1 Introduction

The U.S. Corps of Engineers (USACE) oversees the operations and maintenance of the U.S. Inland River System, which includes 27 rivers, 12,000 miles of inland river channels, 207 Lock chambers at 171 lock sites, all of which carry at least 850 billion tons of a wide variety of commodities each year while benefitting shippers, receivers, and communities (Fig. 1).

Fig. 1.
figure 1

The U.S. navigation system

In the late 1990s and early 2000s, following several controversies in USACE’s analyses of the Upper Mississippi River locks, the National Academy of Sciences was sought out to review USACE’s draft analysis and recommended that they develop an approach to estimate the structure of transportation demands for use in USACE planning models, particularly by analyzing shipper behavior to changes in conditions to the waterways.

Following that time, USACE completed several studies that examined actual and hypothetical behavior on the Upper Mississippi and Illinois River Basins (Train and Wilson, 2004, 2005, 2007a, 2019), the Columbia-Snake Waterway (Train and Wilson, 2006a), the Ohio River (Train and Wilson, 2008c), and the Calcasieu River (Wilson et al., 2011) and more recently the Upper Mississippi River and Ohio River Restudy (Wilson, 2021).Footnote 1 In every case, survey methods focused on shippers of commodities that had a historical presence on the waterway and on shippers of varying distance from the waterway to capture the effects of space that are central to the decision to use the waterway. Using these survey data, demand models have been estimated that yield significant evidence that shippers do respond to changes in rates, time and reliability. The responsiveness is two-fold: shippers’ discrete decisions (where and how to ship the product) and continuous decisions (the volume of shipments) are both embedded in most of the studies. In all cases, the analyses proved that shippers respond to changes in attributes that are affected by USACE infrastructure decisions.

The results of the survey were used to calculate transportation demand functions by mode of delivery which allow for the generation of demand elasticities used in waterway investments. Moreover, these elasticities were then incorporated into various models, such as the USACE Navigation Investment Model, which provided the following outputs:

  • Event trees and hazard functions to model lock failures, closures, and repairs

  • Demand curves by origin, destination, and commodity to define shipping forecasts

  • Optimal configuration of tows for each movement, including selection of towboat, number of barges, and reconfiguration by river segment to minimize cost

  • Congestion-based costs on a lock-by-lock basis and annual systemwide traffic equilibriums

  • Automated calibration of the model to historical traffic using optimization routines

  • Optimal selection and time sequencing of alternatives to improve capacity and reliability

  • Determination of optimal lockage fees

  • All these features help analyze (1) lock reliability and component failures; (2) demand projections versus system capacity to determine equilibrium waterway traffic; and (3) selection and sequence of replacement, repair, or modernization efforts over the planning horizon.

2 Role of Elasticities in Inland Navigation Benefits Analysis

The heart of transportation demand models involves the computation of demand elasticity, which is an economic principle that measures the extent of response to changes in quantity demanded because of a change in price. A variable is said to be elastic (having an absolute elasticity value greater than 1) when it responds more than proportionally to changes in price. In contrast, an inelastic variable (with an absolute elasticity value less than 1) is one which changes less than proportionally in response to changes in price. When there are substitutes available, the elasticity is likely to be higher, as one could switch from one good to another even if the price change is minor. By the same token, the more necessary a good is, the lower its demand elasticity, as people will attempt to buy it no matter the price. Common examples include insulin or a heart transplant. The same economic principle has been applied to carrier when faced with making decisions on various modes of transport (truck, rail or barge) to move its commodities.

Numerous studies have applied the principle of elasticity for various modes of public transportation including automobile usage where the estimated elasticity is between 0.01 and 1.26, urban transit with an estimated elasticity between 0.01 and 1.32, airline travel with an estimated elasticity between 0.36 and 4.60, and rail travel with an estimated elasticity between 0.12 and 1.54 (1). Equally important has been the estimation of freight transportation, i.e. the movement of commodities. The elasticity estimates of these various modes are found to depend heavily upon the commodity being transported but with general elasticity estimates of: rail transportation with an estimated elasticity between 0.02 and 3.50 and motor carrier transportation with an estimated elasticity between 0.14 and 2.96 (1). By examining the response to changes in cost, the cost of alternative movements (in other words) benefits to the waterways can be estimated (Wilson, 2004).

According to the Corps’ Planning Guidance Notebook ER1105-2-100, National Economic Development benefits are “the difference in costs of mode transport between the without-project condition (when rails, trucks or different waterways or ports are used) and the with-project condition (improved locks, waterways or channels). The economic benefit to the national economy is the savings in resources from not having to use more costly mode or point of transport. (Additional benefits can be realized by reductions in costs incurred from trip delays (e.g. reduction in lock congestions), reduction in costs associated with the use of larger or longer tows, and reduction in costs due to more efficient use of barges.”

3 Survey Description

All data used in the recent Ohio and Upper Mississippi River analyses were generated from a survey of agricultural shippers using a survey instrument approved by the U.S. Office of Management and Budget and supplemented with information from the Surface Transportation Board’s Carload Waybill Statistics, USACE river distances, and Google map distances. The goal of the research was to gather data that pertain to all agricultural shippers that could conceivably ship on Ohio River and Upper Mississippi River Basin waterways. Figures 2 and 3 show the shipper locations and destinations.

Fig. 2.
figure 2

Shipper locations for the ohio study shipper destinations for the ohio study

Fig. 3.
figure 3

Shipper locations - upper miss study shipper destinations – upper miss study

More specifically, several thousand shippers were sampled. The sample was stratified by distance from the waterway, with a higher percentage for those located closest to the waterway. For both river systems, corn shipments dominated the sample, representing 65% and 47% for the Upper Mississippi River and Ohio River System, respectively. The remaining commodities included but were not limited to wheat, soybeans, beans, and grain.

Survey questions included grain elevator age, loading capacity, shipment information, last shipment, and shipping alternatives. The meat of the survey contained questions on alternate modes: For example, “If rates went up by X percent, how likely would you switch from water to rail or truck, etc.? (Fig. 4)” Questions were repeated for changes in time and changes in reliability.

Fig. 4.
figure 4

Portion of shipper response survey

4 Revealed Vs. Stated Preference

Revealed data reflect actual decisions made by shippers is very useful in predicting shipper behavior. However, many believe that revealed data’s attributes do not provide a large enough range of data to identify the parameters of interest. Rates per ton-mile, times-in-transit, and reliability each have similar values between the chosen and next-best alternative. Because of limited variation in such statistics, there has been a growing literature on stated preference modeling. A stated preference survey presents survey respondents with a set of hypothetical states, and then solicits a preference. This approach considerably simplifies analysis and the difficulty of collecting survey responses to confidential information. However, it is criticized as being based on hypothetical situations instead of real-world decision-making. This stated preference approach differed from the standard approach in that the stated preference questions were grounded in the revealed decisions made. In particular, survey recipients were asked what they did and what they would do if the chosen alternative were not available. This was taken as their next best alternative. The stated preference questions ask if the shipper would stay with their choice, switch to a different option, or shut-down if an attribute change. For example, for the last shipment, if the attribute changed x percent, would you continue with the original mode and destination or switch to your best alternative choice?). This framing of the question grounds the decision- making not to hypothetical alternatives, but rather to alternatives commonly confronted by the individual making the decision.

In the survey, three such questions related to rate, time, and reliability. The percentage change was randomly offered to each and ranged from 10 to 60%, generating a range of values over which to identify the parameters of the profit-function on which decisions are made. In addition, if the shipper did not switch, they were asked what level of the attribute would induce a switch with outcomes presented in Tables 1, 2, and 3.

For the Ohio River Shipper Survey Report (and similarly applied to the Upper Mississippi River Report), 6 rate changes, from a 10 to 60% increase in rates, were used in the survey. A total of 319 responses were observed. At low values of rate changes, 66% of responses indicated they would not switch to the alternative. As the rate change increased, this proportion fell. However, even for large rate increases, 45% (30 of 66) of respondents report they would still not switch. If they would switch, there were two alternatives selected. First, they could switch to their next best mode/destination. At various rate changes, there were a total of 128 such switches. Second, they could switch to shut-down. Shut-down is and has been a major factor in all of the surveys conducted discussed in the literature. In this sample, 22 of 319 (7%) reported that they would shut-down at the rate increase prompt. As expected, switching to an alternative tends to increase with the magnitude of the rate change.

Table 1. Shipment stated preference – rate responses

The same information with respect to increases in transit time was examined, with transit times defined, again, as including the setup and waiting times and the time once loaded to reach the final destination. There were 316 responses. If time changes, shippers report that a total of 177 (56%) shipments would not change regardless of the time change. As with rates, switch rates generally increase with progressively higher changes in transit times.

The same information as in Tables 1 and 2 with respect to reliability is presented in Table 3, with a total of 412 responses. The same general pattern as with rate and time is indicated (as expected). For decreases in reliability, the switch rate increases with the percentage change in reliability. Generally, Tables 10, 11, and 12 each follow expectations. Further, shippers appear to be more responsive to rates than to time and reliability, particularly for large rate changes.

Table 2. Shipment stated preference – time responses
Table 3. Shipment stated preference – reliability responses

5 Major Report Findings

  1. 1.

    The choice models indicated statistically important responses of shippers to changes in the rates, reliability, and distance. These responses also differed by shipper attributes that included rail car loading capacity and storage capacity.

  2. 2.

    There were important differences in the responses for truck, rail, and barge shipments.

  3. 3.

    Many firms reported limited alternatives in their choice of mode and destination, and many reported that they would shut down in the presence of rate increases or if the chosen alternative was taken away. Unlike previous studies conducted under NETS, the effect of a shut-down alternative was reflected in the choices and explicitly captured in the models of switching behavior.

  4. 4.

    Arc elasticities were calculated for each mode and shipment attribute. Demand was found to be inelastic; that is, the arc-elasticities were all less than one in magnitude.

  5. 5.

    The rate demand elasticities were all inelastic. Barge elasticities ranged from −0.41 to −0.48; rail elasticities ranged from −0.22 to −0.12, and truck elasticities ranged from −0.29 to −0.26.

  6. 6.

    The time demand elasticities were all inelastic, and smaller than rate elasticities. Barge time elasticities ranged from −0.287 to −1.067; and truck elasticities ranged from −0.19 to −0.76.

  7. 7.

    The reliability elasticities were all inelastic and rest between those of rate and time elasticities (in magnitude). Barge reliability elasticities ranged from 0.29 to 1.067; rail elasticities ranged from 0.16 to 0.36 and truck elasticities ranged from 0.19 to 0.76.

  8. 8.

    Annual volume demand elasticities were also estimated for rate, time and reliability. The responses of shippers often pointed to no change in annual volumes from a change in an attribute. A Heckman (1979) model was, therefore, used to estimate the model. The results suggest that shippers with large storage capacities were more likely to adjust volumes in response to rate changes than for smaller capacities. Given a change does occur, the change is driven largely by the level of the change in the attribute. That is, the elasticities conditioned on a change occurred did not vary with shipper attributes or commodity, but, whether or not a change occurred depended on shipper attributes.

  9. 9.

    The Heckman model allows the calculation of two different elasticities. These are a conditional elasticity (given a shipper’s volume changes) and an unconditional elasticity (where a shipper’s volume may or may not change). By definition, the former is larger in magnitude than the latter for each attribute. In some cases, annual volumes, given a change in volume, were responsive to changes in attributes. However, generally the unconditional elasticities were less than one in magnitude, pointing to relatively inelastic demands.

  10. 10.

    Two different rate elasticities are presented – one in which the shipper and its competitors face the same rate change, and one in which the shipper but not its competitors face a rate change. The elasticities calculated from the former are much smaller in magnitude than those calculated from the latter, and in the latter case, there are some unconditional elasticities greater than one in magnitude for the median shipper. For some rate change levels, the conditional elasticities are greater than one in magnitude. This suggests that if there is a rate change that induces a volume change, the change is relatively responsive.

  11. 11.

    Both time in transit and reliability elasticities are nonzero, a finding that suggests shippers do adjust annual volumes to these shipment attributes. As with rates, the unconditional elasticities are less than one in magnitude.

6 Conclusion

This report continues a series of demand studies aimed at providing shipper-level information that can be used by USACE to evaluate the benefits of waterway improvements. The shipper-based surveys that have been developed and modified over the last several years are designed to collect information on shipper and shipments. These data, in turn, are used to estimate the responsiveness of mode, destination choices, and annual volumes to changes in rates, time in transit, and reliability.

The choice models were estimated with a logit methodology applied to both revealed and stated preference data. The results suggest that while demands are responsive to changes in rates, time in transit, and reliability, the response is somewhat small and points to relatively inelastic demands (i.e., demand elasticities less than one in magnitude). The annual volume models were estimated with a Heckman selection model using stated preference data. Generally, the results suggest that shippers respond to rates and time in transit, but as with the choice models, the response is somewhat small, with most elasticities less than one in magnitude.

The demand functions appear to be reasonably steep and point to a large degree of captive shippers (i.e., shippers that do not switch to alternatives even for large changes in the attributes). While this result points to relatively large benefits to infrastructure investments, there are limits. A novelty of this research is the incorporation of the option of no longer shipping (i.e., shutting down). This finding has been a consistent theme throughout this line of research. In the present case, the option to shut down is explicitly represented in the choice model. Hence, attributes, particularly rates, cannot increase without bound because eventually shippers will opt out of the market. This reaction places limits on the benefit calculations necessary for USACE planning models. The resulting elasticities are used widely in the analysis of lock closures, delayed investments and other challenges to the inland waterway system.