USDA’s Economic Research Service (ERS) annually estimates agricultural trade multipliers (ATMs) for U.S. agricultural exports for the most recent calendar year for which data are available. Multiplier analysis helps to quantify the entire impact of a given economic activity (e.g., exporting) on economic sectors, industries, and households. For example, an ATM encapsulates the relative values of farmers' purchases of fertilizer and tractor parts from manufacturers—and the value of farm products sold to food processing plants, feed mills, or other nonfarm businesses. ATMs also include the producing sectors' payments of wages, salaries, and other incomes that accrue to U.S. households, as a result of agricultural trade. The ATMs for 2018-19 are the result of a cooperative research agreement between ERS and Inforum at the University of Maryland. Inforum’s director of research Douglas Meade and his assistants Troy Wittek and Trinity Wade participated in this project via that agreement and estimated its multipliers. Inforum (Interindustry Economic Research Fund, Inc, or IERF) is a nonprofit corporation affiliated with the University of Maryland that is dedicated to improving business planning, government policy analysis, and the general understanding of the economic environment.


The open model of economic activity in this data product measures the direct and indirect effects of an economic activity (exports); that is, the impacts of sales and purchases between all goods and service sectors of the economy, sales to final demand (consumption, investment, government, and net exports), and purchases of land, labor, and capital services. Open-model multipliers are best suited to describe what has already happened in an economy or the interrelatedness of sectors in a base period.

  • Trade Multipliers-Open Model: For agricultural exports in the calendar year, ERS estimates 1) the national employment per $1 billion of agricultural exports of a commodity or from an industry and 2) the total economy wide output per $1 of commodity or sector exports at the producer and port stage of export. Last updated: May 2021.
  • Benchmark Input/Output Trade Margins: Trade margins reflect the value of transportation and wholesale-and-retail trade services provided in delivering commodities from producers to purchasers. The margins are used in the ERS estimates for port-value multipliers. Last updated: May 2021.

Understanding Open Multipliers

To understand the working of the multiplier process, it is useful to keep the different components of a multiplier separate. Open-model multipliers reflect the value of the exported commodity or product to the originating sector (direct effects), plus the value of the activity in supporting sectors (indirect effects)—such as inputs, processing, distribution, and other services. Multipliers are measured either at the producer level (which includes just the activity embodied in the commodity as it leaves the farm gate or manufacturer's door) or at the port level (which includes shipping, handling, and storage charges—in addition to the farm or manufacturing sector's value). Using corn (and 2019 export data) as an example, the producer open- model output multiplier for corn is 2.254.

This multiplier analysis assumes that the only limit on the output of an economy is a lack of markets for its production. I/O models assume that as new demands emerge, such as increased exports, new production to meet these new demands draws upon idle resources (labor, land, and production capacity). These assumptions oversimplify how an economy operates. But simplification is the nature of most economic models, which use simplifying assumptions to distill basic relationships.


Multiplier analysis is an effective method of estimating the economic impact of an economic change or shock. Economists use input-output (I/O) analysis to calculate trade multipliers. Multipliers reflect the impacts of trade in farm and food products, in terms of employment and/or output. The benchmark I/O tables (used by economists to generate trade multipliers) are published by the U.S. Department of Commerce (USDOC), Bureau of Economic Analysis (BEA). These tables show the production of goods and services, and the transaction flows of goods and services, between different producing sectors of the economy and to different components of final use for a specific year (“benchmark year”). I/O analysis uses the information contained in the accounting tables for a benchmark year to provide a snapshot of the interrelationships between the sectors of an economy. The BEA typically publishes its benchmark-year accounting tables every 5 years. The most recent national-level benchmark I/O table was constructed for calendar year 2012.

Definition of Agricultural Trade

Since the late 1970s, ERS has analyzed the economy-wide impacts of agricultural trade, using a consistent grouping of commodities designated as agricultural by USDA. Originally, this definition was drawn from a Congressional directive. However, in January 2021, USDA switched to the World Trade Organization’s (WTO) definition of agricultural products, which contains a broader set of products than USDA’s previous definition. This new definition extends to fuel ethanol, alcoholic beverages in addition to beer and wine, and tobacco manufactures, among others. ERS’s ATM model relies on the WTO definition, for the first time, in the results presented in the 2019 Data Overview. The model also treats biodiesel as agricultural in order to provide more comprehensive insights into the output and employment supported by biofuel exports. USDA's Foreign Agricultural Service (FAS) and ERS are jointly responsible for defining and maintaining U.S. agricultural trade data, which are available to the public via FAS’s Global Agricultural Trade Database (GATS). (For more information, see Foreign Agricultural Trade of the United States (FATUS): Questions and Answers and the U.S. Agricultural Trade Topic on the ERS website.)

ERS’s ATM model consists of several thousand different 10-digit codes listed in the U.S. Harmonized System (HS) that correspond to agricultural products (as defined by the WTO). The codes are matched with the appropriate I/O sectors for analysis. The resulting vector of agricultural exports (i.e., final demand) differs from the definition of agriculture used in the North American Industrial Classification System (NAICS). NAICS only classifies crop and animal production as agricultural, while the various intermediate and consumer-oriented products obtained from crops and animals are treated as manufactures. In contrast, the WTO definition of agricultural products (and the previous USDA definition before it) generally treats crops, animals—and the manufactures produced using crops and animals—as agricultural. Consequently, the employment and output multipliers—and other results reported here—do not necessarily match with other analysis that is based on the NAICS definition of agriculture.

l/O Model Assumptions and Caveats

ERS estimates agricultural trade multipliers using an open I/O model. Analysts assume that 1) the set of industry interrelationships embedded in an input-output benchmark table does not change dramatically over time, 2) the relationships quantified in the 2012 national I/O table adequately describe the current economy, and 3) these relationships do not vary as production rises or falls.

l/O models further assume the only limit on the output of an economy is a lack of markets for its production. That is, as new demands emerge, such as increased exports, an unlimited supply of goods will meet them. The models do not consider capacity, feasibility, or profitability. In practical terms, as the economy expands due to exports, one would expect prices to change. However, I/O-based models do not consider price changes in their equations. These price changes must be addressed exogenously—i.e., outside the model itself—usually by indexing the results.

The employment multipliers estimated by ERS are value-based (i.e., number of jobs per billion dollars). Value-based employment multipliers change as each commodity price changes and as U.S. labor productivity changes. Employment multipliers should also consider the value of, and adjust for, changes in the value of the transportation margin and the wholesale-and-retail trade margin associated with the export of a commodity. Adjusting the margins will affect the total size of an employment or output multiplier.

ERS estimates have already been adjusted by these price and labor productivity indices.

The Open l/O ModelI-O Table 1 thumb

The Open l/O model measures the direct and indirect effects of economic activity (agricultural exports). Those effects include: the impacts of sales and purchases between all goods and service sectors of the economy, sales to final demand (consumption, investment, government, and net exports)—and purchases of land, labor, and capital services. Generally, open-model multipliers are best suited to describe what has already happened in an economy or the interrelatedness of sectors in a base period.

In an open model, the analyst first chooses either a level of exports or a change in exports (it does not matter which; the input-output model is a linear and proportional economic model). The model can express the results as an output or income multiplier by dividing the total output or income by the value of exports (i.e., economic activity per $1 of exports). The model generates a jobs multiplier—the number of jobs required to produce the output that goes for export—by dividing the number of jobs by the total value of exports (i.e., jobs per billion dollars of exports).

Effects of Commodity Prices on the Size of the Multiplier

There is a need to adjust for price changes that occurred between the benchmark year of the l/O tables (2012) and the year of the trade data (2019). When it is not practical to use individual prices, economists use price indices to adjust a trade value to a base year's prices. Using price indices can influence the multiplier estimates. The price index is an average of several prices that are representative of the commodity group for which the price adjustment is being made. For example, feed grain is the commodity group used for corn. The weight given each representative commodity is fixed at the base year's level. For example, in 2012 (the base year), corn accounted for 94 percent of the value of feed-grain exports. When the relative importance of a commodity changes in the mix of agricultural commodities traded, the price adjustment from a fixed-weight price index will adjust—albeit imperfectly, for actual prices.

Effects of Labor Productivity on the Number of Jobs Associated with Exports

Industry employment estimates are derived by ERS analysts, based on data from USDA's Agricultural Resource Management Survey (ARMS) and the U.S. Department of Labor, Bureau of Labor Statistics (BLS), Office of Employment Projections. The open I/O model estimates the number of full-time civilian jobs required, given the levels of economic activity (i.e., exports). Throughout this exercise, the number of jobs is measured in full-time equivalents (FTEs)—a conversion of the number of hours worked to an equivalent number of full-time positions. For its ATM model, ERS uses a ratio of 2,080 hours per year per FTE. Due to changes in labor productivity across time and differences in labor productivity across sectors, the employment multipliers generated by ERS’s ATM model vary by product group and by year measured. ERS’s estimates could very well be more or less than measurements of actual industry employment for the calendar year—given that the model relies on FTEs and does not account for overtime, part time, temporary work, etc.


USDOC defines margin or margin costs as "the value of the trade services provided in delivering commodities from producers' establishments to purchasers, where the purchaser pays for the services." The margins used in ERS’s ATM model come from the benchmark-year I/O accounting tables and reflect national averages of the costs associated with shipping, handling, and distributing commodities for export. By turning these base-year values into a percentage distribution, a modeler can allocate prices paid at the port to the appropriate sector (i.e., producer, transportation, or wholesale and retail trade). This concept is similar to "markups" in retail trade. For every dollar spent by a consumer in a retail establishment, a portion goes directly to the seller or store where the item was purchased. A second portion goes to the trucking company that hauled the item to the store. A third portion, usually the largest of the three, goes to the farm (in the case of commodities) or the manufacturer (in the case of food and nonfood items). Similarly, port-value multipliers can be apportioned into producer, transportation, and wholesale-and-retail-trade margins. The benchmark I/O tables have nine categories of margins, which are summed to three for the ERS estimates of port-value multipliers.

Multiplier Employment Impacts (Producer or Port Stage)

Producer-value multipliers reflect the value of the commodity as it leaves the farm gate or manufacturer's door. Port-value multipliers include the producer value and shipping, handling, and storage charges between the farm and the port.

To approximate the ERS methodology, here is a simplified example of a producer-value-based, open-model multiplier, which estimates the total number of jobs related to a given year's level of commodity exports. In this release, the multipliers are calculated in 2019 prices, which is the same as nominal values. This simplified example starts with a hypothetical nominal value of corn exports of $10 billion. ERS multiplies this export value by an employment multiplier of 9,738 FTEs per billion dollars of corn exports. The value of corn exports ($10 billion), times an employment multiplier of 9,738 FTEs per billion dollars of corn exports, equates to 97,380 FTEs related to total corn exports. This is a producer-value-based multiplier.

To understand port-value-based, open-model multipliers, the simplified example continues. First, the share of the export values related to the producer value, transportation margin, and wholesale-and-trade margin are calculated separately. The producer-value component is 86.21 percent of $10 billion, or $8.621 billion for corn. Multiplying this by the producer-value jobs multiplier for corn (9,738); yields 83,951 FTE’s for corn itself, not including jobs in the margin industries.

Next, we need to add the jobs related to assembling, handling, and shipping from the producer to the port. For transportation services, the $10 billion export value is multiplied by the transportation margin share (0.1278) to yield transportation costs of $1.278 billion. The transportation jobs multiplier is 6,967. Thus, we have the following: $10 billion x 0.1278 (the transportation share of port value) x 6,967 (transportation workers per billion dollars of corn exports), or 8,904 jobs. For wholesale and trade services, the $10 billion export value has a 0.0101 share of trade margin, or $101 million. Thus, we have the following: $10 billion x 0.0101 (the trade share of the total export value at the port) x 5,260 (trade workers per billion dollars of corn exports), or 531 jobs. The jobs total is then the sum of 83,951, 8,904, and 531, or 93,386 workers. All three shares (producer, 0.8621; transportation, 0.1278; and wholesale and trade, 0.0101) add to 1.

The first estimate for jobs related to corn exports, 97,380 workers, is different than the second estimate. This difference is because—in the first estimate, the producer-value multiplier is applied to the full value of exports, which is assumed to be expressed in producer values (that is, with no margins included). The second estimate, 93,386 workers—which includes adjustments of all port-value components including transportation and trade margins—gives a more accurate multiplier, assuming that the export figure is expressed in port values, as are the data in the GATS database.

These simplified examples do not include an adjustment for labor productivity from the base year to the current year. However, such adjustments are included in the ERS estimates.


Base Year Open Model Estimation

The following procedure can be used to estimate employment, output, and/or income related to exports of agricultural commodities when an Input/Output (I/O) transaction table is available.

Income Generation

Since income (or gross domestic product) measures—in an aggregated form—the sum of value added in various I/O sectors, then


Output = ∑ X
Income = ∑ Vj

where Vj is value added in sector j. Under an I/O structure, value added is a fixed proportion of output, so that income can be written in a matrix form as:


Output = X = (I-A) -1 F

Income = Y = vX = v (I-A) -1F


• X = an n x 1 vector of sector outputs
• (I-A)-1 = an n x n I/O total requirements matrix
• F = an n x 1 vector of final demand for agricultural exports
• Y = an n x 1 vector of income originating from each sector of the economy due to agricultural exports
• v = an n x n diagonal matrix of value added per dollar of sector output coefficients

Employment Generation

Using the above notations, employment in each sector of I/O industries is derived as:


E = L (I-A) -1

• (I-A) -1 and F are as previously defined
• L = an n x n diagonal matrix of civilian employment coefficients per dollar of sector output
• E = an n x 1 vector of sector employment needs related to the level of agricultural exports defined in vector F

Nonbase Year Estimation

To estimate output, income, and employment multipliers related to exports for years beyond the published I/O tables, one must work with less information because current year (I-A)-1, v, and L are unavailable. Yet, there are observable changes that can be incorporated into the analysis, such as changes in labor productivity and in the sectoral composition of final demand. Changes in the composition of final demand may also require changes in industry output requirements, which, in turn, change interindustry demand. Likewise, increases in labor productivity imply that the same output can be produced with a smaller workforce or that more output can be produced with the same size workforce.

Changes in the yearly commodity composition of agricultural exports are available from the Foreign Agricultural Trade of the United States (FATUS) calendar year tables.

Nonbase year income is estimated through a modification of equation (2).


Y = qT

• T=v(l-A)-1 F'
• q = an n x n diagonal matrix of output originating price deflators
• F = an n x 1 vector of current year exports

Nonbase year employment is estimated through a modification of equation (3).

Labor productivity changes in farming and in nonfarm sectors are available from USDA and the U.S. Department of Labor, respectively. Therefore, equation (3) is modified to incorporate the effect of productivity change in the generation of employment.


E = pW

• p = an n x n diagonal matrix showing the ratio of base year labor productivity to current year productivity
• W = L(I-A)-1 F'