A Conceptual Model for Demands at the Pool Level

1. A Conceptual Model for Demands at the Pool Level Kenneth D. Boyer Michigan State University Wesley W. Wilson University of Oregon

2. Aim • Pool level demand elasticities • Useful for getting a gross benefit from lock expansion and/or improvement.

3. Criteria for a good model • Based on plausible decision settings • Spatially motivated • Identified • Capable of separating shifts in supply from shifts in demand • At an aggregation level that is useful for policy.

4. Classic problems of Freight Transportation Demand Estimation • Data availability • Confidentiality • Rates quoted at much finer levels of aggregation than quantity data • Econometric identifiability • Complexity of the choice setting

5. Problems are perhaps not as severe here • 100% sample of movements for many years • Rates should not be as unpredictable as for rail or air. • A proxy for rates is available on a weekly basis • Speed can be computed for every movement. • Linearity of movements makes analysis potentially tractable

6. A Sequential Set of Choices • Each farmer decides • How many acres to devote to corn, for example. • The level of effort to devote to the crop • How much of the crop to harvest • When to release the harvest to an elevator. • Whether to deliver the harvest to river port. • Which pool to deliver the harvest to • When to load harvest on a barge to Gulf.

7. Simplifications • If prices of river services get too high, the farmer can: • Delay shipment until rates drop. • Deliver to a pool lower down on the river, thus saving on barge expenses. • Not use the Upper River at all. (This is a leakage.) • Ship to Portland instead • Sell to a local processor. • Ship to St. Louis via land.

8. The Basic Method • Observe harvest in hinterland of each pool • Observe periodic shipments from each pool • Separately for each pool, estimate how shipments are determined by the product of harvest in the pool’s hinterland and seasonality of shipments.

9. For example • We might determine that over a ten year period, increasing harvest in the hinterland of pool 4 by 1 million bushels increase average river shipments by .6 million bushels. • We might determine that on average, July has 10% of the year’s shipments.

10. If shipping charges rise on the upper river, 1 • Some of the grain will be leaked and thus perhaps only .5 million additional bushels are shipped in the case of a 1 million bushel harvest increase. • This is where the PNW-Gulf rate spread will be introduced as a separate regressor. • The response should be higher farther upstream • Closer to PNW • River shipping is larger proportion of delivered cost.

11. If shipping charges rise on the upper river, 2 • The pattern of shipping may change, reducing shipments at high rate periods and increasing them later. • The farther upstream, the more pronounced the effect should be since rate changes will be proportionately larger. • This effect can be confirmed by inventory build-ups following periods of relatively high rates.

12. If shipping charges rise on the upper river, 3 • A shipper may economize on river transportation by delivering the harvest to a lower pool. • Missing bushels in pool n will show up as extra bushels in pool n+1. • In high numbered pools, this effect may result in a complete leakage as the upper river’s locks are not used

13. Measuring rates 1 • For most modes, rate estimates are extremely unreliable • Upper Miss barge traffic seems to be different • Rates = time * cost per hour • Time is observable • Cost per hour can be inferred from index rates

14. Measuring rates 2 • Unsure: how to deal with backhauls • Is this an issue? • Should rates be calculated based on round trip time or one way time? • Can rates be confirmed by difference in bid prices between different pools? • Assumes a competitive market for export grain and arms-length contracts

15. Congestion and rates • Since congestion slows traffic, it should raise rates charged. • Since upstream shippers must traverse lower pools, congestion affects upstream shippers more than shippers closer to St. Louis. • So rate effects should be most pronounced upstream.

16. Rates assumed exogneous at pool level • Hourly cost of using barges and towboats should be based on system-wide supply and demand • Other commodity demands • Other waterways. • Is each pool “small” relative to the whole?

17. Error terms contemporaneously correlated across pools • World demand shocks should simultaneously affect demand for all pools. • Requires that demands for each pool be estimated simultaneously. • Cross-equation error term constraints will also allow us to observe traffic that would normally go to pool n going to pool n+1.

18. Basic Estimating Form • Qyip = Ap(Hyp)(Wyip)β1(Pyip)β2eyip • Where: • Ap is a constant term for pool p. • Hyp is an index of the harvest level in the 12 months prior to year y in the hinterland of pool p. • Wip represents a set of i weekly dummy variables to capture the seasonality of grain shipments from pool p. • Pyip is the price of shipping from pool p to pool 30 in week i of year y • eyip is the error term associated with the southbound movement of grain from pool p in week i of year y.

19. Normal Inventory Levels • One response to higher prices is to change inventory holding patterns. • There is a normal periodic pattern to inventory holding. • If shipping is delayed, inventories should build up, leading to larger shipments later.

20. A modified model • Qyip = Ap(Hyp)(Wyip)β1(Pyip)β2(Syp)β3eyip • Where Syp is a measure of the ratio of the weekly storage to the normal storage level in pool p. • Other variables are as before. • Inventory levels can be directly observed or constructed from lagged error terms.

21. The complete model • Qyip = Ap(Hyp)(Wyip)β1(Pyip)β2(Syp)β3eyip + T+vip-1­((Hyp-1)Pyip-1) – T-vip+1­((Hyp)Pyip) • Where T+vip-1­((Hyp-1)Pyip-1) is the amount of harvest transferred to a pool from the hinterland of the pool immediately upstream.

22. Estimating Elasticities • Once the entire system has been estimated, the slopes of demand curves can be calculated by simulation. • A lock or group of locks is improved, lowering transit times and reducing rates. This: • Changes weekly pattern of movements • Changes pool-to-pool transfer patterns • Reduces leakages out of the river system

23. Any number of elasticities can be calculated • Simulation allows us to estimate the consequence of improvements to any combination of locks.

24. Long run feed back loops • Planting is assumed to be exogenous. • But logically, there must be a relationship between planting and expected delivered price of grain. • This effect is probably too subtle to be visible given the fluctuations in prices in the data set.

25. Another limitation • Planting and storage decisions are based on speculative motivations. We will not try to model expectations in any of the estimations done here. • Instead, we will simply record changes in patterns that can be predicted by changes in transportation costs.

26. A concern • Is there enough price variation to estimate anything? • To the extent that the multiplier follows a seasonal pattern, unchanged from year to year, we can’t disentangle seasonal affects from rate affects • Except for occasional anomalous events, there seems to be small differences in speed across the year

27. Another concern • What is the appropriate period? • We would like to have a match between the price of moving grain and the seasonal pattern of moving grain. • Prices depend on the speed of flow, arguing for a shorter period (a week, for example.) • It appears that flows from pools are irregular, arguing for a longer period (possibly a month.)

28. First results • Tracking sailings is an inappropriate way of organizing the data. • Speed needs to be calculated as median time on a pool-to-pool basis for all tows. • Quantity should be calculated from pool-to-pool aggregate flows over a period.