A Conceptual Model for Demands at the Pool Level

Kenneth D. Boyer

Michigan State University

Wesley W. Wilson

University of Oregon

Aim

• Pool level demand elasticities

• Useful for getting a gross benefit from lock expansion and/or improvement.

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.

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

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

A Sequential Set of Choices

• Each farmer decides1. How many acres to devote to corn, for example.2. The level of effort to devote to the crop3. How much of the crop to harvest4. When to release the harvest to an elevator.5. Whether to deliver the harvest to river port.6. Which pool to deliver the harvest to7. When to load harvest on a barge to Gulf.

Simplifications• If prices of river services get too high, the

farmer can:1. Delay shipment until rates drop.2. Deliver to a pool lower down on the river,

thus saving on barge expenses.3. Not use the Upper River at all. (This is a

leakage.)1. Ship to Portland instead2. Sell to a local processor.3. Ship to St. Louis via land.

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.

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.

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.

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.

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

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

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

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.

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?

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.

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.

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.

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.

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.

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

Any number of elasticities can be calculated

• Simulation allows us to estimate the consequence of improvements to any combination of locks.

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.

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.

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

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.)

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.