Spatial competition and geographic grain transportation demand on the Mississippi and Illinois rivers

Abstract

Using a model of spatial competition between grain elevators, I estimate a model of transportation demand for grain elevators located along the Mississippi and Illinois rivers. This analysis uses a unique set of interview data collected by the Tennessee Valley Authority (TVA). Both the theory and the data suggest that there are geographic patterns in barge demand elasticity–patterns which are empirically uncovered using an endogenous switch point model. These results are of central importance to policy-makers as they call into question assumptions made by the models currently used for measuring the benefits of inland waterway improvements.

Notes

¹ In particular, NRC (2004) states that ‘Price responsiveness is so important to estimating the benefits of waterway improvements that informed judgments about the merit of such improvements cannot be made without careful study of these demand and supply elasticities.’ In addition, NRC (2004) posits that ‘A spatial price model … would gauge the degree to which grain shipments increase, decrease, or move to alternative transportation modes with changes in the cost of waterway transport, a phenomenon described as the ‘elasticity’ of waterway traffic demand.’ The results of this present study directly address both of these concerns expressed by the NRC.

² Henrickson and Wilson (2005) use the same base set of data as are used in this study. However, this previous work makes no attempt to estimate geographic patterns in elasticity nor is there any attempt to incorporate the spatial competition empirical specifications used in this work. In addition, the data used in this current work include numerous data and variable differences which represent better measures of the spatial environment being examined.

³ The focus of this study is on grain products as they are the most common commodity being shipped on the Upper Mississippi and Illinois rivers, with corn being the dominant commodity within the group. As such, it should be noted that spatial competition and spatial relationships have been of particular interest to agricultural markets, e.g. Fackler and Goodwin (2001) and Faminow and Benson (1990). Also worth noting is that, by incorporating the spatial nature of transportation demand, this study addresses one of the NRC's other criticisms of the current ACE planning models (NRC, 2004).

⁴ Estimates which call into question the assumptions made by current planning models used by ACE, while also providing a contribution to the spatial modelling of demand.

⁵ Note that this theoretical model is grounded in a standard Hotelling competition model.

⁶ However, this model is general enough to be adapted to nonlinear distances.

⁷ Note that this assumes that grain is evenly distributed between elevators; however, this model is again general enough to be adapted to a noneven distribution of grain.

⁸ δ _e enters this equation to control for nonprice differences across farmer's utility functions. For example, one farmer may like the options provided to it by using a large multi-plant company's elevator, while a different farmer may prefer his local cooperative elevator. Note that this treatment of farmer preferences is not completely novel in the literature (e.g. Johnson and Wilson, 1993).

⁹ It is assumed that no one elevator prices the other elevators out of the market.

¹⁰ Note that these elevators often provide a considerable amount of service in the form of storage. As demonstrated by Benirschka and Binkley (1995) and Brennan et al. (1997), the elevators not only choose what mode of transportation to use, but also when to ship. Thus, many of these elevators store crops on site for shipment at a later date, contributing to both the service provided and the costs of the elevator. This decision of when to ship is largely based on whether the spot prices for the commodity are higher than the forward prices (backwardation) or the opposite (contango).

¹¹ Note that this problem is really a spatial-temporal problem; however, given the data described later, the time portion of this equilibrium cannot be directly modelled.

¹² There are many ways that the assumption of larger shipments being more difficult to procure can be satisfied; for example, the shipper having to increase its bid prices in order to increase its catchment area or to induce farmers to reach a reservation price.

¹³ As explained by NRC (2004), currently barge shipments must be decoupled to pass through locks, drastically decreasing transit time and increasing transportation costs. Thus, an improvement to the waterway infrastructure would decrease transit times and costs which is similar to the impact of railroad development in the late nineteenth century as described by Solakoglu and Goodwin (2005). Note that this also has implication for any policy whereby locks would be upgraded selectively rather than universally. This may or may not be the case, but in either case, the locks will be improved over a long period of time and will lead to at least temporary differences in costs associated with the upgrade schedule.

¹⁴ This reduction in transportation costs stems primarily from the time savings offered by upgraded locks, which allow barge tows to be brought through a lock without decoupling prior to entering the lock and re-coupling once through the lock.

¹⁵ In addition, it is possible that congestion could actually be higher for firm B as more traffic flows down the river given the infrastructure improvement north of firm B which would further increase firm B's costs and lower their profit-maximizing quantity.

¹⁶ A pool is the area between two locks on the river. In ACE modelling efforts, demands are typically defined at the pool level. That is, they consider the originating-terminating and commodity triple as a demand function that enters into their planning models.

¹⁷ This is done because the alternative rate facing the river terminal is the rate facing nonriver elevators.

¹⁸ According to the United States Department of Agriculture (USDA), corn production is nearly double that of wheat and soya beans.

¹⁹ Note that most studies treat quantity as endogenous and transportation rates as exogenous (see Oum (1989) for a description of this methodology and the associated functional form options). In addition, the NRC (2004) cites the need to ‘estimate the likely reduction in barge shipping rates that would result from improved lock infrastructure’ which could then be ‘incorporated into the spatial models and the models solved to determine increases in river grain flow and increases in economic welfare resulting from these investments’, something which this study directly assesses. However, to first verify this treatment of rates as exogenous in this study, a Hausman test was run using barge capacity data obtained from the US Army Corps of Engineers’ Navigation Data Center. These data allow for the calculation of the barge capacity available in different regions of the Mississippi River System, a supply side variable, as an instrument for barge rates. The results of this test indicate that Ordinary Least Squares (OLS) is consistent, and that an instrumental variables approach is not necessary, although the estimates are numerically similar to those presented in this study when using instrumental variables. Also, note that the precise construction of each of these variables is discussed later in the data section.

²⁰ The results of estimating Equation 7 via OLS are also presented to assess the stability of the results.

²¹ To the extent that these alternative markets impact all elevators within a pool, the FE model should capture this variation. Tests for breaking the sample in two and treating the Upper Mississippi and Illinois rivers separately indicated that such treatment was not warranted.

²² Anselin (1988) provides a detailed development of the spatial-lag model. The alternative spatial model would be the spatial error model. The spatial-lag model is used in this analysis because it is believed that the elevators within a pool are competing with one another to procure their shipments; however, a spatial error model was also estimated and the results were qualitatively identical to those presented for the spatial-lag model.

²³ However, numerous other specifications of the weight matrix were examined and did not qualitatively change the results presented. Row standardization is done such that the sum of each row of the spatial weight matrix sums to one, which places the least structure on the spatial specification.

²⁴ Notice that zero weight is given to all diagonal elements of the weighting matrix to prevent each firm's annual ton-miles from being a function of itself.

²⁵ Note that the Tennessee Valley Authority (TVA) checks these data against the confidential Waterborne Commerce Data.

²⁶ The survey data also contains information on elevators located on other waterways; however, the focus of this study is on the Upper Mississippi and Illinois Rivers. As was noted previously, Fig. 2 provides a visual depiction of the elevators analysed in this study.

²⁷ There are many spatial competition models that have been developed over time; for an overview of such models and the typical assumptions behind them, Tirole (1988) provides for a good reference.

²⁸ The transportation rate from farmer to elevator variable is obtained through the TVA survey and is created from the elevator's answer to the questions in the survey regarding their gathering/catchment area and the cost of relevant rail/truck movement to the elevator. In other words, if the elevator states that their average catchment area is 100 miles and that the cost of using rail/truck in the area is $10 per ton, then the transportation rate from farmer to elevator would be 10/100 = $0.10 per ton-mile.

²⁹ Other variables influencing barge rates come from the supply side of the market including the aforementioned barge capacity available. These variables determine supply which explain the barge rates present; however, the focus of this study is on barge demand and elasticity rather than barge supply.

³⁰ Note that tests indicate no correlation or heteroskedasticity problems in the estimates from these data.

³¹ A regression of catchment area and river miles (measured from Cairo, IL) indicates that catchment areas increase with river mile, and a 100-mile increase in river miles increases the catchment area of an elevator by approximately 4 miles. From the lower reaches of the river to the most northern areas, this suggests a difference in catchment area of approximately 33 miles. Anderson and Wilson (2005) show that this should be the case, as farmers are willing to transport further to the river to take advantage of the chapter barge transportation as the distance to be travelled increases.

³² Note that the number of firms in the pool is not included in the FE model as there is no within pool variation in this variable.

³³ Given the cross-sectional nature of the data used in this study, these estimates should be interpreted as shortrun in nature. However, note that the long run is driven by changes in capacity and location, and Train and Wilson (2004a) show that the short-run responsiveness of location and capacity is small, implying that while the estimates presented here are short run, the short run is a long time.

³⁴ The effect of these variables may be captured in the FE coefficients.

³⁵ Initial work in estimating geographically varying elasticities employed both rolling regressions and locally weighted regressions; however, both these models suffered from a degrees-of-freedom problem which resulted in seriously under-smoothed estimates that were statistically insignificant. The results of these estimation methods are available from the author upon request; however, the results point towards barge transportation demand being more elastic on the northern and southern stretches of the waterway system.

³⁶ Tests indicate that the Mississippi and Illinois barge elasticities are different at the 99% level.

³⁷ The possible break points would be at elevator 2 (meaning that elevator 1 and elevators 2–5 have different elasticities), elevator 3, elevator 4 and elevator 5.

³⁸ The specific break point is at the pool level for the break point that yields the largest test statistic.

³⁹ Note that the elasticity being higher on the Illinois River reaffirms the previous argument that elevators located on the Illinois have more alternatives available to them.