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 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 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: Cant be completed till –final deterministic specification is concurred –Specification/format of conditional expectations on modal rate distributions [Personnelbroken back and bull stampede!]

Goal Review overall approach –Report distributed in two versions Appendix (details on all aspects of data/model) Report (summary of methods and results) pages Present current results Concur/Resolve outstanding issues on –Deterministic model –Risk questions

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

Consumption

World Wheat Consumption

World Corn Consumption

World Soybean Consumption

Change in World Wheat Consumption,

Change in World Corn Consumption,

Change in World Soybean Consumption,

Wheat: Consumption by Selected Importers

Corn: Consumption by Selected Importers

Soybean: Consumption by Selected Importers

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

Income Elasticities for Exporting and Importing Regions

Regression Results for the Income Elasticity Equations

Income Elasticity for Wheat

Income Elasticity for Corn

Income Elasticity for Soybeans

Estimated Income Elasticities for Selected Countries/Regions

Estimated Percent Change in World Consumption,

Forecast Consumption, Selected Countries/Regions,

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

Estimated Wheat Yields for Major Exporting Countries/Regions

Estimated Corn Yields for Major Exporting Countries/Regions

Estimated Soybean Yields for Major Exporting Countries/Regions

Estimated Percent Change in World Production,

Forecast Production, Selected Countries/Regions,

Production Costs

Wheat Costs of Production, , $/mt

Corn Costs of Production, , $/mt

Soybean Costs of Production, , $/mt

Wheat Costs of Production, , $/mt

Corn Costs of Production, , $/mt

Soybean Costs of Production, , $/mt

Soybean Cost of Production

Corn Cost of Production

Wheat Cost of Production

US Consumption and Production

US Consumption Regions

US Production Regions

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

Percent of U.S. Consumption by Crop and Region, 2002

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) Resultsee 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

Calculation of Increased Corn Consumption for Ethanol by Region to 2010

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 (

Domestic and Export Subsidies

Import Tariffs

Modal rates: Rail –Barge –Truck –Ocean –Changes in modal rate competitiveness Barge delay functions and restrictions Competitive routes and arbitrage

Modal Rates: Ocean Rates Data –Maritime Research Inc – –Distances derived for each route –Pooled observations Rates used –Generated from regression –R=f(Size, Miles, Oil, Dummies, trend) –See p. 68 –See projections as well

Rail rates Confidential waybill – –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)

U.S. Corn Rail Rates From Production to Export/Barge Loading Regions, 2002

U.S. Wheat Rail Rates From Production to Export/Barge Loading Regions, 2002

U.S. Soybean Rail Rates From Production to Export/Barge Loading Regions, 2002

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 –4 th Qtr 2003 to 3 rd qtr 2004.

Estimated Relationship Between Distance, Rate/Loaded Mile and Cost/mt

Barge Rates Data source –USDA AMS –For each reach Adjustments –Draft adjustments for above/below St. Louis (see p. 54)

Draft Adjusted Average Barge Rates for Six Reaches ($/mt)

Handling Fees Separate handling fees imposed for additional costs of selected movements –Barges –Great Lakes

Barge Transfer Costs

Handling Fees on the Great Lakes

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 /mt Reach Reach Reach Selected comparisons –See Table 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 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

Barge Loadings Reach 1-6 by Crop,

Barge Loadings by Reach, Corn, Wheat and Soybeans,

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

Barge Loadings for Below L&D27 (Reach 1a) and above (Reach 1b)

Rail Unloads at River Gulf

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 Discuss model and results Highlight –Missing rail rates on PNW –Interpret

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

Objective Function

Restrictions

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 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

Reach Shipments: Corn Preliminary and for Illustration of the MOdel

Reach Shipments: Soybeans Preliminary and for Illustration of the MOdel

Reach Shipments: Wheat Preliminary and for Illustration of the MOdel

Reach Shipments: Corn, Soybeans and Wheat Preliminary and for Illustration of the MOdel

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

Reach Shipments: Forecast Preliminary and for Illustration of the MOdel

Forecast Export Volume by Port Preliminary and for Illustration of the MOdel

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 Assumptions –2002 model Barge and Logistical Restrictions –Barge demand analysis (long-run) –New Orleans –Reach 1 –Expanded system PNW Spreads Panamadecrease shipping costs by $2/mt Free Trade –No subsidies (prod or export) in 2010 Other macro trade –Brazil –China demand

Sensitivities Barge Rates: Long-run Demand Curve Preliminary and for Illustration of the MOdel

Sensitivities: Reach 1 Capacity Preliminary and for Illustration of the MOdel

Sensitivities: New Orleans Rail Capacity Preliminary and for Illustration of the MOdel

Sensitivities: Expanded Lock Capacity Preliminary and for Illustration of the MOdel

Expanded Lock Capacity: US Export Volume by Port Preliminary and for Illustration of the MOdel

Forecast: No subsidies in 2009 Forward Preliminary and for Illustration of the Model

Forecast Export Volume by Port Preliminary and for Illustration of the Model

Sensitivities: China Soybean Demand Preliminary and for Illustration of the Model

Sensitivities: Ethanol Demand Preliminary and for Illustration of the Model

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 –Panamadecrease shipping costs by $2/mt –Free Trade No subsidies (prod or export) in 2010 –Other macro trade Brazil China demand

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 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 Lock capacity Supply riskyield variability Demand risk Modal Rate Risk and Interrelationships (though these are in the objective function)

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 These sources of risk are called right- hand-side uncertainty. Consider an supply constraint for region i and commodity j: Note yield y ij is a random variable.

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 or Prob( ) 1 - ij

Chance Constraints cont Typically choose =0.99, 0.975, 0.95, 0.9, etc. Note, the chance constraint is the cdf of y ij evaluated at S ij /a ij Need to be able to evaluate the cdf of the random variables, –i.e., supply and demand

Chance Constraints cont 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 cont 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 pdfs

Triangular pdfs cont 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 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 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 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 cont 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 = = 0.44 –If each constraint is satisfied with =0.997, joint probability = = 0.95 Prob used to derive distributions for Reach shipments

Distribution Details

Modal Rate Error

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) 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 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 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 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 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 Deterministic resolution and report completion: 2 weeks Risk model: 1 month

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…