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Description of Iowa State Stochastic Model Used in EPA Analysis

Memo to the Docket

2012 Decision in Response to Requests for a Waiver of the RFS

November 15, 2012

The model that was used to estimate the impacts of a mandate waiver solves for market clearing prices 

and quantities in the following eight markets: corn, U.S. corn ethanol, Brazilian sugarcane ethanol, 

soybeans, soybean oil, soybean meal, and U.S. biodiesel. The model is solved 500 times. The following 

variables are varied across the 500 model solutions: U.S. corn production, U.S. wholesale gasoline prices, 

U.S. soybean production, Brazilian soybean yields, Argentine soybean yields, and Brazilian ethanol 

production. Following are summary descriptions of each of these markets.

Corn

U.S. supply for the 2012/13 marketing year equals beginning stocks plus U.S. production. Production 

was treated as a random variable by fixing acres harvested at 87.7 million acres and then varying yields. 

Yields were drawn from a beta distribution with minimum and maximum values determined by the 

minimum and maximum percent errors in production projections as reported by the United States 

Department of Agriculture (USDA). The mean yield was set at USDA’s projected yield for the 2012/13

crop. All exogenously determined U.S. agricultural inputs (e.g., corn production, corn yields, beginning 

stocks) were set to the values provided in USDA’s October 2012 World Agricultural Supply and Demand 

Estimates (WASDE) report.

Linear demand curves were calibrated to WASDE projections of demand for feed, food, and exports. 

Demand elasticities at the WASDE price (mid-point projection) and quantity are -0.25, -0.096, and -0.65 

for these three markets respectively. A beta distribution was used to model stocks to account for the 

likely stock-out condition that the U.S. will likely find itself in during at the end of this marketing year. 

The four demand curves are summed to obtain the non-ethanol corn demand curve. The supply of ethanol 

is derived from the excess supply curve of corn. 

Corn Ethanol

The supply curve for corn ethanol is obtained from the excess supply curve of corn. The quantity of 

ethanol is set equal to the supply of corn multiplied by 2.75 gallons per bushel. The supply price of 

ethanol is the price of ethanol that is needed to cover all variable costs of production.

The demand for ethanol was specified by EPA as a function of the price of ethanol relative to wholesale 

gasoline prices. These specifications were determined in consultation with the U.S. Department of 

Energy based on internal analysis and information provided by the refining industry.

Brazilian Ethanol

The market for Brazilian ethanol closely follows the specification shown in the appendix of Babcock, 

Barr, and Carriquiry (2010).1 Ethanol demand is the sum of hydrous demand and anhydrous demand plus 

export demand. Hydrous demand is a function of the retail price of hydrous relative to gasoline and the 

number of flex-fuel vehicles in Brazil. Anhydrous demand is a function of hydrous demand (more 

hydrous demand means less anhydrous demand because anhydrous is used in gasoline). Supply of 

ethanol is treated as a stochastic variable. Trade with the United States is allowed. Imports flow into 

 

1

“Costs and Benefits to Taxpayers, Consumers, and Producers from U.S. Ethanol Policies.” Staff Report 10-SR 106

July 2010. Center for Agricultural and Rural Development Iowa State.
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Brazil when the domestic Brazilian price of anhydrous ethanol is greater than the U.S. domestic price plus 

transportation costs. Exports flow to the U.S. when the demand for either conventional or advanced 

biofuel pushes the U.S. price of one of these fuels above the Brazilian domestic price plus transportation 

costs. Two way trade in biofuels is allowed in the model.

Soybeans

The world soybean sector is broken down into the U.S., Brazil, Argentina, and the rest of the world. 

Demand for soybean meal and soybean oil create a demand for soybean crush in each of the three 

countries. The amount of crush determines the supply of soybean oil and soybean meal. The supply of 

soybeans equals the products of acreage and yield in the three modeled countries. Distributions of 

soybean yields in Argentina and Brazil are formed from historical de-trended yield data with a mean set 

equal to WASDE projections. WASDE acreage estimates were used. U.S. soybean yields were modeled 

identically to corn yields with harvested acreage fixed at WASDE projected levels and variability 

determined by the historical errors in WASDE projections.

World prices for soybeans, soybean oil, and soybean meal are determined endogenously in the model.

U.S. Biodiesel

The supply of biodiesel is determined by the operating margins of biodiesel plants assuming that soybean 

oil is used as a feedstock. 680 million gallons of biodiesel are produced from feedstocks other than 

soybean oil. The demand for biodiesel is perfectly elastic at a price that is discounted from diesel. The 

diesel price is determined by the stochastic gasoline price.

Model Solution

Market-clearing prices and quantities are solved for given assumptions about the level of mandates and 

for 500 draws of gasoline price, corn production, soybean production in the U.S., Brazil, and Argentina, 

and Brazilian ethanol production.

Equilibrium corn prices clear the market for corn. Ethanol supply prices allow ethanol plants to cover 

their production costs where the quantity of production is determined by the excess amount of corn that is 

available after non-ethanol corn demands are met. The RIN price for conventional biofuel covers any gap 

between the supply price that ethanol plants receive and the demand price that blenders pay. 

Similarly, equilibrium soybean prices clear the crush and export markets for each country. Soybean oil 

demand from biodiesel increases the demand for soybean oil, which leads to an increase in the price of 

soybean oil. Higher soybean oil prices increases the crush margin, which leads to an increase in the 

demand for soybeans. Higher demand for soybeans increases the price of soybeans, which increases the 

supply of soybean meal and soybean oil. Equilibrium prices that clear all three markets (soybeans, 

soybean oil, and soybean meal) are determined endogenously by the model. Any gap between the 

demand price for biodiesel and the supply price that biodiesel plants need to cover the cost of producing 

biodiesel plus their required margin is covered by the biodiesel RIN price. 

Equilibrium in Brazil’s ethanol market is determined jointly with the U.S. ethanol market accounting for 

U.S. demand for Brazilian sugarcane ethanol to meet advanced and possibly conventional mandates and 

Brazilian demand for U.S. ethanol.
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Differences between Current Model and 2008 Model

The model that was used to determine the impact of waiving the RFS mandate in 2008 differs from the 

model that is currently in use in a number of ways. The most prominent differences are as follows:

The current model treats gasoline prices as exogenous. The 2008 model endogenously solved for 

gasoline prices simultaneously with ethanol prices, using an exogenous assumption of crude oil prices 

based on futures market prices for crude oil at that time. 

The 2008 model included heterogeneous efficiency across ethanol plants. The current model 

assumes uniform efficiency.

Because the 2008 modeling exercise was carried out in the spring, there was more uncertainty 

about the level of production so both yield and harvested acreage were made stochastic with a relatively 

high variance. The current model fixes harvested acreage and uses WASDE historical error bounds to 

determine the variance of harvested yield.

The current model models the soybean sector to enable interaction between sugarcane ethanol 

and biodiesel in the advanced biofuel market. The 2008 model did not include soybeans.

The current model includes the Brazilian ethanol sector as both a supplier of sugarcane ethanol 

and as an export market for US corn ethanol.

In 2008, the capacity of the ethanol industry was not known so it was made stochastic. The 

current model does not have this stochastic component.

Corn export demand was made stochastic to capture the effects of volatile exchange rates. The current 

model has a fixed corn export demand curve.