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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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Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

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 Mississippi River:

  • 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 Mississippi River:

  • 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!]


Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332
Goal Mississippi River:

  • 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: Mississippi River:

  • 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


Consumption
Consumption Mississippi River:


World wheat consumption
World Wheat Consumption Mississippi River:


World corn consumption
World Corn Consumption Mississippi River:


World soybean consumption
World Soybean Consumption Mississippi River:








Approach to consumption
Approach to consumption Mississippi River:

  • 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




Income elasticity for wheat
Income Elasticity for Wheat Mississippi River:


Income elasticity for corn
Income Elasticity for Corn Mississippi River:


Income elasticity for soybeans
Income Elasticity for Soybeans Mississippi River:







Production costs
Production costs Mississippi River:

  • 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









Production costs1
Production Costs Countries/Regions








Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

Soybean Cost of Production Countries/Regions


Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

Corn Cost of Production Countries/Regions


Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

Wheat Cost of Production Countries/Regions



Us consumption regions
US Consumption Regions Countries/Regions


Us production regions
US Production Regions Countries/Regions


Estimates of consumption by region
Estimates of consumption by region Countries/Regions

  • 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 Countries/Regions

  • 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 Region to 2010

  • 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)



Import tariffs
Import Tariffs Region to 2010


Modal rates rail
Modal rates: Rail Region to 2010

  • 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 Region to 2010

    • 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 Region to 2010

    • 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 Loading Regions, 2002

    • 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 and Cost/mt

    • Data source

      • USDA AMS

      • For each reach

    • Adjustments

      • Draft adjustments for above/below St. Louis (see p. 54)



    Handling fees
    Handling Fees and Cost/mt

    • 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: and Cost/mtRail/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 and Cost/mt

    • 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 loadings reach 1 6 by crop 1995 2003
    Barge Loadings Reach 1-6 by Crop, 1995-2003 Reach and Existing vs. Expanded Capacity


    Barge loadings by reach corn wheat and soybeans 1995 2003
    Barge Loadings by Reach, Corn, Wheat and Soybeans, 1995-2003 Reach and Existing vs. Expanded Capacity


    Barge restrictions
    Barge Restrictions Reach and Existing vs. Expanded Capacity

    • 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 1b)

    • 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 1b)

    • Discuss model and results

    • Highlight

      • Missing rail rates on PNW

      • Interpret


    Model specification overview
    Model Specification: Overview 1b)

    • 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 1b)

    • 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 1b)

    • 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


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Reach Shipments: Corn 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Reach Shipments: Soybeans 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Reach Shipments: Wheat 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Reach Shipments: Corn, Soybeans and Wheat 1b)

    Preliminary and for Illustration of the MOdel


    Projections existing capacity
    Projections: Existing Capacity 1b)

    • Assumptions

      • WEFA growth in income and popn.

      • No subsidies beginning in 2010

    • With/without expansion in barge capacity


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Reach Shipments: Forecast 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Forecast Export Volume by Port 1b)

    Preliminary and for Illustration of the MOdel


    Reasons
    Reasons 1b)

    • 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 1b)

    • 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


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Sensitivities Barge Rates: Long-run Demand Curve 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Sensitivities: Reach 1 Capacity 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Sensitivities: New Orleans Rail Capacity 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Sensitivities: Expanded Lock Capacity 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Expanded Lock Capacity: US Export Volume by Port 1b)

    Preliminary and for Illustration of the MOdel


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Forecast: No subsidies in 2009 Forward 1b)

    Preliminary and for Illustration of the Model


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Forecast Export Volume by Port 1b)

    Preliminary and for Illustration of the Model


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Sensitivities: China Soybean Demand 1b)

    Preliminary and for Illustration of the Model


    Longer term forecasting of commodity flows on the mississippi river application to grains and world trade 1341332

    Sensitivities: Ethanol Demand 1b)

    Preliminary and for Illustration of the Model


    Next steps
    Next steps 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • Lock capacity

    • Supply risk—yield variability

    • Demand risk

    • Modal Rate Risk and Interrelationships (though these are in the objective function)


    Lock capacity
    Lock capacity 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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 ( 1b)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 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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) 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • 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 1b)

    • Deterministic resolution and report completion: 2 weeks

    • Risk model: 1 month


    Notes
    Notes 1b)

    • 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…