-unit increase in personal income can be represented as follows:

vW vW vVj ¼ $ vYj vVj vYj

(1)

Then the coefficient b can be represented as follows:

vW vYj

b¼

!,

vW vYi

 ¼

vW vVj $ vVj vYj

!,

vW vVi $ vVi vYi

 (2)

Here, the social welfare function is set to be the function of CES type society:

" W ¼

X

#1=13 Vi13

(3)

i˛I

 0) is a parameter which represents the social awareness of equity. The utility function is set to be the CobbeDouglas type function as

3 (3

  ð1BÞ B Vj ¼ V Pj ; Rj ; Yj ¼ Pj Rj Yj

(4)

Pj is the price index of region j, Qj is the housing expense of region j, and Yj is the average personal income. B is the proportion of housing expense to the total family expenditure. Thus, with equations (2)e(4), the regional equity coefficient b can be represented as follows:

b¼

 ð1BÞð13 Þ  Bð13 Þ  3 Pj Qj Yj Pi Qi Yi

(5)

100

J. Shi, N. Zhou / Research in Transportation Economics 36 (2012) 93e100

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