The Agricultural Trade Multipliers measure the impacts of sales and purchases between all goods and service sectors of the economy, sales to final demand (e.g., consumption, investment, government, and net exports), and purchases of land, labor, and capital services. The aim of the Agricultural Trade Multipliers (ATMs) is to provide annual estimates of employment and output effects of trade in farm and food products on the U.S. economy. When expressed as multipliers, these effects reflect the amount of economic activity and jobs generated by agricultural exports. 

Scope/Coverage of Data

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. 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 (e.g., consumption, investment, government, and net exports), and purchases of land, labor, and capital services.

The Agricultural Trade Multipliers are derived from the 2012 Benchmark Input-Output (I/O) tables published by the U.S. Department of Commerce, Bureau of Economic Analysis and include detail on 124 agricultural products and product groups, ranging from soybeans to essential oils, using the World Trade Organization’s (WTO) definition of agricultural products. The Agricultural Trade Multipliers estimates are only for open multipliers at either the producer (i.e., farm or manufacturer) or port stage of export. 

The Agricultural Trade Multipliers App gives users two display options: 

  • Predefined ERS estimates of the economic activity and jobs supported by agricultural exports in the most recent calendar year; or
  • Interactive calculator that enables users to select a basket of exports from the list of predefined estimates and/or apply a new set of trade margins to the commodity or basket of goods (see Overview for step-by-step instructions for using the ATM calculator).

Current data are available in Excel format through the ATM Calculator.


ERS estimates Agricultural Trade Multipliers using an open I/O model. Analysts assume the following: (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.

Model Estimation

In a 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)-1and 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

For nonbase year estimation, there is less information to work with 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 inter-industry demand. Likewise, increases in labor productivity imply the same output can be produced with a smaller workforce or 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)-1F'
    • 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)-1F'

Calculator Methodology

The following describes how to calculate the output and job multipliers for a specific bundle of goods as performed in the calculator application. First, we go over how to obtain the port output multiplier for a custom bundle of commodities. The equation calculates the weighted average (based on export value) of the port multipliers for each commodity in the bundle:

Port output multiplier =


Where n is the number of commodities, M is the producer multiplier for commodity j and X is the export value of commodity j.

We can go through a simple example for the port output multiplier. Say that we want to calculate the bundle for soybeans and corn. Our value n would be 2, and the equation would be:

Port output multiplier = (M1 * X1 + M2 * X2)/(X1 + X2)

Where M1 is the port multiplier for soybeans, X1 is the soybean export value, M2 is the port multiplier for corn, and X2 is the corn export value.

We generalize this equation to calculate the port job multiplier, the producer job multiplier, and the producer output multiplier by substituting the specific multiplier type desired instead of the port output multiplier for every instance of the variable M (i.e. producer job multiplier instead of port job multiplier).

Strengths and Limitations

This multiplier analysis has a year lag and assumes 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.


Related Data and Releases:

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Recommended Citation

U.S. Department of Agriculture, Economic Research Service. Agricultural Trade Multipliers.