SDT 261 AFFORDABILITY OF PUBLIC TRANSPORT: A METHODOLOGICAL CLARIFICATION

Transcription

1 SDT 26 AFFORDABILITY OF PUBLIC TRANSPORT: A METHODOLOGICAL CLARIFICATION Autor: Andrés Gómez-Lobo Ecenique Santiago, Sep. 27

2 Serie Documentos de Trabajo N 26 Affordability of public transport: a metodological clarification Andrés Gómez-Lobo Ecenique Departamento de Economía Universidad de Cile Abstract Tere as been a surge of interest recently on te relation between poverty and transport policies. Wen analyzing te relation between poverty and transport, often te affordability of public transport is estimated. In tis paper we present two alternative definitions of affordability used in te transport literature and discuss teir limitations. Any affordability measure covering only transport expenditure is bound to be a very partial view of ouseold welfare. In addition, te required affordability bencmark to determine weter transport costs are ig or not is arbitrary. Terefore, te approac tat uses te absolute level of tese affordability measures is meaningless. We also sow in tis paper tat te cange in te affordability measures, as opposed to its absolute level, can be given a more rigorous interpretation in terms of traditional welfare economics. In spite of tis last result, we argue tat to analyze weter transport subsidies are meeting teir social or distributional objectives it is muc more fruitful to use traditional income distributional tools suc as te relative benefit curve and its associated Gini coefficient. Keywords: transport subsidies, affordability, equity, welfare impacts

3 Affordability of public transport: a metodological clarification Andrés Gómez-Lobo Department of Applied Economic Analysis University of Las Palmas of Grand Canary Campus Tafira s/n, 357, Las Palmas de Gran Canaria, Spain Abstract: Tere as been a surge of interest recently on te relation between poverty and transport policies. Wen analyzing te relation between poverty and transport, often te affordability of public transport is estimated. In tis paper we present two alternative definitions of affordability used in te transport literature and discuss teir limitations. Any affordability measure covering only transport expenditure is bound to be a very partial view of ouseold welfare. In addition, te required affordability bencmark to determine weter transport costs are ig or not is arbitrary. Terefore, te approac tat uses te absolute level of tese affordability measures is meaningless. We also sow in tis paper tat te cange in te affordability measures, as opposed to its absolute level, can be given a more rigorous interpretation in terms of traditional welfare economics. In spite of tis last result, we argue tat to analyze weter transport subsidies are meeting teir social or distributional objectives it is muc more fruitful to use traditional income distributional tools suc as te relative benefit curve and its associated Gini coefficient. Keywords: transport subsidies, affordability, equity, welfare impacts Permanente Address: Department of Economics, University of Cile, Diagonal Paraguay 257, of. 5, Santiago, Cile. agomezlo@econ.ucile.cl, pone: (562) , fax: (562)

4 . Introduction Tere is a long literature in te transport field justifying public transport subsidies on economic efficiency arguments. Most, but not all, of tese arguments are second best in nature, in te sense tat subsidies compensate for externalities in oter parts of te economic system, namely private transport use, tat cannot be addressed directly. In tis context, public transport subsidies may reduce tese externalities improving resource allocation in society. However, in many situations subsidies are introduced for social or distributive reasons, particularly in developing countries. Te social case for transport subsidies starts by recognizing te importance of accessible and affordable transport for te well being of people. Transport is a complementary input to te obtainment of oter social benefits suc as education, ealt services and employment opportunities, among oters. Tis is sometimes couced in te catc all concept of social inclusion, an appealing term tat is unfortunately ard to define in an operationally useful way for policy decisions. Among te multilateral agencies, te relationsip between poverty and transport as received considerable attention of late. Incorporating poverty issues and pro-poor project design in transport projects as become an important priority for lending by multilateral banks. 2 2 See for example Asian Development Bank (2), Te World Bank (25), capter 3 of Te World Bank (22), Gannon and Liu (997) 2

5 Unfortunately, muc attention in tis field as centered on te affordability of public transport and on policies to make public transport affordable to te poor. 3 However, it is not clear wat is meant by affordable public transport or ow tis concept sould be applied in designing transport policies. In tis paper we examine two definitions of affordability and discuss teir relative merits. We ten sow tat te cange in tese affordability indices can be given a rigorous economic welfare interpretation. However, in spite of tis last result, we argue tat te use of an affordability measure is not te most promising approac to analyze poverty and transport issues. Instead, we argue in favor of a metodological approac more in line wit traditional income distribution analysis. Tis latter approac as been used in a number of recent case studies analyzing te impact of public transport subsidies on poor ouseolds. 2. How to define affordability in te transport sector Most studies on poverty and transport estimate te percentage of montly income or expenditure used on transport by poor families. In more formal terms, tis affordability measure can defines as: Aff N i= = x i ( p, y) i y p () 3 See SITRASS (24a; 24b), Suiying, Han, Weili and Dening (23), Howe and Bryceson (2), Godard and Diaz Olivera (2), and ECORYS and NEA (24) among oters. 3

6 were x i (p i,y) are te number of trips usually public transport trips or work related trips taken during te mont by ouseold member i, and y is ouseold income or expenditure. Te number of trips is presented as an explicit function of te price of trips and ouseold income. Tis measure is ten compared to a bencmark considered affordable to ouseolds. Armstrong-Wrigt and Tiese (987) consider tat tere is an affordability problem wit public transport wen more tan % of ouseolds spend more tan 5% of teir income on work related trips. According to Venter and Berens (25), te Sout African government as establised a % of income as a policy bencmark in its 996 Wite Paper on Transport Policy (Department of Transport, 996). Gomide, A., S. Leite and J. Rebelo (24) use a 6% limit to estimate te affordability of public transport in Bello Horizonte, Brazil. Tis approac is not exclusive to te transport sector. Foster (24) uses a 5% of a ouseold s montly income or expenditure as te limit of affordability of expenditure on tree public services (water, electricity, and gas). In te water sector, tere is a well establised rule of tumb wose origin is attributed to te World Healt Organization (WHO) wereby a water bill representing more tan 5% of montly ouseold income or expenditure is considered unaffordable. Tis 5% limit is used operationally by te Cilean government to estimate te number of water subsidies given eac year and teir value. 4 4 See Gómez-Lobo (2) for more details. 4

7 Altoug intuitively appealing, tere are several problems wit tis affordability measure. Te main one, as noted by Venter and Berens (25), is tat te relation between welfare and te expenditure on transport as a percentage of income may not be monotonic. Terefore, it is not clear tat ouseolds tat spend less tan % of income or expenditure on transport are necessarily better off tan people tat spend more. As an example, it may be tat due to te ig price of public transport very poor people eiter walk or do not make many trips. Tus, teir observed transport expenditure may be low due to a suppression of trips rater tan a ig level of income. 5 In order to overcome te above problem Carruters, Dick and Saurkar (25) use a fixed basket of trips to estimate an affordability index. 6 Tey define affordability as te ability to make necessary journeys to work, scool, ealt and oter social services, and make visits to oter family members or urgent oter journeys witout aving to curtail oter essential activities. Operationally, tey use te percentage of montly per capita income (or te per capita income of te lowest quintile of te income distribution) required to make sixty km trips per mont in eac city. 7 Formally, teir affordability index is defined as: N xi p i= Aff = y (2) 5 Tere is substantial evidence sowing tat te poor coose to walk muc more often tan te non-poor. See Cropper (27), Howe and Bryceson (2), SITRASS (24a, 24b), and Badami, Tiwari and Moan (24) for evidence from developing country cities. 6 Tis approac as also been used by ECLAC (992). 7 In a similar vain, Haider and Badami (24) calculate te fare level tat eac income group could pay in order to afford a 4 work trips per mont for two earner ouseolds in Islamabad, Pakistan. 5

8 were x i, a fixed parameter, replaces te observed number of trips taken by ouseold member i, wic in te case of Carruters, Dick and Saurkar (25) is 6 trips per mont. One of te advantages of using te metodology proposed by Carruters, Dick and Saurkar (25) is tat it makes it easier to estimate comparable affordability indices across cities and countries. Teir main results are reproduced in Table, were te percentage of per capita income required is presented for te average ouseold and for ouseolds in te first quintile of te income distribution. [Table around ere] In spite of its attractiveness, tere are several problems wit tis last affordability measure. First, it ignores possible canges in fares due to supply responses needed to accommodate te fixed number of trips considered. For example, if it were te case tat every person made 6 trips per mont, in most cities aggregate public transport demand would be different (probably muc larger) tan current demand. Terefore, equilibrium fares would also be different unless tere are constant economies of scale in public transport supply. Second, it is not clear eiter ow te results are to be used for policy making. Tere are two possible applications for an affordability measure. 6

9 First, as an indicator to determine weter public transport is too expensive in a given city and terefore tat someting sould be done about it. However, tis would require defining a bencmark of wat is considered affordable. Is it %, 5% or 5%? Any suc bencmark is arbitrary and subject to furter criticisms. For example, imagine two cities, one were te transport affordability index is 5% and anoter were it is %. One migt be tempted to conclude tat efforts sould be made to reduce te transport costs in te first city. However, wat if an analogous affordability index is estimated for food (or water, or watever oter good or service one may care about) and it turns out tat in te first city is represents 45% of income and in te second 5% of income. Is it still te case tat lowering transport cost in te first city is so important? In te end, ouseolds spend te same amount of teir income in bot transport and food. 8 Tis last problem points to te pitfalls of analyzing welfare issues from a sectoral perspective instead of a global perspective. In order to make consistent welfare comparisons, a fixed basket of all te goods and services consumed by an average (or poor) ouseold sould be used to gauge teir welfare, not just of public transport trips. Tis is precisely wat a consumer price index does, allowing welfare comparisons across time. It is also te idea beind te Purcasing Power Parity excange rate index used to compare welfare (real income) across countries. In bot cases, a fixed basket of many goods and services is used. Terefore, te use of an absolute measure of public transport affordability is bound to be problematic and arbitrary. A second possible use of te affordability index is to evaluate te impact of certain policy interventions. For example, it could be used to 8 Tis point is also note in World Bank (22). 7

10 compare te affordability of transport before and after a new subsidy was introduced. Economic teory does not ave a definition of affordability but it does ave well developed concepts to measure welfare canges. Te use of canges in te affordability measure, as opposed to its absolute level, seems like a muc more promising avenue for te practical use of tis concept. Below we will sow tat canges in te affordability index can be given a rigorous economic welfare interpretation. 3. Measuring canges in economic welfare Trougout te unit of analysis will be te ouseold. 9 Te question is to ascertain ow eac ouseold is affected by different policies in te public transport sector. Assume a money metric utility function C( p, U ). Tis function measures ow muc money a ouseold requires to reac a certain level of utility or welfare, and will depend on a ouseold s preferences, te vector of prices of te goods and services consumed, p, and te reference utility or welfare level (U). Te welfare impact on a ouseold of a cange in prices, say from p to p, can ten be measured by te Compensating Variation (CV), tat is, (minus) te amount of monetary resources tat a ouseolds needs to be given or taken away so tat after te cange it can still reac its original utility level or CV = C( p, U ) C( p, U ) were U is te original welfare of te ouseold. Since te money needed to reac te original utility level at te original prices is just te income of te ouseold, te CV measure can also be defined as CV = y C( p, U ) were y is te monetary income of te ouseold. 9 Noting substantive canges if te individual is taken as te unit of analysis. However, it is more common to consider welfare impacts on ouseolds rater tan individuals. 8

11 Tis last expression indicates tat if prices rise, CV would be negative since te money resources needed to reac te original welfare level at tese iger prices is greater tan te original income level of te ouseold. Minus CV is te amount of money tat sould be given to te ouseold in order to compensate for te price cange and allow te ouseold to reac its original welfare level. Anoter measure of te welfare cange on a ouseold brougt about by a cange in prices is te Equivalent Variation. Tis measures te cange in te ouseold s income tat is equivalent to te cange in price. In tis case te reference utility is te final expost utility of te ouseold, U or EV = C( p, U ) C( p, U ) = C( p, U ) y. Since a price rise decreases a ouseold s welfare, reacing tat ex-post level of welfare at te original price level (C(p,U )) requires less financial resources tan te ouseold s monetary income and tus te EV measure is negative, as desired. Often, te cange in consumer surplus is used to gauge te welfare impact of a price cange. Tis is defined as te cange in te area below te demand curve for te good wose price rises or falls. It is well known tat te cange in consumer surplus is not an exact welfare measure but it will always be bounded by te oter two exact measures (CV and EV). For small canges in prices all tree give very similar results, especially if te good represents a small percentage of te ouseold s expenditure (Willig, 976). CV is a welfare cange measurement. Since a price rise is bad for ouseolds, tis measure as to be negative in tis case. Tat is wy it is defined as in te text and te negative of tis measure gives te monetary amount tat would ave to be given to a ouseold to compensate it for a price rise. 9

12 3. First order approximation to te true welfare cange In order to empirically measure te CV (or EV), te analyst needs to know te expenditure function of te ouseold (te money metric utility function), C(p,U). Tis can be recovered from te estimation of a demand system suc as te Almost Ideal Demand System (Deaton and Muellbauer, 98), or its more flexible extension, te Quadratic Almost Ideal Demand System (Banks, Blundell and Lewbel, 997). However, tis requires muc data and effort, and is prone to specification and estimation errors. For most practical purposes, a more useful approac is to use a first order approximation to te true welfare cange. For example, te first order Taylor approximation to te expenditure function is: C( p, U ) C( p = y + = y +, U n i= n i= ) + C( p C( p, U p x i ) ( p p ) i i i, U ) ( p ( p p ) i i p ) (3) were x i is te original level of consumption of te good or service i and te last equality was obtained using Seppard s Lemma. Using tis last expression, a first order approximation to te CV would be: Wen only a single price canges, only te demand for tis good needs to be estimated, a somewat simpler and less data intensive problem. However, tis may still be not possible in many applications.

13 n i= ( p p ) y C(p, U ) x. (4) i i i Tat is, te sum of te pre-cange consumption of eac good times its price cange. Tis quantity does not require estimating a demand system and it will be feasible in most applications. 2 How good is tis first order approximation? Tis will depend on te ouseold s preference structure and te size of te price cange. However, empirical evidence suc as Banks, Blundel and Lewbel (996) using UK ouseold data sows tat even for large price canges it may be a very good approximation. In tat study tey compared te first order approximation wit te welfare cange estimated using te expenditure function recovered from a QUAIDS demand system estimation. Tey found tat for a 2% price rise for a significant expenditure group (cloting) te first order approximation was at most % from te true CV value. 3 Given its simplicity and advantages as regards data requirements, togeter wit evidence tat sows tat it may in fact be a very good approximation, te first order approac seems like te ideal coice to use to study te impact of different policies. Tis is particularly so wen comparing several policy interventions and comparing case studies across several countries, were data availability may be very diverse. 2 Note te similarity of tis result wit ow a consumer price index is calculated. For te EV, te formula would be identical except tat te post-cange level of demand replaces te pre-cange level of demand in te formula. 3 Te estimated value from te demand system is in reality a second order approximation to te true expenditure function, since te QUAIDS is a second order flexible functional form.

14 3.2 A welfare interpretation of te affordability indices Te first order approximation to te economic welfare cange can be used to give a welfare interpretation to te affordability measures discussed earlier. Let us take te first order approximation to te Compensating Variation developed above and assume tat only te price of one transport mode canges. Tus, from (4): ( ) CV v. (5) p v p v were v is te original number of rides in te affected mode and p v is te fare level. Notice tat tis is equal to te difference in expenditure on public transport before and after te price cange (valued at te original number of rides): CV v pv v p v. (6) If tis is ten normalized by te income (or expenditure of te ouseold) ten we ave: CV v pv v pv = ΔAff. (7) y y y Tis last expression is te cange in te affordability index using effective number of rides (or Aff in () above). Tus, te cange in tis affordability measure is proportional to te first order approximation of te Compensating Variation. 2

15 In most studies it is common to estimate te average affordability by income groups say quintiles or deciles of te income distribution. Te average cange in te affordability index in a sub-group of te population is: ΔAff = H = ΔAff H H = CV y H (8) were indexes te ouseold unit. Tis last expression is equivalent to measuring te welfare impact of a price cange using a welfare function approac. Define te social welfare function [ u,..., u ] = W [ v ( p, y ), v ( p, y ),..., v ( y )] W = W u, (9), 2 H 2 2 H p H were, u is te welfare level attained by ouseold, measured by te indirect utility function v (p,y ). Following Stern (987), it is trivial to derive te first order approximation to te cange in social welfare of a price cange as: 4 ΔW = H H q Δp = = = θ θ CV () were θ is te marginal social weigt of eac ouseold and is defined by [, v2,..., v ] W v H ( p, ) θ =. () v y v y 4 Tis derivation uses Roy s identity. 3

16 Terefore, if te marginal social weigt of eac ouseold takes te particular form of θ = (2) y ten te average cange of te affordability index over a group of ouseolds is proportional (by a constant /H) to te (negative) cange in social welfare: ΔAff H H = θ CV ΔW (3) Te use of marginal social weigt inversely proportional to income is very popular among practitioners and is often used in te empirically measure of welfare impact of policies. Tese social weigts are reasonable since tey give iger weigt to lower income ouseolds. However, tey are not free from criticism, as will be discussed below. In summary, te average cange in te affordability measure tat uses effective trips made by ouseolds can be rationalized as a reasonable approximation to te social welfare cange generated by transport policies. Te affordability measure proposed by Carruters, Dick and Saurkar (25) also as a welfare interpretation. However, it is a bit more involved and requires additional information. Appendix presents te details of te results. 4

17 4. Sould we use an affordability measure to analyze social policies? Altoug we can give a welfare interpretation to te cange in te affordability index, it is not recommended tat tis approac be used wen analyzing social policies in te transport sector. First, te definition of any welfare function is arbitrary and subject to te preferences of te analyst. Different studies may arrive at different results simply because tey cose different social welfare functions. Tere in no way to obtain a consensus or unanimous social welfare function specification. 5 Second, te use of te cange in te affordability index as a welfare cange measure requires a very particular social welfare function to be assumed and some very strong assumptions regarding preferences. To be more precise, assume tat te social welfare function is of te Bergson (938) class: W (, p) H v = y + ρ + ρ (4) were ρ is te inequality aversion parameter. Furtermore, assume tat preferences can be represented by a Price Independent Generalized Logaritmic form (Muellbauer, 975): 5 In spite of tis, in te transport literature several autors ave used te welfare function approac to evaluate policies For example, Proost (2), assigns a weigt to lower income ouseolds wic is 2 or 3 times te weigt assigned to iger income ouseolds. Dodgson and Topam (987) also use a welfare function approac, wit a specific functional form due to Feldstein (972). In bot of tese cases te weigts or te welfare function are used to aggregate distributional results allowing quantitative trade-offs to be made between efficiency and equity in te determination of optimal policies. 5

18 ln v ( y, p) ln y ln a b ( p) ( p) =. (5) Te PIGLOG form includes some of te most popular preference representations used in empirical analysis, including te Almost Ideal Demand System (Deaton and Muellbauer, 98) and Exactly Aggregable Translog Model (Jorgensen, Lau and Stocker, 982). Using () and te specified functions, te initial marginal social weigt of eac ouseold is: θ = [ v v,..., v ] W, 2 H v ( p, y ) ρ = ( p) v y, v y y b ( p). (6) If all ouseolds face te same prices, ten p can normalized to and b (p ) can be set to for all ouseolds. Wit tis assumption plus an inequality aversion parameter equal to (ρ =), te marginal social weigt valued at base line prices will be: θ = y as required for te proportionality result (3) to old. If te price vector faced by eac ouseold is different ten even more restrictions must be placed on te social welfare function and preferences. Banks, Blundell and Lewbel (996) sow tat in order to obtain marginal social welfare weigts tat are independent 6

19 of prices and inversely proportional to eac ouseold s income, te social welfare function must be: W = W v [ ( p y ), v2 ( p, y2 ),..., vh ( p, yh )] = ( k ln y a ( p) ) H, (7) = Were k is a constant and a is a function of prices. Tus, te social welfare function must be additive in te indirect utility functions of eac ouseold and in turn tese individual functions must take a particular form given by: v ( p y ) = k ln y a ( p),. (8) Only in tis case will te marginal social weigt be independent of prices and inversely proportional to income: 6 [ v v ] W v =, 2 H v ( p, y ) k θ,..., =. (9) v y y However, tese assumptions imply tat preferences are omotetic (Teorem of Banks, Blundell and Lewbel (996)). Terefore, te income elasticities are equal to one for all goods, wic is clearly unrealistic. 6 Te constant k could be set to /H for eac ouseold to make te relation between te average cange in affordability and te cange in social welfare exact. However, given te ordinal nature of te aggregate social welfare measure, tis is not really required. More troublesome is te fact tat to make (4) valid, k must be te same for all ouseolds, tus ruling out demograpic or oter types of eterogeneity of preferences among ouseolds. 7

20 Terefore, in order for te cange in affordability to represent a social welfare cange, an additive Bergson type welfare function (wit an inequality aversion parameter equal to one) and a PIGLOG preference structure must be assumed. 7 In addition, all ouseolds must face te same prices. Tese are strong conditions, in particular given tat PIGLOG preferences imply sare equations tat are linear in log income. Houseold data, at least from te UK, sows tat real preferences are more complex requiring sare equations tat are quadratic in log income (Banks, Blundell and Lewbel, 997). If prices differ across ouseolds ten even stronger assumptions must be made regarding te welfare function and ouseold preferences. 5. A more convention alternative approac Rater tan aggregate individual ouseold impacts using a welfare function, a more flexible approac is to analyze te social or distributive implications of a subsidy by graping te Lorenz curve or relative benefit curve. Te relative benefit distribution curve (or Lorenz curve) graps te percentage of a certain policy benefit accruing to te first n t rank of ouseolds, according to some measure of income, expenditure or wealt distribution. 8 More formally, te grap of a relative distribution curve can be defined as: r( j) = j = s S 7 Tese are sufficient conditions. Necessary conditions are marginally more flexible. See Lewbel (989). 8 Tis discussion is couced in terms of te distribution of benefits, suc as subsidies. Clearly it also applies to te distribution of costs of a policy measure. 8

21 were denotes te j t ranked ouseold from te lowest to te igest, r(j) is te value of te grap at te ouseold ranked j, s is te benefit (CV for example) accruing to ouseold and S is te total benefit distributed by te policy. Figure gives an example were two curves are graped. Te curve above te 45º line sows a progressive distribution of benefits, since all K% of poorest ouseolds receive more tan K% of te total benefits for watever value of K cosen. Te curve below te 45º line sows a regressive distribution of benefits since poorer ouseolds now receive less of tan a proportional amount of te benefit. Te relative benefit curve is very useful wen comparing te distributive impact of different policies since it gives a grapical representation of te relative incidence of benefits. Wen te curves for different policy interventions are superimposed on te grap it will often be possible to rank tem according to teir distributive impact. Tis will be te case wen te different curves do not cross eac oter, in wic case te igest curve will dominate te oters in terms of progressiveness. [Figure about ere] Associated wit te relative distribution curve is te Gini coefficient wic gives a summary measure of te distributive impact of a policy. Tis coefficient is calculated as te area between te 45º line and te distribution curve (wit a negative value wen te curve is above te 45º line) over te area below te 45º line. Tis is illustrated in Figure 2. Te closer te Gini coefficient is to - te more progressive is te distribution of impacts. [Figure 2 about ere] 9

22 Te distribution curve analysis is muc more flexible tan a welfare function approac since te data required can always be used subsequently to estimate te social welfare cange if desired. However, unlike te welfare function approac, te distributional analysis conveys muc useful information witout aving to assume a particular, and somewat arbitrary, welfare function. Finally, te relative distributional curve approac is consistent wit prior researc on te distributional consequences of transport subsidies. For example, Frankena (973) and Guriai and Gollinz (986) estimates te benefit and tax incidence by income groups of several transport subsidies in Canada and New Zealand, respectively. Calculating incidence by income groups is equivalent to using a step function approximation to te relative benefit curve were instead of graping te incidence of benefits for eac individual ouseold te average over income groups is used. Tis approac as been used in a number of recent case studies analyzing te distributive impact of transport subsidies in several cities around te developing world. 9 Te results sow tat most transport subsidies are badly targeted and in many cases are regressive. As an example of te use of relative distribution curves we present a result te distributive impact of te student preferential fares in Santiago, Cile, taken from Gómez-Lobo (27). Te use of preferential fares for certain groups of users (including students, te elderly, war veterans, etc.) is very common in many countries. However, in 9 See Foster (25) for te case of Buenos Aires, Flynn (27) for te case of México City, Gómez-Lobo (27) for te case of Santiago, Cile, and Crooper (27) for te case of Mumbai, India. 2

23 Santiago, as in most oter cases, tese benefits are funded by te rest of users wo pay iger regular fares. Te distributive impacts of tese cross subsidies for te case of Santiago are sown in Figure 3. From tis figure we can see tat te student preferential fare in te bus system is somewat progressive. Te associated Gini coefficient is -.6, wic is a bit more progressive tan a Gini coefficient of for a neutral distributional impact. However, it can also be seen from te grap tat te funding of tis subsidy is also regressive in te sense tat poorer ouseolds pay a iger proportion of tis tax. Te associated Gini coefficient for te funding of te cross subsidy is -., very close to te coefficient for benefits. Tese results imply tat te student preferential fare is distributing resources from ouseolds witout students to ouseolds wit students. Tis distribution of resources occurs across all deciles of te income distribution. Altoug on average tis subsidy is marginally progressive, te majority of poor ouseolds are urt by tis policy. Te social impact of tis subsidy would improve significantly if its funding came from general taxation instead of te current cross subsidy sceme. Altoug even in tis case, wit a Gini coefficient of -.6, te progressiveness of te policy would still not be very impressive. 2

24 6. Conclusions Lately, tere as been a surge of interest on te relation between poverty and transport policies. Tis stems from te recognition of te importance of transport as a complementary input for access to basic needs suc as ealt, education and employment. Many public transport subsidies are justified on social or distributive arguments. Wen analyzing te relation between poverty and transport, often te affordability of public transport is estimated. Tis usually entails calculating te percentage of montly income spent on public transport and comparing it to an arbitrary bencmark considered affordable. If most poor ouseolds spend more tan tis tresold ten it is deemed tat public transport is unaffordable for te poor and some type of subsidy is warranted. In tis paper we argue tat te above procedure may not be te most fruitful approac to tackle te issue of transport and poverty. We present two alternative definitions of affordability used in te public transport literature and discuss teir limitations. Any affordability measure covering only transport expenditure is bound to be a very partial view of ouseold welfare. In addition, te required affordability bencmark to determine weter transport costs are ig or not is arbitrary. Terefore, te approac tat uses te absolute level of tese affordability measures is meaningless. We also sow in tis paper tat te cange in te affordability measures, as opposed to its absolute level, can be given a more rigorous interpretation in terms of traditional welfare economics. In particular, te average cange in te affordability of public 22

25 transport is a reasonable first order approximation to te cange in social welfare. Tis implies tat te cange in affordability may be a valid approac to study, among oter issues, te social impact of different transport subsidy policies directed to elp te poor. In spite of tis last result, we argue tat to analyze weter transport subsidies are meeting teir social or distributional objectives it is muc more fruitful to use more traditional income distributional tools suc as te relative benefit curve and its associated Gini coefficient. Tis approac as been used in a number of recent case studies analyzing te distributive impact of transport subsidies in several cities around te developing world. Te results sow tat most transport subsidies are badly targeted and in many cases are regressive. Tis implies tat socially motivated transport subsidies are not meeting teir stated objectives and more researc and effort needs to be placed in improving teir design and application. 23

26 Acknowledgements Te paper was written wile te autor was a Visiting Professor at te Department of Applied Economic Analysis (DAEA) of te University of Las Palmas de Gran Canaria, Spain (ULPGC). He would like to acknowledge te splendid academic environment and facilities provided by DAEA and is gratitude for te invitation to visit te ULPGC. Comments by Tómas Serebryski and participants at te 27 World Bank Transport Forum are kindly appreciated. Te usual disclaimer applies. 24

27 References Asian Development Bank (2), Handbook for Integrating Poverty and Impact assessment in te Economic Analysis of Projects, Economics and Development Resource Centre (EDRC), Manila. Armstrong-Wrigt, A. and S. Tiriez (987), Bus Services: Reducing costs, raising standards, Te World Bank, Wasington D.C. Badami, M., G. Tiwari and D. Moan (24), Access and Mobility for te Urban Poor in India: Bridging te Gap between Policy and Needs, paper presented at te Forum on Urban Infrastructure and Public Service Delivery, New Deli, June. Banks, J., R. Blundel and A. Lewbel (996), Tax Reform and Welfare Measurement: do we need demand system estimates?, Economic Journal, 6(438), pp Banks, J., R. Blundel and A. Lewbel (997), Quatratic Engel Curves and Consumer Demanda, Te Review of Economics and Statistics, 79(4), pp Bergson. A. (938), A reformulation of certain aspects of welfare economics, Quarterly Journal of Economics, vol. 52, pp Carruters, R., M. Dick and A. Saurkar (25), Affordability of Public Transport in Developing Countries, Transport Papers TP-3, Te World Bank Group, Wasington D.C., January. Cropper, M. (27), Public Transport Subsidies and Affordability in Mumbai, India, paper prepared for te World Bank. Deaton, A. and J. Muellbauer (98), An Almost Ideal Demand System, American Economic Review, 7(3), pp Department of Transport (996), Wite Paper on National Transport Policy, Sout Africa. Dodgson, J.S. and N. Topam (987), Benefit-Cost Rules for Urban Transit Subsidies, Journal of Transport Economics and Policy, 2(), pp ECLAC (992), Te Impacts of Subsidies, Regulation and Different Forms of Ownersip on te Service, Quality and Operational Efficiency of Urban Bus Systems in Latin America, United Nations Economic Commission for Latin America and te Caribbean. ECORYS Researc and Consulting and NEA Transport Researc (24), Labor Mobility, Beneficiaries of Public Transport Services in Eastern Europe and Central Asia, Final Report prepared for te World Bank Group, Rotterdam, June. Feldstein, M. (972), Distributional equity and te structure of public pricing, American Economic Review, vol. 62, pp

28 Flynn, J. (27), Measures to make urban transport affordable to te poor: Mexico City case study, Jon F. Kennedy Scool of Government, Harvard University, report prepared for Te World Bank, February. Foster, V. (24), Hacia una Política Social para los Sectores de Infraestructura en Argentina: Evaluando el Pasado y Examinando el Futuro, Centro de Estudios Económicos de la Regulación, Universidad Argentina de la Empresa, Buenos Aires. Frankena, M. (973), Income distributional effects of urban transit subsidies, Journal of Transport Economics and Policy, September. Gannon, C. and Z. Liu (997), Poverty and Transport, TWU-3, Te World Bank Group, Wasington D.C., September. Godard, X. and L. Diaz Olvera (2), Poverty and Urban Transport: Frenc Experience in Developing Cities, Final Report, TWUTD, Te World Bank Group, Wasington D.C. Gómez-Lobo, A. (2), Making water affordable: Output-based consumption subsidies in Cile, en Brook, P.J. y S.M Smit (eds), Contracting for Public Services: Output-based aid and its applications, Te World Bank. Gomez-Lobo, A. (27), Public Transport Affordability and Subsidy Policies: A case study of Santiago Cile, report prepared for te World Bank. Gomide, A., S. Leite and J. Rebelo (24), Public Transport and Urban Poverty: A Syntetic Index of Adequate Service, Te World Bank Urban Transport Program in Brazil, Te World Bank, Wasington D.C. Guriai, J.C. and A.A. Gollins (986), Net tax incidence for public transport subsidies in New Zealand, Transportation, 3, pp Haider, M. and M.B. Badami (24), Public Transit for te Urban Poor in Pakistan: Balancing Efficiency and Equity, paper presented at te Forum on Urban Infrastructure and Public Service Delivery, New Deli, June. Howe, J. and D. Bryceson (2), Poverty and Urban Transport in East Africa: Review of Researc and Dutc Donor Experience, Report Prepared for te World Bank, International Institute for Infrastructural, Hydraulic and Environmental Engineering, December. Jorgensen, D.W., L. Lau and T.M. Stocker (982), Te transcendental logaritmic model of aggregate consumer beaviour, in Advances in Econometrics, vol. I, (ed. R. Basmann and G. Rodes), Greenwic, Connecticut: JAI Press. Lewbel, A. (989), Houseold equivalence scales and welfare comparisons, Journal of Public Economics, vol. 39, pp Muellbauer, J. (975), Aggregation, income distribution and consumer demand, Review of Economic Studies, 62, pp

29 Proost, S. (2), Acieving Equity Troug Urban Transport Pricing?, mimeo, University of Leuven. Suiying, Z., W. Han, H. Weili and C. Dening (23), Poverty and Transportation in Wuan, Economic Researc Institute, Wuan University, Report written for te World Bank, revised draft, December 5. SITRASS (24a), Poverty and Urban Mobility in Conakry, Final Report, prepared by te International Solidarity on Transport and Researc in Sub-Saara Africa for te Sub-Saara Policy Transport Program, Te World Bank, November. SITRASS (24b), Poverty and Urban Mobility in Douala, Final Report, prepared by te International Solidarity on Transport and Researc in Sub-Saara Africa for te Sub-Saara Policy Transport Program, Te World Bank, September. Stern, N. (987), Te teory of optimal commodity and income taxation, in Newbury, D. and N. Stern (eds.), Te Teory of Taxation for Developing Countries, Oxford: Oxford University Press. Te World Bank (22), Cities on te Move: A World Bank Urban Transport Strategy Review, Te World Bank, Wasington D.C. Te World Bank (25), Distribution of Benefits and Impacts on te Poor, Transport Note Nº TRN-26, Transport Economics, Policy and Poverty Tematic Group, Te World Bank, January. Venter, C. and R. Berens (25), Transport Expenditure: is te % Policy Bencmark Appropriate?, Proceedings of te 24 t Soutern African Transport Conference, SATC 25, Preotia, Sout Africa, July. Willig, R. (976), Consumer s surplus witout Apology, American Economic Review, 66 (4), pp

30 Appendix: A welfare interpretation to te Carruters, Dick and Saurkar (25) affordability measure Carruters, Dick and Saurkar (25) use as an affordability measure an estimate of te percentage of ouseold income tat is devoted to public transport, considering a fixed and exogenous number of 6 trips per mont. Taking te first order approximation to te Compensating Variation and normalizing tis measure by te ouseold s income or total expenditure, we obtain: y C( p y, U ) x pt ( p p ) pt y pt x = pt p y pt x pt p y pt. We can again interpret te income or expenditure normalization as te social welfare weigt associated to eac ouseold. If we interpret te initial situation as te ypotetical case were te price of public transport is sufficiently low say p pt so tat te ouseold would effectively coose to make tese 6 trips per mont, ten wat Carruters, Dick and Saurkar (25) estimate is te first part of te above equation: x tr p pt y. Tis is te percentage of income tat is spent if tese trips were made at current prices. If we could estimate at wat price te ouseold would effectively make x pt trips tat is an estimate of p pt ten te second part of te equation could be estimated and we can ten use te measure devised by Carruters, Dick and Saurkar (25) as a first order 28

31 approximation to a true welfare measure. Te difficulty lies in aving an estimate of te ouseold s demand for trips. However, even if te original expenditure, x tr p pt y, cannot be estimated, it is reasonable to assume tat it will be more similar across cities and countries tan x tr p pt y. Tis is so because te first measure is bounded below by. Terefore, even if te affordability index of Carruters, Dick and Saurkar (25) varies between cities, from % to % on average according to teir study, te expenditure required at te price for wic ouseolds would effectively make te 6 trips will probably vary by less. If we take te extreme view tat tis expenditure would be te same for eac city or country, w, ten subtracting tis number from te affordability index of Carruters, Dick and Saurkar (25) will give a reasonable welfare comparison of public transport prices across cities: CV y x pt p y pt w. 29

32 Table : Affordability index for different cities assuming 6 trips per person per mont City Affordability Index Average Bottom Quintile Sao Paulo % 7% 2 Rio de Janeiro 6% 63% 3 Brasilia 6% 59% 4 Cape Town 4% 38% 5 Buenos Aires 4% 26% 6 Mumbai 9% 23% 7 Kuala Lumpur 5% 22% 8 Mexico City 3% 9% 9 Cennai 8% 9% Manila 5% 7% Krakow 6% 7% 2 Amsterdam 6% 6% 3 Moscow 4% 5% 4 Guangzou 4% 4% 5 Warsaw 4% % 6 New York 3% % 7 Los Angeles 3% % 8 Cicago 3% % 9 Singapore 2% % 2 Beijing 3% 9% 2 Seoul 4% 9% 22 Sangai 2% 6% 23 Cairo 3% 6% 24 Budapest 3% 6% 25 London 2% 5% 26 Prague 2% 4% 27 Bangkok % 4% Source: Carruters, Dick and Saurkar (25). 3

33 Figure % 45º Line: neutral distribution % of accumulated benefits Progressive distribution Regressive distribution % Houseolds ordered from poorest to ricest % Figure 2 % of accumulated benefits % Gini = A/B ( - < G < ) A < A> B % Houseolds ordered from poorest to ricest % 3

34 Figure 4 Preferential Student Pass in Buses Relative Distribution Curve Houseold rank in income per capita distibution 45º degree line Funding Subsidy Source: Gómez-Lobo (27) 32