Abstract
This paper examines the role of uncertain crude oil prices, uncertain crop yields, and competition for acreage on corn, soybean, and switchgrass prices under biofuel production mandates. We find enforcement of the cellulosic mandate is costly in that it raises equilibrium prices of all three crops through competition for acreage. However, crude oil prices largely determine industry profitability even in the face of high crop prices. Further we find that uncertainty in crude oil prices and crop yields causes higher corn, soybean, and switchgrass prices compared to a baseline with no uncertainty. (JEL Q21, Q42)
I. Introduction
Congress signed into law the Energy Independence and Security Act (EISA) in December 2007.1 The Renewable Fuel Standard, or RFS, in the EISA mandated the use of 36 billion gallons of biofuels by 2022, of which 15 billion gallons can come from corn-based ethanol and 21 billion must come from advanced biofuels—including 16 billion from cellulosic biofuels and 1 billion from biomass-based diesel. In the year 2000, cornbased ethanol production was 1.63 billion gallons, and by the end of 2009 production reached 10.6 billion gallons.2 Along with other factors such as a weak dollar and consumption growth that outpaced production growth, the increase in corn-based ethanol production contributed to record high nominal corn prices in 2008 (Abbott, Hurt, and Tyner 2008, 2009). Competition for acreage transferred the demand pressure in corn markets to other crops, putting upward pressure on these prices as well. As we move into years with binding mandates on biodiesel and cellulosic ethanol production, it seems this trend will continue. Further, since food commodity markets are linked on the supply side by competition for acreage and on the demand side by consumption substitutability, production mandates in one commodity market affect markets in the entire system. The purpose of this paper is threefold: (1) We examine the incentives required to encourage production of the EISA-mandated quantities of biofuels, (2) we quantify the impacts of the RFS on some important agricultural commodity prices, and (3) we quantify acreage allocations for these commodities as well.
Biofuel production mandates, when binding, require that more than the equilibrium quantity of biofuel must be produced, which creates a wedge between the price at which producers are willing to sell and consumers are willing to buy biofuel. To illustrate, the supply and demand for ethanol is represented in Figure 1 by S and D. Given the installed capacity that we have in place, there would be some volume of ethanol produced even if all government programs supporting the industry were eliminated. This level of production is found at point c, where supply equals demand. The free-market price and quantity of ethanol are denoted by P* and Q*.
Now consider what happens when quantity QM is mandated. Because QM exceeds Q*, ethanol producers must be paid a price that exceeds P*. This price is given by point a, where the mandated volume intersects the supply curve. To clear the market, ethanol consumers must pay a price that is less than P*. This price is given by point b, which is where the mandate intersects the demand curve. As shown, the mandate creates a gap equal to a - b between the required producer price and the required consumer price.
The mandated volumes are enforced by the U.S. Environmental Protection Agency (EPA) in two ways. Part of the price gap is made up through the Volumetric Ethanol Excise Tax Credit (VEETC).3 However, it can be that a - b is larger than the VEETC, so to ensure that the mandate is met the EPA created a compliance system whereby each gallon of biofuel produced or imported is assigned a Renewable Identification Number, or RIN. Blenders are assigned a number of RINs that they must give to the EPA each year. Because each gallon of biofuel has a RIN associated with it, producers and importers can obtain RINs by buying biofuels and keeping the RIN. Alternatively, they can enter the RIN market and buy the RIN from somebody else.
We present a model based on the assumption that one can predict the price wedge created by mandated biofuel production levels if one understands the factors influencing the decisions made by agents in the economy. Farmers make planting decisions based on expected market prices. Further, farmers recognize that land devoted to biofuel feedstock production has an opportunity cost, so they will only grow biofuel feedstock such as switchgrass for cellulosic ethanol production if it is profitable to do so. Investors who build biofuel plants do so only if they expect a risk- adjusted return on par with or superior to investments made elsewhere in the economy. Existing plants operate only if the marginal cost of production is less than the value of output. Those who blend and use biofuels do so only if the market price of ethanol is less than the prices of alternatives. When mandated biofuel production is higher than what the market would otherwise provide, a price wedge is created. Historically, the VEETC described above has made up for this price wedge.
We model the decisions of relevant agents in the economy and the market forces guiding them within a stochastic simulation model of U.S. crop and biofuel markets. With this model we can then explore the impact of different elements in the system. We explore the effect energy prices, land-intensive cellulosic feedstock requirements, and the cost of cellulosic ethanol production have on equilibrium agricultural prices, the price wedge in the biofuel market, and equilibrium acreage allocations.
Price Wedge from Mandated Quantity of Biofuel Production
II. Previous Literature
Analysis of the economics of ethanol production garnered interest in the 1970s in part because of the energy crisis at that time (Hammond 1977; Litterman, Eidman, and Jensen 1978; Meekhof, Tyner, and Holland 1980 are examples of this literature). By the mid 1980s oil prices were less of a concern, and industrial and academic interest in this field waned. Interest increased again in the mid 2000s when oil prices rose and corn-based ethanol became a major player in agricultural markets.
De Gorter and Just developed a model of the corn and fuel markets; a long-run equilibrium relationship is the tie that binds the two together in their model. This work was focused on welfare analysis of the ethanol market. They point out that when the intercept of the ethanol supply curve is above the market price of ethanol without any tax credit, much of the tax credit is redundant because a portion of the tax credit is used just to get the ethanol industry to a breakeven level. For example, suppose with a $0.25/gal tax credit the ethanol industry breaks even. Then a $0.45/gal tax credit will stimulate ethanol production only after the first $0.25/gal; the first $0.25/gal is redundant in the sense that no ethanol production resulted from the first $0.25/gal of the subsidy. The redundancy generates welfare losses much larger than standard welfare calculations would suggest (de Gorter and Just 2008, 2009). However, their model is deterministic and focuses on the corn market, which prevents them from dealing with the effects of competition for acreage on commodity prices in multiple markets and from accounting for uncertainty in these markets.
Elobeid et al. (2007) provided a model of the more recent ethanol expansion, which considered domestic and international impacts of expanded ethanol production. Later, Tokgoz et al. (2007) extended this work, strengthening some of its elements. They include equilibrium relationships for prices of biofuel coproducts, most notably distillers' grains. Both use the world agricultural model from the Food and Agricultural Policy Research Institute to determine the potential size of the corn-based ethanol sector and to describe how it affects crop and livestock markets. First, they assume biofuel investments will continue until expected profit is zero, and they calculate the break-even corn price that drives margins on new corn-based ethanol plants to zero. Second, they assume this break-even corn price clears the market, and they calculate the size of the biofuel sector required to bring about this price. Finally, once they determine the break-even corn price, they evaluate its impact on U.S. and world agriculture. They ignore biofuels from cellulose and biodiesel because their results suggest these are not economically viable. They also ignore risks associated with investments in biofuel plants.
Land use has become an important element in the discussion of biofuels and their capacity to reduce greenhouse gas emissions (Fargione et al. 2008; Melillo 2009; Searchinger et al. 2008). The EPA analyzed life cycle greenhouse gas emissions for biofuel production. The lifecycle analysis includes aggregate greenhouse gas emissions—direct and indirect—from all stages of production and distribution. The initial report concluded ethanol produced from corn starch did not meet the required 20% emission reduction threshold. However, a revised version that adjusted crop yields, distillers grains, and solubles feed efficiency concluded that ethanol produced from corn starch does in fact meet the 20% emission reduction requirement (USEPA 2009, 2010).
While our study is not aimed at quantifying greenhouse gas emissions, we assert that land use is an important part of a purely market-based study as well. Using land for the production of corn, soybeans, or anything else has an opportunity cost, and therefore modeling supply and demand for biofuels without considering crops other than corn cannot capture the intricacies of competition for acreage among commodities.
Our model also enhances previous work by incorporating awareness of risk into the decision problem of the biofuel investor. Returns to biofuel production are primarily a function of energy and feedstock prices, which are uncertain. Crude oil prices are the main determinant of the prices of transportation fuels such as gasoline, ethanol, and diesel, while crop yields affect feedstock costs through their effects on equilibrium commodity prices.
By incorporating uncertainty in crude oil prices and crop yields we can compare the risk-adjusted return in the production of each type of biofuel, determining which types are attractive to investors. Basing the investor's decision on risk-adjusted returns is more realistic than using a zero profit condition, which implies a risk-neutral investor. A stochastic model that provides probability distributions over commodity prices and returns in the biofuel industry allows us to build a model in which the investor cares not only about the mean of returns, but also about the variance.
III. The Model Economy
The agricultural economy has three goods: corn, soybeans, and switchgrass.4 Switchgrass and miscanthus are both perennial grasses that are considered by scientists as good candidates for cellulosic ethanol production. Commercial cellulosic ethanol from nonwaste feedstock is almost nonexistent, so it is still uncertain which grass will prevail as the feedstock of choice. However, for the purpose of this study we consider switchgrass since it is native to the U.S. tall-grass prairie and already represents a significant portion of the forage grown for livestock feed in the United States (Anderson et al. 1988; Schmer et al. 2008). The three agents in the model are farmers, consumers, and investors. Consumers buy agricultural commodities and use them as input in producing either food or energy. Investors can choose to build a corn ethanol plant, a biodiesel plant, or a switchgrass ethanol plant; alternatively, they can simply choose to invest in an alternative we call the market portfolio.
We introduce uncertainty through agricultural commodity yields and crude oil prices. Further, we assume the two random variables are independent with joint probability distribution f(ζ,ε) = g(ζ)h(ε), where ζ is a vector of yield realizations and ε is the realization of crude oil prices. By specifying commodity yields and crude oil prices as independent, we implicitly assume that shocks to domestic biofuel production do not influence world crude oil price shocks.
Agents form expectations about crude oil prices and future crop yields. Farmers allocate acreage among corn, soybeans, and switchgrass, and investors plan long-run capacity in the biofuel sectors. Acreage allocation is carried out implicitly through time, and we assume that farmers choose the proportion of land in annual crops (an equilibrium corn-soybean rotation) and land in the perennial, switchgrass. With this we avoid dealing with the difference in the timing of cost and payoff between the annual and perennial crops; what we lose in specificity in the farmer's yearly decision is not pertinent to the results and permits us to work with a more specific model in which we can focus on the long-run results.
Crop supply is determined by acreage allocations and by crop yield realizations. Demand for the commodities comes from the livestock feed, human food, and export sectors but is represented in the model by an aggregate demand function. Demand from the biofuel sectors is determined by production capacity, which is determined by a long-run equilibrium condition. We describe these components of the model in more detail below.
Commodity Supply
We use an aggregate supply function for each crop, with the price of all three crops in the model appearing in each equation. In this way we allow the model to capture aggregate market signals that determine shifts in the planting behavior of farmers. High prices of corn relative to soybeans and switchgrass, for example, will encourage acres to shift from these crops to corn acres; similarly, high prices across all three commodities will encourage more acres to be brought into production that previously had other uses.
We assume crop yields follow a linear trend. We estimate the trend for corn, soybeans, and switchgrass with yield data (per harvested acre) from the National Agricultural Statistics Service (NASS) of the U.S. Department of Agriculture for the years 198O-20O6.5 There are no national yield statistics for switchgrass available; instead we use alfalfa yields as a proxy. The alfalfa production system is similar to that of switchgrass, its mean yield is similar to the academic studies available for switchgrass, and its yield is likely to covary with corn and soybeans in a similar way as switchgrass would. The trend equations used are
Note that t here is the actual crop year. To scale the yields to 2012 levels we used the equation yieldupscaled = yieldactual year t * yieldtrend year 2012/yieldtrend year t.
The random yield realizations, denoted by ζ, introduce uncertainty into the model and are drawn using the smoothed bootstrap method. That is, yield realizations from 19802006 are scaled up to 2012 trend yield levels, then yields are resampled with replacement and perturbed by a random variable with mean zero to smooth the discrete sample (Efron 1979). Resampling with replacement ensures that the simulated yield draws have exactly the covariance structure of the actual yield realizations over the last 20 years. The yield draws are then perturbed by a normal random variable with mean zero and standard deviation equal to half the sample standard deviation. While there is a substantial body of literature regarding choice of smoothing parameter in the context of nonparametric regression, there is not much guidance in the context of simulation modeling. We choose half a standard deviation as the smoothing parameter because it is large enough that it results in a realistic distribution (i.e., not multimodal) of crop yields without causing the variance of the distribution to be artificially high:
[1]Here yj is a 3 × 1 vector containing the scaled up yield from a random year in the sample, 
are standard normal random variables, and 
are the sample standard deviations of each crop. Figure 2 displays the simulated yield distributions.
Bootstrapped Crop Yield Distributions
Before yield is realized, farmers make planting decisions. These decisions combined with random yield realizations form commodity supply. We model the functional form of harvested acres for each crop as
[2]We estimate the parameters of the HA function from NASS data on harvested acres and prices from the previous year for crop years 1991-2009. The parameters used in the simulation model are found in Table 1.
The harvested acres taken with the random yield realizations form the commodity supply function of each crop, 
(p ; yi ,ζi), which depends on the prices of each commodity, the γi vector of supply function parameters, and the random yield realization, ζi:
[3]Parameters Used in Monte Carlo Simulation
Commodity Demand
Demand for commodity i is denoted by 
. The demands are a function of commodity prices, p = [p 1 p2 p3] ', and ni is the amount of biofuel of type i produced. The set of parameters defining the demand function is denoted by Ωi.
In equation [4] we specify a constant elasticity, reduced-form demand function for each crop and use the intermediate-term own and cross-price demand elasticities for beef from the ERS/% trade model6 as our estimates:
The variable ni is the amount of biofuel of type i produced, and δi converts the amount of biofuel produced into the amount of feedstock required to meet that production level. For example, the size of the corn-based ethanol industry in billion gallons per year is n1. Therefore, δj transforms the amount of ethanol produced into the amount of corn required. In reality, biofuel production is expanded in discrete increments, one production plant at a time. A limitation of this model is the treatment of ni as a continuous variable. Doing so cannot properly account for sunk investment in a particular plant, but treating ni as a continuous variable ensures the existence of a long-run equilibrium (conditions for the long-run equilibrium are defined in Section III). In Section IV we explain our assumptions about the δi parameters in more detail.
[4]The Investors
In each period, investors can choose among four different options: a corn-based ethanol plant, a biodiesel plant, a switchgrass ethanol plant, or an alternative investment we call the market portfolio—as in the capital asset pricing model (CAPM) of Sharpe (1964). The market portfolio functions as an option if at the margin, the returns none of the biofuel investments are attractive.
We assume investors seek the largest risk-adjusted return on investment possible, and we assume that there exists a riskless asset in the economy returning the risk-free rate, RFR. Investors use the CAPM to evaluate investment alternatives; they calculate the security market line to measure the required rate of return for an asset, a:
[5]where is the expected return of the market portfolio, M, and βa is defined by
[6]where the variance of returns on the market portfolio is 
and Ra is the return of asset a. The investors calculate the difference in the expected return and required return of asset a as calculated with the CAPM. The investors choose the project with the highest excess returns over the required return. However, if the difference is negative for each of the biofuel plants, an investor will choose to invest in the market portfolio. As long as the biofuel industry earns excess returns over the required return, it will continue to attract investment and, thus, continue to expand.
Returns to Biofuel Production
Input costs in each sector are determined by feedstock, production, and other capital costs. Nonfeedstock production costs and capital costs are exogenous in the model. It is important, however, that we account for technological advancement of cellulosic ethanol production. This is extremely difficult to predict, especially since we have not observed cellulosic ethanol production on a commercial scale to date. This will greatly affect predictions of the model, so later when we present results we include three different technological scenarios. The first assumes a 50% reduction in the cost of cellulosic ethanol production from today's levels (more on the details of this in Section IV), the second assumes a 25% reduction, and the third assumes no reduction in the cost.
As important as process costs are, it is feedstock costs that are the most important input cost to biofuel production, and these are determined by market equilibrium. The annualized per gallon rate of return to producing biofuel of type a is
The per gallon cost of producing biofuel of type a is 
and is composed of per gallon feedstock and nonfeedstock costs as indicated in equation [7]:
[7]where the per gallon feedstock cost is denoted by 
. That is, in the case of corn-based ethanol production, p1pergal is the equilibrium price of corn transformed into a cost per gallon of ethanol; in the case of biodiesel production, ppergal2 is the equilibrium price of soybeans transformed into a cost per gallon of biodiesel; and in the case of cellulosic ethanol, p3pergal is the equilibrium price of switchgrass transformed into a per cost per gallon of ethanol. The nonfeedstock cost of producing biofuel of type a is NFcosta; this includes capital cost, which is expressed per gallon and on an annual basis.
The term qa(ε) is defined by equation [8]:
[8]The market price of biofuel, pa(ε), is a function of the crude oil price realization, ε . In our simulation, crude oil prices are lognormal and calibrated to match current conditions in the futures market. The function of the term wedgea will be more intuitive after defining the long-run equilibrium in the next section, but one can think of it as the shortfall in the price of ethanol that prevents biofuel of type a from being commercially viable.
This relationship essentially measures the annual return on capital invested over input costs of the plant. Notice that the production costs depend on equilibrium commodity prices, which result from uncertain yield realizations and depends on the realization of the commodity prices. For example, in a year when crop yields are relatively poor, biofuel production costs will be higher than expected due to high equilibrium commodity (feedstock) prices. Likewise, high energy prices imply high returns in the biofuel sectors because the output price of biofuel will be high.
This annual framework allows us to proceed with a long-run analysis even though timing of decisions of agents in the model is mismatched. Farmers make annual acreage decisions and earn profits from that decision in the same year. Investors, on the other hand, make a large initial investment in hope of a stream of annual returns for many years into the future.
We implicitly assume that investors form a long-run expectation about the price of crude oil, and then we exploit the stationarity of the crude oil price and crop yield distributions by basing their investment decisions upon the expected return on their investment in a typical year.
Long-Run Competitive Equilibrium
In our agricultural economy, a long-run competitive equilibrium is defined by
pricing functions pi (ζ, ε, n, Ω, θ) for i = 1, 2, 3,
crop demand functions
(p;ni, Ω) for i = 1, 2, 3,
crop supply functions
investment functions ni (p, ε) for i = 1, 2, 3.
Commodity markets clear given the pricing functions, biofuel plants in operation, and realizations of crop yields and crude oil prices. That is,
[9]In addition to the market clearing condition we impose a long-run equilibrium condition that requires, at the margin, the returns of each project equal the required risk-adjusted returns as determined by the CAPM:
where RR is the required return to biofuel production as determined by the CAPM.
The zero excess return conditions ensure we have investment in each sector until the prices of feedstock (corn, soybeans, and switchgrass) are bid up to the point at which an investor is indifferent between any of the biofuel plants and the market portfolio. If the return to biofuel production is less than the required return for all industry sizes, then investment equals zero in this biofuel sector. Or this equilibrium condition allows us to calculate the price wedge generated by the mandated levels of biofuel production.
IV. Implementing The Model
Our question is empirical in nature. The incentives present for the biofuel industry to expand or contract depend on many factors, some of which are the price of crude oil, demand for corn and soybeans for food uses, and weather variability. Exploring more than the most basic results of this model requires us to specify functional forms and evaluate the results numerically via the Monte Carlo method.7 We calibrated the model to the average springtime market conditions from 2005 to 2009, and then ran our scenarios based on 2012 trend yields.
Algorithm for Simulating the Model
Our strategy for simulating the economy is to specify functional forms for both crop supply and crop demand and to calibrate the distribution of crude oil prices and crop yields. A draw from these distributions implies an equilibrium price for corn, soybeans, and switchgrass and thus implies return levels in each biofuel industry. The simulation algorithm is as follows:
Form crop yield and crude oil price distributions and make random draws. Calculate biofuel prices from the crude oil price draws.
Solve for the equilibrium crop prices for each draw using the market clearing conditions on crop supply and demand for a given level of biofuel capacity.
Calculate the implied distribution of returns to biofuel production using the biofuel prices from (1) and equilibrium crop (feedstock) prices from (2).
Use the long run (zero excess return condition) to determine the price wedge on each biofuel type.
For example, setting the levels of biofuel production high (as in the EISA RFS) causes crop prices to increase due to the increase in demand for these commodities. This causes returns to biofuel production to shrink and ordinarily would cause the industry to contract. If this is the case, we calculate the price wedge between the price biofuel producers are willing to accept and biofuel consumers are willing to pay. The following subsections describe the details of implementing this algorithm further.
Accounting for Cellulosic Ethanol from Corn Stover and Wood Chips
Biomass sources that do not compete directly for acres with high-value crops, such as corn and soybeans, do not have large implicit land costs. Since corn stover and woody biomass do not compete for crop acreage, it seems reasonable to assume the RFS for cellulosic ethanol of 16 billion gallons per year will be met only with a contribution of feedstock from these sources, because if more land-intensive biomass like switchgrass is profitable, stover and woody biomass will be profitable also. Because this production occurs outside the framework of our model, we need to make assumptions about how much ethanol will be produced from these sources. We assume ethanol from both corn stover and woody biomass is produced when the economy produces a nonzero amount of switchgrass ethanol. It remains unclear exactly how much cellulosic ethanol will come from the sources not competing for land with traditional crops, so we present several scenarios varying the amount of cellulosic ethanol that must come from switchgrass to meet the mandate.
Calculating Returns to Biofuel Production
Returns to biofuel production are affected most by feedstock costs and governmental policy, with feedstock costs determined endogenously in the model. Ethanol and cellulosic ethanol plants use corn and switchgrass as feedstock, but biodiesel uses soy oil (not soybeans directly) as feedstock. Our model produces equilibrium soybean prices but not soy oil prices. We estimate a simple linear relationship between the price of soybeans and the price of soy oil using recent data:8
Each biofuel production process generates a coproduct, which creates value and offsets some feedstock cost. Corn ethanol produces dried distillers grains, dried distillers grains with solubles (DDGS), or wet distillers grains, which are used in beef, pork, and poultry rations. Distillers' grains have approximately the same digestible energy content as corn, so we give credit to corn ethanol plants for DDGS consistent with its ability to substitute for corn (Shurson et al. 2003). We assume ethanol has a yield of 2.8 gal/bu of corn, and that 17 lbs of distillers grains are produced for every bushel (56 lbs) of corn processed into ethanol. Therefore δ1 = [1 - (17/56)]/2.8 is the amount of corn (net of distiller's grains) required to produce n1 billion gallons of ethanol (Shapouri and Gallagher 2005).
There is not currently a government or industry group publishing annual cost indexes for biofuel production processes. For biofuel production cost estimates we rely on varied sources from the academic literature. Some of these references are becoming dated, however. So in order to impose more realistic production costs, all of the costs mentioned in the paragraphs below are brought forward to December 2009 levels using the Producer Price Index for general chemical manufacturing maintained by the Bureau of Labor Statistics.
The biodiesel production process yields glycerin, fatty acids, and filter cakes. We credit 80/gal to the biodiesel producer, based on recent market value for these coproducts (Paulson and Ginder 2007). In equation [4] the size of the biodiesel industry in billion gallons per year is n2, and δ2 is the conversion factor that calculates the bushels of soybeans needed to produce enough soybean oil to produce n2 gallons of biodiesel. Thus δ2n2 is the amount of soybean oil required to meet the biodiesel production level. Soybean oil weighs 7.3 lbs/gal, and 1 lbs of soybean oil can produce 0.973 lbs of biodiesel, so 7.5 lbs of soybean oil is required to produce 1 gal of biodiesel (Altin, (Cetinkaya, and Yücesu 2001). Assuming soybean oil yield is 11 lbs/ bu, we have δ2 = 7.5/11.
Production of ethanol from switchgrass produces lignin, which is combustible. We assume that this will be used to generate electricity within the facility, or sold back to the electrical grid (Aden et al. 2002). We credit switchgrass ethanol with 100/gal, as suggested by Aden et al. (2002). The per gallon nonfeedstock costs of producing corn-based ethanol and cellulosic ethanol are 760/gal and 970/gal, respectively, while the nonfeedstock cost of producing biodiesel is 550/gal (Paulson and Ginder 2007; Tokgoz et al. 2007). We assume a cellulosic ethanol yield of 70 gal per ton of feedstock. Therefore, in the context of equation [4], δ3 = 1/70.
A biofuel plant's revenue relates directly to crude oil prices through the relationship between crude oil, ethanol, and diesel. We estimate the price of ethanol and diesel as deterministic linear functions of the price of crude oil, using monthly spot prices from January 1994 through August 2007 of the Cushing Oklahoma crude oil, New York Harbor conventional gasoline, and U.S. No. 2 whole- sale/resale markets:9
While other components of the model are calibrated to annual data, here we use monthly data in order to observe more variation in these price relationships, hopefully leading to better estimates. E10 (10% ethanol, 90% gasoline) is used for its ability to oxygenate gasoline, which enhances combustion and reduces emissions (NSTC 1997). Tokgoz et al. (2007) assume that when annual production is greater than 15 billion gallons per year, the E10 market becomes saturated, causing ethanol to be priced at the margin according to its energy value (about two-thirds) compared to gasoline (Shapouri, Duffield, and Graboski 1995). When production is below this threshold, they assume ethanol is priced at a premium to gasoline and valued for its properties as an additive (see also Hurt, Tyner, and Doering 2006). Since the scenarios we consider are all at 15 billion gallons of ethanol production per year, we assume ethanol is priced by
We recognize there has been limited research on the relationship between the wholesale price of ethanol and the price of gasoline. Until further research gives more direction on this, we proceed with this pricing rule.
V. Results
We impose biofuel production at levels set in the RFS of the EISA of 2007 and consider the model's equilibrium outcomes for three different crude oil price scenarios. We set the mean of the crude oil price distribution to $50, $100, and $150 per barrel.10 We also consider the effect of the need to use land-intensive crops to meet the cellulosic mandate by presenting four scenarios. The scenarios vary the amount of land-intensive cellulosic ethanol needed to meet the mandate from zero to 3 billion gallons. Additionally, we present three different cellulosic production cost scenarios: the current level, 25% reduction, and 50% reduction. After imposing mandated biofuel production levels, our model allows us to solve for the price wedge generated by the mandate, which must be met in order to maintain the zero-excess-return condition, in addition to delivering equilibrium crop price distributions and acreage allocations.
The Effect of Energy Prices on the Price Wedge and Land-Intensive Cellulosic Feedstock
Table 2 contains results from the first set of scenarios we consider. The columns correspond to increasing levels of switchgrass ethanol production as indicated in the first row. Numbers in parentheses are volatilities for prices and standard deviations for other stochastic variables. The table also contains price wedge results for the three different crude oil price scenarios. In the zero switchgrass ethanol scenario no switchgrass is used for cellulosic ethanol production, but the model still yields over 65 million acres and 223 million tons of switchgrass production. All of the switchgrass grown is being utilized in one of these alternative uses in this case. Currently switchgrass is not grown on a large scale for cellulosic ethanol production, but it is grown on Conservation Reserve Program (CRP) land, and it is grown for hay and forage of livestock (English et al. 2006). In 2010, CRP enrollment was 31.2 million acres.11 According to the NASS, the number of acres harvested for hay (excluding alfalfa) was 59.7 million. This means that in 2010, 70.2 million acres were enrolled in CRP and harvested for production of hay. This number slightly overestimates switchgrass acres because the harvested acres of hay reported by NASS include hay acres planted to other grasses, and CRP acres contain a small proportion of acres that are planted to trees, but it demonstrates that the order of magnitude of switchgrass acres in our base case is roughly comparable to the number of acres currently in production.
Sensitivity of Crop Prices and Price Wedge to Increasing Switchgrass Ethanol Levels and Crude Oil Prices
The equilibrium commodity prices range from $4.29/bu to $4.82/bu for corn, $13.26/ bu to $15.03/bu for soybeans, and $134.73/bu to $312.94/bu for switchgrass. Figures 3 and 4 display a histogram of the simulated crop price distributions associated with zero switchgrass ethanol production and 3 billion gallons ethanol production. As the amount of switchgrass ethanol produced increases, corn acreage declines from 80.5 million acres to 78.9 million acres, soybean acreage decreases from 70.6 million acres to 68.6 million acres, and switchgrass acreage increases from 65.4 million acres to 74.26 million acres.
The bottom three rows in Table 2 contain the modeled price wedge in the biofuel markets. For the $50/barrel crude oil price scenario the price wedge is $0.52/gal, $3.55/gal, and $1.56/gal for corn ethanol, biodiesel, and cellulosic ethanol, respectively, with zero switchgrass ethanol production. When switch-grass ethanol production is increased to 4 billion gallons per year, the price wedges increase for each commodity due to competition for acreage. The price wedges increase to $0.66/gal, $4.16/gal, and $4.21/gal.
Probability Distribution of Harvest-Time Crop Prices as of Spring Planting Season, No Switchgrass Ethanol Produced
Comparing this with the results associated with a mean crude oil price of $150/barrel we find that the price wedge disappears for corn-based ethanol, and the price wedges are substantially reduced for biodiesel and switchgrass ethanol as well. Notice that we also provide rows corresponding to reduced cellulosic ethanol production costs. In fact, if there were a 50% reduction in the cost of switchgrass ethanol production and crude oil was expected to be $150/barrel, then switchgrass ethanol would be commercially viable up to 3 billion gallons per year.
Probability Distribution of Harvest-Time Crop Prices as of Spring Planting Season, 3 Billion Gallons Switchgrass Ethanol Produced
The Effect of Competition for Acreage
Still focusing on Table 2 we can see the effect of competition for acreage on our results. The top row indicates that switchgrass ethanol production increases as the columns go from left to right. However, corn-based ethanol production and biodiesel production are held constant, so the demand for corn and soybeans is unchanged in the scenarios represented by the columns. As switchgrass ethanol production is increased, more acres are required to meet this new demand. Table 2 shows that harvested acres and production for corn and soybeans decrease while switchgrass acres increase in the columns from left to right. Even though total acreage increases from 216 to 221 million acres, the changes in relative prices of the three crops cause some acres to shift from corn and soybean production. This is associated with the increase in equilibrium price of corn and soybeans from $4.29/bu to $4.82/bu for corn and $13.26/bu to $15.03/bu for soybeans.
These results highlight the fact that when other prices enter a crop's supply function, policies intended to impact just one market affect all the related markets as relative prices of the competing crops change.
Removing Uncertainty from the Model
To obtain the results found in Table 3 we ran the simulation model for deterministic crude oil prices and crop yields set at their mean values. This gives us a baseline we can compare against to explore the effects of uncertain crude oil prices and crop yields on the model. Crude oil price uncertainty affects the beta of biofuel production in equation [5], which determines the required return. Uncertainty in crop yields makes commodity supply uncertain, which causes uncertainty in equilibrium commodity prices. Further, uncertain commodity prices also influence beta in the required return equation.
Comparing Tables 2 and 3 shows the magnitude of these impacts on our model. The presence of uncertainty in the model raises the mean level of commodity prices. This is because the price distributions under uncertainty are skewed to the right. The skewness is driven by crop yield distributions that indicate a small (but positive) probability of very low crop yield realizations; in other words, the crop yield probability distributions are skewed to the left. The small probability of very large prices causes the mean commodity prices to be higher than when we remove uncertainty from the model.
Removing Uncertainty from Crude Oil Prices and Crop Yields
The price wedge is increased in all cases as well when uncertainty is added to the model. The increased price wedge is also due to crop price distributions being skewed to the right. Recall that the price wedge is the difference between the maximum feedstock price biofuel producers can pay, while still earning the required return, and the actual realized market price of feedstock in our model. Since both output prices (the price of ethanol and biodiesel) and input prices have probability distributions, the increased price wedge in the uncertain case means that our model's resulting commodity price distributions are more skewed to the right than the crude oil price distribution we used to generate uncertainty in biofuel prices. Economically, what this means is that biofuel producers are more likely to be negatively affected by a spike in feedstock cost than they are to benefit from a spike in biofuel prices.
Uncertainty does not seem to have a significant impact on each crop's share of harvested acres in our model, nor does it affect total acreage; this is seen by comparing the harvested acres in Table 2 with the harvested acres in Table 3. The fact that each crop's share of acreage stays approximately the same indicates that the increase in price level due to uncertainty affects each crop by a similar magnitude. We see the price level of all three crops increase, but farmers do not change the acreage mix when faced with these higher prices and uncertainty.
Increased Crop Yield Variability
We discovered above that uncertainty has an important effect on commodity prices and the biofuel price wedge, so next we consider what happens in our model in the event that crop yield variability increases as is predicted to happen if climate change accelerates. For purposes of comparison we present only the 1 billion gallon switchgrass ethanol scenario here. Increasing the yield standard deviations12 by 50%, 55%, and 59% for corn, soybeans, and switchgrass, respectively, results in corn prices that are $0.48 higher, soybean prices that are $0.79 higher, and switchgrass prices that are $19.53 higher than in the baseline scenario. This corresponds to 11%, 6%, and 12% price increases in the respective crops. As discussed above, increasing the variance of crop yields makes a severe short crop more likely than a very high yield realization due to the skewness of crop yields. Therefore an increase in the variance of crop yields also results in more extremely high crop prices than it does in low crop prices. This causes the mean of the price distribution to increase.
This means that if climate change increases the variance of yields but does not alter the shape of the distribution, in other words, that yield distributions remain skewed to the right, the negative shocks are more severe than the positive shocks are beneficial. As farmers, biofuel producers, food processors, and others take this into account, they recognize that the likelihood of a very high price realization is greater than the likelihood of a very low price realization, and their price expectation is adjusted accordingly.
Likewise, increased crop yield variability causes the biofuel price wedge to increase in all cases as well. For example in Table 4, with $50/barrel mean crude oil price, the price wedge increases from $0.57/gal to $0.69/gal, $3.73/gal to $4.00/gal, and $2.05/gal to $2.30/ gal for corn-based ethanol, biodiesel, and switchgrass ethanol, respectively. It is important to remember that the price wedge is determined by variables on the revenue side and on the cost side of biofuel production. In this scenario, we increased crop yield variability, which increased the likelihood of high crop price realizations, but we did not increase the variability of crude oil prices. Since this scenario is motivated by climate change impacts on crop yields, this makes sense and results in an increase in the price wedge. If instead we increased variability of both, reflecting general increased market volatility, we could have seen the mean price wedge fall. This is particularly true if increased market variability would impact crude oil prices more; that is, if crude oil price spikes were relatively more likely than crop price spikes.
Long-Run Results under Increased Crop Yield Volatility
VI. Conclusions
We find two elements that most significantly determine the impacts of the RFS in agricultural and biofuel markets: competition for acreage and energy prices. Competition for acreage ensures that policy that provides an incentive to even one type of biofuel will increase the equilibrium prices of all crops. This concern has been the center of the “food verses fuel” debate. However, as is so often the case, we find that the degree of this problem depends on some factors we cannot yet fully quantify. The level of commodity price increase resulting from the RFS for corn ethanol, biodiesel, and cellulosic ethanol will depend on how many low-opportunity-cost acres can produce biofuels. Our model predicted high commodity prices in the case where a large amount of acres must be devoted to switchgrass for cellulosic ethanol production relative to the case where the cellulosic mandate can be met with residue biomass.
Our results show that acreage competition is an important determinant of commodity price levels, and the more acres that must be diverted from other uses in order to meet the mandate, the higher all commodity prices will be in equilibrium. This means that things like corn stover and woody biomass, which do not take food acres out of production, would contribute to meeting the cellulosic mandates without putting upward pressure on commodity prices. Alternatively, the more land-intensive biofuel feedstocks, like switchgrass, that are required to meet the mandate, the higher commodity prices become.
Finally, while energy prices do not impact crop prices when the mandate is binding, they are an important determinant of the price wedge. When energy prices are high, the market incentives to biofuel production are strong. We find the mandate is not binding (i.e., the price wedge is zero) for corn-based ethanol when crude oil is $100/barrel, and the mandate is not binding for modest switchgrass ethanol production when crude oil is $150/ barrel. When crude oil is $50, the RFS is binding and the price wedges are quite large: on the order of $0.58/gal for corn-based ethanol, $3.80/gal for biodiesel, and $2.05/gal to $3.30/gal for cellulosic ethanol depending on the level of land-intensive feedstock needed. This means that energy prices are a primary determinant of market inefficiencies from the RFS outside of the agricultural markets.
Acknowledgments
Mindy Mallory would like to thank members of her dissertation committee, Chad Hart, Sergio Lence, and Arne Hallam, for guidance on an earlier version of this paper. Also, the authors would like to thank Phil Garcia and two anonymous referees for their thoughtful comments. Mindy Mallory is grateful for financial support provided by the Center for Agricultural and Rural Development at Iowa State University.
Footnotes
↵1 HR 6, The Energy Independence and Security Act of 2007, available at http://thomas.loc.gov/cgi-bin/bdquery/z?d110:h.r.00006:.
↵2 Industry-reported levels found at www.ethanolrfa.org/industry/statistics/.
↵3 Read about the VEETC at www.afdc.energy.gov/afdc/laws/law/US/399.
↵4 We consider only corn, soybeans, and switchgrass because we focus on the decision of a farmer who must allocate crop ground. Other cellulosic feedstocks such as woodchips are not well suited to crop ground (Lewandowski et al. 2003).
↵5 Yields are per harvested acre.
↵6 Documentation of the ERS/Penn State Trade Model can be found at trade.aers.psu.edu/pdf/ERS_Penn_State_Trade_Model_Documentation.pdf. Beef demand elasticity is used here as a proxy for aggregate corn demand elasticity because livestock feed is a major usage of U.S. corn and soybean production.
↵7 We use Matlab (MathWorks 2010) to perform all simulations with 5,000 random draws.
↵7 We estimated the relationship from the daily nearest cash prices on the CBOT from October 17, 2005, to September 14, 2007.
↵9 Historical data maintained at http://tonto.eia.doe.gov/dnav/pet/pet_pri_spt_s1_d.htm.
↵10 The $50/barrel scenario is consistent with the Annual Energy Outlook 2010 “low” forecast of the price of oil in 2025. The base crude oil price forecast is $115 per barrel, and the high crude oil price forecast is $196 per barrel.
↵11 CRP information and statistics can be found in the Conservation Programs portion of the USDA Farm Service Agency web site: www.fsa.usda.gov/FSA/webappŒarea = home&subject = copr&topic = rns-css.
↵12 We multiplied the smoothing parameter by three to increase the yield variability while preserving the covariance of the bootstrap sample.
