1. Introduction
The transport sector is very important in a country’s economy. In the case of the US, it accounted for 9.1% and 8.7% of its GDP in 2018 and 2019 (11.6% in 1980), respectively (US Bureau of Transport Statistics, BTS [
1,
2]). In addition to this direct impact, transport modes and their costs are fundamental factors in understanding economic and human geography, as Krugman pointed out in his seminal 1991 article [
3]. As stated by Rodrigue et al., transport is vital to the performance of an economy: “When transport systems are efficient, they provide economic and social opportunities and benefits that result in positive multiplier effects” [
4].
On the other hand, there are major problems of passenger transport inefficiency and its impact in terms of noise emissions, pollutants, and greenhouse gases. Suffice it to give a brief overview of some of these problems. The US transport sector emitted 1836 million metric tons of carbon dioxide in 2022 (US Energy Information Administration, EIA [
5]). The US total was 4964 million metric tons of carbon dioxide, thus making transport the highest-emitting end-use sector. In this US transport service, light trucks (including SUVs, vans, and minivans) account for 37.1% of greenhouse gas emissions, passenger cars for 20.7%, commercial aircraft for 6.6%, other aircraft for 2.0%, ships and boats for 2.8%, and rail for 1.9% [
6]. Global CO
2 emissions from the transport sector grew again in 2022 by 254 Mt [
7].
Moreover, congestion and under-utilisation problems remain severe. Regarding congestion, different examples of problems can be cited: delays (increased fuel consumption, workers’ overtime, passenger compensation); increased operational costs (congestion leads to inefficient routes and queuing patterns); reduced travel frequency or use of higher capacity means of transport, impacting on overall operational efficiency; infrastructure costs (higher investment in infrastructure to avoid congestions); and environmental impact (congestion can lead to increased fuel consumption and greenhouse gas emissions). A variety of different costs stem from overcapacity in passenger transport, including opportunity costs (revenue lost due to oversupply and unrealised demand) and inefficiency (variable cost per passenger increases with a lower margin if prices do not change, and there can be lower profitability due to the need to lower prices to increase demand).
The costs associated with some of those problems have been analysed in the literature. Thus, for example, Schrank et al. [
8] estimated that congestion in road transport generated losses of USD 190 billion (2020 USD) in 2019 due to additional fuel costs and extra travel hours. This is consumption that increases greenhouse gas emissions: “the stop-and-go nature of congestion increasing emissions yet further” (Grote et al. [
9], p. 95). Congestion is thus an important factor in road traffic emissions (op. cit.). The same problem occurs in air traffic, since, as the following was pointed out by Clarke et al. [
10]: “Because of congestion, aircraft are often forced to fly far from the cruise altitude and/or the cruise speed for which they are designed. Such sub-optimality results in unnecessary fuel burn and gaseous emission” (p. 4).
Furthermore, the US Travel Association [
11] deduced that traffic congestion caused Americans to avoid 47.5 million road trips in 2018, which cost the economy nearly USD 30 billion in lost travel spending. Moreover, the cost of delays in 2019 was estimated at USD 33 billion by a Federal Aviation Administration (FAA)-sponsored study [
12]. Additionally, the Travel Industry Association’s estimate of unrealised air travel in 2007 was valued at more than 41 million trips, which would have resulted in additional revenue of more than USD 26 billion (Travel Impact Newswire [
13]). In turn, the problem of airport congestion was quantified in 2008 by Gelhausen et al. [
14], who estimated that 6% of all flights are operated from capacity-constrained airports in the United States. Moreover, as some authors have argued (Burghouwt et al. [
15]), congestion at airports leads to higher fares for air passengers. Finally, among many other issues raised, there is a current trend for airlines to use larger aircraft to cope with transport from congested airports (Pollard [
16]). At the same time, the use of regional airports, currently less in demand, is likely to increase, based on smaller, less noisy, and more environmentally sustainable aircraft (Banchik et al. [
17]). The development of airports and the aircraft type composition of airlines will depend on the evolution of demand and therefore on making a correct demand forecast (NASA Team [
18]). In general, as Severino et al. [
19] state, “transport systems efficiency plays a key role for communities’ liveability and economy, being, in addition, an important factor in the economic integration of countries” (p. 1).
Ultimately, these problems highlight the need to make estimates and projections of the intensity of each of the modes of passenger transport and, consequently, of demand (Nar y Arslankaya [
20]). There are several alternative methods of transport demand forecasting. Very important aspects of current study methods include the use of a large quantity of data collected through smart systems (e.g., use of smart cards, use of payment cards, use of numerical systems to quantify public transport) and, based on artificial intelligence, efforts to make predictions of future demand behaviour. This introduces greater variation of estimation and prediction methods compared to the situation prior to the development of digital traffic management systems and data processing. For example, Nar and Arslankaya [
20] use machine learning algorithms. Çelebi et al. [
21] use neural networks to develop short-term passenger demand forecasting models. Qin et al. [
22] note that recurrent neural networks, convolutional neural networks, and other methodologies are used in road traffic demand management. Orlando et al. [
23] propose spatial models (a modern variation of the old gravity models) and the use of digital public transport data to predict the future frequency of public transport trips. However, all these methodological proposals face the problem of the difficulty of obtaining reliable passenger transport data. One of the most relevant ways of quantifying demand in the passenger transport sector is based on the estimation of its elasticity with respect to income and prices of the most relevant modes. Therefore, quantifying the elasticity of demand for the routes where transport is concentrated is vital to understanding the impact of price changes and income on all the issues outlined above. Li et al. [
24] pointed out that “studying the price elasticity of demand is the only way to formulate scientific road pricing”, which can be extended to all other modes. Moreover, the great relevance of estimating the elasticities of demand is reaffirmed in the scientific literature. For example, Zeng et al. [
25] point out that the research into the price elasticity of demand for travel modes “has become a research hotspot.” (p. 3). In addition, “the sensitivity of demand concerning the monetary price of travelling determines the supplier’s ability to raise revenues by setting fares above the marginal social cost” (Hörcher and Tirachini [
26], p. 2). Above all, forecasting through knowledge of elasticities would provide insight into reactions to future price and income developments, adding an understanding of potential consumer behaviour in different scenarios.
Finally, the movement of passenger demand between modes of transport is an important element in an emission reduction strategy, as rail transport implies lower emissions (e.g., Gama [
27], Zeng et al. [
25]). However, whether such a shift in demand between modes occurs depends, in part, on the value of the cross-price elasticities (the higher their positive value is, the stronger the response to price changes will be).
Although the estimation of passenger transport demand elasticities has been widely addressed in the scientific literature (Oum et al. [
28], Goodwin [
29], Holmgren [
30], Gundelfinger [
31], etc.), the results reveal wide ranges of these estimates (see
Appendix C), meaning that further research is needed to illuminate this issue and approximate this value more accurately. Moreover, there is little recent evidence on the price elasticity of demand for public transport services (Davis [
32]).
Consequently, this study focuses on demand elasticities, an important contemporary scientific research object (Zeng et al. [
25]), and does so with respect to some of the most important routes in the United States. One of the advantages of estimation at the route scale is that it allows for differentiation between distinct cases. For example, factors such as distance, infrastructure, demographic and economic structure, etc., vary from one route to another, and an estimation at the national market level would exclude important existing differences.
Therefore, the present study has a general objective, which is to propose a relatively simple model that can be used to estimate and predict passenger transport demand on different routes, factoring in the various transport modes and making assessments based on accessible data from public statistical agencies. In this way it could be used, without complexity, by companies and public management to obtain a global view (through average values) of the different routes and the pressure of their demand, as well as a relative perspective of each of them, allowing for a comparison between routes. To achieve this objective and to show that it is feasible, the present study includes three intermediate aims, namely, (i) to contribute to estimating the elasticities of demand in passenger transport for domestic routes in the United States, where there is competition between air, road, and rail transport; (ii) to contribute to the comparison of those estimates on the different routes analysed from 2003 to 2019 in order to check whether there are relevant variations between them (which requires comparison on a common basis); and (iii) to draw some conclusions based on the relationship between the estimated demand elasticities and the effectiveness of different public policies to be implemented to improve the sustainability of passenger transport in the United States on domestic routes.
In order to achieve these objectives, 20 routes in the United States have been selected based on the relevance of their passenger volume. Demand elasticities have been estimated using a procedure similar to that applied by Escañuela [
33] when measuring the demand elasticity of the Northeast Corridor of the United States. This study expands the geographic area of study and thus provides a more general and homogeneous view of passenger transport demand in the United States. To obtain this estimation, road passenger data series, for which no accurate records exist in the United States, have been approximated. Making this information available can be seen as one of the indirect contributions of this study.
Demand is measured at the route level as the number of passengers using each mode of transport, meaning that the estimate is conditional on the level of expenditure within the group. A theoretical demand model, the Rotterdam demand model (RDM), which was initially proposed by Barten [
34] and Theil [
35], is applied. The RDM fulfils the different maximisation conditions (whose corresponding theoretical restrictions are detailed in point 2.2 of the methodology section), contributing to the results’ robustness while enabling a comparison between routes.
3. Results
After estimating the elasticities of the 20 routes considered in the study, we can affirm that 19 of them have coefficient estimates whose sign agrees with the theory’s prediction. The one exception is the Portland–Seattle route, which has signs of estimated coefficients contrary to the theory’s predictions (so that the Slutsky matrix is not negative semidefinite). The explanation for this seems to lie in a series of events that make the series non-homogeneous, with exogenous impacts on supply, masking the impact of prices and rents on demand (see
Appendix B,
Table A5).
Moreover, almost all estimated income elasticities were significant (for a maximum p value of 0.1) for road and air transport modes, but not for rail transport. A total of 40 estimates of income elasticity were significant (38 without the Portland–Seattle route), 11 (10 without the Portland–Seattle route) were not statistically significant and, except for 2 of them, all referred to passenger rail transport.
Regarding the price elasticities of demand, approximately three-quarters of the coefficients were statistically significant when estimating demand for two modes of transport (air versus car/bus), but this significance decreased for estimates of routes with competition among all three modes of transport. On routes with three modes, about 45% of the price elasticities were statistically significant. The price elasticities of demand involving the rail mode of transport were generally not statistically significant. Finally, the application of the corresponding statistical tests, whose results are included in
Appendix B at the end of
Table A4 and
Table A5, confirmed that the vast majority of routes supported the validity of the regression hypotheses (no autocorrelation, homoscedasticity, normality, or relevance of the multi-equation conditions imposed).
Regarding air and road transport, the estimated average income elasticities show that air travel has an inelastic demand (0.94), while that of road travel is elastic (1.11). The coefficient of variation indicates the existence of some heterogeneity. As such, the median of each distribution was also calculated (0.95 air, 1.06 road), confirming the conclusions drawn from the average. The estimates made for rail transport were highly heterogeneous (with a high coefficient of variation), including both positive and negative estimates. The average is 0.05 (the median being 0.20). These estimates can be compared with those given in
Table A6,
Table A7 and
Table A8 in
Appendix C. The quantification obtained is within the ranges observed in the scientific literature, although the income elasticity of road transport in the scientific literature is sometimes lower and that of air transport higher. After analysing a sample of 22 income elasticities from the literature, Holmgren [
30] pointed out that the income elasticity of public transport demand ranged from −0.82 to 1.18, with an average of 0.17. Thus, on the one hand, looking at the values in the tables in
Appendix C and in Holmgren’s study, there is a large dispersion of estimates, which underlines the need for further research. On the other hand, the low estimate of the income elasticity of the train is justified by the fact that many customers buy a car when their annual income reaches a certain level, which reduces the demand for public transport (train and bus modes).
The Hicks elasticities were negative in terms of the price itself and positive for the price of the competing modes (net substitutes). However, the substitution effects were all weak (a 10% increase in the price itself would generate, on average, a drop in demand for this mode of transport of −2.4% for air transport, −1.3% for road transport, and −8.2% for train transport). The Hicks cross-price elasticities were also weak. The median of each distribution confirmed the conclusions drawn from the average.
The Marshall elasticities show inelastic demands for all modes of transport. A 10% increase in the price itself implies, on average, a reduction of −6.2% for air, −6.9% for road transport, and −8.2% for train transport. All cross-price elasticities are weak. These elasticities are sometimes negative because the income effects dominate the substitution effects (grossly complementary to one another) (income effects predominate for air transport demand relative to road transport prices, as well as for road transport relative to the prices of the other two modes (the strongest effect is the 6% fall in road transport demand due to the 10% increase in air transport prices)).
For example, considering the route from Chicago to Orlando, a 10% increase in air transport prices causes a −6.8% reduction in the number of passengers using air transport and a −2.2% reduction in those using road transport. Moreover, a 10% increase in road transport prices causes a −5.6% reduction in the demand for air transport and a −6.2% reduction in the demand for passenger transport using cars or buses. Taking, for example, the Los Angeles to San Francisco route, a 10% increase in the price of rail would imply a −16.5% decrease in the use of rail, with almost imperceptible changes in the use of air (+0.4%) and cars or buses (−0.9%). The percentage change in the price of air travel would mean an increase in train use (14.1%) and a reduction in air travel (−5.9%) and car/bus use (−7.6%).
Different causes can be found for the nonstatistical significance of the coefficients calculated for rail transport and the variability of the estimated values. This is a problem that has been raised, in one form or another, in previous analyses. There are few studies of passenger rail elasticities in the United States. Some of the studies that have been performed estimate coefficients that are not statistically significant. Finally, there is a great deal of variability in the elasticities calculated. See
Appendix C,
Table A8. On the one hand, the demand for rail transport might be influenced by some factors not considered in the model. The conclusions of Wardman [
99], who points out in his UK study that “the critical importance of GDP for rail demand growth is quite clear” (p. 15), may be relevant. On the other hand, the lack of rail demand data concerning seat types, tickets for journey types, etc., and the fact that the data sample is smaller in size make this value difficult to estimate. The complexity of the pricing strategy and the importance of detailed data on the prices paid by different demanders is highlighted in the study of Cirillo and Hetrakul [
40], who stated that “Amtrak’s pricing strategy is more complicated than the one presented in this paper. We have not taken into account cancellation behaviour, various discounts, guest reward programmes and special fare schemes” (p. 21). In general, data on and knowledge of Amtrak’s fare policy need to be improved.
4. Discussion
Based on the objectives set out at the beginning of this research, the following results have been obtained. On the one hand, the method used and the way of obtaining the data and reconstructing the usable series have been shown to enable comparisons of the quantifications made for the different routes and conclusions to be reached for the routes as a whole and for each route individually. In this sense, the procedure makes it possible, in a relatively simple and rapid way, to relate the elasticities of demand thus estimated and the effectiveness of the different public policies to be applied to improve the sustainability of passenger transport in the United States on domestic routes using the data available from public statistical bodies. In summary, a method based on microeconomic theory and annually available data has been applied with relative success. On the other hand, the elasticities of demand for passenger transport on domestic routes in the United States have been estimated, although the estimate is not significant in relation to rail transport. Further research is needed on the explanatory factors of transport and the need for a more reliable understanding of the behaviour of rail passenger transport.
A statistically significant estimate of the elasticity of demand for air and road passenger transport has been achieved for the main US domestic routes: the average values calculated for the routes indicate that all income elasticities are positive (normal goods). While air transport demand is slightly inelastic and road transport demand is slightly elastic, both close to unity, rail demand is highly inelastic (although the estimate is not reliable due to the high coefficient of variation). This implies a crucial fact for planning future transport infrastructure and services in the United States: future income increases in the United States will lead to a roughly proportional increase in demand for air and road transport at the route level (somewhat higher for the latter mode). Although the exact value of the income elasticity of rail transport in the US has not been quantified with certainty, it should be reasonably low. It appears that demanders, given the current characteristics of rail transport in the US, tend to increase their demand for this mode very little in response to rising incomes. Thus, demand pressure will be differential for each of the modes. However, it is possible to note, at least as an approximation, the apparent differences between the different routes.
All the Hicksian elasticities show consistent signs of being competing services, with all the modes of transport being net substitutes. However, these elasticities are very low, and the price substitution effects are relatively weak. Moreover, all modes of transport have negative Marshallian demand own-price elasticities, although their values are less than one. Increases in transportation prices or costs produce a less-than-proportional reduction in the use of this service. This means that demanders have little propensity to stop using a transport type or to switch between transport modes. That is, in the face of price movements and differential price changes between modes, the demander has a high propensity to continue to use a particular mode of transport on US domestic routes. This can be because “transport is a derived demand and tends to be inelastic” (Oum et al. [
28], p. 8). Moreover, the Marshallian demand for air and car/bus transport shows that the two are strongly complementary to each other. This is because the income effect has a much stronger impact than the substitution effect; that is, the change in real income resulting from a change in prices has a greater influence than the direct impact of prices on switching between modes.
In general, the proportionally smaller demand response to price increases, and the reduced or non-existent transmission of demand from one mode to another at the route level (as shown by the values of the cross-price elasticities), indicate that fiscal or carbon price actions require very high price increases to produce significant reductions in transport demand, which are always proportionally smaller than the price increase and, consequently, entail high costs for consumers. While the fact of the inelastic price elasticity of demand for energy implies as an additional effect that a tax on CO
2 production would strongly increase tax revenues (Halsnaen et al. [
100], p. 153), it should be asked, in the face of high increases in transportation costs, what social and political impact this would have. Barrett and Chen indicate that “prices, particularly of food and fuel, seem to be particularly important” for explaining recent social unrest [
101]. This would indicate that public policy interventions through regulation would be more successful in the interests of sustainability (legal changes to the types of vehicles or types of fuel to be used). The most notable measure of this kind is that from the State of California, which has banned new gas-powered cars by 2035 (Emma Newburger [
102]). Nakamura and Hayashi [
103] argue that the introduction of a price on CO
2 output would reduce emissions by 5%, while the fuel efficiency improvement is estimated to be more than 20% (although it could generate the opposite effect of increasing travel demand and traffic congestion). Major investments in the infrastructure of different modes are also possible at the route level, which would change either the time taken from one end of the route to the other by each mode, or the possibility of interchanging one mode for another (e.g., rail terminals in the vicinity of airports). Major changes in infrastructure would also change the demand for each mode.
Moreover, since increased income generates greater proportional increases in the demand for road transport, investment policies for this mode are needed in anticipation of an expanding economic cycle to avoid infrastructure congestion. Similarly, as the substitution effect between modes is very weak, measures should be taken to increase the exchange of demand between modes. The direct interconnection of airports by rail and via the routes offered by Amtrak seems to be a crucial element. Such a connection already exists, for example, at the Baltimore/Washington International Airport station, and allows travellers to arrive or depart on Amtrak’s Northeast Corridor routes (Amtrak [
69]). In addition, price elasticity is also key in estimating the impact of changes in fuel prices based on oil price fluctuations.
Another interesting result of this study is the existence of a certain heterogeneity in the distribution of the estimated demand elasticities. This necessarily requires the study of the underlying and differential factors of each route, as well as the design of efficient public transport policies for each route. However, any effective public policy should quantify costs and benefits, which requires a view of all transportation routes as a whole.
Overall, therefore, a strategy for reducing greenhouse gas emissions into the environment should seek to replace fossil fuels with cleaner modes of energy, especially for those modes that will see the greatest increase in demand: planes, cars, and buses. This should primarily be performed with electric engines using electricity produced from renewable sources or sustainable aviation fuel (OEE&RE [
104], or otherwise using equivalents for vehicle engines.
This research could be extended in several directions in future research. The first and most immediate objective in this field is to confirm the findings of this research by analysing domestic routes in other locations and expanding the sample size to achieve greater precision. In particular, it is necessary to further estimate the demand for intercity trains in the United States and, in general, in all countries of the world. In addition, the geographical expansion of the study would benefit from extending the research to international transport routes. On the other hand, constructing and estimating a dynamic demand model that considers the possible impact of time would also be of great interest. Moreover, incorporating additional factors related to consumer preferences into the model would be of great value.