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Data

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 of 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: November 2013.
  • 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. They are used in the ERS estimates for port-value multipliers. Last updated: December 2014. 

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 as an example and 2009 export data, the producer open model multiplier for corn is 3.55.

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 uses 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.

Assumptions

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. Benchmark I/O tables that economists use to generate trade multipliers are published by the U.S. Department of Commerce, 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. I/O tables are prepared primarily from U.S. Census data.

ERS annually estimates trade multipliers for agricultural and food exports for the most current calendar year available. The employment and output multipliers reflect 2007 levels adjusted for changes in prices and labor productivity to the most recent year available.

The several thousand (over 2,000 import and over 1,200 export) FATUS 10-digit U.S. HTS codes that USDA defines as agricultural are bridged into the appropriate Input-Output sectors for analysis using the Concordance between 2007 Input-Output Commodity Codes and Foreign Trade Harmonized Codes found in the BEA’s Benchmark Input-Output 2007 Data Files.

This "vector" of agricultural exports (i.e., final demand) differs from the definitions of agriculture used in most studies of industry contributions to national income as well as those used by BEA and the U.S. Department of Labor, Bureau of Labor Statistics (BLS). Consequently, the employment and output multipliers and other results reported here will not match with BEA and other data analysis that is based on North American Industrial Classification System (NAICS) definitions of production agriculture. Agricultural exports included in the FATUS definition include nonfarm exports from the food processing, pharmaceutical, organic chemical, adhesive and other sectors which BEA does not include in its definition. Out of 396 I/O-NAICS sectors, 56 produced FATUS-defined agricultural exports.

Background

Since the late 1970s, ERS has analyzed the economy-wide impacts of agricultural trade using a consistent annual grouping of commodities designated as agricultural by USDA in accordance with a congressional directive. USDA's Foreign Agricultural Services (FAS) and ERS are jointly responsible for defining and maintaining U.S. agricultural trade data which they do through the Foreign Agricultural Trade of the United States (FATUS) database. The several thousand (over 2,000 import and over 1,200 export) FATUS 10-digit U.S. HTS codes defined as agricultural are bridged into the appropriate Input-Output sectors for analysis using the Concordance between  Input-Output commodity codes and Foreign Trade Harmonized Codes found in the BEA's Benchmark Input-Output  Data Files.

Because this "vector" of agricultural exports (i.e., final demand) is different from the definitions of production agriculture used in the North American Industrial Classification System (NAICS), the employment and output multipliers and other results reported here will not match with BEA and other data analysis based on NAICS definitions of agriculture. Agricultural exports included in the FATUS definition include nonfarm exports from the food processing, pharmaceutical, organic chemical, adhesive, and other sectors that BEA does not. Out of 396 I/O-NAICS sectors, 56 produced FATUS- defined agricultural exports.

For further information, please see Foreign Agricultural Trade of the United States (FATUS): Questions and Answers and the U.S. Agricultural Trade Topic.

Multiplier analysis helps quantify the entire impact of a given economic activity (e.g., exporting) on economic sectors, industries, and households. For example, an agricultural trade multiplier 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. Agricultural trade multipliers also include the producing sectors' payment of wages, salaries, and other incomes that accrue to U.S. households as a result of agricultural trade.

I/O analysis uses the information contained in "benchmark" year accounting tables to provide a snapshot of the interrelationships between the sectors of an economy. The BEA typically publishes benchmark-year accounting tables every 5 years. The most recent national-level benchmark I/O table was constructed for calendar year 2007.

I/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 2007 national I/O table adequately describe the current economy, and 3) these relationships do not vary as production rises or falls.

I/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. Price change must be dealt with exogenous to, or outside of, the model itself, usually by indexing the results.

The ERS estimated employment multipliers are value based (i.e., number of jobs per billion dollars). Value-based employment multipliers change as each commodity price changes and as the Nation's labor productivity changes. Employment multipliers should also consider the value of, and adjust for, changes in the value of the transportation and wholesale-and-retail trade margins 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 I/O Model

I-O Table 1 thumbOpen I/O models measure the direct and indirect effects of economic activity (agricultural 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. 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

The need to adjust for price change arises because so many separate commodities are traded that the only meaningful way to report aggregate trade data is in value terms. 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 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 2007 (the base year), corn accounted for 89 percent 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 and BLS's Office of Employment Projections. The open I/O model estimates the amount of jobs required given the levels of economic activity (i.e., exports).  The employment multipliers in the ERS estimates will vary according to the commodity and/or group of commodities chosen and year measured due to labor productivity changes.  The resulting ERS estimates could very well be more or less than measurements of actual industry employment for the calendar year--given that the model uses full-time equivalent jobs and does not account for overtime, part time, temporary work, etc. 

Margins

The U.S. Department of Commerce 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 included in the ERS I/O model used to calculate agricultural trade multipliers 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 actual 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. The third, and usually largest, portion goes to the farm (in the case of commodities) or 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.  This simplified example starts with a nominal value of corn exports of $10 billion.  The export value is converted to real terms by using the indexed prices received by farmers for feed grains.  This results is a real (inflation-adjusted) value of corn exports of $6.173 billion.  We multiply this real export value by an employment multiplier of 18,140 workers per billion dollars of corn exports.  The value of corn exports ($6.173 billion) times an employment multiplier of 18,140 workers per billion dollars of corn exports equates to 111,975 jobs 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 value related to transportation and wholesale and retail trade, or "margins," is removed so that the multiplier applies only to the producer value of this $6.173 billion of corn exports. With a producer share of corn exports of 62 percent, the number of jobs related to corn exports therefore is $6.173 billion x 0.62 x  18,140 (the number of required farmworkers), or 69,425 jobs.

To use a port-value multiplier correctly, one needs 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 adjusted using an index of transportation prices, which computes to $8.06 billion.  Thus, we have the following: $8.06 billion x 0.16 (the transportation share of port value) x 12,948 transportation workers per billion dollars of corn exports, or 16,698 jobs. For wholesale and retail trade services, the $10 billion export value is adjusted using an index of trade prices, which computes to $8.81 billion. Thus, we have the following: $8.81 billion x 0.22 (the trade share of the total export value at the port) x 18,771 trade workers per billion dollars of corn exports, or 36,382 jobs. The jobs total is 69,425 +16,698 + 36,382, or 122,505 workers. All three shares (producer, 0.62; transportation, 0.16; and wholesale and retail trade, 0.22) add to 1.

The first estimate for jobs related to corn exports, 111,975 workers, is lower than the second estimate because the adjustment for the feed grain price change applies to the full value of exports, even the transportation and wholesale-and-retail-trade portions. The second estimate, 122,505 workers, which includes adjustments of all port price components rather than the full value of exports, gives the most accurate multiplier.

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.

Methodology

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

(1)

n
Output = ∑ X
j=1

n
Income = ∑ Vj
j=1

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:

(2)

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

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

Where:

  • 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:

(3)

E = L (I-A)-1 F

Where:

  • (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).

(4)

Y = qT

Where:

  • T = v(I-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.

(5)

E = pW

Where:

  • 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'