# 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'