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Longer-Term Forecasting of Commodity Flows on the Mississippi River: Application to Grains and World Trade. Project report to the ACE Penultimate for discussion and direction July 6, 2005. Purpose/Overview.

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slide1

Longer-Term Forecasting of Commodity Flows on the Mississippi River: Application to Grains and World Trade

Project report to the ACE

Penultimate for discussion and direction

July 6, 2005

purpose overview
Purpose/Overview
  • Collection and analysis of important data impacting world trade in grain and oilseeds.
    • These include data on production, consumption, imports, interior shipping and handling costs, and international shipping costs.
  • Development of an analytical model to analyze world grain and oilseeds trade.
    • Specifically, a large scale linear programming model will be developed.
  • Risk analysis
    • Derive probabilities and risk measures about critical variables (reach shipments)
    • Determine how far forward it is practical to generate projections
      • Ie how do their accuracy change for different forecast horizons
3 major glitches
3-major glitches
  • Back-casting
    • Shorter-term concept
    • Compatible with econometrics
    • Longer-term projections imply longer-term adjustments not compatible with back casting
  • Reach allocations and shipments
    • Allocation of shipments between/within Reaches is challenge
    • Other studies simply refer to “barges” without attention to Reach allocations
    • Study has to embrace
      • Extreme macro phenomena e.g., production costs in Ukraine, at the same time it considers
      • Inter-reach-inter-modal allocations of shipments
  • Risk: Can’t be completed till
    • final deterministic specification is concurred
    • Specification/format of conditional expectations on modal rate distributions
  • [Personnel—broken back and bull stampede!]
slide4
Goal
  • Review overall approach
    • Report distributed in two versions
      • Appendix (details on all aspects of data/model)
      • Report (summary of methods and results) 20-30 pages
  • Present current results
  • Concur/Resolve outstanding issues on
    • Deterministic model
    • Risk questions
background data
Background data:
  • Consumption
  • Production costs
  • Yields
  • Trade and Agriculture Policies
  • Modal rates
    • Rail
    • Barge
    • Truck
    • Ocean
    • Changes in modal rate competitiveness
  • Barge delay functions and restrictions
  • Competitive routes and arbitrage
approach to consumption
Approach to consumption
  • Changes in consumption as countries’ incomes increase
  • Econometrics:
    • C=f(Y)
      • For each country and commodity using time series data
      • Use to generate elasticity for each country/commodity
    • E=f(Y)
      • Non-linear
      • Across cross section of time series elasticity estimates
      • Allow elasticities for each country to change as incomes increase
  • Derive projections
    • Use WEFA income and population estimates
    • Derive consumption as
      • C=C+%Change in Y X Elasticity
production costs
Production costs
  • Yields
    • Yields by crop and country
  • Costs
    • From WEFA
      • Cross-sectional for most producing countries/regions
      • Costs per HA
      • Variable costs were used
    • Generate costs per metric tonne using estimated yields
estimates of consumption by region
Estimates of consumption by region
  • No estimates are available for consumption by region or state, through time
    • USDA and others only provide national estimates
    • Anecdotal estimates exist by state for selected crops e.g. ethanol
  • Approach: Combine the below
    • National use by crop and through time
    • Production
    • Rail shipments from each reach; and imports to each region; all relative to national consumption
    • Derive estimates of consumption in each region
    • See attached4
ethanol
Ethanol
  • Derived additional demand due to ethanol consumption of feed grains by region and state…for the current and projection period.
  • Adjustments for
    • State/regional ethanol planned production
    • Existing capacities and those planned
      • Most of planned expansions are in W. corn belt
    • Assume extraction rates
    • DDG used locally and demand adjusted due to different species (Cattle, swine and poultry)
  • Result—see attached
    • Estimate of the net added corn demand, which results in reduced exportable surplus by region
    • Notable increase in W. Corn belt, followed by E. Corn belt and C. Plains.
    • Total: 24 mmt or about 10% of corn production
trade and agriculture policies
Trade and Agriculture Policies
  • Model includes the impacts of
    • Domestic subsidies
    • Export subsidies
    • Import tariffs
    • Import restrictions/relations
      • US/Canada on wheat
      • Mercursor
      • Other minor
  • Data: Agricultural Market Access Database (www.amad.org)
modal rates rail
Modal rates: Rail
    • Barge
    • Truck
    • Ocean
    • Changes in modal rate competitiveness
  • Barge delay functions and restrictions
  • Competitive routes and arbitrage
modal rates ocean rates
Modal Rates: Ocean Rates
  • Data
    • Maritime Research Inc
    • 1994-2004
    • Distances derived for each route
    • Pooled 7000+ observations
  • Rates used
    • Generated from regression
    • R=f(Size, Miles, Oil, Dummies, trend)
    • See p. 68
    • See projections as well
rail rates
Rail rates
  • Confidential waybill
    • 1995-2002
    • Regions redefined on be compatible with flows
    • Concern:reporting of flows/rates from this data
  • Matrixes developed for each crop
    • Domestic
    • Export
  • Missing observations
    • Either non-movement, or, non-reported movement
    • Replaced during projection period with “estimated” rate function
      • Estimated to reflect a consistent relationship with contiguous rates
      • See text p. 46-……
    • Specifications
      • R=f(Distance, distance to barge, spread (pnw-gulf)
      • R=f(distance)
truck rates
Truck rates
  • Used to allow for truck to barge shipping locations
  • Distance matrix estimated:
    • centroid of each prod region to export and barge loading regions, and domestic regions
  • Rate function derived from trucking data from USDA AMS
    • 4th Qtr 2003 to 3rd qtr 2004.
barge rates
Barge Rates
  • Data source
    • USDA AMS
    • For each reach
  • Adjustments
    • Draft adjustments for above/below St. Louis (see p. 54)
handling fees
Handling Fees
  • Separate handling fees imposed for additional costs of selected movements
    • Barges
    • Great Lakes
selected comparisons rail barge via reach 1 vs rail barge direct
Selected Comparisons: Rail/Barge via Reach 1 vs. Rail/Barge Direct
  • Problem
    • Rail rates from origins to local barge points vs. St. Louis (Reach 1)
      • Rates to St Louis have declined selectively
      • In some cases, lower in absolute value than the local Reach
  • Analysis: For comparison
    • Derive comparative rail advantage of rail to reach 1 and then barge; vs., Rail to local reach (3 or 4) and then barge
    • 2002 barge rates for comparisons
      • Reach 1 4.99/mt
      • Reach 2 12.98
      • Reach 3 16.66
      • Reach 4 10.43
  • Selected comparisons
    • See Table 6.6.4-6.6.6
  • Major point
    • Selectively, rails have lowered rates to Reach 1 (and in some cases US Gulf) to favor that movement, vs., shipment to local reaches.
    • Model:
      • Major shift in optimal solution to favor rail to StLouis flows
      • See below
barge delay functions
Barge delay functions
  • Barge rates were: B=B+D where B is barge rate above, plus D=delay cost
  • Delay costs
    • Derived for each reach 1-4
    • Oak Ridge Model
      • Average wait time=f(volume)
      • Cost=f(wait time)
    • Assume “normal traffic” for other commodities
    • Current and expanded lock system
  • See attached
relationship between change in barge rate and volume by reach and existing vs expanded capacity
Relationship Between Change in Barge Rate and Volume by Reach and Existing vs. Expanded Capacity
relationship between change in barge rate and volume by reach and existing vs expanded capacity1
Relationship Between Change in Barge Rate and Volume by Reach and Existing vs. Expanded Capacity
barge restrictions
Barge Restrictions
  • In light of
    • rail rate declines to St Louis
    • and to US Gulf,
    • both selectively,
    • prospective shifts in flows
  • St Louis area restriction on transfer
    • Reach 1 split above and below L&D 27
    • About 4-5 mmt enter above 27;
    • and 2-4 below, but, this has been increasing
  • US Gulf
    • Similar issues
    • Average rail unloads 5.9 mmt
restrictions
Restrictions
  • If run model w/o any restrictions large shift to
    • Rail to StL and barge transfer; or direct to USGulf
  • Restrict
    • St. L transfer (below 27) 6 mmt
    • US Gulf 5.9 mmt
  • Discussion 1
    • Is this apparent?
    • Is it due to rail to barge transfer? Or rail to elevator transfer? Or due to rail capacity?
  • Effect
    • Limits volume of grain by rail to either StL or USGulf
    • Force grain onto barges in Reaches 2-4
  • Discussion
    • Other studies:
      • Not apparent they encountered this issue
      • Likely a recent phenomena
      • Also apparent in econometrics of rail rates where negative trend is significant (vs. barges not)
    • How defendable is this?
    • Is this a short term or longer-term effect (Mosher,…is it sustainable?)
    • Alternatives
      • Retain as assumption
      • Estimate w/wo restriction
      • Rail capacity restriction (not so easy)
      • Handling fees: Increasing function of volume (how to parameterize)
      • Risk model: Captures this through rate functions, but, problem remains
      • others
section 9
Section 9
  • Discuss model and results
  • Highlight
    • Missing rail rates on PNW
    • Interpret
model specification overview
Model Specification: Overview
  • Model is nonlinear (due to delay costs) where
  • Objective
    • Minimize costs
      • Costs include: production, interior shipping, handling, ocean shipping costs adjusted for production and export subsidies, and import tariffs
    • Subject to
      • Meeting demands
      • Area planted restrictions in each region (total arable land is restricted)
      • Rail, barge transfer
      • Barge capacity (as delay functions)
  • Selected other restrictions (see Table 10.1 p. 104)
    • Wheat
results
Results
  • Base Case, calibration and back casting
  • Projections
  • Sensitivities
  • All should be viewed as Preliminary and for Illustration of the MOdel
base case calibration and back casting
Base Case, calibration and back casting
  • See attached
  • Backcasting:
    • Short-run observations vs. longer term adjustments!
    • Calibrate for particular year, then impose on other years precludes capturing peculiarities of individual years
  • Results
    • See attached
    • Generally respectable of general trends
slide84

Reach Shipments: Corn

Preliminary and for Illustration of the MOdel

slide85

Reach Shipments: Soybeans

Preliminary and for Illustration of the MOdel

slide86

Reach Shipments: Wheat

Preliminary and for Illustration of the MOdel

slide87

Reach Shipments: Corn, Soybeans and Wheat

Preliminary and for Illustration of the MOdel

projections existing capacity
Projections: Existing Capacity
  • Assumptions
    • WEFA growth in income and popn.
    • No subsidies beginning in 2010
  • With/without expansion in barge capacity
slide89

Reach Shipments: Forecast

Preliminary and for Illustration of the MOdel

slide90

Forecast Export Volume by Port

Preliminary and for Illustration of the MOdel

reasons
Reasons
  • US land area
    • limited…
    • in many cases decreasing
  • Increased domestic consumption ..reduces exportable supplies
  • Competing countries land area
    • expanding
  • Trending yields have differential impacts on prod costs
    • US losing advantage in wheat costs
sensitivities
Sensitivities
  • Assumptions
    • 2002 model
  • Barge and Logistical Restrictions
    • Barge demand analysis (long-run)
    • New Orleans
    • Reach 1
    • Expanded system
  • PNW Spreads
  • Panama—decrease shipping costs by $2/mt
  • Free Trade
    • No subsidies (prod or export) in 2010
  • Other macro trade
    • Brazil
    • China demand
slide93

Sensitivities Barge Rates: Long-run Demand Curve

Preliminary and for Illustration of the MOdel

slide94

Sensitivities: Reach 1 Capacity

Preliminary and for Illustration of the MOdel

slide95

Sensitivities: New Orleans Rail Capacity

Preliminary and for Illustration of the MOdel

slide96

Sensitivities: Expanded Lock Capacity

Preliminary and for Illustration of the MOdel

slide97

Expanded Lock Capacity: US Export Volume by Port

Preliminary and for Illustration of the MOdel

slide98

Forecast: No subsidies in 2009 Forward

Preliminary and for Illustration of the Model

slide99

Forecast Export Volume by Port

Preliminary and for Illustration of the Model

slide100

Sensitivities: China Soybean Demand

Preliminary and for Illustration of the Model

slide101

Sensitivities: Ethanol Demand

Preliminary and for Illustration of the Model

next steps
Next steps
  • Resolve modeling issues above
  • Planned Sensitivities
    • Barge and Logistical Restrictions
      • Barge demand analysis (long-run)
      • New Orleans
      • Reach 1
      • Expanded system
    • PNW Spreads
    • Panama—decrease shipping costs by $2/mt
    • Free Trade
      • No subsidies (prod or export) in 2010
    • Other macro trade
      • Brazil
      • China demand
summary of results
Summary of Results
  • Major changes impacting barge flows
    • Increased rail competitiveness for selected shipments to:
      • Reach 1 and direct to US Gulf
    • Expansion of domestic use of some grains in selected regions:
      • reducing export demand
    • Higher cost of production in selected crops/regions
      • Brazil N is not low cost vs. US soybean regions
      • Peculiar quality requirements in wheat provide an advantage, despite they are not lowest cost
    • Delay functions become important at Reach 1
    • Farm/trade policies
    • Fastest growth markets for US grains/Oilseeds
      • SE Asia; China (Soybeans); N. Africa……
risk model
Risk Model
  • Model Overview
    • Minimize costs
    • Subject to
      • Normal constraints
      • Chance Constraints
    • Costs inclusive of all above
  • Purpose:
    • Quantify risks
    • Determine how far forward in future it is relevant to project
sources of risk
Sources of Risk
  • Lock capacity
  • Supply risk—yield variability
  • Demand risk
  • Modal Rate Risk and Interrelationships (though these are in the objective function)
lock capacity
Lock capacity
  • Due to supply and demand risks
    • the quantity arriving at each lock is random
    • Can total volume pass through a given lock?
  • Objective function addresses by
    • rate functions increase with volume;
    • cost of delay increases with volume.
  • Model rations lock capacity
    • Model evaluated with and without planned expansions.
supply and demand uncertainty
Supply and Demand Uncertainty
  • These sources of risk are called “right-hand-side” uncertainty.
  • Consider an supply constraint for region i and commodity j:

Note yield yij is a random variable.

chance constraints
Chance Constraints
  • Model right-hand-side uncertainty with chance constraints (Charnes and Cooper 19XX)
  • With chance constraints, model will satisfy constraint with probability 
  • Prob( ) ij

= Prob( ) ij

orProb( )  1 - ij

chance constraints con t
Chance Constraints con’t
  • Typically choose =0.99, 0.975, 0.95, 0.9, etc.
  • Note, the chance constraint is the cdf of yijevaluated at Sij/aij
  • Need to be able to evaluate the cdf of the random variables,
    • i.e., supply and demand
chance constraints con t1
Chance Constraints con’t
  • Source of randomness = error terms from econometric estimation of supply and demand equations
  • Error terms are distributed as normal with mean zero
  • No closed form solution to evaluate cdf of the normal distribution
chance constraints con t2
Chance Constraints con’t
  • Approximating distribution
    • Triangular distribution is often used to approximate many other distributions including the normal
    • Has closed form cdf, finite tails, can be symmetric about mean
triangular pdf s con t
Triangular pdf’s con’t
  • A triangular distribution with =0 and 2=1 has
    • endpoints of
    • 95% confidence interval of (-1.90,1.90)
      • For comparison, normal dist. (-1.96,1.96)
chance constraints cont
Chance Constraints (cont.)
  • Chance constraint
    • For each producing regioncommodity
    • For each consuming region commodity
  • Need to assure that
    • the joint probability of satisfying all constraints simultaneous is  some specified level, e.g., 0.99, 0.975, 0.95…
grand unifying chance constraint
“Grand Unifying” Chance Constraint
  • We specify one chance constraint that guarantees that all supply and demand constraints are satisfied with some specified probability
  • Need to evaluate the joint cdf of all constraints
  • Joint cdf of multivariate triangular?
evaluating joint triangular cdf
Evaluating Joint Triangular cdf
  • Error terms from regression models are the sources of randomness
    • Regression models correct for correlated error terms, so final error terms are uncorrelated (read: independently distributed)
  • Can evaluate the probability of satisfying each supply and demand constraint independently
  • Multiply to get joint probability of satisfying all constraints simultaneously
joint cdf con t
Joint cdf con’t
  • Note each constraint must be satisfied to a very high level of probability
  • Example
    • consider 4 regions and 4 commodities = 16 constraints
    • If each constraint is satisfied with =0.95, joint probability = 0.9516 = 0.44
    • If each constraint is satisfied with =0.997, joint probability = 0.99716 = 0.95
  • Prob used to derive distributions for Reach shipments
modal rates
Modal Rates
  • Experimentation
    • Supply/demand by mode (structural equations) and reduced form models
      • Supply functions for rail do not exist
        • Oligopoly results in supply function not defined
        • Reduced form is what is needed: R=f(exog variables)
    • Barge:
      • Barge supply and level of exports are highly correlated
      • Use export levels as that is tied to optimization model
  • Resolve
    • Modal pricing equations reflective of reduced form specifications
  • Alternative:
    • Some type of “supply relation”, but, unclear how this would be specified
modal rates model logic suggestions welcome
Modal Rates: Model logic (suggestions welcome)
  • Ocean shipping costs:
    • O=f(distance, dummies by port, fuel, trend)
    • Used to determine rates levels and spreads
  • Barge rates (pooled)
    • B=f(exports, dummy by reach origin, dummy by exports, spread)
      • Trend not significant
    • Used to estimate barge rates for each region
  • Rail: Export (pooled)
    • R=f(distance, distance to barge, Reach origin, barge rate at each origin (1,4) trend)
  • Rail domestic:
    • R=f(distance, distance to barge, spread, barge. selectively)
  • Summary:
    • Oil impacts ocean and spreads;
    • Barge impacted by exports and spread
    • Rail export: impacted by barge rates, trend
    • Rail domestic: somewhat independent..
modal rates estimation details
Modal Rates: Estimation details
  • Ocean shipping costs:
    • O=f(distance, dummies by port, fuel, trend)
    • China ore or trend;
    • R2=.42
  • Barge rates (pooled)
    • B=f(exports, dummy by reach origin, dummy by exports, spread)
      • Trend not significant; exports, ocean spread sign
      • Differential interaction between R2, R3, R4 and export level
    • R2=.95
  • Rail: Export (pooled)
    • R=f(distance, distance to barge, Reach origin, barge rate at each origin (1,4) trend)
    • Corn good R2=.77; Sbeans .65, OK Wheat .68
    • Corn and wheat have more complicated interactions between barge rates at the reach level
  • Rail domestic:
    • R=f(distance, distance to barge, spread, barge. selectively)
  • Rail export: impacted by barge rates, trend
    • Rail domestic: somewhat independent..
modal rate functions concerns
Modal rate functions: Concerns
  • Technology change
    • Significant in rail corn,…
    • Not significant in barges
    • Over time: Rail rates decline at log(t)
  • Fuel not significant in rail or barge
    • Estimated prior to 2004 when fuel surcharges began\
    • Oil cost will not naturally/directly impact rates in simulations
  • Relationships loosely tied to ocean spreads
  • Relationships somewhat inconsistent (in significance) across grains
  • System:
    • Pooled: In each case, but, in all cases “unbalanced”
    • Estimated as non-system due in part to
      • Non-compatible time periods, geographic scope etc
    • Normally: estimate as system, but, requires compatible time periods, cross-sectional observations etc.
outstanding issues
Outstanding Issues
  • WEFA Projections of Macro ($10K) variables
  • Forecasting error increasing in time.
    • Variance of error terms increase over time.
    • At some point
      • forecasting error will make it impossible to satisfy chance constraint with any reasonable degree of confidence!
      • We will measure this
  • Communication of results: how to present results in meaningful (to USACE) way

Graph cost vs. alpha?

expected timeline
Expected Timeline
  • Incorporating rate functions
    • In progress
    • Completed by end of July
  • Programming/testing of chance constraints
    • In progress
    • Completed by August
  • Evaluation of scenarios
    • Completion fall of 2005
outlook to complete
Outlook to Complete
  • Deterministic resolution and report completion: 2 weeks
  • Risk model: 1 month
notes
Notes
  • Trend yields vs. log trend
  • Check projections…w/wo can restriction..etc
  • Run with vc=0
  • Pnw spreads.
  • Sign of trend in rail vs. barge…
  • Is base about 50 mmt or 60 mmt…
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