Optimal Fuel Taxes and Heterogeneity of Cities


In the United States all levels of jurisdictions are allowed to levy supplements to the federal fuel tax level. While fuel tax differentials at the state level are substantial, there is a relatively small differentiation across cities. This seems surprising given the heterogeneity of U.S. metropolitan areas. Against this background, the objective of the present paper is to analyze whether the current small level of tax differentiation across heterogeneous metropolitan areas is justified on efficiency grounds. We employ a spatial urban computable general equilibrium approach and calculate optimal gasoline taxes for an average U.S. prototype urban area characterized by a medium degree with respect to the spatial distribution of jobs (implying a medium spatial expansion of the urban area, medium degree of externalities, medium public transit share etc.) and for cities that differ with respect to these and further characteristics. We find that in our prototype urban economy the optimal gasoline tax is higher than current rates as suggested by previous studies calculating nationwide optimal gasoline taxes. Furthermore, it is shown that optimal tax levels may vary considerably across heterogeneous cities, much more than actual tax rates. This implies that stronger spatial fuel tax differentiation across cities could raise social welfare. However, we also show that setting an optimal spatially uniform tax, i.e. a uniform tax that maximizes the sum of the benefits generated in all cities, is capable to generate a significant fraction of the maximum achievable welfare gain under optimal city specific locally differentiated gasoline taxes. Interestingly, such an optimal uniform tax could deviate from all city specific optimal fuel tax levels. This suggests that the additional benefit from spatial fuel tax differentiation might actually be relatively small, in our case the efficiency premium is less than one-thirds.

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  1. 1.

    Generally, the tax is composed of a federal tax, a state excise tax and other state or local taxes such as applicable sales or use taxes, gross receipts taxes, oil inspection fees, county and local taxes, underground storage tank fees and other environmental fees (API 2014).

  2. 2.

    In this paper we focus on U.S. passenger transport and, thus, use the terms ‘gasoline’ and ‘fuel’ synonymously.

  3. 3.

    The composition is as follows: federal tax: 18.40 \(\text{c}\!\!\!/\) pg; state excise tax: 20.51 \(\text{c}\!\!\!/\) pg; other taxes: 10.71 \(\text{c}\!\!\!/\) pg.

  4. 4.

    According to the literature local fuel taxes may be influenced through tax competition among municipalities (e.g. Zodrow and Mieszkowski 1986; Wilson 1986; Wildasin 1988); cross-border shopping (Kanbur and Keen 1993; Nelson 2002; Nielsen 2001) or yardstick competition (Besley and Case 1995) which could explain the small differences. Here we study optimal local fuel taxes in the absence of tax competition to derive a first efficiency related basis for evaluating tax differences across MSAs. There is some reasoning for this choice since evidence on horizontal fuel tax competition is rather inconclusive (Egger et al. 2005; Devereux et al. 2007; Nelson 2002). As far as MSAs are not closely located, cross-border shopping is hardly possible and horizontal tax competition among MSAs will probably be weak or absent.

  5. 5.

    Bento et al. (2009) also examine impacts of an increase in U.S. gasoline taxes. However, they do not focus on calculating an optimal tax but on distributional aspects of the tax considering different household types using an approach different to that of Parry and Small (2005). Parry (2008) calculates the optimal tax on diesel fuel use of heavy duty trucks in the U.S. finding that the optimal tax on diesel is much higher than the benchmark tax of 0.45 $/gallon. Optimal fuel tax studies for other countries are provided by Tscharaktschiew (2014) for Germany, Parry and Small (2005) for UK, and Antón-Sarabia and Hernández-Trillo (2014) for Mexico.

  6. 6.

    Parry and Timilsina (2010) analyze optimal pricing schemes, e.g. gasoline taxation, for a specific city (Mexico City). Anas and Hiramatsu (2012) study the effects of a whole gasoline price increase on an urban economy, using the city of Chicago as example.

  7. 7.

    For further empirical evidence on metropolitan decentralization see also Anas et al. (1998), Jordan et al. (1998), Mieszkowski and Mills (1993), and White (1999). There is also a large body of literature on subcenter formation, see e.g. Giuliano and Small (1991; 1999), and McMillen and McDonald (1998).

  8. 8.

    We will discuss the implications of a relaxation of this assumption in the concluding section.

  9. 9.

    See also some related applications and further developments provided by Anas and Hiramatsu (2012, 2013); Anas and Liu (2007); Tscharaktschiew and Hirte (2010b, 2012). Anas (2012) provides a theoretical exposition.

  10. 10.

    For simplicity, Figure 1 shows only a section of the circular urban area. Note that due to accessibility advantages the innermost zone of the city will in fact endogenously become the city center where, e.g., land rents are highest.

  11. 11.

    Hereafter the terms ‘household’, ‘worker’, ‘resident’ and ‘traveler’ are used synonymously.

  12. 12.

    More general, the government uses \(\tau ^{ls}\) to balance its budget (\(\tau ^{ls}>0:\) tax; \(\tau ^{ls}<0:\) transfer).

  13. 13.

    This is a reasonable assumption particularly for U.S. Transit Authorities of cities dominated by rail such as ‘MTA New York City Transit, Brooklyn, NY’; ‘Washington Metropolitan Area Transportation Authority’; or ‘Massachusetts Bay Transportation Authority, Boston, MA’ (see Parry and Small 2009). As opposed to that, this treatment is, however, a simplification for cases where public transport is dominated by bus, e.g. ‘Los Angeles County Metropolitan Transportation Authority’. Parry and Small (2009) cite evidence that for the 20 largest U.S. Transit Authorities most passenger miles driven can be attributed to rail (72 vs. 28 % in 2003). In addition, in the long-run increased passenger demand could be satisfied by replacing smaller buses by larger vehicles implying that there would not necessarily be an increase in traffic. We therefore think that this assumption affects the quantitative results derived here only to a moderate degree.

  14. 14.

    The function was estimated by fitting a polynomial to the performance of the Geo Prizm, one of the car brands in the study by Davis and Diegel (2004) based on real data.

  15. 15.

    There is empirical evidence that about half of the long-run price responsiveness of gasoline consumption is due to changes in vehicle miles traveled while the other half comes from changes in average fleet fuel economy (see e.g. Parry and Small 2005).

  16. 16.

    See Parry and Small (2005) and Parry (2011) who also apply a constant elasticity relationship.

  17. 17.

    In the benchmark simulation \(\tau _{0}^{g}=\tau ^{g}\), implying that \(g_{i}^{auto}=\hat{g}_{i}^{auto}.\)

  18. 18.

    According to U.S. Environmental Protection Agency (2005), CO\(_{2}\) emissions from one gallon of gasoline amount to 2421 g\(\times 0.99\times (44/12)=8788\) g. The carbon content per gallon of gasoline (2421 g) is multiplied by the oxidation factor 0.99 assuming that 99 % of the carbon is eventually oxidized while 1 % remains un-oxidized and is multiplied by \(44/12\) in order to convert carbon emissions into emissions of carbon dioxide. The last factor is the ratio of the molecular weight of CO\( _{2}\) (m.w. 44) to the molecular weight of carbon (m.w. 12).

  19. 19.

    The first term on the right-hand side of \(\Delta _{ij}\) is divided by 2 because traffic originating and terminating in a zone is assumed to traverse one half of the zone length.

  20. 20.

    Subscript a \(\left( a\in I\right)\) in the formulas for shopping and outdoor leisure traffic flows is here the employment location of a worker residing in zone i.

  21. 21.

    Although this is simplifying assumption, it is much less restrictive than it appears to be at first glance. Even though travel to work has historically defined peak travel demand, non-work related trips are a major portion of all trips at all times of the day (Nelson and Niles 2000). The National Household Travel Survey provides evidence that a significant number of non-work vehicle trips are made during peak periods by now implying that there is a considerable overlap of work and non-work travel during the peak travel periods. Currently, more than half of peak period person trips in vehicles are not related to work. For example, in 2009 the total number of work related daily vehicle trips at morning peak period only slightly exceeded the total number of daily vehicle trips with respect to non-work related personal travel (including shopping) while at evening peak period daily commuting trips were even lower (U.S. Department of Transportation 2011).

  22. 22.

    This is a widely adopted standard assumption in studies on optimal fuel taxes (see Parry and Small 2005; Parry and Timilsina 2010; Parry 2011). It also presumes that marginal external pollution and accident costs do not depend on traffic conditions (congestion) in the urban area. For example, it has been suggested that there might be an inverse relationship between traffic congestion and road accidents. On the one hand, under congested traffic conditions, the average speed of traffic is normally lower which is likely to result in less serious injuries or fatalities. On the other hand, however, on congested roads traffic volume is higher which likely increases the number of accidents. As a consequence, the net effect of the relationship between accident costs and congestion is ambiguous. In fact, in a recent case study for London, Wang et al. (2009) find that traffic congestion has only little or even no impact on accidents.

  23. 23.

    For the sake of simplicity in the following we provide a qualitative description in regard to the characteristics of the government sector. The full formulas of the public budget constraints and the ‘balance of payment’ (see below) aggregate the different sources of tax revenues and travel mode specific transport costs over households, locations and tax/cost categories. We assume that the urban area is a single tax district.

  24. 24.

    For example one might think of parks and other ‘green’ recreational areas.

  25. 25.

    In the U.S. public transport is heavily subsidized. For example, Parry and Small (2009) cite evidence that across the 20 largest transit systems in the U.S. (ranked by passenger miles), the subsidy – as measured by the difference between operating costs and passenger fare revenues – ranges from 29 to 89 % of operating costs for rail and from 57 to 89 % for bus (in 2003). According to Buehler and Pucher (2011) the share of operating expenses covered by fare revenue fell from 37 % in 1992 to less than 33 % in 2007 (U.S. average).

  26. 26.

    This procedure has the advantage of being able to generate differentiated scales of employment decentralization without assuming that urban firms (located in different cities) differ in their production technology or other characteristics. Consequently, it avoids the fact that results could be driven by differences in production technology. Besides, it is not implausible to assume that exports are more service-oriented in some cities (with production being more centralized employing relatively more labor as input) while exports are more manufacturing-oriented in other cities (with production being more decentralized employing relatively more land).

  27. 27.

    In contrast to urban residents we assume that absentee landowners are not subject to income taxation. The main reason is that considering income taxation would require to make assumptions about the place of residence (which state or even whether to live abroad) and particularly about the number of absentee landowners. Because of the fact that the range of possible assumptions concerning these issues is considerably large, the results would become more doubtful rather than more comprehensive and insightful.

  28. 28.

    Implying an average household size of 2.5 (U.S. average household size was 2.53 in 2010; see also Tscharaktschiew and Hirte 2010b). Accordingly, total population in the whole metropolitan area is assumed to be 2 million. Given the spatial expansion of the urban area with radius 16.5 miles in the benchmark, the total land area amounts to 855 square miles. As a result, population density then is 2339 persons per square mile (ppsqmi). For comparison: Milwaukee-Waukesha-West Allis MSA: 1079 ppsqmi; Detroit-Warren-Livonia MSA: 1104 ppsqmi; Los Angeles-Long Beach-Santa Ana MSA: 2692 ppsqmi; New York-Northern New Jersey-Long Island MSA: 2983 ppsqmi; Detroit (city) 5144 ppsqmi; Los Angeles (city): 8092 ppsqmi; Chicago (city) 11,842 ppsqmi; New York (city): 27,013 ppsqmi (US Census data).

  29. 29.

    Not only exogenous parameters had been tried to refer to the year 2009 but also endogenous variables/figures which equilibrate the benchmark urban economy.

  30. 30.

    The middle column of Table 4 shows further prototype city characteristics (e.g. wage and rent profiles) of the pre-policy benchmark case.

  31. 31.

    Parry and Small (2004, 2005) consider a range of 1.5–9.0 \(\text{c}\!\!/\) mile with a central value of 3.5 \(\text{c}\!\!/\) mile for the U.S. as a whole. This estimate is based on an assessment that averages the marginal congestion costs for representative road classes not only across urban but also across rural areas.

  32. 32.

    Parry and Small (2009) estimated these urban specific costs from data on average delay. This average delay was then multiplied by a factor (3.7) which reflects typical estimates of the ratio of marginal to average delay cost on urban highways.

  33. 33.

    This is in line with ranges suggested by the empirical literature (see Small and Verhoef (2007) and Small (2012) for corresponding overviews).

  34. 34.

    However, it is taken into account that road infrastructure (supply) density is generally higher at central locations. For example, considering only the city (zones 4–8) 22 % of the entire land area is allocated to roads, implying that in the suburbs the share is less than 11 %. Although U.S. data concerning land shares with respect to roads are scarce, we believe that a share of 11 % for the whole metropolitan area is reasonable given that there is a higher share of urban road infrastructure in the U.S. compared to European countries. For example, Tscharaktschiew and Hirte (2010a) cite evidence that about 15 % (17 %) of the total land area is allocated to roads (2007 data) in the city of Berlin (Munich).

  35. 35.

    The aggregate benchmark time delay of automobile travelers was calculated by comparing actual aggregate road traffic travel time with hypothetical automobile travel time occurring when the same benchmark equilibrium traffic flows would take place under uncongested (free-flow) conditions.

  36. 36.

    According to www.carbonfund.org (using several data e.g. from Transportation Energy Data Books) CO\(_{2}\) emission factors for urban rail (bus) are 160 (300) gCO\(_{2}\)/passenger mile. By weighting these numbers with relative shares of rail (0.72) and bus (0.28) transit passenger miles driven (20 largest U.S. Transit Authorities; see Parry and Small, 2009) one obtains \(\xi =199\) gCO\(_{2}\)/passenger mile.

  37. 37.

    Marginal costs used by Parry and Small (2009) range from 23–66 \(\text{c}\!\!\!/\) /passenger-mile for Los Angeles and Washington, DC.

  38. 38.

    In the benchmark all densities peak in the city and decline with distance from the city center as observed in real urban areas. For example, household density [HH/square mile] is 1742 in the city (zones 4–8) and 725 in the suburbs (zones 1–3 + zones 9–11); and employment density [jobs/square mile] is 1935 in the city and 675 in the suburbs.

  39. 39.

    The significant share of non-work related trips accentuates the importance of considering not only commuting but also non-work related trips. Note that in order to calculate the trip purpose shares (commuting, shopping, leisure according to our definition) we assigned the NHTS trip purpose ‘other family and personal errands’ with weight 2/3 to shopping trips and with weight 1/3 to leisure trips (in addition to ‘social and recreational’). As a result, we get the distribution of trips by purpose as reported in Table 3. See also Anas (2007) who discusses the trip distribution based on transportation surveys 1969/1977–1995.

  40. 40.

    Based on a federal tax of 18.4 \(\text{c}\!\!\!/\) pg and a state tax (U.S. average) of 22.8 \(\text{c}\!\!\!/\) pg (including e.g. inspection and environmental fees) in 2009.

  41. 41.

    See also Graham and Glaister (2002) and Brons et al. (2008). The latter found a slightly higher elasticity of -0.3.

  42. 42.

    This includes the prototype city described here as well as all further cities under consideration. For comparison, Parry (2011) assumes an overall elasticity of gasoline consumption with respect to the fuel price of -0.4. Small and Van Dender (2007) find a (long-run) price elasticity of -0.363 (over the entire sample using data from 1966–2004). This elasticity declines in magnitude to -0.237 when considering only more recent data over 5 years from 2000–2004. Hence, their analyses suggest that fuel consumption by passenger vehicles has become more price-inelastic over time. In fact, most recent evidence provided by Havranek et al. (2012) finds that after correction for the aspect that the literature suffers from publication selection bias the average long-run elasticity reaches –0.31.

  43. 43.

    For example, Parry and Small (2005) take the central value to be 0.06 $/gallon with range 0.002–0.24 $/gallon whereas Parry (2011) assumes 0.09 $/gallon as benchmark and 0.70 $/gallon for sensitivity analysis. It should be noted, however, that all these figures are lower than cost rates usually applied in, e.g., European project studies.

  44. 44.

    Both values chosen refer to Parry (2011). Parry and Small (2005) use a central value of 0.02 $/mile with range 0.004–0.10 $/mile for local pollution damages and 0.03 $/mile with range 0.012–0.075 $/mile for marginal external accident costs. See Parry and Small (2004) for an extensive discussion on external pollution and accident costs.

  45. 45.

    On the one hand, an increasing scale effect for suburban production could be justified by, e.g., better interstate highways accesses or better parking opportunities in less central locations while, on the other hand, an increasing scale effect for urban production could reflect higher productivity in central location due to a stronger spatial proximity of firms causing, e.g., scale economies in shopping or knowledge spillovers. Consequently, setting a constant scale effect implies that such effects are assumed to be approximately balanced.

  46. 46.

    Sales taxes and fuel excise taxes are not included in the combined effect because they are explicitly treated separately.

  47. 47.

    Sales taxes on general consumption and corresponding tax laws are – as in the case of fuel sales taxes – quite heterogeneous not only among U.S. states, but also among cities/counties within the same state levying local sales taxes in addition to the state tax. For example, New York’s State and local sales tax burden is high relative to most other states, ranking fourth in the nation with an aggregate average State and local rate of 8.45 %. This is in part because of the high local sales tax, which accounts for 4.875 percentage points of the total sales tax. All of New York State’s counties and many of its cities (including New York City) impose a local sales tax in addition to the State sales tax where the most common local sales tax rate is 4 % with 38 of 57 counties (excluding the boroughs of New York City) currently levying this amount (Office of the New York State comptroller 2010). In contrast, sales tax rates in most other States are lower, ranging from 4–7 % in most cases.

  48. 48.

    For empirical evidence see, e.g. Cox (2013), Levine (1998), or Sultana (2002).

  49. 49.

    We calculated effects in the range of 0.0 $/gallon – 4.0 $/gallon using an interval of 0.05 $/gallon.

  50. 50.

    In the figures ‘urban welfare’ represents effects on urban residents including the impacts of congestion (delays and fuel consumption) but excluding impacts related to pollution and accidents.

  51. 51.

    Note that the sum of the benefit from external cost reduction and the value of the negative tax interaction effect (see Table 6) almost exactly reflects the social welfare gain of setting the gasoline tax at its optimal level.

  52. 52.

    Note that endogenous mileage related marginal external costs hardly go down in Figure 3 because reduced external costs (expressed in $/mile) as a result of a higher gasoline tax are multiplied by increased (improved) fuel economy (expressed in miles/gallon).

  53. 53.

    Because g depends on the gasoline price and so on the gasoline tax (see Eq. (13)) \(\tau _{C}^{g}\) also appears on the right-hand side. The calculation therefore relies on numerical simulation.

  54. 54.

    If we assume instead that the share of land which has become non-urban as a result of the higher gasoline tax is not used productively the latter effect vanishes and the optimal gasoline tax were 1.00 $/gallon. Thus the basic results remain the same, i.e. the optimal local tax is higher than the benchmark tax, but lower than the marginal cost of car driving and an approximated corrective tax.

  55. 55.

    This approximately matches the spatial pattern of the prototype city (see Table 1).

  56. 56.

    Examples for the former are Atlanta-Sandy Springs-Marietta MSA: 9/27; Dallas-Fort Worth-Arlington: 11/23; St. Louis MSA: 14/25; examples for the latter are Akron MSA: 25/44; Albany-Schenectady-Troy MSA: 24/40; Harrisburg-Carlisle MSA: 29/42; Lancaster MSA: 30/38 (Kneebone 2009).

  57. 57.

    For comparison, according to Kneebone (2009), Las Vegas (30/63) and Virginia Beach (36/46) are among the most centralized MSAs whereas Detroit (7/16) and Los Angeles (8/26) are among the most decentralized MSAs. Note that in order to generate even more decentralized or centralized cities one would have to modify additional parameters than only the export shares so that both employment distribution patterns constitute our extreme cases.

  58. 58.

    For example, population density in Los Angeles, CA (decentralized job distribution) is considerably lower, only around one-fourth, than that in New York, NY where jobs are relatively centralized.

  59. 59.

    There are indeed considerable wage differences across MSAs for, of course, a large variety of reasons (see U.S. Bureau of Labor Statistics 2013).

  60. 60.

    Clearly, our conclusions are derived from cities with a specific set of characteristics. Given the huge heterogeneity of MSAs with respect to those characteristics, we were forced to create a specific bunch of features. However, two of the cities under consideration can be seen as some kind of extreme cases whereas our prototype city is in turn some kind of an average since it lies in between both other cities with respect to all variables. Therefore our results can to some extent be interpreted as lower/upper bounds.

  61. 61.

    Concerning alternative policies and measures one can also think of cordon tolls (Anas and Hiramatsu 2013), traffic regulations (De Borger and Proost 2013; Nitzsche and Tscharaktschiew 2013), land use restrictions (Rhee et al. 2014), or public facility location planning (Müller et al. 2008). See also Proost and Van Dender (2012) for a discussion on policy mixes.


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We wish to thank the guest editor, Rüdiger Hamm, and two anonymous referees for their constructive comments.

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Correspondence to Stefan Tscharaktschiew Ph.D..

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Hirte, G., Tscharaktschiew, S. Optimal Fuel Taxes and Heterogeneity of Cities. Rev Reg Res 35, 173–209 (2015). https://doi.org/10.1007/s10037-014-0095-z

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  • Fuel tax
  • Gasoline tax
  • Urban economics
  • Tax differentiation
  • Job sprawl

JEL classification

  • H21
  • H71
  • R13
  • R14
  • R48
  • R51