United States

Department of

Agriculture

Economic

Research

Service

Technical

Bulletin

Number 1933

July 2012

Dynamic PEATSim Model

Documenting Its Use in Analyzing 

Global Commodity Markets

Agapi Somwaru and Steve Dirkse
The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs 

and activities on the basis of race, color, national origin, age, disability, and, where 

applicable, sex, marital status, familial status, parental status, religion, sexual 

orientation, genetic information, political beliefs, reprisal, or because all or a part of an 

individual's income is derived from any public assistance program. (Not all prohibited 

bases apply to all programs.) Persons with disabilities who require alternative means 

for communication of program information (Braille, large print, audiotape, etc.) should 

contact USDA's TARGET Center at (202) 720-2600 (voice and TDD). 

To file a complaint of discrimination write to USDA, Director, Office of Civil Rights, 1400 

Independence Avenue, S.W., Washington, D.C. 20250-9410 or call (800) 795-3272 

(voice) or (202) 720-6382 (TDD). USDA is an equal opportunity provider and employer.

Recommended citation format for this publication: 

Somwaru, Agapi, and Steve Dirkse. Dynamic PEATSIM Model: 

Documenting Its Use in Analyzing Global Commodity Markets, TB-1933, 

U.S. Department of Agriculture, Economic Research Service, July 2012.

Use of commercial and trade names does not imply approval or constitute 

endorsement by USDA.

www.ers.usda.gov

Visit Our Website To Learn More!

www.ers.usda.gov
United States

Department

of Agriculture

www.ers.usda.gov

A Report from the Economic Research Service

Abstract

This report documents the updated version of the Partial Equilibrium Agricultural 

Trade Simulation (PEATSim) model developed by USDA’s Economic Research Service. 

PEATSim is a global model, covering 31 commodities and 27 countries/regions. The 

model, consistent with economic theory, provides a flexible country and commodity 

aggregation and accounts for cross-commodity linkages and interactions. The report 

includes a presentation and discussion of the structure and specific features of the 

revamped model, along with the theoretical underpinnings. It also documents an application of the model to illustrate its dynamic structure and to demonstrate the differential 

behavior. 

Keywords: Partial equilibrium, dynamic, trade, multi-commodity markets, agriculture, 

global model

Acknowledgments

The authors thank the following individuals for their valuable insights and recommendations: John Dyck, William Liefert, Suchada Langley, and Danny Pick of USDA’s 

Economic Research Service, and three anonymous reviewers. The authors also thank 

John Weber and Wynnice Pointer-Napper for editorial and design assistance. 

About the authors

Agapi Somwaru is a former senior economist with USDA’s Economic Research Service. 

Steve Dirkse is Director of Optimization with GAMS Development Corporation.

Dynamic PEATSim Model

Documenting Its Use in Analyzing 

Global Commodity Markets

Technical

Bulletin

Number 1933

July 2012

Agapi Somwaru and Steve Dirkse
ii

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Contents

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Methodology and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Model Structure, New Features, and Modifications . . . . . . . . . . . . . . . . 3

Geographic Scope and Flexible Country Aggregation . . . . . . . . . . . . . . . 3

Commodity Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Supply/Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Trade and Model Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Nontraded Commodities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Data Sources and Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Appendix: Mixed Complementarity Problem . . . . . . . . . . . . . . . . . . . . . 41
iii

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Summary

Background

PEATSim (Partial Equilibrium Agricultural Trade Simulation) is a dynamic, 

partial equilibrium, mathematical-based model that enables users to reach 

analytical solutions to problems, given a set of parameters, data, and initial 

conditions. This theoretical tool developed by ERS incorporates a wide range 

of domestic and border policies that enables it to estimate the market and 

trade effects of policy changes on agricultural markets. PEATSim captures 

the economic behavior of agricultural producers, consumers, and markets in a 

global framework. It includes variables for production of crops and livestock 

activities, consumption, exports, imports, stocks, world prices, and domestic 

producer and consumer prices. 

In 2010, ERS updated and modified the model extensively. The original 

model, static in its specification, was developed through a collaborative 

effort between ERS and Pennsylvania State University. This report supports 

requirements for documentation and information quality as specified by the 

U.S. Office of Management and Budget. 

What Is the Contribution?

PEATSim’s innovative and flexible design enables users to analyze a variety 

of domestic and trade policy issues. The model is written in GAMS (General 

Algebraic Modeling System) using PATH, a Mixed Complementarity 

Problem (MCP) solver. MCP enables PEATSim to account for a discontinuous policy regime, such as a tariff rate quota or a trade ban. This report 

makes the model transparent and available to a larger audience. 

In 2010, PEATSim was modified to include new features and enhanced 

capabilities:

•	PEATSim was augmented to incorporate different sets of production

activities; links between upstream and downstream sectors; and interactions of producers, processors, and consumers at a global level.

•	Unlike previous versions, the updated model’s dynamic specification and

enhanced flexibility enable researchers to analyze short-term and longterm effects of domestic and border policies.

•	The model accounts for simultaneous interactions between livestock and

crop activities and has the ability to capture and solve different sets of 

production activities worldwide.

•	PEATSim now includes 27 countries/regions, up from 12 in the previous

version. The updated version also allows flexible aggregation of the countries in the model to accommodate various modeling needs.

•	The updated model includes 31 agricultural commodities in addition to

3 biofuel-related commodities (ethanol, biodiesel, and distillers’ dried 

grains with solubles). 
iv

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

•	The data in PEATSim calibrate to USDA Agricultural Projections to 

2019 and OECD-FAO Agricultural Outlook 2010-2019, while an innovative econometric method (i.e., cross entropy) equilibrates supply and use.

•	PEATSim uses transparent, clearly listed programming codes, data

inputs, equations, data rules, policies, and parameters.

How Was the Study Conducted?

This report documents the latest version of PEATSim. To illustrate the model’s 

capabilities, we evaluate the effects on the biofuels sector of alternative macroeconomic conditions and crude oil prices, taking into account biofuel production on a global scale from different feedstocks across countries. 
1

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Introduction

This report documents the latest version (2010) of the Dynamic Partial 

Equilibrium Agricultural Simulation (PEATSim) model and discusses specific 

modified features and structures, such as commodity/country coverage and 

updates of trade policies. It also presents an empirical application of the model 

on the global biofuels sector under alternative macroeconomic conditions and, 

especially, crude oil prices (testing for high/low levels). 

PEATSim is a simulator in the sense that it is a mathematical-based system 

that attempts to find analytical solutions to problems, given a set of parameters, data, and initial conditions. Previous versions of the PEATSim model 

have been used in numerous studies (see Blayney et al., 2006; Dyck et al., 

2008; Langley et al., 2003, 2005, 2006; Stillman et al., 2005; Zahniser et 

al., 2010; Valdes et al., 2010, Meade et al., 2010; and Shane et al., 2009). For 

example, PEATSim was used to analyze global dairy markets, examine the 

effects of agricultural trade liberalization, estimate the effects of biofuels 

expansion on global agricultural production and trade, and analyze the impacts 

of biofuel mandates on worldwide grain, livestock, and oilseed sectors (see 

Peters et al., 2008, 2009, 2010; and Stillman et al., 2007, 2008a, 2008b). 

In previous versions of the model, biofuels were represented by “stylized” 

biofuels activities, which do not fully capture the complexity and interaction 

of biofuels production patterns. An analysis of global expansion of biofuels 

production calls for an innovative way to incorporate these activities into 

the model and capture their impacts and links between upstream and downstream activities of the biofuels “module.” For this reason, PEATSim was 

augmented to incorporate a module that links farm activities/sectors with 

downstream industries on a global basis. 

The documentation of the static version of the model, the ERS/Penn State 

Trade model, was developed by ERS’s James Stout in collaboration with 

David Abler of the Pennsylvania State University (2004).1 In fall 2005, the 

model was revamped and extended to include the complementarity features 

of PATH, a state-of-the-art program (Dirkse, 1994; Dirkse and Ferris, 

1994b, 1994c). In 2010, the dynamic version of the model was developed 

and extended to include the global biofuels module and the use of maximum 

entropy techniques for data consistency.

1The theoretical underpinnings 

for the static version of the model 

were developed by a modeling 

team, including David Abler, David 

Blandford, Karl Meilke, Ian Sheldon, 

GianCarlo Moschini, Mary Bohman, 

and Praveen Dixit.
2

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Methodology and Data 

PEATSim’s multiple-commodity, multiple-region structure enables it to 

account for simultaneous interactions between livestock and crop activities 

while maintaining identities such as supply and use. PEATSim covers major 

crops, oilseed and oilseed products, livestock, and dairy activities. It also 

incorporates explicit representation of each country’s domestic and trade 

policies pertaining to agricultural commodities. PEATSim has the ability to 

model different sets of production activities; links between various crops and 

livestock sectors both upstream (at the farm gate) and downstream (such as 

biofuels and dairy processing); and interactions of producers, processors, and 

consumers on a global level. The model’s innovative and flexible specification 

enables researchers to analyze a variety of domestic and trade policy issues.

PEATSim is a reduced-form model that captures the economic behavior of 

producers, consumers, and markets in a global framework. It includes variables 

for production of crops and livestock activities, consumption, exports, imports, 

stocks, world prices, and domestic producer and consumer prices. Commoditybased markets are modeled such that quantities and prices clear the market 

(Hamilton, 1994, pp. 324-327). This implies that market-clearing quantities 

are the sum of beginning stocks, production, and imports and equal to the sum 

of exports, consumption, and ending stocks. These equilibrating conditions 

hold at commodity levels and at world markets. The model is used to simulate 

“what-if” scenarios for comparison with base year(s) results. Constant elasticity 

functions are selected because of their ease of interpretation and well-behaved 

properties. They can be viewed as first-order approximations to underlying 

supply and demand functions (see Stout and Abler, 2004).

The PEATSim model is written in GAMS (General Algebraic Modeling 

System, Brooke et al., 1988) programming language using PATH, a Mixed 

Complementarity Problem (MCP) solver developed by Dirkse (1994a), 

Dirkse and Ferris (1994b), and Dirkse et al. (1994c) (see appendix). MCP 

enables PEATSim to generate a model with different production-consumption 

regimes and functional form discontinuities. Thus, PEATSim can incorporate 

discontinuous functional forms such as tariff-rate quotas (TRQs) and discontinuous demand issues created by mandates, targets, and other complicated 

policy instruments. MCP also allows for endogenous determination of active 

regimes and the consequences of regime shifts, such as the shift from an 

“in-quota” tariff to “over-quota” tariff. For example, PEATSim endogenously 

determines the TRQ price and quantity and makes the need for the arbitrary 

quota rent allocation obsolete. 
3

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Model Structure, New Features, 

and Modifications

Given the complexity of global agricultural markets, it is not easy to 

evaluate the implications of a growing global market for biofuels because a 

model would need to account for biofuel production and its links with other 

agricultural and nonagricultural sectors worldwide. PEATSim was extensively modified to include additional sectors involved in biofuels and their 

byproducts, including conventional ethanol and biodiesel, on a global basis, 

such as the AGLINK-COSIMO (OECD-FAO, 2010) and FAPRI (FAPRI, 

2010) models. 

The interactions of biofuel and agricultural markets are inherently multisectoral because of the interactions between energy, farm inputs, crops, feed, 

food consumption, and trade. Continued long-term growth in the use of food 

and feed products and in the production of fuel have made it difficult to assess 

the impacts of such growth on the global market. For these reasons, ERS 

augmented and revised the model with a global biofuels module.

Theoretically, the model was modified incorporating detailed global ethanol 

and biodiesel markets. The new global biofuel component of PEATSim 

includes ethanol and biodiesel from a variety of feedstocks, such as corn, 

wheat, rapeseed, soybeans, sugarcane, and sugar beets, as well as downstream production activities related to biofuels for all countries in the model.

Also, the expanded database includes biofuel production from sources other 

than feedstocks. For the nonfeedstock-related biofuel production processes, 

such as that for cellulosic ethanol, detailed technical data are unavailable. 

However, nonfeedstock sources, or “other” biofuels, are accounted for in 

PEATSim given data availability in the AGLINK-COSIMO (OECD-FAO, 

2010) model and its database.

Geographic Scope and Flexible Country Aggregation

PEATSim was updated to include 27 countries/regions. The country coverage 

is Argentina, Australia, Bangladesh, Brazil, Canada, China, European 

Union (EU-27), Egypt, Indonesia, India, Iran, Japan, South Korea, Mexico, 

Malaysia, New Zealand, Pakistan, Philippines, Russia, Saudi Arabia, South 

Africa, Thailand, Turkey, Ukraine, United States, Vietnam, and the rest of 

the world (see fig. 1). The latest version allows flexible aggregation of the 

countries in the model. For example, a user can aggregate the model into 

fewer countries if needed.

Commodity Coverage 

The model covers 31 agricultural commodities: 11 crops (rice, wheat, corn, 

other coarse grains, soybeans, sunflower, rapeseed, cotton, sugarcane, 

sugar beets, and sugar (semi-processed)); 10 oilseed, oil, and meal products (soybeans, soybean oil, soybean meal, sunflower seed, sunflower oil, 

sunflower meal, rapeseed, rapeseed oil, rapeseed meal, and other oilseed oil); 

4 livestock and livestock-related products (beef and veal, pork, poultry, and 

raw milk); and 6 dairy products (fluid milk, butter, cheese, nonfat dry milk, 
4

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

whole dry milk, and other dairy products). In addition, coverage includes 

three biofuel commodities and byproducts (ethanol, biodiesel, and dried 

distillers’ grains with solubles (DDGs)).

Sectors

The model includes the crop sector, livestock and products sector, 

and the food processing sector. These sectors are related to each other 

through production processes, commodity prices, and their use of shared 

resources, such as land. The model includes four types of production 

activities: crop production (includes sugarcane and sugar beets), livestock 

production (includes raw milk), oilseed product production, and dairy 

product production.

Argentina–9%

Australia–5%

Brazil–6%

Canada–1%

EU27–50%

India–2%

Rest of

world–10%

U.S.–17%

World biodiesel production

Argentina–0.41% Australia–0.74%

Brazil–29.82%

Canada–1.93%

China–5.14%

EU27–7.08%

India–2.66%

Mexico–0.08%

Rest of

world–2.67%

U.S.

49.46%

Figure 1

PEATSim countries/regions, 2009

World ethanol production
5

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

The crop sector comprises grains (rice, wheat, and corn), oilseeds, upland 

cotton, and sugarcane and sugar beets. “Other coarse grains” are primarily 

barley, sorghum, millet, and oats. Livestock sector includes beef and veal, 

pork, poultry, and raw milk. Sugarcane and sugar beet crops are newly introduced to the model, as are the complementarity conditions between sugar 

feedstocks (sugarcane and sugar beets) and processed/refined sugar. The 

revised model also includes sugar that is processed/refined, with cane and 

beet sugar combined into a single commodity. 

Supply/Production

Crop production in the model is determined by acreage harvested and yield 

per harvested acre, while both acreage harvested and yield are determined 

endogenously. The latest version of the model is dynamic, and in an attempt 

to capture the relative profitability of farmers, acreage response equations 

are specified to reflect farmers’ perceptions of expected prices and yields. 

In documenting the Food and Agricultural Policy Simulator (FAPSIM), 

Gadson et al. (1982) wrote: “Farmers can base future yield perceptions on 

past or experienced yield levels or alternatively discount abnormal weather 

conditions in past years and base their expected yield perceptions on yields 

realized under normal weather conditions” (see also Westhoff et al., 1990). 

At planting time, acreage harvested and yields are not known. Assuming 

an adaptive expectations hypothesis of farmers’ perceptions, we use lagged 

or past acreage harvested, yields, and price to explain crop production. 

Following FAPSIM, the reduced form equations of acreage response and 

yields are specified to represent farmers’ price expectations based on past or 

experienced yield levels and market prices prior to planting.

Crops

Crop production, PRDi,r,t, is defined as the product of acreage harvested, 

AHVi,r,t, and yield, YLDi,r,t, while producer prices are allowed to adjust. 

Area harvested of crop i in country r and year t is a function of area and the 

crop’s own producer price and producer prices of other crops, which may be 

complementary or competing for acreage as follows:

,

, , , , |(1) ,, 1 ,,, 1 ,

(1) i r ij n

irt irt irt i jrt i j

AHV a AHV PPR λ ε

− −

  =   ∏

 

where αi,r,t|(1) is a measure that captures the past interaction between the 

producer price and crop area,2 AHVi,r,t-1 is lagged area of crop i, λi,r is 

a partial adjustment parameter, PPRi,r,t-1, is own lagged producer price, 

PPRj,r,t-1 is lagged producer prices of other crops j, and εi,j is cross price elasticities for crop area. 

As explained earlier, the reduced form yield equation is then specified as 

a function of the ith crop’s lagged yield and lagged producer price of crop 

PPRi,r,t-1 as follows:

, ,

, , , , |(2) ,, 1 ,, 1 (2) i r i rirt irt irt irt YLD a YLD PPR μ η

− − =

2This modeling is appropriate when, 

for example, the production technology is described by a Cobb-Douglas 

function, such as: Y(L,K) = ALbK1-b

where Y represents total production, L, represents labor, K represents 

capital, and A represents total factor 

productivity, which includes effects 

from technology, efficiency, and scale. 

Given that A varies over time, we can 

use it as a variable to help calibrate the 

long-term projections.
6

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

where αi,r,t|(2) is a measure that captures the past interaction between the 

producer price and yield, μi,r is a partial adjustment parameter, ηi,r is the price 

elasticity of the yield for crop i, and PPRi,r,t-1 is own lagged producer price.

Oilseed products

As stated earlier, the model includes 10 oilseed, oil, and meal products. The 

“other oilseed oil” aggregate includes canola oil, flax seed oil, and tropical 

oils (palm oil, olive oil, coconut oil, and other oil). 

Production of oilseed products i in country r at time t(PRDi,r,t) is determined 

by the quantity of jth oilseed crushed and by an exogenous extraction rate as 

follows:

, , ,, ,,, (3) irt jrt i jrt i

PRD CRU ERT = ∑

where CRUj,r,t is the crush of the associated oilseed and ERTi,j,r,t is the 

extraction rate assuming fixed proportion in the technology of meal and oil 

production. The determinants of oilseed crushing are discussed later in equation 15.

Livestock products

Production of livestock product i in country at r year t, PRDi,r,t, is a function 

of its own producer price and the producer prices of the other livestock products, a feed cost index for that product, and production of that product in the 

previous year as:

, , , ,

,, ,, ,, 1 ,,, 1 , , (4) i r i jr i r

n

irt irt irt i jrt irt

j livestock

PRD PRD PPR FeCost λ η σ β − − ∈= ∏

where βi,r,t is a measure that captures the past interaction between (1) the 

producer price and feed costs and (2) production, PRDi,r,t-1 is production of 

ith livestock product the previous year, λi,r is a partial adjustment parameter, 

PPRi,j,r,t is the producer price of i livestock products (own) and the producer 

prices of other livestock products j (cross price) in country r, σi,j,r is the price 

elasticity of production, FeCosti,r,t is the feed cost index for each livestock 

product i, and ηi,r is the elasticity of production with respect to input prices.

The feed cost index, FeCosti,r,t, is a function of feed use and feed prices and is 

specified as:

, , ,,, ,, (5) irt i jrt jrt j feeds

FeCost FeedUse PPR == ∑

where FeedUsei,j,r,t is the jth feed used in the production of livestock product 

i, in country r at time t, and PPRj,r,t, is the price of feed j in country r at

time t. There are nine commodities in the model that can potentially be used 

as livestock feed: wheat, corn, other coarse grains, DDGs, and all meals 

(byproducts of soybeans, sunflower seeds, and rapeseeds).
7

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Dairy products

As mentioned earlier, the model identifies six dairy products. The “other 

dairy products” aggregate includes ice cream, yogurt, and whey. Dairy products are processed from raw milk, one of the four livestock products in the 

model. In some regions, production of one or more dairy products is zero or 

negligible, in which case production is set equal to zero in the model. 

Production of dairy products i at year t is modeled as proportional to the total

quantity of raw milk processed , ,

' ', ,

irt

processed milk r t

PRD

PRD (because all 

processed dairy products are derived from raw milk) and the price of dairy 

products.3 With this specification, a change in the price of one processed 

dairy product relative to another leads to changes in the mix of processed 

dairy products made from raw processed milk. The equation is as follows:

,

, , ,, 1 , ,

, , , ,

' ', , ' ', , 1

(6) 

i r

irt irt i jr

irt jrt

processed milk r t processed milk r t j dairyproducts

PRD PRD

PPR PRD PRD

λ

σ β −

− ∈

   

= ∏          

where PRDi,r,t is production of the ith dairy product in country r at time t, 

PRD'processed milk' ,r is total production of raw processed milk,

, ,

' ', ,

irt

processed milk r t

PRD

PRD is the proportionality, which indicates that the 

production of the ith dairy product varies in direct proportion with the total

production of raw processed milk, ,, 1

' ', , 1

irt

processed milk r t

PRD

PRD −

− is the

proportionality lagged one year, PPRj,r,t is the producer price of dairy product 

j, βi,r,t is a technology parameter that determines the production of dairy 

products over time, λi,r represents the rate of adjustment, and σi,j,r is the own 

and cross-price elasticity of supply for dairy products.

Biofuels

Production of biofuels, PRDi,r,t, is expressed as the summation of biofuels 

from the various feedstocks, BioPRDi,j,r,t, and production of biofuels from 

nonfeedstock, OthPRDi,j,r,t, as follows:

, , ,,, ,,, (7) irt i jrt i jrt

j

PRD BioPRD OthBioPRD = + ∑

where i indicates the type of biofuels (ethanol, biodiesel), j indicates feedstocks, r indicates country, t indicates time, and OthBioPRDi,j,r,t denotes 

“other” agricultural and nonagricultural related sources, such as corn residues (stover), fermentation of molasses, wheat byproducts (i.e., Australia), or 

forest byproducts. Note that OthBioPRDi,j,r,t, depicts biofuel production from 

other sources, such as corn stover, wheat straw, and sugarcane residue, driven 

by data availability in the database and is expressed as the summation of 

biofuels from other resources. 

3The supply of dairy products is 

modeled as proportional to the total 

quantity of raw milk (proportionality) 

and the previous year's proportionality. 

Although dairy products and raw milk 

are perishable, the supply of dairy 

products at the first stage of processing

(i.e., milk processing plants) can be 

subject to the longrun equilibrium 

specification.
8

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

The production of biofuels, both ethanol and biodiesel, from all categories of feedstocks, BioPRDi,j,r,t, is an intermediate production process and 

depicts the interindustry technological relation of biofuels and feedstocks in 

each country in the model. This production process captures the technology 

balance of converting feedstocks to biofuels. The process is characterized by 

each country’s technological advances depending on the type and availability 

of alternative feedstocks and can be represented as follows:

,,, , , , , (8) i jrt j r t i biofuels j r t i biofuels BioPRD Conv Fue = = =

where i indicates type of biofuel (ethanol, biodiesel), j indicates feedstocks, 

r indicates country, t indicates time, Fuej,r,t|i=biofuels indicates alternative 

feedstocks for biofuels, and Convj,r,t|i=biofuels is the technical coefficient for 

converting feedstocks to biofuels. In other words, the process captures the 

technological interindustry relation of converting and producing biofuels 

from alternative feedstocks in each country in the model. 

The main byproducts of corn ethanol, for example, in the case of the U.S. 

dry-corn milling industry, are DDGs. DDGs are a substitute for corn (as feed) 

and are used as a protein source for animals in feedlots, particularly finishing 

cattle and poultry. The production of DDGs, or PDR'DDGs', r,t, in the corn 

ethanol process is proportional to a technical coefficient that captures the 

technological relation of corn-ethanol production and DDGs. This complementarity relationship between primary product (corn ethanol) and byproduct 

is linear and can be stated as follows:

' ', , ' ', , ' ', , (9) PRD ddgsConv Fue DDGs r t = corn r t corn r t

where r indicates country, t indicates time, ddgsConv is the technical coefficient that depicts the conversion of corn feedstocks to DDGs in the production 

of DDGs, and Fue'corn',r,t is corn feedstocks in the production of corn ethanol. 

Sugar 

Sugar production, PRD'sugar',r,t, from sugarcane and sugar beet feedstocks is 

defined as follows: 

' ', , ,,| , , (10) sugar r t i r t i sugar i r t

i

PRD sugCon Foo = ∑ =

where i indicates the type of sugar-producing crop, r indicates country, t

indicates time, and sugConi,r,t\i=sugar denotes a technology-related concept 

in the sugar-processing sector determining the technological relationship 

between processed sugar (output) and sugarcane and sugar beets (inputs) in 

each country in the model. Finally, Fooi,r,t denotes sugarcane and sugar beets 

used (or demanded) by the refined sugar processing sector (an intermediate 

processing sector), where i refers to sugarcane and sugar beets for refined 

sugar-processing products. 

Demand

The model includes various types of consumption activities, such as food, 

feed, and fuel demand. The model is specified to maintain consistency 

between consumption and its subcomponents.
9

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Food demand

Food demand exists for all commodities in the model except raw milk and 

the three oilseed meals. Food demand is specified as per capita and aggregate. Per capita food demand PcFOOi,r,t for commodity i in country r at 

time t is a function of consumer price, PCNi,r,t, and per capita income in real 

terms, PcRGDPr,t, as follows: 

, , ,

,, ,, ,, , (11) i jr i rirt irt irt r t

i

PcFOO PCN PcRGDP σ ε = β ∏

where βi,r,t is a measure that captures the interaction between the consumer 

price, the per capita demand, and per capita income; σi,j,r is the own- and 

cross-price elasticity of demand; and εi,r denotes the income elasticity of food 

demand for commodity i in country r at time t.

Aggregate food demand for all commodities, FOOi,r.t, is specified as a function of per capita commodity demand and population:

, , ,, , (12) FOO PcFOO POP irt = irt rt

where PcFOOi,r.t is per capita food demand and POPr,j denotes population in 

country r at time t. 

Feed demand

Each region in the model has four feed demand equations, one for each of its 

four livestock products. As noted earlier, there are seven commodities in the 

model that can be used as livestock feed: wheat, corn, other coarse grains, 

soybean meal, sunflowerseed meal, rapeseed meal, and DDGs. In some 

regions, the use of a particular feed for one or more livestock products is zero 

or negligible, in which case feed demand is set to zero in the model.

Feed demand, FEESi,k,r,t, is specified as a function of livestock production 

(PRDk,r,t), feed conversion ratios (FRi,k,r,t), and feed prices (PFEi,r,t) as follows:

,,,

,,, ,,, ,, ,,, , , (13) ijktikrt ikrt krt ikrt irt

i feed

FEES PRD FR PFEσ β ∈= ∏

where i depicts feed category, k depicts livestock/meat category, r indicates 

country, t indicates time, βi,k,r,t is a measure that captures the interaction 

between the feed price and feed demand, PRDk,r,t depicts production of livestock/meat, and FRi,k,r,t indicates feed used by livestock/meat category. Feed 

prices are depicted as PFEi,r,t, while σi,j,k,r is the own feed price elasticity of 

demand for i=j and the cross-price elasticity of feed demand for i≠j for meat 

and milk k. 

Aggregate feed demand across all livestock, FEEi,r,t, is specified as the 

summation of feed demand by each livestock type k as follows:

, , ,,, (14) irt ikrt

k

FEE FEES = ∑
10

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Crush 

Oilseed crush, CRUi,r,t, is specified as a function of lagged crush, CRUi,r,t-1, 

and crush margins, MGNi,r,t, as follows:

, , ,

,, ,, ,, 1 , , (15) i r i jrirt irt irt irt

j oilseeds

CRU CRU MGN λ σ β − ∈= ∏

where i depicts oilseed category, r depicts country, t indicates time, and βi,r,t

is a measure that captures the past interaction between the crush margin 

and crushing. In this specification, the demand for crush increases with 

increases in the processing/crushing margins and vice versa. In other words, 

as the crush margin increases, there will be a greater demand for oilseeds 

for crushing, resulting in a gradual rise in oilseeds prices. Conversely, when 

the margin starts falling, one can expect weaker demand for oilseeds and 

falling oilseeds prices, σi,j,r is the crush elasticity with respect to own price 

(i) and cross price (j) of oilseeds in country r, and λi,r is a partial adjustment 

parameter.

The crushing margin, MGNi,r,t, is specified as a function of the extraction 

rate of crush products, the prices of crush products (meal and oil), and the 

consumer prices for oilseeds:

,,, ,,

, ,

, ,

(16) 

i jrt jrt

j

irt

irt

ERT PPR

MGN

PCN

∑

=

where i indicates oilseed category, such as soybeans, rapeseeds, and sunflower 

seeds, j indicates crush products (meal and oil), r indicates country, t indicates 

time, ERTi,j,r,t is the extraction rate of oilseed crush (meal and oil), PPRj,r,t is 

the price of crush products, and PCNi,r,t is the consumer price of oilseeds.

Raw milk processing

Raw milk processing demand, CONi,r,t, for j dairy products, such as fluid 

milk, cheese, butter, nonfat dry milk, whole dry milk, and other dairy products, is specified as a function of lagged raw milk demand, CONi,r,t-1, and the 

ratio of the value of the processed dairy product to the value of raw milk used 

(needed) in processing:

,

,

,, ,, ,, 1 ,, ,, (17) 

i r

i r

irt irt irt jrt jrt

j

CON CON PRD PPR

σ

λ β −

  =   ∑

 

where i indicates raw milk, j indicates dairy processed products, r indicates 

country, t depicts time, βi,r,t is a measure that captures the past interaction between processed dairy products and the demand for raw milk to be 

processed (as projected in the AGLINK-COSIMO (OECD and FAO model/

baseline). PPRj,r,t is the producer price of processed dairy products (j = 

fluid milk, cheese, butter, nonfat dry milk, etc.), PCNi,r,t is the price of raw 

milk, λi,r is the partial adjustment parameter, and σi,r is the price elasticity of 

demand for raw milk in the processing of dairy products. In this specification, 
11

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

PRDj,r,t depicts (over time t) demand of dairy products, while CONi,r,t depicts 

demand of raw milk for processing.

Biofuels-Ethanol

The demand for ethanol FUE'ethanol',r,t is specified as a function of ethanol 

price, PCN, the price of gasoline, pGAS, and real income, RGDP, as follows:

'

' ', , ' ', , ' ', , ' ', , , , (18) r r r FUE a PCN pGAS RGDP ethanol r t ethanol r t ethanol r t gasoline r t r t

σ ε φ =

where r denotes country at time t, α'ethanol',r,t is a measure that captures the 

interaction between the ethanol price and ethanol demand, σr

 is the ethanol 

price elasticity of demand, εr

 is the gasoline price elasticity of demand for 

ethanol, and φr

 is the income elasticity of demand for ethanol.

Biofuels-Biodiesel

The demand for biodiesel, FUE'biodiesel',r,t, is specified as a function of the biodiesel 

price, PCN, the price of diesel, pDSL, and real income, RGDP, as follows:

' ', , ' ', , ' ', , ' ', , , , (19) r r r e FUE biodiesel r t biodiesel r t biodiesel r t diesel r t r t a PCN pDSL RGDP ρ η =

where r denotes country, t indicates time, α'biodiesel',r,t is a measure that 

captures the interaction between the biodiesel price and biodiesel demand, ρr 

is the biodiesel price elasticity of demand, er is the diesel price elasticity of 

demand for biodiesel, and ηr

 is the income elasticity of demand for biodiesel.

Biofuels-Feedstock

The demand for feedstocks, Fuej,r,t|biofuels, is an intermediate production 

activity and thus depends on the prices of feedstocks (upstream inputs) and 

biofuels (downstream outputs). The allocation (demand) of feedstocks for 

alternative biofuels, Fuej,r,t|biofuels, is specified as a function of the price of 

biofuels and the price of feedstock as follows:

, , ,

, , , , ,, ,, (20) ( ) i jr j r e

j r t biofuels j r t biofuels irt jrt i biofuels

Fue PPR PCN εα == ∑

where i denotes biofuels (ethanol and biodiesel), j denotes feedstocks (such 

as corn, soybean oil, sugarcane, sugar beets, and rapeseed oil), r denotes 

country, t denotes time, αj,r,t|biofuels is a measure that captures the interaction 

between biofuel prices and the demand for feedstock for alternative fuels, 

PPRi,r,t denotes the producer price of biofuels i, εi,j,r is the price elasticity of 

demand for feedstocks in production of biofuel type/category, PCNj,r,t is the 

consumer price of feedstocks j, and ej,r represents the feedstock price elasticity of demand for biofuels. 
12

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Demand for sugarcane and sugar beets

The demand for sugarcane and/or sugar beets, FOOi,r,t\i=sugarcane / sugar-beets, 

is defined as follows:

, ,

, , / , , ' ', , , , (21) i r i r FOOi r t i sugarcane sugar beets irt PPR PCN sugar r t irt

φ θ α = − =

where i denotes sugarcane/sugar beets, αi,r,t is a measure that captures the 

interaction between (1) the prices of both sugar feedstock and refined sugar 

and (2) the demand for sugarcane or sugar beets in country r and year t, 

PPR'sugar',r,t is the producer price of refined sugar, φi,r is the price elasticity of 

demand for sugarcane/sugar beets for the production of refined sugar, PCN

is the consumer price of sugarcane/sugar beets, and θi,r represents the price 

elasticity of demand for sugarcane/sugar beets in country r at time t.

Other demand

Other use demand is generally small, and it is assumed to change over time 

by the same proportion as the change in the sum of food, fuel, feed, and 

crush, as follows:

, , ,, ,, ,, ,,

, ,' ' , ,' ' , ,' ' , ,' ' , ,' '

(22) irt irt irt irt irt

i r baseline i r baseline i r baseline i r baseline i r baseline

Oth FUE FOO FEE CRU

Oth FUE FOO FEE CRU

+ ++ = + ++

Total 

Total demand of all commodities i in country r at time t except raw milk is 

specified as the summation of the components food, fuel, feed, crush, and 

other, as follows:

,, ,, ,, ,, ,, ,, (23) CON FEE FOO FUE CRU OTH irt irt irt irt irt irt =+ +++

Stocks

Ending stocks for crops ESTi,r,t are specified as a function of ending stocks in 

the previous period and the ratio of commodity world reference prices over 

lagged world reference prices for crops:

, , , ,

,, ,, ,, 1

,, 1

(24) 

irt

irt

irt irt irt

irt

PRFC

EST EST

PRFC

ε

α −

−

  =      

where αi,r,t is a measure that captures that past interaction between world 

references prices and ending stocks for crops, i indicates commodity, r

indicates country, t indicates time, PRFC denotes transmitted world price 

of a commodity i in country r at time t, and εi,r,t is the ending stocks price 

elasticity of demand. The proportionality of stocks at time “t” over stocks at 

time “t-1” (ESTi,r,t / ESTi,r,t-1) for a commodity depends on the proportionality of the transmitted world price of commodity i in country r at time “t” 

over price at time “t-1” (PEFCi,r,t / PRFCi,r,t-1). If this were not the case, the 
13

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

demand for commercial stocks would be a function of the good’s expected 

price, that is, the demand for stocks would be speculative (Meilke, 1999; 

Gadson et al., 1982).

Prices

Domestic prices are endogenously determined in the model. World prices 

are in U.S. dollars, and all domestic prices and policies are expressed in 

local currency. Real exchange rates are treated as exogenous. In each region, 

domestic prices for all traded commodities (except raw milk, fluid milk, and 

other dairy products) depend on world prices, exchange rates, transportation 

costs, and country-specific policies that affect prices. 

World prices

PRFi,t depicts the world reference price of commodity i, while PRFCi,r,t

depicts the transmitted world price of commodity i to country r at time t. 

The transmitted world price to country r is defined as a function of the world 

reference price, PRFi,t, (see equation 40) expressed in U.S. dollars as follows:

, , ,, , , (25) PRFC TRANSM PRF REXR irt = irt it rt

where TRANSMi,r,t represents a price transmission mechanism used in the 

model to capture the effects of world reference price on a country’s price, 

and REXRr,t is a real exchange rate for a tradable commodity i in country r at 

time t. Note that the world reference price is indexed over commodity i and 

time t while the transmitted world price commodity to a country is indexed 

over commodity i in country r at time t. Real exchange rates are exogenous in 

the model, while the transmission parameters are assigned or have the value 

of 1 for all tradable commodities.4

Domestic prices 

For most region/commodity pairs, the domestic price PDOMi,r,t is defined as 

a weighted average of export prices, PEXi,r,t, and import prices, PIMi,r,t. The 

model assumes homogenous products, such that one domestic price is specified as:

,, ,, ,, ,, ,, (26) (1 ) PDOM PEX irt irt irt irt irt = +− θ θ PIM

where θi,r,t is the weight (0 ≤ θi,r,t ≤1 )and is equal to the baseline-years 

exports divided by the sum of baseline exports and baseline imports, 

, ,

,, ,, ( )

irt

irt irt

EXP

EXP IMP +

Producer prices

Producer prices, PPRi,r,t, are specified as a function of the domestic prices 

adjusted by producer subsidies or taxes for commodity i in country r at time 

t. Producer subsidies in the model can be either exogenous or endogenous 

4Because of either policies (such as 

domestic price support or consumer 

subsidies) or weak market infrastructure, the transmission of changes in 

agricultural border prices to domestic 

prices within countries might be 

incomplete (less than one). This could 

especially be the case for many developing countries. Given that country 

coverage was expanded in this version 

of the model, particularly to include 

more emerging market and developing 

economies, future efforts will be 

devoted to determining more accurate 

price transmission parameters.
14

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

(e.g., subsidies that vary depending on the domestic price or other variables 

in the model): 

, , ,, ,, (27) PPR PDOM TW irt = + irt irt

where TWi,r,t represents variable production subsidies (if any) associated with 

target price policies.

Consumer prices

Consumer prices, PCNi,r,t, for commodity i in country r at time t are specified as a function of domestic prices adjusted by consumer subsidies (by 

subtracting) or taxes (by adding) as follows: 

, , , , , , (28) (1.0 ) PCN PDOM TC irt = ± irt irt

where TCi,r,t represents consumer subsidies/taxes. Consumer subsidies/

taxes can be either exogenous or endogenous (i.e., subsidies/taxes that vary 

depending on other variables in the model).

Feed prices

Feed prices for feed category i in country r at time t, PFEi,r,t, are specified as 

a function of consumer prices (used as a proxy for the feed price at the retail 

level) adjusted for any difference between country/region consumer prices 

and the transmitted world price to the country r:

,, ,, ,, ,, ,, (29) ( ) PFE PCN FeedPRFAC PRFC PCN irt irt = + irt irt irt −

where the feed price, FeedPRFACi,r,t, captures the difference (if any) between 

domestic consumer prices and world prices. Feed prices within the model 

can differ from domestic consumer prices by any endogenous or exogenous 

amount, added or subtracted, on an ad valorem or specific basis. However, as 

of this time, no policies have been introduced into the model for any countries that could cause feed prices to deviate from domestic consumer prices. 

Consequently, FeedPRFACi,r,t is set equal to zero due to lack of data availability, except for wheat and other coarse grains in Japan.

Import prices

Import prices, PIMi,r,t, are specified as a function of world prices adjusted for 

an ad valorem tariff (i.e., first tier, or in-quota rate, Tm1i,r,t, and second tier, or 

over-quota rate, Tm2i,r,t) and transportation costs, Transi,r,t , as follows: 

, , , , ,, ,, ,, , , (30) (1.0 1 * 2 ) PIM PRFC Tm Z Tm Trans irt irt = ++ + irt irt irt irt

where PRFCi,r,t denotes the transmitted world price to country r of 

commodity i at time t while Zi,r,t relates to the TRQ. Zi,r,t is bounded with 

values ranging from 0 to 1 [0,1] and solves endogenously for the level

where the quota operates. If the quota is not binding, it takes the value of 0; 
15

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

otherwise, it takes the value of 1 (see also equation 33). Instead of “tariffication” of TRQs or linear approximations, TRQs are specified as functions and 

are solved explicitly in the model, taking account of the discontinuity in the 

tariff rate using the MCP formulation.5

Export prices

Export prices, PEXi,r,t, are specified as a function of the transmitted world prices 

to country r, PRFCi,r,t, adjusted for export subsidies and/or taxes as follows:

, , ,, ,, (31) (1.0 exp ) PEXirt irt irt = + Sub PRFC

where i denotes commodity, r denotes country, t denotes time, PRFCi,r,t

denotes the transmitted world price to country r, and exp Subi,r,t denotes ad 

valorem export subsidies or taxes. Note that the transmitted world price to a 

country r depends on the world reference price (see equation 25).

Producer price for nontraded commodities

The domestic prices for nontradable commodities (raw milk, fluid milk, 

other dairy products, sugarcane, and sugar beets) are determined by domestic 

supply-demand equilibria, or the material balance equation holds:

,, ,, 1 ,, ,, (32) 0 PRD EST CON EST irt irt irt irt + − −= −

where i denotes nontraded commodity, and r denotes country at time t.

Policies

The core set of policies includes both specific and ad valorem import and 

export taxes/subsidies, TRQs, and producer and consumer subsidies. In addition, the model includes other policies that constitute important aspects of 

agricultural policy in particular countries. 

In particular, for the United States, the model includes loan rates with 

marketing loan benefits for crops and export subsidies for dairy products. For 

the EU, the model includes export subsidies and production quotas for raw 

milk and sugar. For Canada, the model includes production quotas for milk 

that target producer prices.

Tariff-rate quotas 

A TRQ is a policy in which imports are subject to one (low) tariff below a 

specified quantity of imports and a second higher tariff on imports in excess 

of this limit. To model a TRQ directly, we use complementarity to capture 

this switching from one regime to another. 

There are two issues in modeling TRQs: how to model a switch from one 

regime to another and how to handle the boundary case where imports are 

exactly at the quota limit. In the latter case, we have a range of possible supply 

5The MCP formulation allows in the 

absence of TRQs the actual applied 

tariff rates to be used. The model uses 

actual applied tariff rates rather than 

World Trade Organization bound rates 

whenever such data are available. 

For most of the agricultural products 

imported by the United States, Canada, 

and Mexico, tariffs under the North 

American Free Trade Agreement 

(NAFTA) are more important than 

Most Favored Nation tariffs because 

more agricultural imports are from 

within NAFTA than outside NAFTA. 
16

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

prices whose bounds are determined by the below- and above-quota tariffs. The 

model determines a supply price in this range such that markets clear.

Our TRQ policy for an imported commodity i in country r at time t is defined 

by a lower (tier 1) tariff, Tm1i,r,t, an upper (tier 2) tariff, Tm2i,r,t, a TRQ quota 

limit, Tarqtai,r,t, and the import quantity qi,r,t (aka IMPi,r,t). Note that the 

over-quota tariff is the sum Tm1i,r,t + Tm2i,r,t, and both Tm1i,r,t and Tm2i,r,t 

are positive—if not, we have one regime (i.e., a normal tariff). If we introduce a variable Zi,r,t in [0,1] complementarity to a function:

( ) , , ,, ,, , , (33) : = 0 1 F Tarqta q irt irt irt Zirt • − ⊥ ≤≤

then by definition (see appendix), below-quota imports imply that Zi,r,t = 0. 

To see this, observe that below-quota imports imply that Fi,r,t > 0, so by definition, Zi,r,t must be at its lower bound. Similarly, above-quota imports imply 

that Zi,r,t = 1. At-quota imports imply that Fi,r,t = 0, so that Zi,r,t is allowed to 

float between 0 and 1. Note that in this specification, Fi,r,t is perpendicular to 

Zi,r,t even though Fi,r,t does not depend on Zi,r,t. 

Given this behavior for Zi,r,t, we can write the function determining the 

supply price for this import as in equation 30 or:

PIMi,r,t = PFRCi,r,t (1.0 + Tm1i,r,t + Zi,r,t * Tm2i,r,t) + Transi,r,t

where we would have used only Tm (or tariff rate) for a “simple” tariff case. 

With this, we get the (tier 1) tariff Tm1i,r,t below the quota, the (tier 2) tariff 

Tm1i,r,t+ Tm2i,r,t above the quota, and the possibility to choose any value in 

between these two when we are at the quota. The at-quota behavior allows the 

model to choose Zi,r,t in [0,1] so that the supply price is equal to the demand 

price at equilibrium.

Variable production subsidies

In the presence of variable production subsidies for certain agricultural 

commodities, producers receive government payments when the domestic 

price falls below a certain level known as the target price. The payment 

amount is equal to some fixed percentage of the price shortfall. We assume 

that the payment is zero when the domestic price is at or above the target 

price. To implement these subsidies, we introduce a price wedge TWi,r,t (variable production subsidy) equal to the maximum of and a percentage of the 

price shortfall. To compute, we utilize the complementarity framework as 

follows:

, , ,, ,, ( , , ) , , 0 irt irt irt irt irt (34) TW PtargetFac Ptarget PDOM TW ≥ − ⊥≥

where Ptargeti,r,t is the target price, PtargetFaci,r,t is the percentage, and 

PDOMi,r,t is the domestic price for a commodity i in country r at time t. 

Complementarity implies that TWi,r,t takes on the desired maximum (max) 

value:

(35) TWirt , , max 0, PtargetFac Ptarget PDOM irt irt ,, ,, ( irt , , ) = −    
17

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Production quotas

The model incorporates production quotas for policies that limit production by placing explicit upper bounds on the quantity produced. When such 

a quota for a commodity is binding, the producer price for that commodity 

in the production equation (called the area harvested equation in the case of 

crops) is adjusted endogenously by adjustment factor (ShadSlki,r,t).6

Complementarity allows this endogenous adjustment factor ShadSlki,r,t to be 

nonzero only if production is at the quota level for a commodity i in country r

at time t. To implement this, we replace the producer price PPRi,r,t in production 

equations with the adjusted price and set:

,, ,, , , (36) 0 ProdLim PRD ShadSlk irt irt ≥⊥ ≥ irt

Price supports

In the absence of price supports, we have at equilibrium that the producer 

price PPRi,r,t is equal to the domestic price PDOMi,r,t. Note that the consumer 

price in the absence of policy-distorted taxes and or subsidies is equal to 

the domestic price. If the government has a price support policy (i.e., it 

pays producers the shortfall between the producer price and the announced 

support price), then the equality will not hold when the price drops below 

the support price. In this case, the producer sets output at a level consistent 

with the higher support price and the consumer sets demand/consumption 

consistent with the lower consumer price to clear the market. This happens 

when we set a lower bound on the producer price and equate producer and 

consumer prices as follows:

, , , , , , , , (37) _ PPR PDOM PPR PPR Support irt ≥ ⊥≥ irt irt irt

Trade and Model Closure

Global net trade in each commodity must be zero for international markets 

to clear. The model is nonspatial in the sense that a region’s imports and 

exports are not distinguished by their source or destination, respectively. It is 

a gross trade model that accounts for total exports and total imports of each 

commodity in every region. This is accomplished in most cases by distinguishing gross exports and gross imports as follows: the smaller of the two 

(exports or imports) in a region is governed by a behavior equation that is 

consistent with historical trade, while the larger of two (exports or imports) 

adjusts to clear global agricultural markets. For the nontraded commodities, 

supply and demand in each region must be equal. The revamped model was 

extended and includes a separate module to handle bilateral trade flows.

Internationally traded commodities

The model balances supply and demand for each tradable commodity i in 

region r at time t as follows:

,, ,, ,, 1 ,, ,, (38) NET PRD EST CON EST irt irt irt irt irt =+ −− −

6In the previous (static) version of the 

model (ERS/Penn State Trade model), 

when a quota for a commodity was 

binding, the producer price for that 

commodity in the production equation 

(called the area harvested equation 

in the case of crops) was replaced by 

an endogenous shadow price that was 

assumed to be equal to marginal cost. 

In that specification, the shadow price 

was equal to the producer price when 

the quota was not binding. In the latest 

version of PEATSim, when a quota for 

a commodity is binding, the producer 

price for that commodity in the production equation (called the area harvested 

equation in the case of crops) is adjusted 

endogenously by an adjustment factor 

(ShadSlki,r,t ). Complementarity allows 

this endogenous adjustment factor to 

be nonzero only if production is at the 

quota level. The complementarity condition holds for current production. Note 

that the adjustment factor is not the 

shadow price.
18

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

where PRDi,r,t is production, ESTi,r,t-1 is lagged ending stocks (or beginning 

stocks for time t), CONi,r,t is consumption, and ESTi,r,t is ending stocks. 

Equilibrium conditions for world markets require that the sum of exports, 

EXPi,r,t, be equal to the sum of imports, IMPi,r,t, across regions for tradable 

commodity i in region r and year t:

, , , , (39) irt irt r r

∑ ∑ EXP IMP =

and under the complementarity condition, the world price, PFRi,r,t is the 

equilibrating variable in the world balance equation, or 

, , , , , , (40) 0 irt irt irt r r

∑ ∑ EXP IMP PRF = ⊥≥

Trade

For any tradable commodity i in region r and time t, one of the export/import 

pairs is specified as a function of price while the other is left relatively free 

to allow the market to clear. In the description that follows, we consider the 

case where export quantities are determined as a function of export price and 

imports float to clear the market. The case where the roles are reversed is 

treated similarly.

The complementarity conditions determining the import and export quantities when ,

,, ,, i rirt irt PEXε

α is positive are:

,

,

,, ,, ,, , , , ,

,, ,, ,, ,, , ,

,, ,, ,, ,

(41) 0

(42) 0

(43) 

i r

i r

irt irt irt irt irt

irt irt irt irt irt

irt irt irt i

EXP PEX Neterr EXP

PEX Neterr NET Neterr

IMP EXP NET IMP

ε

ε

α

α

≥ + ⊥≥

+≥⊥ ≥

≥− ⊥ , 0 r t ≥

where αi,r,t represents a technology-related attribute, PEXi,r,t is the price of 

export-bounded commodity, εi,r is an export elasticity, and Neterri,r,t is an endogenous variable used as a correction factor to ensure that EXPi,r,t ≥ NETi,r,t. When ,

,, ,, i rirt irt PEXε

α is not positive, we use these conditions:

,, ,, , , (44) 0 EXP NET EXP irt irt ≥⊥ ≥ irt

,, ,, ,, , , (45) 0 irt irt irt irt IMP EXP NET ≥− ⊥ ≥ IMP

Import quantity, in this case, is the equilibrating variable.

Nontraded Commodities

For commodity i in region r at time t that is not traded internationally, domestic 

supply must be equal to domestic demand (i.e., NETi,j,t must be zero):

, , (46) 0, , NET for i j nontraded commodities i jt = ∈
19

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Data Sources and Calibration

Currently, the model utilizes the domestic USDA baseline, the CountryCommodity Linked System, and the AGLINK-COSIMO model of OECD 

and FAO. The Linked System joins ERS foreign country models and is 

used to perform the first rounds of projections for the international baseline. 

PEATSim uses the AGLINK-COSIMO database for all dairy products, sugar, 

sugarcane and sugar beets, and biofuels. The data in PEATSim calibrate 

to USDA Agricultural Projections to 2019 and 2019 AGLINK-COSIMO 

(OECD-FAO, 2010) projections.

We develop a suite of programs in GAMS for accessing, calibrating, and 

performing consistency tests: (1) the OECD AGLINK baseline database, 

and (2) the USDA Baseline with the Linked System’s foreign country 

models in conjunction with the AGLINK databases. This involves reading 

the databases from various formats and platforms (i.e., Microsoft Excel and 

Microsoft Access) into GAMS and, using an Information-Theoretic estimation procedure (cross entropy), we estimate a new set of information (or data 

in a general context) close to the prior (or available data). In other words, 

the objective of this approach, which aims to use all available information, 

is to minimize the entropy between the probabilities that are consistent with 

the information in the data and the priors (see Judge et al., 1985; Golan et 

al., 1996; and Golan, 2002). In PEATSim, we ensure the basic identities of 

supply equal use (material balanced): 

Σ(Production, Imports, Beginning Stocks)= Σ(Consumption, Exports, 

 Beginning Stocks)

and similarly,

Consumption=Σ(of sub-consumption component)=Σ(Food, Feed, Fuel, 

 Crush, Other)

This way, we ensure the base data clear the markets and, hence, the model’s 

price solutions are consistent with market-clearing conditions. We develop an 

approach in GAMS for calibrating the rest of the world as a region along with 

the specific countries and the world, while maintaining the integrity of the U.S. 

baseline, by the use of maximum-entropy econometrics (though without using 

a penalty approach). Maximum entropy econometrics provides a procedure for 

economic and statistical models that may be nonregular in the sense that they 

are ill-posed or underdetermined and the data are partial or incomplete (Golan 

et al., 1996; and Golan, 2002). By using the maximum entropy formalisms 

and techniques used in the physical sciences, we are able to recover information about economic systems such as the USDA Baseline. Since entropy is a 

measure of uncertainty for a single random variable, we use entropy econometrics as a measure of uniformity (Golan and Gzyl, 2003).

Values for elasticities and other parameters in the model are drawn from 

studies; reviews of the literature; other trade models, such as Abler (2001), 

Dyck (1988), Hahn (1996), Hertel et al. (1989), Huang (1993), and Regmi 

(2001); and other models, such as European Simulation Model (ESIM), 

ERS Baseline Projections Model, FAPSIM, and the IMPACT Model – 

International Food Policy Research Institute. In the past, certain models’ 
20

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

elasticities that account/depend on the base data were derived in spreadsheets. At present, we developed a process that integrates the derivation of 

these elasticities in GAMS. This way, the elasticities are revised/updated 

when the model is calibrated to different base years. 

We also are in the process of updating trade policies using the World 

Integrated Trade Solution (WITS), a software developed by the World Bank 

in close collaboration with various international organizations, including 

United Nations Conference on Trade and Development (UNCTAD), 

International Trade Center (ITC), United Nations Statistical Division 

(UNSD), and the World Trade Organization. WITS gives access to major 

international trade, tariff, and nontariff data (http://wits.worldbank.org/wits).
21

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Application

The global biofuels sector is growing rapidly, and the expansion of biofuel 

production is changing agricultural markets worldwide. The revamped 

version of PEATSim includes a biofuels-feedstock module that allows an 

indepth examination of the effects of global biofuels expansion on agricultural production and trade, accounting for links between relevant upstream 

(inputs) and downstream (outputs) industries. Our empirical application 

examines the impact of alternative petroleum prices and macroeconomic 

conditions on the demand for biofuels and their feedstocks on global agricultural markets. 

As different countries use different feedstock sources for the production of 

biofuels, the challenge is to capture and properly model both the demand 

for biofuels and the supply response specific to each country. A “stylized” 

representation of biofuels production would fail to capture the complexity 

and interaction of biofuel/feedstock production. For this reason, it is important that each country’s production of biofuels be explicitly represented in 

the model to consistently account for links between biofuels and feedstock 

needed/used and their interaction with other sectors. This calls for an innovative way to capture the impacts of biofuels expansion from the producer 

level all the way to the global agricultural markets and trade. We focus on 

accessing variability of the simulation under alternative levels of real gross 

domestic product (GDP) and prices of crude oil in the long run.

The expansion of biofuel production and consumption is not limited to the 

United States. For example, over the last several decades, production of 

crop-based biofuels increased in Brazil as it used sugarcane as a feedstock 

to produce ethanol and then used ethanol on a large scale to fuel vehicles. 

The EU has used rapeseed oil to produce biodiesel for fuel use in relatively 

large quantities over the last decade. Government policies are also influencing 

biofuel industries in Canada, Argentina, China, countries of the former Soviet 

Union, India, and Indonesia. A number of developed and developing countries have instituted programs to promote biofuel production and consumption 

and have set targets for increasing the use of biofuels.

Scenarios

We consider alternative scenarios that focus on the variability of ethanol and 

biodiesel production worldwide under various crude petroleum price levels 

and macroeconomic conditions in the long run. In particular, we utilize the 

long-term 30-year projections for the United States from the Information 

Handling Services (IHS) Global Insights as posted on www.ihsglobalinsight.

com. Following Global Insights, we adopt three projections characterized 

by different long-term outlooks: optimistic, pessimistic, and the “middle” 

projection, or baseline. According to Global Insights, under the optimistic 

projection, economic growth proceeds smoothly but more rapidly than under 

the baseline. Under the pessimistic projection, economic growth proceeds 

smoothly but more slowly than under the baseline. The assumptions on the 

long-term optimistic and pessimistic projections form a bandwidth around 

the baseline. For this reason, the baseline’s results are omitted. We adopt the 

same assumptions of economic growth for all countries in the model. 
22

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

In the long term, scarcity of energy supplies and/or sources tends to bid 

energy prices up, while new technologies tend to hold them down. In the end, 

according to Global Insights projections, these two forces are more likely to 

balance out, and real crude oil prices are projected to remain flat over the 

baseline projection, especially over the long-term forecast period. For each of 

the macroeconomic scenarios, we consider three alternative crude petroleum 

prices: low ($70/barrel), medium ($90/barrel), and high ($120/barrel). A 

crude oil price outcome higher than the baseline projection could result from 

stronger demand growth (perhaps notably in China) and/or weaker supply. 

Although crude oil prices and growth tend to move together, a crude oil price 

outcome lower than the baseline projection could result from higher efficiency standards, recession, and/or better supply prospects (http://myinsight.

ihsglobalinsight.com/servlet/cats?filterID=876&serviceID=1784&typeID=4

410&pageContent=report).

The macroeconomic conditions and the price of crude oil are exogenous 

to the model, and the scenario analyses account for demand and supply 

responses for both upstream and downstream sectors/industries and their 

interdependence on the global modeling framework. Given the structure of 

the model, producers and consumers are allowed to respond to these exogenous changes by making adjustments that affect world prices and production 

of each commodity as well as prices and production for each country/region, 

but the impacts vary among sectors and countries/regions. In turn, these price 

and production changes that are generated by links between, for example, 

producers and consumers or between imports and exports depict new longterm solutions. 

We employ the “bootstrap” technique (see Efron and Tibshirani, 1994; Varian, 

1996) in assessing the variability of the scenario results generated by exogenous 

variables in the model. In particular, we draw 5,000 bootstrap samplings of real 

gross domestic product for each macroeconomic projection and 5,000 bootstrap 

samplings of crude oil prices for each alternative crude oil petroleum price 

(high, medium, and low). The model is solved 5 times 5,000 (or 25,000 simulations were performed in all), and estimates of the mean, variability, and confidence intervals of the simulations outcomes are obtained. 

Since the purpose of this report is to illustrate how PEATSim can be used 

for scenario analyses, only selective model results are reported. The source 

of variability also illustrates the purpose, since many other sources of variability, such as yield and exchange rate, are not considered.

Results

Overall, the model simulations show that the price of crude petroleum oil, 

leaving other factors unchanged, has a larger effect on feedstock use for 

biofuel production than do long-term macroeconomic projections of the 

world’s economy (tables 1-6 and figures 2-5). Biofuel production from various 

feedstocks is affected more by alternative crude oil prices than by alternative 

economic conditions. 
23

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Table 1

Global ethanol production (in million metric tons) from various feedstocks, under alternative 

macroeconomic projections and crude oil prices, 2010-49

Optimistic projection Pessimistic projection

Mean Standard 

deviation

Lower

bound

Upper

bound Mean Standard deviation

Lower

bound

Upper

bound

High oil price High oil price

EU27 Corn 2.320 0.201 2.260 2.369 2.275 0.190 2.222 2.326

Wheat 0.681 0.299 0.602 0.751 0.744 0.274 0.676 0.808

Sugar beets 1.802 0.190 1.754 1.852 1.793 0.193 1.747 1.844

China Corn 1.375 0.258 1.307 1.440 1.383 0.247 1.329 1.441

Argentina Sugarcane 0.562 0.118 0.531 0.593 0.531 0.096 0.506 0.555

Brazil Sugarcane 43.470 7.530 41.334 45.720 40.716 5.879 38.976 42.492

U.S. Corn 50.732 3.065 49.783 51.477 49.881 2.977 49.048 50.619

Canada Wheat 0.166 0.070 0.146 0.188 0.184 0.064 0.165 0.200

Corn 0.705 0.044 0.692 0.718 0.693 0.044 0.678 0.705

India Sugarcane 0.237 0.050 0.220 0.252 0.224 0.041 0.212 0.236

Medium oil price Medium oil price

EU27 Corn 1.947 0.132 1.914 1.979 1.906 0.115 1.875 1.933

Wheat 0.685 0.299 0.606 0.764 0.755 0.278 0.682 0.827

Sugar beets 1.563 0.157 1.521 1.601 1.548 0.163 1.509 1.592

China Corn 1.160 0.216 1.096 1.206 1.153 0.216 1.095 1.204

Argentina Sugarcane 0.490 0.102 0.465 0.514 0.460 0.081 0.440 0.480

Brazil Sugarcane 37.553 6.307 35.634 39.488 35.015 4.725 33.554 36.393

U.S. Corn 42.814 1.500 42.407 43.186 41.990 1.364 41.611 42.315

Canada Wheat 0.168 0.070 0.146 0.189 0.185 0.065 0.167 0.206

Corn 0.595 0.025 0.588 0.603 0.582 0.027 0.574 0.591

India Sugarcane 0.198 0.041 0.186 0.210 0.186 0.033 0.176 0.196

Low oil price Low oil price

EU27 Corn 1.057 0.117 1.029 1.091 1.016 0.121 0.988 1.055

Wheat 0.704 0.309 0.626 0.784 0.776 0.286 0.704 0.842

Sugar beets 0.923 0.171 0.882 0.976 0.901 0.183 0.860 0.949

China Corn 0.633 0.188 0.589 0.685 0.615 0.194 0.569 0.671

Argentina Sugarcane 0.294 0.066 0.278 0.311 0.271 0.051 0.259 0.284

Brazil Sugarcane 22.010 3.730 20.923 23.189 20.235 2.682 19.485 21.085

U.S. Corn 23.559 2.772 22.888 24.423 22.760 2.775 22.073 23.578

Canada Wheat 0.172 0.072 0.151 0.191 0.191 0.066 0.170 0.208

Corn 0.328 0.049 0.315 0.347 0.317 0.054 0.302 0.337

India Sugarcane 0.107 0.024 0.100 0.114 0.098 0.018 0.094 0.104
24

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Table 2

Global biodiesel production (in million metric tons) from various feedstocks, under alternative 

macroeconomic projections and crude oil prices, 2010-49

Optimistic projection Pessimistic projection

Mean Standard 

deviation

Lower

bound

Upper

bound Mean Standard deviation

Lower

bound

Upper

bound

High oil price High oil price

EU27 Rapeseed oil 5.611 0.417 5.492 5.717 5.615 0.409 5.493 5.715

Other oil 0.426 0.118 0.395 0.456 0.427 0.119 0.397 0.456

Soybean oil 0.465 0.118 0.437 0.496 0.465 0.118 0.437 0.495

Argentina Soybean oil 1.909 0.200 1.859 1.963 1.909 0.199 1.859 1.959

Brazil Soybean oil 1.027 0.234 0.956 1.098 1.027 0.234 0.967 1.096

U.S. Soybean oil 2.656 0.221 2.588 2.711 2.656 0.223 2.587 2.709

Canada Rapeseed oil 0.055 0.018 0.049 0.060 0.055 0.018 0.049 0.059

India Rapeseed oil 0.146 0.025 0.139 0.155 0.146 0.025 0.139 0.153

Medium oil price Medium oil price

EU27 Rapeseed oil 4.461 0.214 4.399 4.512 4.480 0.201 4.423 4.535

Other oil 0.342 0.095 0.317 0.365 0.357 0.087 0.334 0.379

Soybean oil 0.390 0.108 0.361 0.414 0.415 0.099 0.389 0.443

Argentina Soybean oil 1.515 0.158 1.479 1.559 1.598 0.134 1.562 1.631

Brazil Soybean oil 0.857 0.204 0.794 0.910 0.919 0.188 0.862 0.974

U.S. Soybean oil 2.110 0.111 2.077 2.136 2.113 0.108 2.076 2.141

Canada Rapeseed oil 0.047 0.016 0.042 0.052 0.051 0.015 0.047 0.055

India Rapeseed oil 0.126 0.024 0.119 0.132 0.137 0.018 0.132 0.142

Low oil price Low oil price

EU27 Rapeseed oil 1.746 0.457 1.634 1.901 1.749 0.471 1.635 1.893

Other oil 0.148 0.072 0.129 0.167 0.152 0.072 0.134 0.171

Soybean oil 0.188 0.097 0.163 0.214 0.199 0.094 0.176 0.224

Argentina Soybean oil 0.603 0.208 0.552 0.670 0.632 0.204 0.585 0.693

Brazil Soybean oil 0.402 0.151 0.357 0.451 0.431 0.142 0.393 0.477

U.S. Soybean oil 0.849 0.176 0.806 0.909 0.847 0.176 0.804 0.899

Canada Rapeseed oil 0.024 0.011 0.020 0.027 0.025 0.010 0.023 0.029

India Rapeseed oil 0.064 0.024 0.058 0.071 0.069 0.021 0.063 0.077
25

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Table 3

Global ethanol production (in million metric tons) from various feedstocks, optimistic projection

High oil price Medium oil price Low oil price

Mean Standard 

deviation Mean Standard deviation Mean Standard deviation

2010-19

EU27 Corn 2.319 0.209 1.950 0.128 1.058 0.122

Wheat 0.683 0.300 0.685 0.303 0.705 0.314

Sugar beets 1.805 0.190 1.561 0.157 0.924 0.184

China Corn 1.386 0.261 1.157 0.215 0.634 0.195

Argentina Sugarcane 0.562 0.118 0.493 0.102 0.293 0.065

Brazil Sugarcane 43.528 7.638 37.448 6.338 22.087 3.771

U.S. Corn 50.721 3.328 42.828 1.571 23.594 3.042

Canada Wheat 0.165 0.070 0.168 0.071 0.173 0.073

Corn 0.705 0.045 0.596 0.025 0.328 0.055

India Sugarcane 0.238 0.049 0.198 0.042 0.107 0.024

2020-29

EU27 Corn 2.323 0.206 1.951 0.127 1.058 0.124

Wheat 0.690 0.305 0.689 0.302 0.709 0.308

Sugar beets 1.796 0.191 1.561 0.157 0.928 0.189

China Corn 1.378 0.261 1.162 0.218 0.632 0.190

Argentina Sugarcane 0.561 0.118 0.488 0.101 0.294 0.066

Brazil Sugarcane 43.384 7.586 37.502 6.337 22.040 3.735

U.S. Corn 50.720 3.345 42.813 1.626 23.639 3.180

Canada Wheat 0.166 0.070 0.168 0.071 0.173 0.073

Corn 0.705 0.044 0.595 0.025 0.328 0.055

India Sugarcane 0.237 0.049 0.199 0.042 0.107 0.024

2030-39

EU27 Corn 2.323 0.203 1.949 0.134 1.056 0.123

Wheat 0.673 0.299 0.685 0.302 0.707 0.309

Sugar beets 1.800 0.191 1.563 0.157 0.925 0.188

China Corn 1.375 0.256 1.154 0.214 0.635 0.197

Argentina Sugarcane 0.563 0.119 0.488 0.100 0.293 0.065

Brazil Sugarcane 43.426 7.408 37.502 6.225 22.013 3.710

U.S. Corn 50.734 3.281 42.812 1.612 23.576 3.023

Canada Wheat 0.166 0.070 0.167 0.071 0.174 0.073

Corn 0.704 0.046 0.595 0.025 0.327 0.055

India Sugarcane 0.238 0.049 0.199 0.040 0.107 0.024

2040-49

EU27 Corn 2.319 0.207 1.948 0.131 1.057 0.124

Wheat 0.675 0.300 0.679 0.299 0.706 0.313

Sugar beets 1.804 0.192 1.563 0.157 0.924 0.186

China Corn 1.377 0.257 1.153 0.212 0.629 0.193

Argentina Sugarcane 0.561 0.117 0.490 0.102 0.295 0.065

Brazil Sugarcane 43.225 7.706 37.564 6.331 22.013 3.765

U.S. Corn 50.759 3.225 42.807 1.621 23.554 2.995

Canada Wheat 0.166 0.071 0.169 0.071 0.172 0.073

Corn 0.706 0.045 0.595 0.025 0.327 0.053

India Sugarcane 0.237 0.050 0.197 0.042 0.107 0.024
26

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Table 4

Global biodiesel production (in million metric tons) from various feedstocks, optimistic projection

High oil price Medium oil price Low oil price

Mean Standard 

deviation Mean Standard deviation Mean Standard deviation

2010-19

EU27 Rapeseed oil 5.611 0.425 4.464 0.219 1.747 0.502

Other oil 0.424 0.118 0.344 0.096 0.148 0.076

Soybean oil 0.463 0.117 0.390 0.108 0.188 0.099

Argentina Soybean oil 1.911 0.202 1.516 0.160 0.606 0.229

Brazil Soybean oil 1.028 0.234 0.855 0.203 0.403 0.157

U.S. Soybean oil 2.655 0.238 2.108 0.119 0.847 0.187

Canada Rapeseed oil 0.055 0.019 0.047 0.016 0.024 0.012

India Rapeseed oil 0.146 0.025 0.125 0.024 0.064 0.025

2020-29

EU27 Rapeseed oil 5.611 0.431 4.464 0.212 1.749 0.499

Other oil 0.429 0.119 0.341 0.094 0.146 0.073

Soybean oil 0.468 0.119 0.389 0.108 0.188 0.099

Argentina Soybean oil 1.909 0.203 1.512 0.157 0.597 0.207

Brazil Soybean oil 1.025 0.234 0.859 0.206 0.404 0.158

U.S. Soybean oil 2.658 0.227 2.109 0.116 0.851 0.196

Canada Rapeseed oil 0.055 0.018 0.047 0.016 0.024 0.012

India Rapeseed oil 0.146 0.025 0.126 0.024 0.064 0.025

2030-39

EU27 Rapeseed oil 5.611 0.441 4.459 0.220 1.747 0.499

Other oil 0.427 0.118 0.341 0.094 0.147 0.075

Soybean oil 0.466 0.117 0.387 0.109 0.191 0.102

Argentina Soybean oil 1.908 0.198 1.517 0.160 0.605 0.224

Brazil Soybean oil 1.027 0.234 0.857 0.205 0.400 0.152

U.S. Soybean oil 2.656 0.236 2.111 0.113 0.851 0.195

Canada Rapeseed oil 0.055 0.018 0.047 0.016 0.023 0.011

India Rapeseed oil 0.146 0.025 0.126 0.024 0.064 0.026

2040-49

EU27 Rapeseed oil 5.609 0.437 4.457 0.221 1.738 0.483

Other oil 0.425 0.119 0.342 0.095 0.149 0.076

Soybean oil 0.462 0.118 0.392 0.109 0.187 0.098

Argentina Soybean oil 1.908 0.202 1.514 0.159 0.603 0.221

Brazil Soybean oil 1.028 0.237 0.859 0.203 0.402 0.155

U.S. Soybean oil 2.655 0.238 2.110 0.113 0.849 0.191

Canada Rapeseed oil 0.054 0.018 0.047 0.016 0.023 0.011

India Rapeseed oil 0.145 0.025 0.126 0.024 0.064 0.025
27

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Table 5

Global ethanol production (in million metric tons) from various feedstocks, pessimistic projection 

High oil price Medium oil price Low oil price

Mean Standard 

deviation Mean Standard deviation Mean Standard deviation

2010-19

EU27 Corn 2.274 0.194 1.903 0.119 1.018 0.131

Wheat 0.750 0.277 0.752 0.278 0.773 0.282

Sugar beets 1.790 0.192 1.549 0.162 0.903 0.191

China Corn 1.385 0.251 1.152 0.217 0.614 0.199

Argentina Sugarcane 0.533 0.097 0.462 0.083 0.271 0.051

Brazil Sugarcane 40.715 6.050 34.920 4.766 20.211 2.679

U.S. Corn 49.868 3.208 41.971 1.505 22.792 3.119

Canada Wheat 0.183 0.064 0.186 0.064 0.190 0.067

Corn 0.692 0.044 0.582 0.027 0.315 0.057

India Sugarcane 0.224 0.042 0.187 0.034 0.099 0.018

2020-29

EU27 Corn 2.277 0.196 1.905 0.120 1.022 0.139

Wheat 0.749 0.274 0.752 0.275 0.774 0.286

Sugar beets 1.790 0.192 1.548 0.164 0.903 0.199

China Corn 1.377 0.245 1.145 0.216 0.617 0.205

Argentina Sugarcane 0.533 0.097 0.461 0.082 0.272 0.051

Brazil Sugarcane 40.655 6.046 35.037 4.779 20.255 2.707

U.S. Corn 49.879 3.123 41.993 1.438 22.794 3.146

Canada Wheat 0.183 0.063 0.184 0.064 0.190 0.066

Corn 0.693 0.044 0.582 0.027 0.317 0.059

India Sugarcane 0.224 0.041 0.187 0.033 0.098 0.018

2030-39

EU27 Corn 2.276 0.194 1.905 0.121 1.020 0.136

Wheat 0.746 0.277 0.758 0.281 0.776 0.289

Sugar beets 1.797 0.194 1.545 0.162 0.899 0.188

China Corn 1.379 0.247 1.151 0.216 0.609 0.192

Argentina Sugarcane 0.532 0.097 0.462 0.082 0.270 0.050

Brazil Sugarcane 40.582 5.924 34.918 4.749 20.265 2.674

U.S. Corn 49.925 3.089 41.972 1.483 22.769 3.118

Canada Wheat 0.182 0.063 0.185 0.066 0.190 0.066

Corn 0.693 0.045 0.582 0.027 0.316 0.059

India Sugarcane 0.223 0.041 0.186 0.034 0.099 0.019

2040-49

EU27 Corn 2.277 0.200 1.906 0.118 1.017 0.127

Wheat 0.742 0.276 0.750 0.279 0.775 0.283

Sugar beets 1.790 0.191 1.544 0.164 0.902 0.192

China Corn 1.387 0.248 1.154 0.219 0.612 0.196

Argentina Sugarcane 0.532 0.097 0.458 0.081 0.273 0.052

Brazil Sugarcane 40.748 5.932 35.062 4.734 20.237 2.682

U.S. Corn 49.957 3.031 42.007 1.410 22.796 3.123

Canada Wheat 0.184 0.064 0.184 0.064 0.191 0.067

Corn 0.692 0.045 0.582 0.027 0.316 0.059

India Sugarcane 0.224 0.040 0.186 0.033 0.099 0.018
28

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Table 6

Global biodiesel production (in million metric tons) from various feedstocks, pessimistic projection

High oil price Medium oil price Low oil price

Mean Standard 

deviation Mean Standard deviation Mean Standard deviation

2010-19

EU27 Rapeseed oil 5.606 0.435 4.483 0.207 1.735 0.484

Other oil 0.427 0.119 0.357 0.087 0.150 0.071

Soybean oil 0.464 0.118 0.415 0.099 0.200 0.097

Argentina Soybean oil 1.905 0.198 1.597 0.134 0.637 0.222

Brazil Soybean oil 1.026 0.235 0.919 0.188 0.434 0.156

U.S. Soybean oil 2.663 0.221 2.111 0.119 0.848 0.191

Canada Rapeseed oil 0.055 0.018 0.051 0.015 0.025 0.011

India Rapeseed oil 0.146 0.025 0.137 0.018 0.070 0.023

2020-29

EU27 Rapeseed oil 5.609 0.429 4.483 0.207 1.739 0.490

Other oil 0.426 0.118 0.355 0.086 0.151 0.071

Soybean oil 0.465 0.118 0.414 0.098 0.200 0.096

Argentina Soybean oil 1.911 0.202 1.597 0.134 0.637 0.222

Brazil Soybean oil 1.034 0.239 0.915 0.187 0.430 0.150

U.S. Soybean oil 2.657 0.233 2.111 0.118 0.852 0.200

Canada Rapeseed oil 0.055 0.019 0.051 0.015 0.025 0.011

India Rapeseed oil 0.146 0.025 0.137 0.018 0.069 0.023

2030-39

EU27 Rapeseed oil 5.615 0.431 4.479 0.207 1.760 0.536

Other oil 0.427 0.118 0.357 0.087 0.152 0.074

Soybean oil 0.465 0.118 0.417 0.099 0.200 0.097

Argentina Soybean oil 1.912 0.204 1.595 0.134 0.633 0.217

Brazil Soybean oil 1.028 0.236 0.917 0.186 0.431 0.149

U.S. Soybean oil 2.658 0.233 2.111 0.121 0.846 0.189

Canada Rapeseed oil 0.055 0.018 0.051 0.015 0.026 0.011

India Rapeseed oil 0.146 0.025 0.137 0.018 0.069 0.023

2040-49

EU27 Rapeseed oil 5.619 0.426 4.486 0.201 1.745 0.500

Other oil 0.425 0.117 0.357 0.087 0.152 0.075

Soybean oil 0.464 0.118 0.415 0.100 0.198 0.093

Argentina Soybean oil 1.907 0.201 1.598 0.134 0.636 0.221

Brazil Soybean oil 1.029 0.234 0.916 0.188 0.430 0.149

U.S. Soybean oil 2.654 0.237 2.115 0.113 0.845 0.187

Canada Rapeseed oil 0.055 0.018 0.051 0.015 0.026 0.011

India Rapeseed oil 0.146 0.025 0.137 0.018 0.069 0.023
29

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

The Global Perspective: Alternative Macroeconomic 

Conditions Versus Crude Oil Prices 

Under alternative prices of crude oil, the demand for feedstock for the 

production of biofuels varies considerably. Figures 2 through 5 and tables 1 

and 2 capture the demand/consumption of feedstock (mean, variance, and 

confidence intervals) for the production of ethanol and biodiesel under high, 

medium, and low crude oil prices and alternative long-term macroeconomic 

projections at the global level (comparing left and right panels).

The long-term macroeconomic conditions under alternative economic growth 

perspectives have a rather small impact on the demand of feedstock used for 

the production of ethanol, both at the mean and variance (figs. 2 and 3 and 

table 1). Unlike the effect of economic growth projections (i.e., optimistic 

vs. pessimistic), the level of the crude oil price significantly affected demand 

(both the mean and variance) for the relevant feedstocks in the production 

of ethanol. Interestingly, the effect of crude oil prices on feedstock demand 

is not symmetric. In this sense, the mean values of feedstock demand under 

high and medium crude oil prices are not quite the same as feedstock demand 

under low crude oil prices. On the other hand, the variability measured by the 

standard deviation of the feedstock demand in the case of medium and low 

crude oil prices is much smaller than in the case of the higher crude oil prices 

(fig. 3 and table 1). 

At the mean, the feedstock demand/consumption for biodiesel production 

is much smaller than the demand of feedstock for the production of ethanol 

worldwide (figs. 4 and 5, table 2). Again, the impact of long-term macroeconomic projections, such as optimistic vs. pessimistic, on global demand for 

feedstock for biodiesel production is small compared with the impact of crude 

oil prices. The variability measured by the standard deviation of the demand 

for feedstock is larger for the case of high crude oil prices and almost the 

same for the medium and low crude oil prices. Under the pessimistic outlook 

projection, the variability of global demand of feedstock is smaller than under 

the optimistic outlook projection (fig. 5 and table 2). The 90-percent confidence interval of the mean measured by the lower and upper bound indicates 

the probability that the confidence interval contains the true population mean.

In sum, crude oil prices have a larger effect on the demand for feedstock for 

ethanol and biodiesel production than macroeconomic growth projections. 

At the global level, both the mean and variance are affected considerably by 

the level of crude oil, but the effect is asymmetric. The variability depends 

on feedstock demand and is different for the demand/consumption of feedstock for ethanol than for biodiesel. Note that we do not conduct any formal 

testing on the causal relationship of crude oil prices and the first and second 

moments (mean and variance) of the distribution of the feedstock productions. Such an effort is beyond of the scope of this report. 

The Country Perspective: Diverge Variability of Production 

of Feedstock for Ethanol 

A variety of feedstock is used for the production of ethanol worldwide. 

Tables 3 and 4 present the model results (mean and standard deviation) of 

feedstock demand for the production of ethanol by country under alternative 
30

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Figure 2

Global ethanol production (mean) under alternative crude oil prices and macroeconomic projections 

2010 15 20 25 30 35 40 45

97.5

98.0

98.5

99.0

99.5

100.0

100.5

101.0

2010 15 20 25 30 35 40 45

86.2

86.4

86.6

86.8

87.0

87.2

87.4

87.6

2010 15 20 25 30 35 40 45

49.0

49.2

49.4

49.6

49.8

50.0

50.2

50.4

High crude oil price, pessimistic projection

Mil. metric tons

Medium crude oil price, pessimistic projection

Mil. metric tons

Low crude oil price, pessimistic projection

Mil. metric tons

High crude oil price, optimistic projection

Mil. metric tons

Medium crude oil price, optimistic projection

Mil. metric tons

Low crude oil price, optimistic projection

Mil. metric tons

2010 15 20 25 30 35 40 45

97.2

97.4

97.6

97.8

98.0

98.2

98.4

98.6

98.8

99.0

99.2

99.4

2010 15 20 25 30 35 40 45

82.6

82.8

83.0

83.2

83.4

83.6

83.8

84.0

84.2

84.4

2010 15 20 25 30 35 40 45

46.4

46.6

46.8

47.0

47.2

47.4

47.6

47.8
31

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Figure 3

Global ethanol production variability (standard deviation) under 

alternative crude oil prices and macroeconomic projections 

High crude oil price, standard deviation

Mil. metric tons

Medium crude oil price, standard deviation

Mil. metric tons

Low crude oil price, standard deviation

Mil. metric tons

2010 15 20 25 30 35 40 45

0.70

0.90

1.10

1.30

1.50

Optimistic projection

Pessimistic projection

2010 15 20 25 30 35 40 45

0.50

0.70

0.90

1.10

2010 15 20 25 30 35 40 45

0.50

0.60

0.70

0.80

0.90

Optimistic projection

Pessimistic projection

Optimistic projection

Pessimistic projection
32

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Figure 4

Global biodiesel production (mean) under alternative crude oil prices and macroeconomic projections 

High crude oil price, pessimistic projection

Mil. metric tons

Medium crude oil price, pessimistic projection

Mil. metric tons

Low crude oil price, pessimistic projection

Mil. metric tons

High crude oil price, optimistic projection

Mil. metric tons

Medium crude oil price, optimistic projection

Mil. metric tons

Low crude oil price, optimistic projection

Mil. metric tons

2010 15 20 25 30 35 40 45

12.22

12.24

12.26

12.28

12.30

12.32

12.34

12.36

12.38

2010 15 20 25 30 35 40 45

9.74

9.76

9.78

9.80

9.82

9.84

9.86

9.88

9.90

9.92

2010 15 20 25 30 35 40 45

3.90

3.92

3.94

3.96

3.98

4.00

4.02

4.04

4.06

4.08

2010 15 20 25 30 35 40 45

12.18

12.20

12.22

12.24

12.26

12.28

12.30

12.32

12.34

12.36

2010 15 20 25 30 35 40 45

9.98

10.00

10.02

10.04

10.06

10.08

10.10

10.12

10.14

2010 15 20 25 30 35 40 45

4.00

4.02

4.04

4.06

4.08

4.10

4.12

4.14

4.16
33

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Figure 5

Global biodiesel production variability (standard deviation) under 

alternative crude oil prices and macroeconomic projections 

High crude oil price, standard deviation

Mil. metric tons

Medium crude oil price, standard deviation

Mil. metric tons

Low crude oil price, standard deviation

Mil. metric tons

Optimistic projection

Pessimistic projection

Optimistic projection

Pessimistic projection

2010 15 20 25 30 35 40 45

0.150

0.155

0.160

0.165

0.170

0.175

0.180

0.185

0.190

2010 15 20 25 30 35 40 45

0.090

0.095

0.100

0.105

0.110

0.115

0.120

0.125

2010 15 20 25 30 35 40 45

0.130

0.135

0.140

0.145

0.150

0.155

0.160

0.165

0.170

0.175

Optimistic projection

Pessimistic projection
34

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

macroeconomic conditions and crude oil prices. Again, the results clearly 

indicate that at the country level, the price of crude oil has a much larger 

effect on feedstock demand/production, both at the mean and standard deviation, than the long-term macroeconomic projections/conditions. Furthermore, 

the price of crude oil affects the demand for feedstock for ethanol asymmetrically while the variability of feedstock in the production of ethanol depends 

considerably on the type of the feedstock. 

For example, under the high crude oil price scenario, Brazil’s sugarcane 

feedstock demand (at the mean) is 15 percentage points higher than under the 

medium crude oil price (scenario). The demand/production of feedstock (at 

the mean) for ethanol in all countries in the model exhibits the same pattern 

as that in Brazil (tables 3 and 4). In other words, the higher the crude oil 

price, the larger the demand/production of feedstock for ethanol. 

Under the low crude oil price scenario, Brazil’s sugarcane feedstock demand (at 

the mean) is about 40 percentage points lower than under medium prices during 

the period under study (2010-49) (tables 3 and 4). The model results indicate 

that under the low vs. medium crude oil price scenario, the demand/production of sugarcane (India and Argentina), sugar beets (EU), and corn (United 

States, Canada, and the EU) follow the same pattern as that of Brazil over the 

long-term 40-year projections. However, under the low crude oil price level, 

the feedstock demand/production for ethanol from corn in China and wheat 

from Canada and the EU is only 11 percentage points different than that under 

medium price level (tables 3 and 4). Furthermore, the production/demand for 

feedstock (at the mean) for ethanol follows the similar pattern under the alternative long-term scenarios (optimistic vs. pessimistic projection).

In conducting the scenarios, we treat all commodities and/or countries similarly under the same specifications of the long-term projections (www.ihsglobalinsight.com). Note that by only employing the bootstrapping technique, 

we are able to access the variability of the simulation results and derive estimates of the underlying statistics (mean, standard deviation, and confidence 

intervals) as the outcomes of simulated scenarios completely lack any statistical property. Since the bootstrapping procedure is distribution independent, 

it provides us with an indirect method to assess the distributional properties of the underlying outcomes/sample. Using the bootstrapping technique 

along with simulation matters as the outcomes are associated with stochastic 

properties that also matter. A Monte-Carlo type of stochastic simulation that 

accounts for cross-commodity correlations would greatly enhance the procedure. However, such a simulation is beyond the scope of this report.

The variability of feedstock production depends on the kind of feedstock used 

for the production of ethanol. Under the optimistic projection, Brazil’s sugarcane variability (standard deviation) is higher under high crude oil prices than 

under medium or low crude prices. In this sense, it is almost 20 percentage 

points higher when under high vs. medium prices and 40 percentage points 

lower under low vs. medium crude oil prices. U.S. corn, EU sugar beets, and 

China corn feedstock demand/production variability (standard deviation) is 

much larger under high and low crude oil prices than under medium crude oil 

prices. The use of bootstrapping indicates that if there are policies in place in a 

certain country that are targeting certain levels of production of ethanol, which 
35

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

is associated with certain levels of feedstock production, the level and the variability of the relevant feedstock must be considered. 

Under the pessimistic projection and for all levels of crude oil prices, variability follows the same pattern as that of the optimistic projection but at a 

smaller magnitude (tables 3 and 4). 

The Country Perspective: Diverge Variability of Production 

of Feedstock for Biodiesel 

Overall feedstock demand/production for biodiesel is much smaller than 

feedstock demand/production for ethanol. The simulation results again indicate that crude oil prices have a much larger asymmetric effect on feedstock 

demand (mean and standard deviation) for the production of biodiesel than do 

the long-term macroeconomic projections/conditions. 

The EU is the largest biodiesel producer followed by the United States, 

Argentina, and Brazil. While the EU uses a variety of feedstocks for the 

production of biodiesel, the United States, Argentina, and Brazil use soybean 

oil (tables 5 and 6). In the case of the EU, rapeseed oil feedstock demand 

(at the mean) is 25 percentage points higher than under medium crude oil 

prices (high vs. medium crude oil price) and declines by 60 percentage 

points under low crude oil prices (low versus medium crude oil price). For 

the United States, the price of crude oil affects the demand for soybean oil 

for the production of biodiesel (at the mean) considerably, but its fluctuation increases when crude oil prices decline. The same is observed with 

Argentina’s and Brazil’s soybean production and India’s rapeseed production 

for biodiesel (tables 5 and 6).
36

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Conclusion

This report documents the latest version of the PEATSim model and illustrates global biofuel production/demand under various crude oil prices and 

economic growth (macroeconomic conditions) scenarios. 

PEATSim is a partial equilibrium, multiple-commodity, multiple-region 

dynamic model of agricultural policy and trade for policy analysis and 

reforms on a multilateral and bilateral basis.

Policy specification is treated on a policy-by-policy basis rather than 

being aggregated and introduced as price “wedges,” as is done in several 

Computable General Equilibrium models.

The partial equilibrium approach allows the use of commodity-specific elasticity specifications. These features can reflect own- and cross-price elasticities much better than could ever be achieved in a general equilibrium model 

that has far less flexibility in the assignment of parameters that determine the 

production/consumption response of each particular commodity. The specification of PEATSim is consistent with economic theory due to the imposition 

of symmetry and homogeneity conditions on elasticity assignments in the 

model wherever appropriate.

The report also examines an application of the model to illustrate its 

dynamic structure and to demonstrate the differential behavior of global 

commodity markets. In particular, the application examines the impact of 

macroeconomic conditions and crude oil prices on the feedstock demand for 

ethanol and biodiesel. Based on a comparison of the outcomes of alternative scenarios, the application finds that unlike macroeconomic conditions, 

crude oil prices have a profound effect on feedstock demand for ethanol and 

biodiesel production. At the global level, both the mean and variance are 

affected considerably by the level of crude oil prices, but the effect is asymmetric. Overall, the scenario simulations show that the effects on feedstock 

demand/production for biodiesel are much smaller than those on demand/

production of feedstock for ethanol.
37

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

References

Abler, D., D. Blandford, M. Bohman, P. Dixit, and J. Stout. “Development of 

and Initial Results from the ERS/Penn State WTO Model,” International 

Agricultural Trade Research Consortium Meeting, Washington, DC, May 

18-20, 2001, Supported by Cooperative Agreement No. 43-3AEK-8-80117 

between USDA, Economic Research Service and Penn State University.

Blayney, D., M. Gehlhar, C. Bolling, K. Jones, S. Langley, M.A. Normile, 

and A. Somwaru. U.S. Dairy at Global Crossroads, Economic Research 

Report No. 28, U.S. Department of Agriculture, Economic Research 

Service, November 2006, www.ers.usda.gov/publications/err28/

Brooke, A., D. Kendrick, and A. Meeraus. GAMS-General Algebraic 

Modeling System, A User’s Guide, The Scientific Press, 1988.

Dirkse, S. Robust Solution of Mixed Complementarity Problems, A Thesis 

Submitted in Partial Fulfillment of the Requirements for the Degree 

of Doctor of Philosophy, Computer Sciences, University of Wisconsin, 

Madison, 1994.

Dirkse, S., and M. Ferris. “The PATH Solver: A Non-Monotone Stabilization 

Scheme for Mixed Complementarity Problems,” Optimization Methods 

and Software, 1994. 

Dirkse, S., M. Ferris, P. Preckel, and T. Rutherford. “The GAMS Callable 

Program Library for Variational and Complementarity Solvers,” Working 

Paper, Computer Science Department, University of Wisconsin, 1994.

Dyck, J., M. Gehlhar, B. Meade, A. Regmi, R. Seeley, A. Somwaru, and R. 

Stillman. “ERS Tariff Line Model, PEATSim, GTAP: Complementary 

Tools for US-Korea Trade Analysis,” International Agricultural Trade 

Research Consortium (IATRC), Summer Symposium Meeting, Seoul, 

Korea, June 30-July 1, 2008.

Dyck, J. Demand for Meats in Japan: A Review and an Update of Elasticity 

Estimates, U.S. Department of Agriculture, Economic Research Service, 

Staff Report No. AGES 880525, 1988.

Efron, B., and Tibshirani, R.J. An Introduction to the Bootstrap, Boca Raton, 

FL: CRC Press, 1994.

Food and Agricultural Policy Research Institute (FAPRI). FAPRI U.S. and 

World Agricultural Outlook, Iowa State University and the University of 

Missouri, Columbia, 2010.

Gadson, K., J.M. Price, and L. Salathe. Food and Agricultural Policy 

Simulator (FAPSIM): Structural Equations and Variable Definitions, 

Staff Report No. AGES 820506, May 1982.

Golan, A. “Information and Entropy Econometrics—Editor’s View,” Journal 

of Econometrics, 107, 2002: 1-15.
38

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Golan, A., and H. Gzyl, “Priors and Information-Theoretic Estimation,” 

American Statistical Association Proceedings, 2003.

Golan, A., G. Judge, and D. Miller. Maximum Entropy Econometrics, Robust 

Estimation With Limited Data, San Francisco: John Wiley & Sons, 1996.

Hahn, W.F. An Annotated Bibliography of Recent Elasticity and Flexibility 

Estimates for Meat and Livestock, U.S. Department of Agriculture, 

Economic Research Service, Staff Report No. AGES 9611, 1996.

Hamilton, J. Time Series Analysis. Princeton, NJ: Princeton University Press, 

1994.

Hertel, T.W., V.E. Ball, K.S. Huang, and M.E. Tsigas. Computing General 

Equilibrium Farm Level Demand Elasticities for Agricultural 

Commodities, AES Research Bulletin No. 988, Purdue University, 1989.

Huang, K.S. U.S. Demand for Food: A Complete System of Quantity Effects 

on Prices, U.S. Department of Agriculture, Economic Research Service, 

Technical Bulletin No. 1795, 1993.

Judge, G.G., R.C. Hill, W.E. Griffiths, H. Lütkepohl, and T.C. Lee. The 

Theory and Practice of Econometrics, San Francisco: John Wiley & Sons, 

1985.

Langley, S., D. Blayney, J. Stout, A. Somwaru, M.A. Normile, J. Miller, 

and R. Stillman. “Trade Liberalization in International Dairy Markets,” 

American Agricultural Economics Association Meeting, Montreal, July 

27-30, 2003.

Langley, S., A. Somwaru, M.A. Normile. “A Trade Liberalization in 

International Dairy Markets,” International Agricultural Trade Research 

Consortium, June 19-21, Seville, Spain, 2005.

Langley, S., A. Somwaru, and M.A. Normile. Trade Liberalization in 

International Dairy Markets, Economic Research Report No. 16, U.S. 

Department of Agriculture, Economic Research Service, 2006, www.ers.

usda.gov/publications/err16/

Meade, B., C. Arriola, and A. Somwaru. “Argentina’s Biofuel Production and 

Trade Impacts,” AEDA Congress, Buenos Aires, Asociación de Economía 

para el Desarrollo de la Argentina (AEDA), September 20-21, 2010.

Meilke, K. “A Proposed Framework for an International Multicommodity 

Trade Model,” Working Paper, Department of Agricultural Economics 

and Business, University of Guelph, January 1999.

Morath, T., and I. Sheldon. “The Economics of Modeling Tariff-Rate 

Quotas,” Economic Research Service and Ohio State University, Working 

Paper, February 1999.

Moschini, G. “Specification of the Demand Structure of National Models and 

Welfare Calculations,” Working Paper, Iowa State University, 1999.
39

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Organisation for Economic Co-Operation Development and the Food 

and Agriculture Organization of the United Nations (OECD-FAO), 

Agricultural Outlook 2010-2019, June 2010.

Peters, M., A. Somwaru, R. Stillman, J. Hansen, D. Kelch, and R. Seeley. 

“Modeling Biofuels: Global Production and Trade Implications,” 

International Agricultural Trade Research Consortium (IATRC) Annual 

General Meeting Scottsdale, AZ, December 7-9, 2008.

Peters, M., A. Somwaru, J. Hansen, R. Seeley, and S. Dirkse. “Modeling 

Biofuels Expansion in a Changing Global Environment,” International 

Association of Agricultural Economics Conference, Beijing, China, 

August 16-22, 2009.

Peters, M., R. Stillman, and A. Somwaru. “Bio-Fuels Expansion in a 

Changing Economic Environment: A Global Modeling Perspective,” 

in Ball, E.V., Fanfani, R., Gutierrez, L. (eds.), The Economic Impact of 

Public Support to Agriculture, New York: Springer, 2010.

Regmi, A. (ed). Changing Structure of Global Food Consumption and 

Trade, Agriculture and Trade Report No. WRS No. 01-1, U.S. Department 

of Agriculture, Economic Research Service, 2001, www.ers.usda.gov/

publications/wrs011/

Shane, M., W. Liefert, M. Morehart, M. Peters, J. Dillard, D. Torgerson, 

and W. Edmondson. The 2008/2009 World Economic Crisis—What It 

Means for U.S. Agriculture, E-Outlook No. WRS-09-02, U.S. Department 

of Agriculture, Economic Research Service, 2009, www.ers.usda.gov/

publications/wrs0902/

Stillman, R., S. Langley, A. Somwaru, and M.A. Normile. “PEATSim: 

Analyzing the Dairy Market,” International Agricultural Trade Research 

Consortium (IATRC), San Diego, CA, December 5, 2005.

Stillman, R., J. Hansen, R. Seeley, D. Kelch, A. Somwaru, and E. Young. 

“Analyzing the Impacts of Biofuel Mandates on World-Wide Grain, 

Livestock, and Oilseed Sectors,” Domestic and Trade Impacts of U.S. 

Farm Policy: Future Directions and Challenges, Washington, DC, 

November 15-16, 2007.

Stillman, R., A. Somwaru, M. Peters, E. Young, and S. Dirkse. “Bio-Fuels: 

Impact on the World Grain, Livestock, and Oilseed Sectors,” American 

Agricultural Economics Association Annual Meeting, Orlando, FL, July 

27-29, 2008a.

Stillman, R., A. Somwaru, M. Peters, E. Young, and S. Dirkse. “Biofuels and 

Trade: World Agricultural Market Impacts,” GTAP Conference, Helsinki, 

Finland, June 12-14, 2008b.

Stout, J., and D. Abler. ERS/Penn State Trade Model Documentation, August 

2003, Updated Version, October 2004.
40

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

U.S. Department of Agriculture, Office of the Chief Economist, World 

Agricultural Outlook Board. USDA Agricultural Projections to 2019, 

Long-Term Projections Report OCE-2011-1, February 2010.

Valdes, C., C. Arriola, A. Somwaru, and J. Gasques. “Brazil’s Climate 

Adaptation Policies: Impacts on Agriculture,” International Agricultural 

Trade Research Consortium, Stuttgart, Germany, June 27-29, 2010.

Varian, H. Computational Economics and Finance: Modeling and Analysis 

with Mathematica, New York: Springer-Verlag, May 1996.

Westhoff, P., R. Baur, D. Stephens, and W. Meyers. FAPRI U.S. Crops Model 

Documentation, Technical Report 90-TR17, Center for Agricultural and 

Rural Development, Iowa State University, 1990.

Zahniser, S., C. Arriola, and A. Somwaru. “The European Union’s 

Framework for Climate Change Adaptation: Implications of Agriculture’s 

Adaptation through Sustained Yield Growth,” International Agricultural 

Trade Research Consortium, Stuttgart, Germany, June 27-29, 2010.
41

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933 

Economic Research Service/USDA

Appendix: Mixed Complementarity Problem

Complementarity problems are used extensively in economics because the 

concept of complementarity is intimately linked with the notion of system 

equilibrium. The balance of supply and demand in economics is often 

described by a complementary relationship between price and excess supply. 

In this case, the complementarity condition requires that the excess supply 

of a commodity must be zero if its price is positive, and the price of the 

commodity must be zero if there is positive excess supply. 

Nonlinear complementarity problems, NCP( F ), seek to find an x ∈ Rn

given a nonlinear function defined as F: Rn → Rn, such that 

NCP( F ): 0 ≤ x ⊥ F ( x ) ≥ 0

where the perpendicular notation “⊥” indicates that in addition to the above 

inequalities, the equation xTF (x) = 0 also holds. This equation can be stated as:

0 ≤ x, F ( x ) ≥ 0, xi

Fi( x ) =0, i =1,2,...,n

In other words, complementarity implies that for each variable, either the 

variable or its complement (i.e., either xi or Fi

 ( x )) must be zero for each 

i =1,2,...,n.

Complementarity problems of this form are associated with the KarushKuhn-Tucker conditions of a constrained nonlinear program as follows:

minimize θ( x )

subject to g( x ) ≤ 0, x ≥ 0

where θ: Rn → R is a continuously differentiable real-valued function and 

g: Rn → Rm is a continuously differentiable vector-valued function.

The NCP( F ) can be generalized by the introduction of (possibly infinite) 

lower and upper bounds on the variable x. This results in the MCP( F,L,U )

defined as follows: 

given F: Rn → Rn and bounds L,U where , and n n L U ∈R − ∞ ∈R + ∞  

find: 

x ∈ [L,U]

s.t. ∀ i, one of the following conditions holds:

 i) Fi

( x ) =0

 ii) Fi

( x ) >0 and xi = Li

 iii) Fi( x ) <0 and xi = Ui.

The NCP( F ) is a special case of MCP( F,L,U ) obtained by setting L = 0

and U = −∞. 
42

Dynamic PEATSIM Model: Documenting Its Use in Analyzing Global Commodity Markets / TB-1933

Economic Research Service/USDA

Another special case occurs if we set L = −∞ and U = +∞; then alternatives 

(ii) and (iii) above are impossible and we have Fi

( x ) = 0 (i.e., a smooth 

system of nonlinear equations). This concept is applied to discontinuous 

functions in PEATSim, such as production quotas, tariff-rate quotas, and 

discontinuous demand issues created by mandates or targets.