Methodology for Estimating Impacts on Food Expenditures, CPI for Food

and CPI for all Items

November 15, 2012

Impact on Food Expenditures:

The impact on food expenditures assumes that the effects of the RFS on corn prices would lead 

to corresponding adjustments in the prices for other feed grains (grain sorghum, barley, and 

oats), distillers dried grains and soybeans. The adjustments in the prices of other feed grains are 

based on historical price relationships of these commodities with corn. Other feed grains 

compete with corn in the feed market and to a lesser extent for acreage. Distillers dried grains 

are a byproduct produced when corn is converted into ethanol and competes with corn in the feed 

market. Soybeans compete with corn for acreage. Any adjustment in the price of soybeans is 

assumed to lead to a corresponding change in the prices for soybean oil and soybean meal. 

These two products are produced from soybeans when soybeans are crushed, with soybean meal 

used as an animal feed and soybean oil used for human consumption.

The changes in commodity prices are assumed to be fully passed on to consumers at the retail 

level. Therefore, the change in food expenditures for each commodity is estimated by 

multiplying the price change by the quantity of the commodity used domestically, including food 

and feed use. Feed use is included to capture the effects of the change in the price of the 

commodity on livestock producers’ production costs and, ultimately, the effects on retail 

livestock prices as livestock producers adjust production in response to changes in commodity 

prices. 

Since the model assumes no response by producers or consumers to changes in commodity 

prices, the model may overstate the change in food expenditures. However, previous research 

suggests that the demand for food is very inelastic and, therefore, the model should provide a

close approximation of the change in food expenditures. 

Change in Food Expenditures=Sum of (Change in Price Commodityi)(Domestic Use 

Commodityi)

Commodity1 = corn; Commodity2 = grain sorghum; Commodity3 = barley; Commodity4 = oats; 

Commodity5 = soybean oil; Commodity6 = soybean meal, Commodity7= distillers dried grains.

Change in Price of Corn=Given

Change in Price of Grain Sorghum=0.93 times Change in Price of Corn

Change in Price of Barley=0.88 times Change in Price of Corn

Change in Price of Oats=0.72 times Change in Price of Corn

Change in Price of Soybean Oil=Given

Change in Price of Soybean Meal=Given

Change in Price of Distillers Dried Grains per pound=Change in Price of Corn/56

Domestic Use Commodityi; See United States Department of Agriculture, World Agricultural 

Supply and Demand Estimates, October 11, 2012.
Impact on CPI for Food:

The CPI for food as measured by the Bureau of Labor Statistics (BLS) consists of two 

components--the CPI for food at home and the CPI for food away from home with the CPI for 

food away from home having a weight of 0.40 and the CPI for food at home having a weight of 

0.60. In turn, the CPI for food at home consists of several components, including the CPI for 

cereal and bakery products, CPI for meats, poultry, fish and eggs, CPI for dairy and related 

products, CPI for fruits and vegetables, CPI for nonalcoholic beverages, CPI for sugar and 

sweets, CPI for fats and oils, and the CPI for other foods. Any change in the price of corn could 

be reflected in the CPI’s for cereal and bakery products, nonalcoholic beverages, sugar and 

sweets, and fats and oils, since corn is used to produce cereal, cooking oil and high fructose corn 

syrup for use in soft drinks and many other products. To determine the effects of changes in 

corn prices on the CPI for food would require information on the products that the BLS tracks in 

determining the various CPI’s, the amount of corn used in those products, and the relative 

weights of the products containing corn in the various CPI’s. Unfortunately, this information is 

not available.

To estimate the change in the CPI for food caused by a change in the price of corn and associated 

changes in other commodity prices, we use the estimated change in food expenditures. The 

following equation represents baseline food expenditures,

 Eo = PoQo

where Eo is baseline food expenditures, Po is the baseline price for food and Qo is the baseline 

quantity of food purchased. Now, assume the following equation represents food expenditures 

after the change in corn and related commodity prices,

 E1 = P1Q1

where E1 is food expenditures, P1 is the price for food and Q1 is the quantity of food purchased. 

We also know from previous research that the quantity of food purchased is very inelastic with 

respect to price. So, if we assume that Qo=Q1, then we can derive and use the following 

relationship 

 E1/Eo = P1/Po

to estimate the change in the price or the CPIfor food. Therefore, if there is no change in 

quantity of food consumed, the percentage change in the CPI for food will equal the percentage 

change in food expenditures. We used the above equation to approximate the change in the CPI 

for food. 

Since the model assumes no response by consumers to changes in food prices, the model may 

overstate the change in the CPI for food. However, previous research suggests that the demand 

for food is very inelastic and, therefore, the model should provide a close approximation of the 

change in the food CPI.
Impact on All Item CPI:

As measured by the BLS, the CPI for food has a weight for 0.14 in the all item CPI. This implies 

that for every 1 percent increase in the CPI for food the CPI for all items would increase by 0.14 

percent. We use this relationship to estimate the change in the CPI for all items. 

Change in CPI, Food CPI, and Food Expenditures

Units (0.07) (0.58) (1.86)

Food CPI without Waiver Index 242.98 242.98 242.98

Food CPI with Waiver Index 242.88 242.13 240.23

 Difference Index -0.10 -0.85 -2.75

 % Change Percent -0.04 -0.35 -1.13

All Item CPI without Waiver Index 232.73 232.73 232.73

All Item CPI with Waiver Index 232.72 232.62 232.36

 Difference Index -0.01 -0.11 -0.369

 % Change Percent -0.006 -0.049 -0.158

Food Expenditures without 

Waiver Bil. $

1139.4 1139.4 1139.4

Food Expenditures with Waiver Bil. $ 1138.9 1135.4 1126.5

 Difference Bil. $ -0.5 -4.0 -12.9

 % Change Percent -0.04 -0.35 -1.13

Change in Corn Price (Dollars per 

Bushel)
Changes in Consumer Expenditures with and without RFS mandate

All Consumers Lowest 20 Percent

Average annual expenditures (1) $49,705 $22,001

Food $6,458 $3,547

Percent of Expenditures on Food 13.0 16.1

$0.07 Scenario

With Mandate

Average annual expenditures (1) 49705.0 22001.0

Food (2) $6,458 $3,547

Percent of Expenditures on Food (2) 13.0 16.1

Without Mandate

Food (2) $6,455 $3,546

Percent of Expenditures on Food (2) 13.0 16.1

$0.58 Scenario

With Mandate

Average annual expenditures (1) $49,705 $22,001

Food (2) $6,458 $3,547

Percent of Expenditures on Food (2) 13.0 16.1

Without Mandate

Food (2) $6,435 $3,535

Percent of Expenditures on Food (2) 12.9 16.1

$1.86 Scenario

With Mandate

Average annual expenditures (1) $49,705 $22,001

Food (2) $6,435 $3,547

Percent of Expenditures on Food (2) 12.9 16.1

Without Mandate

Food (2) $6,362 $3,507

Percent of Expenditures on Food (2) 12.8 15.9

(1) Source: ftp://ftp.bls.gov/pub/special.requests/ce/standard/2011/quintile.txt

(2) Derived, based on changes estimated for food cpi.
Iowa State 

Mean Estimate

Iowa State 

Mandate Binds 

Iowa State "Worst 

Case" Example

Units

Change in Corn Price with Waiver $/bu -$0.07 -$0.58 -$1.86

Change in Food CPI with Waiver percent -0.04 -0.35 -1.13

Change in Annual Expenditures on Food For 

Average Household with Waiver $ -$2.59 -$22.68 -$73.11

Change in Annual Expenditures on Food For 

Lowest Qunitile Households with Waiver $ -$1.42 -$12.46 -$40.15

Change in Food Expenditures as a 

Percentage of Consumer Expenditures for 

Average Household with Waiver percent -0.005 -0.047 -0.151

Change in Food Expenditures as a 

Percentage of Consumer Expenditures for 

Lowest Quintile with Waiver percent -0.007 -0.061 -0.197

Change in Food Expenditures as a 

Percentage of Income After Taxes for 

Average Houshold with Waiver percent -0.005 -0.046 -0.147

Change in Food Expenditures as a 

Percentage of Income After Taxes for 

Lowest Quintile with Waiver percent -0.0065 -0.057 -0.183