Economic

Research

Service

Technical 

Bulletin 

Number 1940

May 2015

United States Department of Agriculture

How USDA Forecasts Retail 

Food Price Inflation

Annemarie Kuhns, Richard Volpe, Ephraim Leibtag, 

and Ed Roeger
Economic Research Service 

www.ers.usda.gov

The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on 

the basis of race, color, national origin, age, disability, and, where applicable, sex, marital status, familial 

status, parental status, religion, sexual orientation, genetic information, political beliefs, reprisal, or because 

all or a part of an individual’s income is derived from any public assistance program. (Not all prohibited 

bases apply to all programs.) Persons with disabilities who require alternative means for communication of 

program information (Braille, large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 

720-2600 (voice and TDD). 

To file a complaint of discrimination write to USDA, Director, Office of Civil Rights, 1400 Independence 

Avenue, S.W., Washington, D.C. 20250-9410 or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA 

is an equal opportunity provider and employer.

United States Department of Agriculture

Access this report online:

www.ers.usda.gov/publications/tb-technical-bulletin/tb1940

Download the charts contained in this report:

• Go to the report’s index page www.ers.usda.gov/publications/

 tb-technical-bulletin/tb1940

• Click on the bulleted item “Download tb1940.zip”

• Open the chart you want, then save it to your computer

Recommended citation format for this publication:

Kuhns, A., R. Volpe, E. Leibtag, and E. Roeger. How USDA Forecasts Retail Food Price 

Inflation, TB-1940, U.S. Department of Agriculture, Economic Research Service, May 

2015.

Cover image: Shutterstock.

Use of commercial and trade names does not imply approval or constitute endorsement by USDA. 
United States Department of Agriculture

Economic 

Research 

Service

Technical 

Bulletin 

Number 1940

May 2015

Abstract

Wholesale and retail food price forecasts are useful to farmers, processors, wholesalers, 

consumers, and policymakers alike, as the structure and environment of food and 

agricultural economies are continually evolving. USDA's Economic Research Service 

analyzes food prices and provides 12- to 18-month food price forecasts for 7 farm, 6 

wholesale, and 19 retail food categories. In 2011, ERS’s forecasting procedure was 

updated to employ a vertical price transmission method that incorporates input prices at 

each stage of production. Where this is not possible, an autoregressive moving average 

approach is used. This report provides a detailed description of the revised methodology 

as well as an analysis of the overall accuracy and performance of individual forecasts. 

The revised forecasting methods show modest increases in forecast accuracy compared 

with simple univariate approaches previously used by ERS. 

Keywords: Food Price Outlook, food prices, Consumer Price Index (CPI), Producer 

Price Index (PPI), forecasts, vertical price transmission model, autoregressive moving 

average approach, error correction model, autoregressive distributed lag, univariate 

moving average approach

Acknowledgments

The authors thank Pat Canning and Ted Covey, USDA, Economic Research Service 

(ERS); Gonzalo Varela, World Bank; and Chris Gilbert, University of Trento, for their 

peer/technical reviews. They also thank Ryan Kuhns, Steve Martinez, and Tim Park, 

USDA, Economic Research Service, for their comments and suggestions and Maria 

Williams and Cynthia A. Ray, USDA, ERS, for editorial and design assistance.

Annemarie Kuhns, Richard Volpe, Ephraim Leibtag, 

and Ed Roeger

How USDA Forecasts Retail Food 

Price Inflation
ii

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Contents

Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

What Are the Major Determinants of Food Prices?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Forecasting Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Structural Breaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Vertical Price Transmission Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Autoregressive Moving Average Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Post-Estimation Evaluation and Forecast Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Comparing Forecast Performance of Previous and Revised Forecasting Methods. . . . . . . . . . . 20

Comparing Forecast Accuracy Across Vertical Price Transmission Approaches. . . . . . . . . . . . 22

Conclusion: Ongoing and Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
United States Department of Agriculture

A report summary from the Economic Research Service

ERS is a primary source 

of economic research and 

analysis from the U.S. 

Department of Agriculture, 

providing timely information on economic and policy 

issues related to agriculture, 

food, the environment, and 

rural America.

www.ers.usda.gov

Economic

Research

Service

Technical 

Bulletin 

Number 1940

May 2015

United States Department of Agriculture

How USDA Forecasts Retail 

Food Price Inflation

Annemarie Kuhns, Richard Volpe, Ephraim Leibtag, 

and Ed Roeger

May 2015

Find the full report at 

www.ers.usda.gov/

publications/tb-technical-bulletin/tb1940

Annemarie Kuhns, Richard Volpe, Ephraim Leibtag, and Ed Roeger

How USDA Forecasts Retail Food 

Price Inflation

What Is the Issue?

Each month, USDA's Economic Research Service (ERS) publishes wholesale and retail price 

forecasts for various food categories and subcategories, and policymakers, food suppliers, and 

researchers rely on these numbers. In recent years, as commodity and food prices have become 

more volatile and less easily predicted, users of the forecasts have expressed a greater need for 

more accurate forecasts. 

ERS continually explores ways to improve its forecasts as new data and methods become available. In 2011, ERS revised its food price forecast methodology to use more rigorous statistical 

techniques and capture the impacts of the multistage U.S. food supply system on wholesale and 

retail food price formation. This updated approach incorporates far richer data available for 

farm, wholesale, and input prices, which could lead to more accurate forecasts. 

What Did the Study Find?

• The precision of ERS food price forecasts has observably improved with the revised methodology. As a result, ERS food price forecasts are, on average, closer to the realized inflation 

figures.

• ERS forecasts using the new methodology required fewer and smaller revisions. For a given 

year, forecasts are subject to revision during a 17-month period. An average of 3.2 changes 

were made per food category using the new, current forecasting methods compared with 3.7 

revisions using the previous method, and the average size of the adjustments dropped from 

2.6 to 2.1 percentage points. 

• Another measure of forecast accuracy was the extent to which initial forecasts differed from 

the actual Consumer Price Index (CPI) values. Using revised forecast methodology, the 

average difference from CPI values was 2 percentage points, compared with 2.6 percentage 

points for the previous methods.

• Although forecast accuracy and precision have improved relative to less rigorous 

approaches used by ERS before 2011, more years of data are needed to fully assess forecast 

performance.
How Was the Study Conducted?

For those food categories with a sufficiently lengthy time series of historical retail and input prices, as well as 

reliable measures of forecast input prices, four separate vertical price transmission models are used to predict 

farm, wholesale, and retail-level food prices. The vertical price transmission approach relies on price forecasts 

at earlier stages of the production process, which are then “passed through” to forecast the CPI for food. For 

those categories subject to data limitations that preclude use of the vertical price transmission method, the 

autoregressive moving-average approach is used, which relies on lagged and current values of the CPI being 

forecast, as well as a time trend. 

The accuracy of the current forecasting method is compared with the forecasting method used by ERS before 

2011. Performance of the current forecasting methods is evaluated over the 2011-2013 period and compared 

with the performance of the previously used univariate moving average approach, which is evaluated over 

the 2003-2010 period. Various measures of forecast accuracy and adjustments are used to evaluate forecast 

performance. 

Finally, the forecasting accuracies of the four vertical price transmission models are compared with each 

other using various performance statistics over the 2012-2013 period. Several accuracy tests were conducted, 

including a directional analysis to examine the extent to which the forecast models anticipate changes in the 

direction of price movements.

www.ers.usda.gov
1

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

How USDA Forecasts Retail Food 

Price Inflation 

Introduction

Food prices are fundamental to research related to the economics of food choices and the 

dynamics of food market competition. USDA, Economic Research Service (ERS) produces 12- to 

18-month forecasts of the Consumer Price Index (CPI) and Producer Price Index (PPI) as indicators of where U.S. retail and wholesale food prices are headed.1,2 The forecasting procedure has 

been significantly updated and extended in recent years. This report presents the food price forecasting methodology currently used at ERS, discussing its performance as well as the limitations 

and challenges facing forecasters. 

Food price inflation forecasts are used in a number of ways. Researchers and policy analysts rely 

on them to anticipate changes that may be necessary in the structure, size, or regulations of various 

food assistance programs. Professionals working throughout the food industry use ERS’s forecasts 

to project costs, expenditures, or demand for their products and services. Because we analyze individual food categories separately, revealing changes in prices relative to other food categories, with 

implications for consumer choice, the forecasts inform research and decision-making on dietary 

quality. Throughout academia and other outlets, the CPI forecasts have been used and cited in 

applied economic research on retail price transmission and formation. Finally, the media regularly 

and extensively uses ERS forecasts to inform U.S. consumers about expected changes in their expenditures and costs of living. 

ERS has forecasted food prices for decades. Recently, the methodology has been updated substantially since the previous report on the forecasting approach (Joutz et al., 2000). The improvements 

to the forecasting procedure came about as the culmination of several factors. Forecasting in a 

multivariate framework that is supported by economic theory requires longitudinal data for the same 

variables. Over the past two decades, the data available for forecasting food prices have become 

far richer, with more information on farm, wholesale, and input prices. The fields of econometrics 

and statistics have advanced, and the forecasting toolkit has become more versatile, accessible, and 

effective. ERS stakeholders have also become more interested in retail food prices as they have 

grown more volatile and inflation has accelerated. Between 1990 and 2006, the food-at-home CPI 

(supermarket prices) increased by an average of 2.4 percent per year with a standard deviation of 

0.85 percentage points. Since 2006, the average annual increase has been 3.1 percent with a standard 

deviation of 2.45 percentage points. Food price inflation has become far less predictable from year to 

year, and ERS has responded to this transition with greater scrutiny and analysis.

ERS’s Food Price Outlook topic page features the CPI and PPI forecasts, available at: http://www.

ers.usda.gov/data-products/food-price-outlook.aspx#.UqiO_dJDseE. Inflation forecasts for the 

current year are always available, and from July to December, ERS also forecasts inflation for the 

1The CPI is a widely used measure of inflation of consumer goods and services, including food. The CPI is produced 

by the U.S. Bureau of Labor Statistics.

2The PPI is a measure of inflation for the selling prices received by domestic producers of goods and services. The PPI 

is produced by the U.S. Bureau of Labor Statistics.
2

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

upcoming year. The topic page is updated monthly with changes to the forecasts, as needed, and 

includes a discussion of food price trends during the prior month.3 The documentation portion of the 

topic page provides a nontechnical overview of the ERS forecasting procedure, a discussion of the 

most important determinants of food prices, and highlights of relevant ERS research on retail food 

price formation and variation.

3The Food Price Outlook is updated monthly, as opposed to quarterly or yearly, to coincide with the release of PPI and 

CPI data, which are also published monthly. 
3

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

What Are the Major Determinants of Food Prices?

Commodity prices, transportation costs, manufacturing costs, and retailing costs are all factors to 

consider when modeling food price inflation. Measurements of these factors serve as the regressors 

in the econometric forecast models. Much research has been devoted to the determinants of food 

prices and food price volatility, but for the most part, these studies have focused on the agricultural 

commodity sector (Gilbert, 2010; Mitchell, 2008; Timmer, 2008). While there is little question 

that agriculture commodities are the most vital input to the food industry, the impact of commodity 

prices on retail food prices is a nuanced one in industrialized nations such as the United States. 

Food in the United States travels from farms to supermarkets, restaurants, and other outlets through 

a supply system with multiple segments and industry sectors, each of which collects a share of every 

retail food dollar spent (fig. 1). The procedure varies across products and categories, but most foods 

undergo transportation, processing, and packaging to various degrees before reaching the retail 

sector. At one or more stages along this distribution chain, most foods also accrue additional costs, 

including advertising, finance, and labor wages, which factor into all industries involved in food 

supply systems. 

When constructing a time series model of retail food prices based on input costs, researchers need 

to consider the extent to which input costs vary over time. There are a large number of potential 

input costs to consider, and since many are likely to be highly correlated over time, it is not feasible 

to include measurements for all of them. Factors that vary little over time will have no predictive 

power for food price variation. Similarly, inputs that are too closely interrelated will pose estimation 

Source: Authors’ calculations based on USDA, Economic Research Service’s Food Dollar Series, Food-at-home dollar, 

2012. 

Figure 1

The industry groups’ shares of the food dollar

Farm & agribusiness, 18.2% 

Food processing, 24%

Packaging, 3.1%

Transportation, 4.7%

Wholesale trade, 13.9%

Retail trade, 22.6%

Energy, 6.3%

Finance & insurance, 3.6% 

Other, 3.6%
4

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

problems and complicate the interpretation of coefficients. For example, crude oil and motor fuel are 

both key inputs to the food processing and transportation process. The prices for these commodities 

correlate very closely, and if both are included in the same model, it may be impossible to identify 

the respective impacts of each.

Examining the changes in selected input costs over time (fig. 2) quickly illustrates which factors 

vary over time. Energy costs, including motor fuel and electricity rates, fluctuate greatly from year 

to year, regularly increasing or decreasing by more than 10 percent. The same is true for farm 

commodity prices. However, financial services and advertising costs (for which only a short time 

series is available) are far less volatile. Average hourly wages are also among the less volatile series, 

but wages do not seem to closely correlate with other input costs. Additionally, wages for industries 

specific to the food supply system may behave differently from those in other industries over time.

Taken in sum, previous research and data on prices in the industries contributing to the U.S. food 

supply suggest that our efforts in modeling and forecasting retail food prices are best focused on 

commodity and energy prices (Lamm and Westcott, 1981; Trostle, 2008). The estimated industry 

shares reported in figure 1 represent averages across all food and likely vary meaningfully across 

products and categories. Transportation and packaging costs may be important factors for certain 

foods that fluctuate considerably over time. Data on these industries, specific to their roles in food 

supply, are difficult to find. Fortunately, research has shown that fuel costs are the major drivers 

of transportation rates (Volpe et al., 2013). Additionally, packaging is an energy-intensive industry 

for which energy use has increased considerably in recent years (Canning et al., 2010). Therefore, 

accounting for energy prices may suffice to account for the roles played by these industries.

Source: Consumer Price Index (CPI), U.S. Bureau of Labor Statistics. 

Figure 2

Annual percent changes in the food CPI and selected input costs, 1980-2012

Percent change

-40

-30

-20

-10

0

10

20

30

40

50

1980 1984 1988 1992 1996 2000 2004 2008 2012

Food CPI

Motor fuel

Electricity

Financial services

Advertising agencies

Farm products

Hourly wages
5

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Forecasting Methodology

In this chapter, the two types of forecasting methods are broadly defined and then each approach is 

discussed more in depth. Food CPI forecasts are of great interest to ERS data users and are some 

of the most cited and discussed estimates produced by ERS. However, it is not clear how to model 

effectively food CPI trends for such a disparate set of food categories in a forecasting framework. 

For example, what is the best way to select agricultural commodities most relevant to the food CPI? 

Or, if an aggregate commodity price index is preferable, how can we obtain reliable forecasts of such 

an index? 

Owing to complications such as these, ERS forecasts individual CPI subcategories for which 

modeling is more tractable and for which data, including upstream forecasts, are more readily available. In 2011, ERS revised its forecasting procedure to improve precision. CPI subcategories are 

now forecasted using two distinct statistical methodologies: the vertical price transmission and the 

autoregressive moving-average approach. Which of the two methods is used depends entirely on data 

availability. In those categories for which we have a sufficiently long time series of data on historical 

retail and input prices, as well as a reliable measure of forecasted input prices, we use a vertical 

price transmission pass-through approach.4,5 For those categories subject to data limitations, we 

apply the autoregressive moving-average approach, which relies on historical measures of economywide price movements, as well as a time trend.6

The forecasts for larger categories—including food-at-home and other aggregations such as meats or 

fruits and vegetables—are calculated as the weighted averages of the forecasted CPI subcategories. 

The weights for this process are drawn from the Bureau of Labor Statistics (BLS) relative importance shares, which are estimates of the shares of the average consumer’s expenditures attributable 

to each spending category.7 An example of an ERS CPI forecast table, as posted on the ERS website 

(table 1), helps illustrate how the various CPI categories relate to one another.

The food CPI constitutes 100 percent of consumer food spending, and all relative importance shares 

have been recalculated based on this denominator.8 Food spending can be broadly organized into 

food at home (FAH) (60.1 percent) and food away from home (FAFH) (39.9 percent) spending.9

Given the intrinsic differences in price formation between these two markets, one plausible approach 

to forecasting the food CPI is to forecast the FAH and FAFH CPIs individually and then weight the 

respective forecasts by their relative importance shares. However, the FAH CPI itself consists of 

an array of food categories and subcategories, each subject to unique modeling considerations and 

data demands. The boldfaced CPI categories in table 1 are those that ERS forecasts directly. The 

remaining categories are aggregates and consist of weighted averages of forecasts.

4The historical CPI and PPI data we use date back to 1974.

5Pass-through approach refers to using first stage forecasts as inputs to the second stage forecast.

6An autoregressive model specifies that forecasts are estimated based on weighted sums of pervious values.

7Relative importance weights are updated in December of each year.

8For example, according to BLS, meats account for approximately 1.1 percent of all consumer spending, and since food 

represent 13.9 percent of spending, meats account for 7.9 percent of food spending.

9Food at home includes food purchased at food stores (grocery stores, supermarkets, etc.), other stores (commissary, 

military exchanges, etc.), home delivery and mail order, or purchases directly from farmers, manufacturers, and wholesalers. Food away from home includes purchases made at eating and drinking places, hotels and motels, retail stores, 

direct selling establishments, recreational places, schools, and colleges. 
6

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table 1

A sample CPI forecast update from the ERS Food Price Outlook topic page

Relative 

importance

Month-toMonthYear-overYear Annual Annual Forecast Forecast

Item

Sept 2013 

to Oct 2013

Oct 2012 to 

Oct 2013 2011 2012 2013 2014

(Percent) Consumer Price Indices (Percent change)

All food 100.0 0.1 1.3 3.7 2.6 1.5 to 2.5 2.5 to 3.5

Food away from home 39.9 0.1 1.9 2.3 2.8 2.0 to 3.0 2.5 to 3.5

Food at home 60.1 0.2 0.8 4.8 2.5 1.0 to 2.0 2.5 to 3.5

Meats, poultry, and fish 12.9 0.6 3.1 7.4 3.6 1.5 to 2.5 2.5 to 3.5

Meats 8.3 0.4 2.0 8.8 3.4 1.0 to 2.0 2.5 to 3.5

Beef and Veal 3.9 0.3 1.4 10.2 6.4 2.0 to 3.0 2.5 to 3.5

Pork 2.5 0.6 3.7 8.5 0.3 0.5 to 1.5 2.0 to 3.0

Other meats 1.9 0.4 0.9 6.4 1.7 -0.5 to 0.5 2.0 to 3.0

Poultry 2.4 0.7 5.1 2.9 5.5 4.0 to 5.0 3.0 to 4.0

Fish and seafood 2.1 1.1 5.0 7.1 2.4 2.0 to 3.0 2.5 to 3.5

Eggs 0.8 1.1 0.9 9.2 3.2 2.0 to 3.0 2.0 to 3.0

Dairy products 6.3 -0.2 -0.2 6.8 2.1 0.0 to 1.0 2.5 to 3.5

Fats and oils 1.8 0.2 -1.8 9.3 6.1 -1.0 to 0.0 1.5 to 2.5

Fruits and vegetables 9.0 0.4 2.7 4.1 -0.6 2.0 to 3.0 2.5 to 3.5

Fresh fruits & vegetables 6.9 1.0 3.7 4.5 -2.0 2.5 to 3.5 2.5 to 3.5

Fresh fruits 3.7 1.5 1.2 3.3 1.0 2.0 to 3.0 2.5 to 3.5

Fresh vegetables 3.2 0.5 6.5 5.6 -5.1 4.0 to 5.0 2.0 to 3.0

Processed fruits & 

vegetables 2.1 -1.5 -0.5 2.9 3.8 0.0 to 1.0 2.5 to 3.5

Sugar and sweets 2.1 0.4 -2.1 3.3 3.3 -2.0 to -1.0 2.0 to 3.0

Cereals and bakery 

products 8.6 -0.2 0.9 3.9 2.8 1.0 to 2.0 2.0 to 3.0

Nonalcoholic beverages 6.6 0.4 -1.3 3.2 1.1 -1.0 to 0.0 2.5 to 3.5

Other foods 12.0 -0.3 -0.4 2.3 3.5 0.0 to 1.0 2.0 to 3.0

Notes: This table is reproduced from the November 27, 2013 update of the Food Price Outlook Topic Page. Some formatting has been 

changed slightly. The U.S. Bureau of Labor Statistics (BLS) published the relative importance shares in December 2012. BLS is the source 

for the month-to-month and year-to-year changes. Numbers in green indicate an upward revision in the annual forecast; numbers in red indicate a downward revision. Consumer Price Index (CPI) categories in bold are those which ERS forecasts directly using statistical methods. 

Source: USDA, Economic Research Service Food Price Outlook topic page.
7

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

In the remainder of this chapter, we first introduce the concept of structural breaks, followed by 

a detailed discussion of the two broad types of forecasting methods used for forecasting the CPI 

subcategories. The type of forecasting method used for each food category is summarized in table 2. 

Table 2

Forecasting method used for each CPI food category

CPI Category Model

All Food Weighted average

Food away from home Autoregressive moving-average approach

Food at home Weighted average

Meats, poultry, and fish Weighted average

Meats Weighted average

Beef and veal Vertical price transmission ECM approach

Pork Vertical price transmission ECM approach

Other meats Autoregressive moving-average approach

Poultry Vertical price transmission ECM approach

Fish and seafood Autoregressive moving-average approach

Eggs Vertical price transmission ARDL approach

Dairy products Vertical price transmission ECM approach

Fats and oils Vertical price transmission ECM approach

Fruits and vegetables Weighted average

Fresh fruits and vegetables Weighted average

Fresh fruits Vertical price transmission ARDL approach

Fresh vegetables Vertical price transmission ARDL approach

Processed fruits and vegetables Autoregressive moving-average approach

Sugar and sweets Autoregressive moving-average approach

Cereals and bakery products Vertical price transmission ECM approach

Nonalcoholic beverages Autoregressive moving-average approach

Notes: ECM = Error Correction Method, ARDL = Autoregressive Distributive Lag.

The indentation scheme illustrates how certain Consumer Price Index (CPI) categories comprise smaller subcategories. 

Food away from home, which is not disaggregated, contains no subcategories.

Source: USDA, Economic Research Service record of the methodology used with each category of CPI data.
8

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Structural Breaks

As discussed in the following sections, we test for the presence of structural breaks in our forecasting models. Whether food prices are forecasted using a vertical price transmission pass-through 

approach or an autoregressive model, the potential role of structural breaks must be considered in 

any time series analysis. Structural breaks occur when a time series variable undergoes a fundamental shift, which usually manifests as a change in the statistical distribution via the mean, variance, or both. If structural breaks are not accounted for, forecasting errors can result and a number 

of statistical tests can be rendered invalid.10

It is common practice to test for structural breaks in instances where they are suspected to occur. In 

a well-known example, economists modeling macroeconomic indicators over time typically find a 

structural break in time series when analyzing gross domestic product (GDP), a common measure 

of economic growth, for the years of World War II (Ben-David et al., 2003; Strazicich et al., 2004). 

Examining annual changes in U.S. GDP over many decades (fig. 3) illustrates this idea. Note that 

GDP growth is highly volatile for nearly 10 years before the war, which the United States entered 

in 1939, and during the war itself. Approximately at the end of the war, around 1945, the volatility 

significantly decreases, and economic growth follows a fairly steady pattern of mild ups and downs 

for several decades. Any attempt to model or forecast U.S. economic growth that did not account for 

the level of volatility toward the end of World War II would result in biased regression coefficients, 

as several researchers have found.

10If a structural change has occurred, it would bias the Dickey-Fuller test toward the nonrejection of the null that a unit 

root exists (Perron, 1989).

Source: U.S. Department of Commerce, Bureau of Economic Analysis. 

Figure 3

Annual percent changes in U.S. gross domestic product, 1930-2012

Percent

-30

-20

-10

0

10

20

30

40

1930193319361939194219451948195119541957196019631966196919721975197819811984198719901993199619992002200520082011
9

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

An additional modeling complication arises when it is not obvious where structural breaks may 

occur. In these cases, structural breaks may be endogenous, and tests have been developed to identify multiple structural breaks in the absence of additional information. For our purposes, these tests 

are especially important because a number of factors may abruptly alter the course of food prices 

over time. For example, the imposition or elimination of Federal marketing orders can have discrete 

and significant impacts on prices in commodity markets, and researchers interested in commodityspecific supply and demand elasticities typically account for these (Russo et al., 2008).11

Other examples that may be pertinent to agriculture include the dynamics of international trade, 

food safety concerns, and severe weather events. We employ, whenever applicable, a technique 

derived by Kejriwal and Perron (2010) to identify endogenous structural breaks in the variables in 

the forecast models. The approach is rooted in deriving the limiting distribution of the Sup-Wald 

test on the error term of the model being estimated and then sequentially testing the null hypothesis of an autoregressive unit root with k breaks versus the alternative that there are k + 1 breaks.12

Structural breaks are incorporated into regression models using dummy variables. 

Vertical Price Transmission Approach 

In this section, we discuss the approach of vertical price transmission forecasting used to make 

monthly forecasts for each CPI subcategory. Because of the multiple stages involved in the U.S. 

food supply system, we chose a vertical price transmission framework to capture the impacts of 

this process on food price formation. Before considering the statistical framework of the model 

in detail, it is important to understand the steps involved in the vertical price transmission passthrough approach, as well as the underlying data (fig. 4). Pass-through models are the incorporation 

of first-stage forecasts as explanatory variables of the final forecasted output of interest. Given data 

availability, the ERS forecast model uses farm price projections to forecast the relevant farm PPI. 

The predicted farm PPI is then used as the key input to predict the wholesale PPI, which in turn is 

“passed through” to forecast the CPI in the final stage.

Forecasts of the Farm PPI

In the first step of the vertical price transmission process, ERS farm forecasts are used as the 

primary independent variable to predict the farm PPI for most food subcategories. The availability 

of these forecasts is a primary limiting factor in applying the vertical price transmission approach 

across food categories. The livestock and crop prices used as input variables include steers, barrow 

and gilt, broilers, turkeys and hens, farm eggs, farm milk, farm wheat, and soybeans.13

The farm forecast data on average monthly prices are available for soybeans and wheat. The PPI 

and CPI data are also produced monthly, so these forecasts can be used directly in the forecast 

models. However, the farm forecasts for steers (cattle), barrow and gilt (hogs), broilers, turkeys and 

hens, eggs, and milk reflect average quarterly prices.14 To adjust the quarterly forecasts to a monthly 

11Federal marketing orders are initiated by industry and may enforce quality, regulate product flow to the market, etc.

12Perron (1989) discusses the difference between a one-time change versus change in a trend. Both non-trending and 

trending instances are examined. The Sup-Wald test is used because it helps ease size distortions associated with the 

regular Wald test. For more information, see Kejriwal and Perron (2010).

13For poultry, wholesale prices are the farthest upstream point because the prevalence of contracting between farm and 

wholesale stages has made the farm price inconsistently related to wholesale price.

14ERS farm forecasts for these commodities reflect average quarterly pricing, but are updated monthly as new data 

becomes available. 
10

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

frequency, we employ the locally weighted scatter plot smoothing (Lowess) function. The Lowess 

function, developed by Cleveland (1979) and Cleveland and Devlin (1988), works to smooth the data 

by estimating the relationship between the historical quarterly commodity forecast and PPI series 

via regression. The estimated relationship from this regression is used to interpolate monthly average 

values for each of the quarterly commodity farm forecast series, which are then imported into the 

forecast models.

For fresh fruits and vegetables, the pass-through model goes directly from farm to retail. These 

retail foods are highly perishable and are thus defined by fixed proportions among inputs 

(Wohlgenant, 2001). Therefore, the wholesale stage adds little information, for the forecast model 

and price transmission may occur in these categories in under a month. For these categories, ERS 

farm forecasts are not available, so we use an augmented autoregressive distributed lag (ARDL) 

model to forecast future values of the respective PPI indices from historical data.

ARDL models use lagged (and potentially current) values of a variable of interest to forecast future 

values, in addition to current and lagged explanatory variables. In all applications of the ARDL 

approach, we take advantage of the lengthy time series of PPI and CPI data available to run in-sample 

forecasts to determine the optimal lag specification.15 We allow for lags as long as 12 months.16 By 

15In this case, lagged values are used as predictors for the future value. The optimal lag must be determined so that the 

model can pick up the true error process. Not having enough lags takes away the residuals’ ability to act as white noise. 

Whereas having too many lags reduces the ability of the Dickey-Fuller test to reject the null of a unit root. 

16Lag length is determined using the Hannan-Quinn information criterion.

Notes: PPI = Producer Price Index. CPI = Consumer Price Index.

Source: USDA, Economic Research Service. 

Figure 4

Illustration of the vertical price transmission pass-through model

ERS farm forecasts

•Steers

•Wholesale broilers

and turkeys 

•Barrows and gilts

•Farm eggs

•Farm milk

•Farm wheat

•Soybeans

•Note: There is no

farm forecast for

fruits or vegetables.

Farm and wholesale

PPI forecasts 

•Beef

•Processed poultry

•Pork

•Eggs

•Processed milk

•Wheat flour

•Fats and oils

•Fresh fruits

•Fresh vegetables

CPI forecasts

•Beef and veal

•Poultry

•Pork

•Eggs

•Dairy

•Bread

•Fats and oils

•Fruits

•Vegetables
11

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

comparing actual future values with predicted values, we calculate prediction errors and select the 

model with the best performance. 

Our model for fresh fruit and vegetable farm PPIs is estimated using 1972-2013 PPI data and takes 

the form

(1) FarmPPIi t PPI diesel sbreaks

j

j i t j d t    s i , , ’ ’ +1 = + α β ∑ − + + β β + β q i i t quarters + , ε

where i is fruits or vegetables, t is month, and j is a lag length specification. The number of lags used 

and their lengths are decided individually for fresh fruits and vegetables using the criterion of lowest 

overall prediction error, as discussed above.17 The model includes the diesel PPI to capture the 

role of transportation costs. The vector of structural breaks, which are incorporated into the model 

as dummy variables, are determined using the Kejriwal and Perron (2010) approach.18 Finally, 

quarterly dummies account for seasonality.19

Some of the model inputs are also forecasted values. Given the monthly frequency of the BLS data 

and fact that ERS regularly forecasts inflation for the coming calendar year, equation (1) is used 

each month to forecast between 6 (in June) and 18 (in July) months of future values. Therefore, in 

many cases, both the lagged farm price values and the current diesel prices are themselves predicted 

values. For example, to forecast the fresh vegetable PPI 10 months ahead calls for the diesel PPI 9 

months in the future, which necessarily must be a predicted value. Diesel prices are also forecasted 

using an ARDL approach.20

For the remaining categories for which we have proprietary farm forecasts, we forecast the farm PPI 

by estimating equation (1) but substituting the forecasted farm price from ERS for the autoregressive 

PPI forecasts. In these cases, equation (1) is no longer an ARDL model. For all other food categories 

forecasted using the error correction model (ECM), the farm forecast takes the following form:

(2) FarmPPIi t ERS Farm diesel sbreak

j

j i t j d t    s , ,

’ +1 = + α β ∑ _ − + + β β s quarters i q + + β ε i i t

’

,

where i represents the food category, t is month, and j is a lag length specification. The number of 

lags used and their lengths are decided individually. This model includes ERS farm forecasts in 

place of the farm PPI. The model also includes the diesel PPI to capture, again, the role of transportation costs.

17For fresh vegetables, the optimal distribution of lags is 1, 2, 6, 9, 10, and 11 months. For fresh fruit, it is 1, 6, 7, and 

10 months. The remaining optimal lag distributions for food price indices are available from the authors upon request.

18The Kejriwal and Perron algorithm identified structural breaks for vegetable prices in April 1978, December 1986, 

and November 1996. For fruit prices, the most recent break was found in January 1997, and the fruit forecast models 

work with data starting at that date. The endogenously determined structural breaks for the remaining variables in the 

forecast models are available upon request.

19Seasonal dummies are necessary as seasonality plays a major role in agriculture, and we are using the non-adjusted 

CPI and PPI data.

20The diesel PPI was not found to have any endogenous structural breaks. The optimal lag distribution was determined 

to be 1, 2, 4, 5, 7, and 8 months. The remaining optimal lag distributions for input prices are available from the authors 

upon request.
12

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

With the farm PPI forecasts in hand, it is now possible to estimate a series of equations, for each 

food category, intended to measure the transmission of input prices throughout the food supply 

system and thereby enable forecasting. The farm forecast is used as an input to predict inflation at 

either the wholesale or retail level. There are two types of pass-through models to forecast the CPI—

those that involve one stage of pass-through (farm to retail) and those that involve two (farm to 

wholesale and wholesale to retail). As shown in figure 4, some categories feature two stages of passthrough while some feature only one (table 3), depending on data availability and industry structure.

Table 3

The forecast models and U.S. Bureau of Labor Statistics (BLS) indices used

Food category Industry sectors Forecasted variable Key explanatory variable

Beef and veal Farm to wholesale Beef and veal products, fresh or 

frozen PPI

WPU022101

Slaughter cattle PPI

WPUSOP0131

Wholesale to retail Beef and veal CPI

CUUR0000SEFC

Beef and veal products, fresh or 

frozen PPI

Pork Wholesale to retail Pork CPI

CUUR0000SEFD

Pork products, fresh, frozen, or 

processed PPI

WPU022104

Eggs Farm to retail Eggs CPI

CUUR0000SEFH

Chicken eggs PPI

WPU017

Poultry Wholesale to retail Poultry CPI

CUUR0000SEFF

Processed poultry PPI

WPU0222

Dairy Farm to wholesale Dairy products PPI

WPU023

Raw milk PPI

WPU016

Wholesale to retail Dairy and related products CPI

CUUR0000SEFJ

Dairy products PPI

Cereals and bakery Farm to wholesale Wheat flour PPI

WPU021203

Wheat PPI

WPU0121

Wholesale to retail Cereals and bakery products CPI

CUUR0000SAF111

Wheat flour PPI

Fats and oils Farm to wholesale Fats and oils PPI

WPU0113

Soybeans PPI

WPU01830131

Wholesale to retail Fats and oils CPI

CUUR0000SEFS

Fats and oils PPI

Fresh fruits Farm to retail Fresh fruits CPI

CUUR0000SEFK

Fresh fruits and melons PPI

WPU0111

Fresh vegetables Farm to retail Fresh vegetables CPI

CUUR0000SEFL

Fresh and dry vegetables PPI

WPU0121

Fish and seafood 

(preliminary)

Wholesale to retail Fish and seafood CPI

CUUR0000SEFG

UBC Wholesale seafood price index

Notes: The BLS series IDs are provided beneath the series descriptions. CPI = Consumer Price Index. PPI = Producer Price Index. 

UBC = Urner Barry Comtell.

Source: USDA, Economic Research Service record of the sources of data used in the forecast models.
13

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Farm-to-Wholesale, Farm-to-Retail, and Wholesale-to-Retail Models

The farm-to-wholesale model, when applicable, is as follows:

(3) WholesalePPI FarmPPI electricity i t

j

j i t j  ,

 e

t , +1 = + α β ∑ − + + β βd t s i

k

k i t k i t

diesel  + sbreaks

+ + ∑ −

’

^

, ,

β

β ε ε

In this setting, the wholesale PPI is modeled as a function of a lag distribution for the predicted farm 

PPI. We also include the electricity PPI as a key measure of operating and processing costs at this 

stage, which similarly is forecasted using the ARDL process outlined above. When we estimate the 

wholesale beef PPI only, the electricity PPI is replaced by the slaughtering wage PPI.21 Diesel is 

included here to represent transportation costs from the farm to wholesaler.

Importantly, equation (3) explicitly includes information from lagged residuals, or error terms, when 

applicable. This information forms the foundation of the ECM forecasting approach. There are many 

varieties of ECMs, and they are commonly used for forecasting (Ghosh, 1993; Granger and Lee, 

1989) because they account for both short- and longrun impacts of a key independent variable (X) 

on the dependent variable of interest (Y). The underlying premise of the ECM approach is that X 

and Y share a longrun equilibrium relationship that largely defines the trajectory of Y and can be 

estimated. To parameterize this longrun relationship requires a lengthy time series of data, and this 

step is the primary reason that the existing data are insufficient to apply the vertical price transmission approach to selected CPIs. 

Changes in X or in other variables in the model can cause deviations from the equilibrium in the 

short run. The magnitude of these deviations can also be estimated and incorporated into the model, 

which for forecasting purposes increases precision (Greene, 2008). In our model, equation (3), these 

deviations manifest as a distribution of lagged residuals, which is established on a case-by-case basis 

using an algorithm developed by Nielsen (2001). The process essentially repeats the search pattern 

used to find the optimal lag distribution for X or the input price series, in our case, given the basic 

longrun relationship between X and Y.

Establishing the equilibrium relationship between X and Y is a process that depends on the 

statistical properties of the variables being studied. Every price index used in the forecast models is 

initially subjected to the augmented Dickey-Fuller test to test for the presence of an autoregressive 

unit root (Dickey and Fuller, 1981).22 Time series variables with unit roots are said to be 

nonstationary and are problematic in regression analysis and particularly forecasting. Regressions 

conducted on nonstationary variables are often spurious, because the relationship described between 

key variables of interest is an artifact of the data and does not reflect reality. In the cases where 

the Dickey-Fuller test indicates the presence of a single unit root, which is very common in time 

series data, variables are integrated to the order 1 (I(1)), which means that they are stationary if 

21The slaughtering wage is used specifically for beef, as it well represents the main processing cost to produce beef, 

whereas electricity better represents processing costs for other food categories.

22A process that has a unit root means that the mean is not stationary; it changes over time. Therefore, the null hypothesis of the Dickey-Fuller test is that the data needs to be differenced to make it stationary, and the alternative hypothesis 

is that the data is already stationary and does not need to be differenced. 
14

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

first differenced.23 Further action may be necessary in these cases, and Hamilton (1994) provides a 

thorough discussion of stationarity, unit roots, and the solutions to relevant problems. 

Having tested for unit roots, we next test for cointegration for all pairs of stationary I(1) indices to be 

modeled.24 Cointegration occurs when a linear combination of nonstationary variables is stationary. 

In other words, the variables share a stable relationship over time that can be described, in our case, 

as a*X + b*Y where a and b are constants. Engle and Granger (1987) developed a well-known test 

for cointegration and established the importance of cointegration for ECM estimation. In essence, 

the stationary, linear relationship that defines cointegration also provides the longrun equilibrium 

between X and Y. We apply the Engle Granger test and find that most of our key pairs of price 

indices are cointegrated.25 For all estimations involving pairs of cointegrated indices, we apply a 

series of ECMs to conduct our forecasts. In the remaining cases, we use ARDL models, which have 

been shown to be comparable under a wide range of circumstances (Keele and De Boef, 2004). For 

these estimations, equation (3) does not include lagged residuals. 

We next test for endogenous structural breaks. We apply the Kejriwal and Perron (2010) procedure 

for identifying multiple structural breaks at unknown intervals in the data to the joint probability 

distribution of X and Y. That is, we test for shifts in the statistical properties of both key indices 

simultaneously. This procedure is applied whether or not the two series were found to be cointegrated. Doing so can greatly improve precision and accuracy in forecasts, relative to running the 

algorithm individually for X and Y. This explains why, in some cases, we do not use the full time 

series available from BLS when estimating our models. For example, a structural break in fruit 

prices leads us to use only CPI and PPI data for fruit from 1997 on.

The final step in crafting the ECMs is to determine the appropriate lag length of X, or the farm 

PPI series. Unlike estimating ARDL models, ECMs are constrained in that the lags of X must be 

consecutive. We, therefore, follow a standard procedure of beginning with the default option of a 

single lag of 1 month and extending the model from there. The optimal lag distribution is chosen 

as the one that minimizes the Hannan-Quinn information criterion (HQIC), a common model 

selection statistic that is rooted in the sum of squared errors (Hannan and Quinn, 1979).26 The 

selected lag distribution must also be logically appropriate for the industry sectors to which it is 

being applied. For example, the HQIC may be minimized for a lag distribution that is implausible for a given food, either too long or too short to facilitate pass-through. For this reason, ERS 

subject specialists for the relevant commodities and markets have been consulted for their input 

and guidance on model selection.

23Multiple unit roots are possible though less common in time series analysis. Stationary (d) indicates a variable that 

must be differenced d times in order to be stationary.

24Results from the unit root tests are available from the authors upon request.

25We also apply other established tests for cointegration, including that devised by Phillips and Perron (1988), to find 

the same effect throughout.

26The HQIC is one of three very common model selection criteria; the others are the Akaike Information Criterion and 

the Schwartz Information Criterion. For very large sample sizes, there is no meaningful difference among the three, but 

for small to moderate sample sizes, as is the case in our forecast models, the three differ in the extent to which they penalize the differences between predicted and actual values of the dependent variable. The HQIC, in these cases, is neither 

the most nor the least penalizing criterion.
15

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Each of the steps outlined for the estimation of equation (3) also apply to the farm-to-retail and 

wholesale-to-retail models. Price transmission to the retail sector is modeled in the same way, 

regardless of the nearest downstream sector. The regression equation is:

(4) CPI PPI gsw diesel sbreaks i t

j

j i t j e d t s i

 , ,   ’

+1 = + α β ∑ − + + β β +β + + ∑ −

^

, ,

k

k i t k β ε i t ε .

where the only substantive change from equation (3) is the use of the grocery store wage, another 

PPI, as a key input price.27 It is used to capture labor costs. In this equation, diesel is used to represent the cost of transport from wholesale to retail.

Estimation of Forecasting Models

For those pairs of series found to be cointegrated, there are a number of estimation options within 

the ECM family, including the threshold, symmetric, and asymmetric. When exploiting a longrun 

equilibrium between X and Y using an ECM, the default choice is to estimate a symmetric ECM. 

This model treats deviations from the equilibrium in the same manner, regardless of direction. Two 

other options that may be suitable for our purposes are the asymmetric ECM and the threshold ECM 

and they are worth discussing briefly.

The asymmetric ECM, developed by Granger and Lee (1989), posits that the dependent variable 

may respond differently to deviations from the longrun equilibrium, depending on the direction. 

Practically, this effect requires estimating separate coefficients for lagged residuals for deviations 

upward and downward. For our specific purposes, the effect implies that agents in the food supply 

chain may respond differently to price increases and decreases. A lengthy literature of theoretical 

and applied research examines asymmetric price transmission and input price pass-through. (See 

Meyer and von Cramon-Taubadel, 2004 for a review of the work specific to food prices.) Kinnucan 

and Forker (1987) found evidence that input price increases are passed along faster and more 

completely than are decreases.28

The threshold ECM treats deviations from the longrun equilibrium differently depending on their 

magnitude. Balke and Fomby (1997) argued that market forces may not always be strong enough 

to drive a relationship back to equilibrium in the short run. If adjustment costs, as an example, are 

higher than the deviation, then agents have no incentive to return to equilibrium. We are motivated 

to apply this model to food prices based on the empirical evidence that food prices are rigid—that 

they do not change as frequently as theory would suggest they ought to (Bils and Klenow, 2004). 

Menu printing costs are commonly cited as a cause of retail food price rigidity. Even small supermarkets have thousands of products with prices posted on the shelves. The labor and printing costs 

associated with frequently changing these prices have been estimated to be high (Levy et al., 1997), 

potentially contributing to a threshold approach in price adjustment.

27The PPI variable here can be interchanged with the farm and wholesale PPI, depending on the food category being 

forecasted. Farm-to-retail models use the Farm PPI, and the wholesale-to-retail models use the wholesale PPI.

28The complete theoretical underpinnings of such a finding, as well as the consensus or lack thereof with respect to this 

phenomenon, are beyond the scope of this bulletin. However, industrial organization theory suggests that, in certain conditions, retailer incentives favor passing cost increases on to consumers to protect profits, while absorbing cost decreases 

to widen margins. 
16

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

We provide a summary of the results of cointegration testing, the estimated importance of error 

correction, and the lag length specifications (table 4). For egg, fruit, and vegetable prices, we are 

unable to apply ECMs due to the lack of cointegration, but the BLS data are rich enough to enable 

the estimation of ARDL models. Also notable is that for all three of these foods, prices are estimated to pass-through (at least partially) from farm to retail in under a month. These are foods characterized by minimal processing and high perishability. 

Autoregressive Moving Average Approach

For the remaining CPIs that ERS forecasts directly—other meats, fish and seafood, processed fruits 

and vegetables, sugar and sweets, nonalcoholic beverages, other foods, and food away from home—

the data currently available do not enable use of any of the vertical price transmission models 

discussed above. Therefore, since it is not necessary to examine the statistical properties of more 

Table 4

Diagnostics used to determine the ideal forecasting approach, by model

Category Model Cointegration1 Error correction2 Timing3

Beef Farm to wholesale Yes Symm. ECM 1

Wholesale to retail Yes Threshold ECM 1 to 2

Asymm. ECM 1 to 5

Pork Wholesale to retail Yes Symm. ECM 1 to 3

Threshold ECM 1 to 3

Eggs Farm to retail No None (ARDL) 0 to 5

Poultry Wholesale to retail Yes Threshold ECM 1 to 4

Symm. ECM 1 to 4

Dairy Farm to wholesale Yes Symm. ECM 1 to 2

Wholesale to retail Yes Threshold ECM 1

Asymm. ECM 1 to 2

Bread Farm to wholesale Yes Symm. ECM 1

Wholesale to retail Yes Threshold ECM 1 to 4

Asymm. ECM 1 to 4

Fats & Oils Farm to wholesale Yes Symm. ECM 0 to 2

Wholesale to retail Yes Asymm. ECM 1 to 3

Threshold ECM 1 to 5

Fresh Fruit Farm to retail No None (ARDL) 0, 11, 12

Fresh Vegetables Farm to retail No None (ARDL) 0 to 3, 6 to 8

1Each pair of indices was tested for cointegration using the approach developed by Engle and Granger (1987).

2These are the ECM models that were found to be statistically significant for each category. For the cases in which cointegration was rejected, the ARDL model was used.

3These give the lag distribution of the key independent variable that minimized prediction error. 

Notes: ECM = Error Correction Method, ARDL = Autoregressive Distributive Lag. 

Source: USDA, Economic Research Service record of the methodology used for each forecasted category.
17

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

than one index for these CPI subcategories, tests for cointegration or joint probability distribution are 

not applicable. 

At this time, ERS forecasts these CPIs using an autoregressive moving average (ARMA) approach 

that is designed to capture the general trajectory of the prices in question.29 The model used to forecast these CPIs is as follows:

(5) CPI CPI CPI CPI i

k

k i t k i Lag Year i Lag Years

 = + α β ∑ , , − + + β β 1 1 2 2 , + β3

5

3

4 1 5

3

j

t

i LagjYears

i Lag Year i Lag

CPI

AllCPI AllCPI

=

−

∑

+

+

,

β β , , 2 6

5

3

3 Years

j

t

i LagjYears

s i t t

AllCPI

+ + sbreaks t + + rend =

−

∑β β β , ’ ’

εi t, .

Model (5) contains two lag structures, one monthly and one yearly. Indexed by k, the monthly lag 

structure includes lagged and current values of the CPI being forecasted and captures seasonality 

without adding unnecessary structure. For example, it is not clear that the standard four-quarter 

approach serves as a meaningful control for fish prices, even though its usefulness for products such 

as fresh produce is well established. The number of lags used depends on the month in which the 

forecasts are made. For current-year forecasts, the distribution begins with December of the previous 

year for the January forecast and is extended with each available month of data, through the June 

forecast, which includes data through May. Forecasts for the upcoming year begin each July, and 

the monthly lags include all data available for the current year. This lagging scheme is intended to 

capture and account for deviations from expected price movements in recent history. 

The yearly lag structure includes the realized CPI values for the previous 2 years as well as the average 

for the 3 years prior, incorporating data from 5 historical years in total. This data-generating process 

cannot forecast or correct for extreme shocks, such as severe weather events, but captures longrun 

trajectory of average prices, which is seen by a plot of annual changes in the food CPI over the years 

(fig. 5). From 1991 to 2013, food prices have increased by an average of about 2.6 percent. Deviations 

from this average value are followed by changes in the opposite direction, effectively returning the 

course of inflation back to normal.30 We apply these annual lags to both the forecasted CPI and the 

all-items CPI, which is the index used by BLS to measure economywide inflation across all consumer 

spending. In this way, we attempt to capture the cyclicality of the economy as a whole. 

Structural breaks are once again determined, on a univariate basis, following the Kejriwal and 

Perron (2010) approach. They are then incorporated into equation (5) using dummy variables. 

Selected estimations of equation (5) include a linear time trend. Trends are commonly used in time 

series analysis to capture intangibles such as technological change. In our case, a time trend is used 

in those cases for which a joint test of significance rejects the importance of the yearly lag structure 

for the forecasted CPI. The rejection of this hypothesis indicates that recent changes in the CPI do 

not effectively explain the direction of prices and the time trend is used to capture a potentially more 

nuanced pattern than that shown in figure 4. 

29An ARMA model applies both autoregressive and moving average analysis to the time series data. The model assumes the time series data is stationary around a time-invariant mean. 

30Though not explicitly tested (as it is not forecasted directly), the food CPI almost surely exhibits structural breaks 

that very nearly follow calendar decades. Over time, food price inflation has fallen considerably in both average levels 

and volatility. During the 1970s, the average annual increase in the food CPI was over 8 percent. In the 1980s, it was over 

5 percent.
18

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Note: CPI = Consumer Price Index.

Source: U.S. Bureau of Labor Statistics and USDA, Economic Research Service calculations.

Figure 5

Annual changes in the food Consumer Price Index, 1991-2013

Percent

0

1.0

2.0

3.0

4.0

5.0

6.0

20-year historical average: 2.6%
19

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Post-Estimation Evaluation and Forecast Intervals 

Whether CPI forecasts are made using the vertical price transmission approach or the autoregressive methodology, the forecasted estimates are evaluated in light of the breadth of current knowledge on the relevant commodity markets and price trends. As an example, when ERS conducted 

the CPI forecasts in June 2012, a drought of potentially historic proportions was settling on the 

Midwest United States. Although the relevant crop forecasts lacked the information to incorporate 

the drought’s impact, the drought’s size suggested that the forecast models for certain affected foods 

underestimated inflation and, therefore, needed a post-estimation adjustment. 

Each month, ERS forecasters consult a variety of sources for information on food price trends. 

These sources include the respective ERS Outlook publications for the various commodities used 

in the forecast models, updates from USDA’s World Agricultural Supply and Demand Estimates 

(WASDE) and USDA’s Foreign Agricultural Service (FAS), as well as publications of the 

International Monetary Fund (IMF) and selected private forecasters. In most instances when information drawn from outside the forecast models motivates a change in the forecast, ERS forecasters 

discuss the potential change with the appropriate ERS commodity or crop subject specialist to 

confirm that the adjustment is reasonable in both magnitude and direction.

For the vertical price transmission estimations with established cointegration, the forecast models 

uniformly produce four forecast estimations—symmetric ECM, asymmetric ECM, threshold ECM, 

and ARDL. In nearly all cases to date, the four estimates suggest the same direction for food price 

inflation (upward or downward), but the magnitude can vary. The ARDL result is typically apportioned the least weight of the four in determining the published forecast, though it is useful as a 

measure of the robustness of the forecast. Among the ECM results, the symmetric ECM result is 

given the greatest weight for all estimates of price transmission to the wholesale sector. For transmission to the retail sector, those estimations for which error correction was found to be significant 

are given greater weight (see table 4). In the following paragraphs, we discuss more in-depth the 

model diagnostics and the relative performance of these four estimation methods.

The monthly frequency of the BLS data, which contrasts with the annual frequency of the ERS forecasts, provides an additional measure for the post-estimation calibration of forecasts. Each month, 

ERS calculates the average value for each forecasted CPI to date in the current year. Typically, ERS 

forecasters then impute CPI values for the months remaining in the current year according to a 

selection of hypothetical scenarios, including no changes to food prices or heavy inflation—e.g. 0.5 

percent, each month. Then the actual and imputed monthly values for the current year are averaged 

and compared to the realized annual CPI of the previous year to obtain point estimates of inflation. 

This approach is of very limited value early in the calendar year, and it is not used to generate forecasts. However, as the year progresses, the approach is very helpful in judging how well the forecast 

estimates from our models compare to the behavior of prices. For the year’s final few months, enormous price shocks would be required for forecasts to deviate from the inflation estimates calculated 

using this approach.

With a forecast point estimate in hand, after running the models and calibrating as needed using 

additional information, we construct an interval of 1 percentage point in order to report the forecasts 

(see table 1).31 Doing so accounts for some degree of inherent uncertainty in forecasting, as well as 

31Rounded 1-percentage-point intervals are used for ease of communicating with the general audience.
20

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

the specific factors that cannot be forecasted rigorously in our case, particularly the weather. Each 

month, a new set of point estimates is calculated across the food categories and compared to the 

published intervals. When a forecast’s point estimate lies outside of the current interval, the forecast 

is updated accordingly to capture the revised point estimate. 

Comparing Forecast Performance of Previous and Revised 

Forecasting Methods

Prior to 2011, ERS food price forecasts were conducted using primarily a univariate moving average 

approach, the details of which are available in Joutz et al. (2000). Given that we have electronic 

records of monthly forecast releases dating back to January 2003, it is appropriate to apply the 

vertical price transmission pass-through and augmented ARMA approaches to conduct out-ofsample forecasts for the period 2003-2010 and compare accuracy and precision between the previous 

and current methodologies.32,33 However, the 2003-2010 forecasts, in the same manner as those 

made today, also incorporated institutional knowledge drawn from commodity market experts, farm 

price forecasts, and financial markets to adjust the point estimates drawn from the forecast models. 

Given that it is not possible to access the same portfolio of institutional information available to ERS 

forecasters at the time older forecasts were made and subsequently adjusted, directly comparing the 

previous and revised approaches over the 2003-2010 period is not appropriate. As an alternative, we 

present statistics on aggregate forecast performance of both the revised methods over the 2011-2013 

period and the previous method over the 2003-2010 period (table 5) for readers to compare. We also 

provide statistics on the overall volatility of food prices and input costs during these two time periods. 

All of the statistics presented indicate an increase in forecast accuracy and precision using the 

revised forecasting methods. Changes in the quality of forecast performance can reflect perceived 

shocks to food prices that could not be predicted (e.g. severe weather events), but if all else is equal, 

fewer forecast revisions indicate greater forecast accuracy. Recall that ERS forecasts for any given 

year are published and subject to revision for 17 months. On average, per category, 3.7 changes were 

made between 2003-2010 and 3.2 changes from 2011-2013. 

We also measured, in absolute terms, the extent to which initial forecasts differed from the realized 

CPI values. From 2003-2010, initial forecast midpoints were 2.6 percentage points removed from 

actual values, while the average difference was 2 percentage points for 2011-2013.34 There is also 

a notable difference in the maximum divergence between the initially forecasted and actual CPI 

outcomes over the two time periods. From 2003-2010, the maximum difference between initially 

forecasted and realized values averaged 12.5 percentage points. From 2011-2013, this value was only 

6 percentage points. This disparity indicates that under the revised forecast methodology, initial 

predictions were closer to the ultimately realized CPI value. The statistics for forecast adjustments, 

by year and category, are available in table A.1 of the appendix.

32An out-of-sample forecast uses historical and current data to make forecasts into the future. We then wait until that 

future date to compare the predicted with the actual amounts.

33The published forecasts for any period of time from 2003 onward are available from ERS upon request.

34Given that ERS forecast intervals are 1 percentage point, an alternative measure of forecast precision is to measure 

the difference between the forecast bounds and the realized CPI values. In this setting, the average differences were 2.1 

percentage points for 2003-2010 and 1.5 percentage points for 2011-2013.
21

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

The challenges associated with forecasting are directly related to the volatility of the variables of 

interest. An economic indicator that varies little over time and follows a clear trajectory is relatively 

easy to forecast with precision. Therefore, we compare the volatility of food prices and key measures 

of upstream costs across the two time periods. We measure volatility in two ways. One common 

measure of dispersion is the coefficient of variation (CV), which is calculated as the sample standard 

deviation divided by the sample mean. The other is the average absolute value of the monthly change 

in indices, which is reported in percentage points. Under certain circumstances, the two measures 

can give conflicting results.35 But the overall pattern that emerges is that wholesale and retail food 

35For example, the average annual CVs suggest that diesel prices were more volatile from 2003-2010, while the average 

monthly changes showed slightly greater volatility during 2011-2013. The CV increases as variables trend away from 

their measure of central tendency. The diesel PPI exhibits large swings over time, which typically feature increases followed by decreases of comparable size. In the first time period, the magnitudes of the swings were larger on average. But 

in the second time period, the increases were relatively larger than the decreases, resulting in a clear upward trend.

Table 5

Aggregate statistics on forecast adjustments, performance, and price volatility, 2003-2010 and 2011-2013

2003-2010 2011-2013

Average forecast changes, across categories, per year 81.37 71.33

Average forecast changes, per category, per year 3.69 3.24

Average forecast change (% points), across categories 2.61 2.07

Average minimum adjustment per year (% points), across categories 0.13 0.08

Average maximum adjustment per year (% points), across categories 12.56 6.08

Average annual CVa

Food CPI 0.008 0.006

Food-at-home CPI 0.010 0.006

Crude foods and feeds PPI 0.052 0.034

Intermediate foods and feeds PPI 0.028 0.024

Finished consumer foods PPI 0.014 0.011

Diesel PPI 0.216 0.097

Electricity PPI 0.036 0.053

Average monthly change (%)b

Food CPI 0.556 0.525

Food-at-home CPI 0.758 0.691

Crude foods and feeds PPI 3.427 3.586

Intermediate foods and feeds PPI 1.958 1.975

Finished consumer foods PPI 1.239 1.114

Diesel PPI 7.070 7.567

Electricity PPI 1.735 1.736

Notes: Average forecast changes, per year: total number of times the forecast was changed, either across all 19 categories or by individual category. Average forecast change (percentage points): change in the forecast in percentage point terms across categories. Average 

minimum adjustment per year: the average minimum percentage point change per year. Average maximum adjustment per year: the average 

maximum percentage point change per year. 

aCV is the coefficient of variation, calculated as the sample standard deviation divided by the sample mean. It is a unitless measure of 

dispersion. We calculated the CV for each year to measure volatility across the months, then calculated average annual CVs for the two time 

periods of our analysis.

bU.S. Bureau of Labor Statistics (BLS) calculates monthly percentage changes for all Consumer Price Indices (CPIs) and Producer Price 

Indices (PPIs). These are averages of the absolute values of the changes, taken across all monthly observations within each time period. 

Source: USDA, Economic Research Service (ERS) calculations using ERS Food Price Outlook forecast data and BLS’s CPI and PPI.
22

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

prices, as well as energy prices, were slightly more volatile during the 2003-2010 period. The difference is not economically significant; for example, the average monthly change in the food CPI across 

the time periods is 0.03 percentage points. 

Taken together, the findings support the notion that overall forecast accuracy is improved since the 

methodology was revised. However, it is important to note that more years of data are needed to 

properly assess forecast performance. Moreover, there is substantial room for improvement among 

the forecasts conducted from 2011-2013. In the Conclusion, we discuss options under exploration for 

improving and refining the ERS forecast methodology. 

Comparing Forecast Accuracy Across Vertical Price 

Transmission Approaches

As outlined in the description of the forecast methodology, the vertical price transmission passthrough models are estimated in four distinct, but related, ways. In this section, we analyze a series 

of quarterly forecasts conducted using symmetric ECM, asymmetric ECM, threshold ECM, and 

ARDL for all of the categories featuring sufficient data. As previously noted, the significance or lack 

thereof of error components suggests the models that are most likely to fit the data and perform well 

for forecasting purposes (see table 4). For this exercise, the forecasts produced by the models have 

not been adjusted using additional information. We conduct out-of-sample, one-quarter ahead forecasts for all of the price transmission models estimated in our vertical price transmission approach 

(fig. 6). We compare the forecasts to actual CPI and PPI values for the years 2012-2013.

Forecasting favors techniques that produce the smallest errors, or alternatively achieve the greatest 

precision, over time. To assess precision, we employ a series of diagnostics. The first measure of 

precision that we calculate is the mean squared error (MSE), which is a measure of forecast error 

dispersion. The MSE has been used as a forecasting diagnostic tool for decades and is appropriate in 

a wide range of circumstances and model specifications (Gneiting, 2014). Choosing the method with 

the smallest MSE is equivalent to selecting the model with the smallest sum of squared residuals in 

typical regression analysis—the model of best fit.36 The equation used to calculate the MSE is:

(6) MSE e n t

n

= t

=

( ) ∑ /

1

2

where e y y t t = − t

 , the forecast error, and n represents the number of observations. Granger and 

Newbold (1986) developed a methodology for testing the null hypothesis of equality in MSE across 

forecast models.37 We apply this method here to test if there are significant differences in performance across the pass-through models by food category. 

36R2 is not an appropriate measure of fit in terms of forecasting models (Diebold, 2006), and hence it is not included in 

this analysis.

37The test for equality in MSE across models consists of testing that the variances in the errors across models are 

equal, or Var(e1) – Var(e2) = 0, for models 1 and 2. Simple arithmetic boils this testing if (e1 + e2) and (e1 - e2) are correlated. One of the assumptions underlying this test is that models 1 and 2 are unbiased over time, and in the pages that 

follow, we demonstrate evidence that this may not be true in some cases. Therefore, particularly in those cases where bias 

cannot be ruled out, the tests of equality in MSE must be considered with that caveat in mind. The complete details of 

this test are available from Granger and Newbold (1986).
23

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Note: m = month (as in “2012m1”). ECM = error correction model. ARDL = autoregressive distributed lag. CPI = Consumer Price Index.

Source: USDA, Economic Research Service.

Figure 6

One-quarter ahead in-sample forecasts, by vertical price transmission approach, compared with realized 

CPI values

Index value Index value

Index value Index value

CPI 

Symmetric ECM 

Asymmetric ECM 

Threshold ECM

ARDL 

Index value Index value

Index value Index value

Index value

240

245

250

255

260

265

270

275 Beef

180

190

200

210

220

230

240

250 Eggs

205

210

215

220

225

230

235

240

Poultry

195

197

199

201

203

205

207

209

211

213

215

Pork

200

205

210

215

220

225

230

Dairy

305

310

315

320

325

330

Bread

320

325

330

335

340

345

350

355

360 Fruit

300

305

310

315

320

325

330

335

340

345

350 Vegetables

220

222

224

226

228

230

232

234

236

238

240 Fats and Oils
24

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

The MSE does not measure the relative scale of the error across the food categories. Therefore, we 

also calculate the mean squared percentage error (MSPE), which measures the dispersion of forecast 

error as a percentage of the estimated value (Diebold, 2006). This is useful for our purposes in that 

BLS indices can vary substantially in magnitude. Here the MSPE is calculated using the following 

equation:

(7) MSPE y y y

n

t

n

t h t h t h

= − ( ) = ∑ + + + 1

2

100

[( ) / ]

*

^

.

One of the most basic forecasting diagnostic is the mean error (ME), which is simply the average 

forecast error across the time series. The ME is calculated as follows:

(8) ME e n

t

n

= t

=

( ) ∑ /

1

.

The key distinguishing characteristic among ME and MSE, MSPE, and other commonly used 

metrics such as the mean absolute error is that it maintains the sign of residuals. In doing so, 

information can be lost when calculating the mean because overestimations are canceled out by 

underestimations. Therefore, the ME is of limited use in determining the precision of forecast 

models, but it is helpful in establishing whether or not models are biased. Statistically, a forecast 

model is biased if it is significantly more likely to over- or underestimate the variable of interest 

over time. The Congressional Budget Office identifies bias as a major priority in assessing the 

performance of agency forecasts and relies chiefly on the ME to test for bias (Burns, 2013).

A series of statistical tests have been devised to establish biasedness based on ME and related 

metrics. Most, however, rely on large samples of data, and we are limited in that regard. Croushore 

(2012) developed a test for the null hypothesis that the forecast error has a mean of zero (ME = 0), 

which is valid in small samples. The test consists of regressing the forecast error, as defined above, 

against an intercept only and testing if the estimated intercept term is equal to zero. 

Next, we calculate Theil’s U statistic, another measure of relative forecasting error. Theil’s U 

compares forecasted values using our vertical price transmission approaches with a naïve forecast 

that draws on only information from the preceding time period. In essence, this technique compares 

forecast results to a random walk of value for the variable of interest. Following Diebold (2006), 

Theil’s U statistic is calculated as follows:

(9) Theil sU y y

y y

t

n

t t t

t

n

t t

’ , ( )

( ) = −

−

− + +

− +

∑

∑

1 1 1

2

1 1

2

where yt+1,t is referred to as the naïve forecast. The resulting value is a ratio, where a value of one 

indicates that the forecast values are as likely to be as correct as those drawn from a random walk, 

or by guessing. Values less than one indicate forecasting performance greater than a random walk, 

and values greater than one indicate forecasting performance that is no superior to guessing. Diebold 

(2006) notes that, in select circumstances, it is not appropriate to equate these naïve forecasts with a 

random walk. Therefore, for our purposes, we compare Theil’s U statistics across models and ascertain that, according to this metric, the model yielding the lowest value has thus far produced the 

most precise forecast estimates. 
25

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

The different model performance statistics (table 6) do not always yield a consensus as to which 

approach performs the best over time. It is worth stressing that these forecast models have only 

been in use by ERS for a short time and, given more data, it will likely become clearer which is 

the preferred approach. The MSE and MSPE mostly yield qualitatively similar rankings across 

the models. For fruits, vegetables, and eggs—the categories for which cointegration could not be 

established and error correction components were insignificant—the ARDL model performs best 

or nearly best. However, the ARDL also is more accurate for fats and oils and dairy retail prices, 

raising questions about the stability of the longrun equilibria governing the two price series. 

Comparing forecast accuracy across the different vertical price transmission models is useful in 

attributing weight to the forecasted point estimates each month when studying the updated BLS data 

and considering forecast revisions. For some categories, the model with the lowest MSE performed 

significantly better than at least one alternative. This was true for the following CPIs: Beef, Eggs, 

Pork, Dairy, Vegetables, and Fats and Oils—and for the Fats and Oils PPI. In other cases, one model 

performed significantly better than all of the other choices. For example, the threshold ECM is 

clearly favored when forecasting the Beef CPI, and therefore, this point estimate is given the greatest 

consideration in the analysis. It is also notable that the threshold error component was found to be 

highly significant in the beef CPI models (see table 4). Alternatively, for the case of the Eggs CPI, 

the ARDL model has the lowest mean squared error, but this difference is only significant when 

compared to the threshold ECM. Therefore, when evaluating point estimates for this category, the 

threshold ECM result is of interest only for checking robustness while the three remaining estimates 

are given approximately equal weight.

The diagnostics indicate that some of the forecast models may be biased. As with any regression 

model, the forecast errors should be random over time, indicating that the estimated coefficients are 

correct on average. Evidence to the contrary suggests that the forecast model requires changes to 

the specification or more information. In some cases, only some of the pass-through models exhibit 

evidence of bias. For example, the asymmetric ECM and ARDL models do not reject the null 

hypothesis of zero average mean error despite potential problems with the symmetric and threshold 

ECMs. However, ERS consistently overestimates inflation for the Dairy and Vegetable CPIs while 

underestimating in the case of retail egg prices. As with all of our forecast point estimates, the 

output of these models is consistently considered in tandem with additional information from 

the underlying commodity markets and other sources, which serves to mitigate the issue of bias. 

Moreover, the time series for these ECM and ARDL models is too short to facilitate traditional tests 

of model bias, which have more power. In practice, ERS forecasters treat evidence of bias similar to 

significant differences in MSE across models. Those specifications exhibiting the greatest likelihood 

of bias, within product categories, are afforded the least weight in the forecast adjustment procedure. 

By and large, Theil’s U statistic supports the notion that all four models yield highly comparable 

forecast estimates. However, the metric also reveals some interesting comparisons across models 

that warrant further observation given a longer time series of data. For example, the asymmetric 

ECM clearly outperforms all other models in forecasting the beef CPI. This result is consistent 

with the notion that retailers pass on upstream beef price increases quickly and more completely to 

consumers than they do decreases. Alternatively, the asymmetric ECM performs rather poorly for 

the poultry CPI while the threshold ECM performs the best. This result suggests that retail poultry 

prices require greater input price shocks before adjusting than do, for example, pork or beef prices. 

The threshold ECM is also the best performing model for breads and cereal products. 
26

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table 6

Performance statistics for the four vertical price transmission, out-of-sample forecasting approaches, 

by category and stage of processing

Mean Squared Errora Mean Squared % Error

Price Transmission

Threshold ECMAsymm. 

ECM

Symm. 

ECM ARDL

Threshold ECMAsymm. 

ECM

Symm. 

ECM ARDL

Cattle PPI – beef PPI 5.46 5.57 5.70 6.38 2.72 2.78 2.84 3.20

Beef PPI – beef CPI 1.96 2.77 2.55 2.36 0.74 1.05 0.97 0.89

Eggs PPI – eggs CPI 10.77 9.39 9.18 8.62 4.92 4.29 4.20 3.94

Poultry PPI – processed poultry CPI 3.04 1.71 2.63 1.71 1.34 0.76 1.16 0.75

Pork PPI – pork CPI 3.58 4.07 4.24 4.18 0.38 0.43 0.45 0.44

Milk PPI – dairy PPI 7.92 8.10 8.09 8.08 3.60 3.68 3.69 3.69

Dairy PPI – dairy CPI 3.01 3.18 3.27 2.79 1.39 1.47 1.51 1.29

Wheat PPI – wheat flour PPI 14.09 13.00 12.87 10.21 6.10 5.63 5.57 4.45

Wheat flour PPI – bread CPI 3.44 3.16 3.13 3.11 1.08 1.00 0.98 0.98

Fruit PPI – fruit CPI 7.39 9.43 7.55 6.76 2.16 2.80 2.24 2.00

Vegetables PPI – vegetables CPI 18.18 18.80 17.74 18.18 5.87 6.07 5.72 5.86

Soybeans PPI – fats and oils PPI 9.16 10.57 9.34 8.01 3.12 3.60 3.20 2.78

Fats and oils PPI – fats and oils CPI 3.90 4.57 3.55 3.05 1.68 1.97 1.53 1.31

Mean Errorb Theil’s U Statistic

Price Transmission

Threshold ECMAsymm. 

ECM

Symm. 

ECM ARDL

Threshold ECMAsymm. 

ECM

Symm. 

ECM ARDL

Cattle PPI – beef PPI 3.40* 3.26* 3.45* 1.36 1.15 1.14 1.13 1.03

Beef PPI – beef CPI 1.13* 1.89 0.21 -0.62 1.13 0.81 1.08 1.17

Eggs PPI – eggs CPI 7.33*** 5.83*** 5.46** 5.26** 1.25 1.29 1.30 1.27

Poultry PPI – processed poultry CPI 2.84*** 0.29 2.41*** 0.70 0.57 0.96 0.66 1.09

Pork PPI – pork CPI -0.07 -1.49 -0.89 -1.54 0.62 0.71 0.68 0.70

Milk PPI – dairy PPI 1.04 0.60 -0.58 -2.54 0.85 0.86 0.87 0.89

Dairy PPI – dairy CPI -1.65** -2.77*** -3.01*** -2.25*** 0.76 0.78 0.77 0.73

Wheat PPI – wheat flour PPI 11.74*** 10.98*** 10.73*** 2.98 0.85 0.84 0.84 0.82

Wheat flour PPI – bread CPI 0.95 -1.25 -0.13 -1.47 0.67 0.74 0.72 0.83

Fruit PPI – fruit CPI 4.02** -8.31*** -4.88*** -3.97** 1.16 1.12 1.14 1.13

Vegetables PPI – vegetables CPI -14.36*** -14.42*** -12.62*** -11.78*** 0.86 0.87 0.85 0.83

Soybeans PPI – fats and oils PPI 1.83 0.40 0.58 -5.75** 0.85 0.82 0.82 0.75

Fats and oils PPI – fats and oils CPI 3.84*** 4.57*** 3.39*** 0.21 1.17 1.15 1.18 1.15

aDifferences were tested in MSE across models following Granger and Newbold (Granger, C.W., and P. Newbold. 1986. Forecasting 

Economic Time Series, 2nd Edition. Orlando, FL: Academic Press). Following Park (Park, T.A. 1990. “Forecast Evaluation for Multivariate 

Time-Series Models: The U.S. Cattle Market,” Western Journal of Agricultural Economics 15(1):133-143), the lowest MSE per category is 

italicized, and those MSEs that are statistically higher than the minimum are boldfaced. 

bForecast bias was tested for, following Croushore (Croushore, D. 2012. “Forecast Bias in Two Dimensions,” Working paper 12-9, Federal 

Reserve Bank of Philadelphia. Available at:http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2040747), modifying the classic test of 

biasedness for small samples. If the average mean error is statistically different from zero, then the forecast model is said to yield biased 

results that are statistically more likely to over- or underestimate the actual value. 

*indicates that the mean error is statistically different from zero at the 0.10 level; **at the 0.05 level; and ***at the 0.01 level. 

CPI = Consumer Price Index. PPI = Producer Price Index.

Source: USDA, Economic Research Service (ERS) calculations using ERS Food Price Outlook forecast data.
27

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Lastly, we perform a directional analysis to examine the extent to which the forecast models anticipate changes in the direction of price movements. We calculate the number of times the forecast 

predicts a movement in the same direction as the index throughout the time series—that is, how 

effective the models are at predicting directional changes in the variables of interest.38 The optimal 

forecast for our purposes minimizes expected loss, where loss is defined as incorrectly forecasting 

the sign of monthly price changes. The loss function is written as follows:

(10) : , , ( )

LossFunction L y y if sign y sign y

 ( ) =  1 ( ) ∆ ≠ ∆

0, ( if sign ( ) ∆y s = ∆ ign y)

{ 

In our setting, this function is useful for identifying two key types of forecasting errors. Using standard statistical terminology, forecasts can result in two potential errors with respect to directional 

changes: type I and type II. Type I errors occur when a directional change is forecasted but no 

such event takes place in the data. Type II errors occur when a directional change in the data is not 

correctly forecasted. Both occurred regularly throughout the 2012-2013 time period (table 7).

Contrary to the discussion of MSE, there are no clear differences in performance across the models. 

The threshold ECM and ARDL committed the fewest type II errors while the asymmetric ECM 

produced the fewest type I errors. In many cases, a substantial share, or even the majority, of directional changes were not accurately predicted. Additionally, for a number of models, more of the 

predicted directional changes proved to be false than occurred as predicted in the data. Many of the 

errors portrayed in table 7 are the result of very small or brief directional changes in the data. As 

discussed in the Conclusion, further statistical analysis is called for to understand the extent to which 

directional changes with significant economic implications are accurately predicted in our forecasting framework.

38Mathematically, directional changes are extrema in the price indices. Both local and global maxima and minima 

represent points at which the trend changes from positive to negative or vice versa. Directional changes are distinct from 

turning points, in which the series of interest changes direction and maintains the new course for a period of time (Wecker, 1979). Most food prices increase steadily over time, meaning that turning points are uncommon. For this reason, we 

restrict our analysis to directional changes.
28

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table 7

Results of the directional analysis, by category and out-of-sample forecasting method, 2012-2013

Threshold ECM Asymmetric ECM Symmetric ECM ARDL

Price Transmission

Directional 

Changesa

Type I 

Errorsb

Type II 

Errorsc

Type I 

Errors

Type II 

Errors

Type I 

Errors

Type II 

Errors

Type I 

Errors

Type II 

Errors

Cattle PPI – beef PPI 11 6 3 6 3 6 3 6 3

Beef PPI – beef CPI 8 6 3 8 4 7 3 9 3

Eggs PPI – eggs CPI 15 4 7 4 8 4 8 4 8

Poultry PPI – 

proc. poultry CPI 12 5 5 3 5 4 5 4 5

Pork PPI – pork CPI 9 6 6 6 5 6 6 6 6

Milk PPI – dairy PPI 7 8 4 5 4 5 4 5 4

Dairy PPI – dairy CPI 6 7 4 6 5 8 5 5 4

Wheat PPI – wheat 

flour PPI 10 5 5 6 4 6 4 5 5

Wheat flour PPI – 

bread CPI 15 4 8 4 9 3 8 3 8

Fruit PPI – fruit CPI 7 7 2 9 3 9 3 9 2

Vegetables PPI – 

vegetables CPI 7 7 5 5 4 5 5 6 4

Soybeans PPI – 

fats and oils PPI 8 6 4 3 5 3 5 3 4

Fats and oils PPI – 

fats and oils CPI 13 4 3 3 4 4 3 4 3

Total 128 73 59 68 63 70 62 69 59

aDirectional changes occur when the index being forecasted changes direction over the time period.

bType I errors occur when the forecast model predicts a directional change that does not take place in the data when predicted. Type II errors 

occur when the forecast model fails to predict a directional change.

cType I errors occur when the forecast model predicts a directional change that does not take place in the data when predicted.

CPI = Consumer Price Index. PPI = Producer Price Index.

Source: USDA, Economic Research Service (ERS) calculations using ERS Food Price Outlook forecast data.
29

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Conclusion: Ongoing and Future Work

Model performance statistics and diagnostics indicate that the precision of ERS’s food price forecasts has somewhat improved with the new technique. While the model has improved, potential 

forecast bias is still a concern regarding forecast accuracy. Additionally, some aspects of the forecasting methodology remain ad hoc due to data limitations or modeling complications. A number 

of efforts, either in the planning stage or already underway at ERS, aim to expand and enhance the 

food price forecasting methodology.

Weather stands as the greatest source of uncertainty in forecasting food prices. ERS cannot accurately predict severe weather events, such as droughts. However, it may be possible to incorporate 

seasonal and climatic forecast data from sources such as the National Oceanic and Atmospheric 

Administration to better account for expected weather patterns. With a better understanding of 

expected deviations from seasonal temperature and precipitation norms in agricultural regions, ERS 

may be better able to anticipate commodity price fluctuations. 

Moreover, given that the most important mechanism by which weather affects food prices is through 

commodity price changes, ERS has a strong incentive to fill the gaps in the economic understanding 

of commodity price transmission. The review by Meyer and von Cramon-Taubadel (2004) concludes 

that much of the empirical research on this topic fails to reach consensus and often conflicts with 

theory. To help foster consensus, ERS has ongoing collaborations with academic researchers to study 

commodity price transmission using proprietary datasets of retail food prices. 

The directional analysis, based on equation (9), indicates that the forecasts are prone to errors with 

respect to directional changes in the CPIs and PPIs. However, it is clear that many of the directional 

changes that the models fail to anticipate (type II errors) are either very small in magnitude, very 

short lived, or both. Additionally many of the false directional changes suggested by the models 

(type I errors) simply take place 1 to 2 months following the prediction. Therefore, a number of 

actual directional changes in the data simultaneously generate errors of both kinds. To identify 

precisely where the models have the greatest shortcomings in predicting price changes that impact 

inflation estimates, more work is called for in delineating between large and small directional 

changes, as well as developing time intervals to place around the points at which the models predict 

directional changes.

Given the impact that changes in the food price forecasts can have on policy, the decisions made 

by agents in the food supply chain, and the outlook of U.S. consumers, ERS strives to minimize 

the number of forecast revisions while maximizing precision. The annual forecast for each CPI is 

subject to revision for 17 months. Examining the frequency of forecast revisions by month, the distribution peaks at about the midpoint of the year being forecasted (fig. 7).39 That is, in May or June, 

with about half of the year’s CPI monthly values realized, ERS researchers obtain a clearer picture 

of food prices on the year and adjust forecasts accordingly. However, a disproportionate share of 

revisions takes place early, and many of these early forecast changes are ultimately reversed, either 

partially or completely.40 This finding likely indicates that a number of forecast revisions are made 

too early and with too little information. ERS is conducting a statistical analysis of revisions that 

39The complete set of forecast revisions, by month and by CPI, is available in the appendix in table A.2.

40For example, ERS adjusted the 2012 forecast for the eggs CPI five times over the 18-month period. But the final 

forecast, made in December 2012, matched the initial forecast made in July 2011.
30

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

were reversed, drawing in part on the information from the loss function analysis, to reduce the incidence of these occurrences.

Work is underway in applying the vertical price transmission pass-through methodology to additional food categories. The stage-of-processing PPIs for carbonated beverages, juices, and other 

drinks may provide enough information to establish a longrun equilibrium relationship with the 

nonalcoholic beverages CPI and, therefore, apply ECM approaches. Similarly, a weighted combination of PPIs for canned, frozen, and juiced fruits and vegetables offers promise for the processed 

fruits and vegetables CPI. ERS has acquired a subscription to the Urner Barry Comtell seafood price 

data. Researchers are working on constructing a price index for wholesale fish and seafood that is 

intended to serve as the foundation for an ECM framework applied to the fish and seafood CPI. 

Kumcu and Okrent (2014) illustrate the construction of price indices for FAFH prices. Applying the 

ECM methodology to these indices may allow for subcategories of FAFH, such as fast food or fullservice restaurants to be forecasted. 

Finally, an avenue by which ERS food price forecasts have the potential to inform policy decisions 

is through the expected impacts of food price changes on food price expenditures. BLS’s Consumer 

Expenditure Survey (CE) measures and reports information on household food expenditures by 

category and across a range of demographics. A simple comparison of annual food price inflation 

and changes in spending according to the CE in recent years reveals that spending does not increase 

proportionally with prices. Households economize, shift their expenditures among supermarkets and 

restaurants, and impacts vary substantially by income and geographic region, among other factors. 

ERS is currently exploring how food price forecasts may be used to produce food expenditure forecasts, drawing on information from both the CE and proprietary data sources.

Note: Each year’s forecasts are initially released in July of the previous year, and at this point, 18 months of data are 

forecasted. The inaugural forecasts are not counted as changes or revisions.

Source: USDA Economic Research Service calculations based on changes made to ERS Food Price Outlook forecasts.

Figure 7

Total number of forecast changes, by month

Number of changes

0

10

20

30

40

50

60

70

80

90

100

17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Months of forecasted data
31

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

References

Balke, N.S., and T.B. Fomby. 1997. “Threshold Cointegration,” International Economic Review

38(3):627-645.

Ben-David, D., R.L. Lumsdaine, and D.H. Papell. 2003. “Unit Roots, Postwar Slowdowns, and 

Long-Run Growth: Evidence from Two Structural Breaks,” Empirical Economics 28(2):303-319.

Bils, M., and P.J. Klenow. 2004. “Some Evidence on the Importance of Sticky Prices,” Journal of 

Political Economy 112(5):947-985.

Burns, S. 2013. “CBO’s Economic Forecasting Record: 2013 Update,” Congress of the United States 

Congressional Budget Office.

Canning, P. 2011. A Revised and Expanded Food Dollar Series: A Better Understanding of our 

Food Costs, ERR-114, U.S. Department of Agriculture, Economic Research Service.

Canning, P., A. Charles, S. Huang, and K.R. Polenske. 2010. “Energy Use in the U.S. Food System.” 

ERR-94, U.S. Department of Agriculture, Economic Research Service.

Cleveland, W.S. 1979. “Robust Locally Weighted Regression and Smoothing Scatterplots,” Journal 

of the American Statistical Association 74(368):829-836.

Cleveland, W.S., and S.J. Devlin. 1988. “Locally Weighted Regression: An Approach to Regression 

Analysis by Local Fitting,” Journal of the American Statistical Association 83(403):596-610.

Croushore, D. 2012. “Forecast Bias in Two Dimensions,” Working paper 12-9, Federal Reserve Bank 

of Philadelphia Available at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2040747.

Dickey, D.A. and W.A. Fuller. 1981. “Likelihood Ratio Statistics for Autoregressive Time Series 

with a Unit Root.” Econometrica, 49, 1057-1072.

Diebold, F.X. 2006. Elements of Forecasting: South-Western College Publishing.

Engle, R.F., and C.W. Granger. 1987. “Co-Integration and Error Correction: Representation, 

Estimation, and Testing,” Econometrica 55(2):251-276.

Ghosh, A. 1993. “Hedging with Stock Index Futures: Estimation and Forecasting with Error 

Correction Model,” Journal of Futures Markets 13(7):743-752.

Gilbert, C.L. 2010. “How to Understand High Food Prices,” Journal of Agricultural Economics

61(2):388-425.

Gneiting, T. 2014. “Making and Evaluating Point Forecasts,” Journal of the American Statistical 

Association 106(494):746-762.

Granger, C.W., and T.H. Lee. 1989. “Investigation of Production, Sales and Inventory Relationships 

Using Multicointegration and Non-symmetric Error Correction Models,” Journal of Applied 

Econometrics 4(S1):S145-S159.
32

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Granger, C.W., and P. Newbold. 1986. Forecasting Economic Time Series, 2nd Edition. Orlando, FL: 

Academic Press.

Greene, W. 2008. Econometric Analysis. Upper Saddle River, NJ: Pearson Education.

Hamilton, J.D. 1994. Time Series Analysis. Princeton, NJ: Princeton University Press.

Hannan E.J. and B.G. Quinn. 1979. “The Determination of the Order of an Autoregression,” Journal 

of the Royal Statistical Society. Series B (Methodological), 41(2 ):190-195.

Joutz, F.L., R.P. Trost, C.B. Hallahan, A.L. Clauson, and M. Denbaly. 2000. “Retail Food Price 

Forecasting at ERS: The Process, Methodology, and Performance From 1984 to 1997,” TB 1885, 

U.S.Department of Agriculture, Economic Research Service.

Keele, L., and S. De Boef. 2004. “Not Just for Cointegration: Error Correction Models with 

Stationary Data,” Department of Politics and International Relations working paper, Nuffield 

College and Oxford University.

Kejriwal, M., and P. Perron. 2010. “Testing for Multiple Structural Changes in Cointegrated 

Regression Models,” Journal of Business and Economic Statistics 28(4):503-522.

Kinnucan, H.W. and O.D. Forker. 1987. “Asymmetry in Farm-Retail Price Transmission for Major 

Dairy Products,” American Journal of Agricultural Economics, 69(2):285-292.

Kumcu, A., and A. Okrent. 2014. “Methodology for the Quarterly Food-Away-From-Home Prices 

Data,” TB 1938, U.S. Department of Agriculture, Economic Research Service.

Lamm, R.M. and P.C. Westcott. 1981. “The Effects of Changing Input Costs on Food Prices,” 

American Journal of Agricultural Economics, 63(2):187-196.

Leibtag, E. 2009. “How Much and How Quick? Pass Through of Commodity and Input Cost 

Changes to Retail Food Prices,” American Journal of Agricultural Economics 91(5):1462-1467.

Levy, D., M. Bergen, S. Dutta, and R. Venable. 1997. “The Magnitude of Menu Costs: Direct 

Evidence From Large U. S. Supermarket Chains,” The Quarterly Journal of Economics

112(3):791-824.

Meyer, J., and S. von Cramon-Taubadel. 2004. “Asymmetric Price Transmission: A Survey,” Journal 

of Agricultural Economics 55(3):581-611.

Mitchell, D. 2008. “A Note on Rising Food Prices,” World Bank Policy Research Working Paper No. 

4682. 

Nielsen, B. 2001. “Order Determination in General Vector Autoregressions,” Working paper, 

Department of Economics, University of Oxford and Nuffield College. Available at http://ideas.

repec.org/p/nuf/econwp/0110.html.

Park, T.A. 1990. “Forecast Evaultion for Multivariate Time-Series Models: The U.S. Cattle Market,” 

Western Journal of Agricultural Economics 15(1):133-143.
33

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Perron, P. 1989. “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,” 

Econometrica, 57(6):1361-1401.

Phillips, P.C., and P. Perron. 1988. “Testing for a Unit Root in Time Series Regression,” Biometrika

75(2):335-346.

Roeger, E. and E. Leibtag. 2011. “How Retail Beef and Bread Prices Respond to Changes in 

Ingredient and Input Costs,” ERR 112, U.S. Department of Agriculture, Economic Research 

Service.

Russo, C., R. Green, and R.E. Howitt. 2008. “Estimation of Supply and Demand Elasticities 

of California Commodities,” Working paper no. 08-001, Department of Agricultural and 

Resource Economics, University of California. Available at http://papers.ssrn.com/sol3/papers.

cfm?abstract_id=1151936.

Strazicich, M.C., J. Lee, and E. Day. 2004. “Are Incomes Converging among OECD Countries? 

Time Series Evidence with Two Structural Breaks,” Journal of Macroeconomics 26(1):131-145.

Timmer, C.P. 2008. “Causes of High Food Prices,” Working paper series 128, ADB Economics.

Trostle, R. 2008. “Global Agricultural Supply and Demand: Factors Contributing to the Recent 

Increase in Food Commodity Prices,” WRS-0801, U.S. Department of Agriculture, Economic 

Research Service.

Volpe, R.J., E. Roeger, and E. Leibtag. 2013. “How Transportation Costs Affect Fresh Fruit and 

Vegetable Prices,” ERR-160, U.S. Department of Agriculture, Economic Research Service.

Wecker, W.E. 1979. “Predicting the Turning Points of a Time Series,” The Journal of Business

52(1):35-50.

Wohlgenant, M.K. 2001. Marketing Margins: Empirical Analysis, eds. B. Gardner and G. Rausser. 

Amsterdam, Netherlands: Elsevier Science.
34

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table A.1

Total number of forecast revisions, magnitudes of forecast changes, and volatility, 

by year and CPI category, 2003 to 2013—continued

CPI category 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

All food Revisions

Change

1

0.5

3

1.0

2

1.0

0

N/A

4

1.0

5

2.5

5

2.5

3

2.5

2

1.5

1

0.0

3

1.5

Avg. CPI ∆ 0.59 0.43 0.45 0.46 0.81 1.01 0.37 0.33 0.90 0.37 0.30

Food away 

from home

Revisions

Change

0

N/A

1

0.5

0

N/A

0

N/A

1

0.5

2

1.0

2

1.0

3

2.5

2

0.25

1

0.75

1

0.25

Avg. CPI ∆ 0.40 0.47 0.51 0.52 0.67 0.87 0.34 0.27 0.56 0.49 0.41

Food at home Revisions

Change

3

1.0

4

2.0

2

1.0

1

0.5

5

1.5

5

3.0

6

3.5

2

2.0

4

2.5

2

0.5

4

2.0

Avg. CPI ∆ 0.75 0.58 0.62 0.67 0.91 1.31 0.77 0.46 1.22 0.44 0.41

Meats, poultry, and fishRevisions

Change

4

1.5

7

5.0

2

0.5

2

1.0

4

2.5

2

1.0

5

5.0

1

0.5

5

4.75

4

0.0

3

1.0

Avg. CPI ∆ 1.68 0.84 0.50 0.56 1.01 1.39 0.79 1.32 1.45 0.80 0.86

Meats Revisions

Change

7

4.0

9

6.0

2

0.5

3

0.5

4

2.5

2

1.0

6

6.6

2

1.5

5

6.0

2

0.25

3

1.75

Avg. CPI ∆ 2.13 1.03 0.62 0.55 1.03 1.48 1.04 1.61 1.74 0.79 0.77

Beef and veal Revisions

Change

6

5.5

8

8.0

2

0.0

2

0.0

5

3.5

3

1.5

6

7.5

2

1.5

5

7.25

5

0.25

3

2.0

Avg. CPI ∆ 3.56 1.77 1.50 1.23 1.50 2.07 1.98 2.00 2.49 1.29 0.87

Avg. wholesale PPI ∆ 6.62 6.16 3.55 2.38 4.68 4.66 4.77 6.37 6.05 5.23 2.98

Avg. farm 

PPI ∆ 6.75 4.49 4.32 3.21 3.13 4.61 3.09 4.82 5.26 4.52 2.70

Pork Revisions

Change

2

1.0

5

3.5

2

0.5

4

1.5

6

1.0

1

0.5

6

7.5

6

4.5

5

5.25

4

3.75

5

1.5

Avg. CPI ∆ 1.59 1.98 1.20 0.97 2.03 2.22 1.49 2.93 2.22 1.56 1.81

Avg. wholesale PPI ∆3.11 3.74 2.96 4.13 3.60 5.50 2.08 4.38 3.83 5.25 4.67

Other meats Revisions

Change

5

3.5

5

3.0

1

0.5

2

0.5

3

1.0

2

2.0

2

1.5

4

3.0

3

4.75

1

0.75

4

3.0

Avg. CPI ∆ 2.12 1.23 1.08 1.43 2.18 1.78 1.68 1.70 1.65 1.28 1.51

Poultry Revisions

Change

2

0.5

8

6.0

2

0.5

6

4.0

6

3.5

4

2.5

4

3.5

1

1.0

1

0.75

2

2.25

3

1.75

Avg. CPI ∆ 1.24 1.48 1.59 1.23 1.58 1.29 1.33 1.40 1.10 1.83 1.65

Avg. wholesale PPI ∆ 1.29 2.61 1.88 2.85 2.20 1.46 2.38 2.48 1.58 1.87 1.32

Fish and 

seafood

Revisions

Change

3

0.5

3

1.5

1

1.0

3

2.0

5

0.5

4

2.0

5

1.0

4

3.0

4

4.25

3

1.5

2

0.0

Avg. CPI ∆ 1.45 1.28 1.29 1.38 1.43 1.98 1.57 2.22 1.81 1.48 2.42

Eggs Revisions

Change

6

11.0

8

3.5

10

15.0

4

2.5

8

23.0

5

16.5

7

18.5

7

0.0

4

6.0

5

0.0

2

0.0

Avg. CPI ∆ 5.30 6.53 5.29 6.68 8.64 4.77 6.64 9.02 3.56 5.15 3.57

Avg. farm 

PPI ∆ 10.80 15.53 13.88 18.25 20.42 20.53 16.37 22.32 17.86 18.60 19.29

continued—
35

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table A.1

Total number of forecast revisions, magnitudes of forecast changes, and volatility, 

by year and CPI category, 2003 to 2013—continued

CPI category 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Dairy

products

Revisions

Change

2

0.0

8

7.0

3

2.0

3

2.0

6

7.5

4

6.0

5

11.0

1

1.0

4

3.5

3

0.75

3

3.25

Avg. CPI ∆ 1.31 2.31 1.19 0.88 2.13 1.51 1.98 0.93 1.54 1.09 0.72

Avg. wholesale PPI ∆ 1.77 4.66 1.33 1.59 3.43 2.78 3.71 2.33 3.93 3.18 1.77

Avg. farm 

PPI ∆ 4.13 7.91 2.52 3.35 5.60 5.43 6.34 4.78 6.30 6.55 3.68

Fats and oils Revisions

Change

3

0.5

9

4.5

3

3.0

4

0.5

2

0.5

11

11.0

1

0.5

4

3.0

7

7.25

5

1.5

4

3.25

Avg. CPI ∆ 1.34 1.68 1.90 1.71 1.23 3.31 1.07 1.33 2.57 1.37 1.14

Avg. wholesale PPI ∆ 4.39 3.27 1.48 2.20 5.18 13.98 5.30 3.68 5.80 2.90 2.47

Avg. farm 

PPI ∆ 6.08 12.38 7.53 4.32 10.27 16.77 18.81 7.60 8.49 13.75 12.08

Fruits and 

vegetables

Revisions

Change

3

1.0

1

1.0

2

1.0

2

1.5

7

0.0

6

3.0

5

6.0

5

2.5

3

1.75

6

2.75

3

0.5

Avg. CPI ∆ 2.12 3.57 4.64 3.19 4.35 3.25 1.84 3.48 2.84 2.06 2.07

Fresh fruits 

and vegetables

Revisions

Change

3

1.0

5

0.5

4

0.5

4

2.0

7

1.5

4

2.0

5

9.5

5

2.5

3

2.0

6

4.0

3

1.25

Avg. CPI ∆ 3.13 5.62 6.85 4.59 6.50 4.12 2.95 5.39 3.95 3.00 2.79

Fresh fruits Revisions

Change

3

0.5

2

2.0

4

0.0

5

2.5

5

0.5

5

1.5

5

10.5

3

3.0

3

0.75

5

0.75

3

0.5

Avg. CPI ∆ 3.45 7.04 5.91 3.53 6.64 7.23 3.39 7.75 5.24 4.78 3.42

Avg. farm 

PPI ∆ 5.62 8.37 6.17 9.71 10.54 5.95 5.23 9.41 6.70 3.68 5.03

Fresh vegetablesRevisions

Change

4

3.5

3

0.0

7

1.0

9

1.5

7

2.0

5

2.0

4

7.5

5

1.5

4

3.25

5

7.5

4

1.75

Avg. CPI ∆ 3.55 6.04 8.28 7.28 7.37 4.95 4.63 4.95 7.09 3.63 4.95

Avg. farm 

PPI ∆ 12.81 19.17 15.54 19.93 20.76 16.14 14.98 26.11 31.81 11.49 24.88

Processed 

fruits and 

vegetables

Revisions

Change

4

1.5

4

1.0

2

1.5

4

1.5

3

0.5

5

6.5

2

3.0

4

3.5

3

0.25

1

0.75

2

1.75

Avg. CPI ∆ 0.96 1.05 1.29 0.70 1.02 1.86 1.15 1.36 1.39 1.01 1.24

Sugar and 

sweets

Revisions

Change

4

0.5

1

1.0

2

0.0

5

3.0

1

0.5

4

2.5

1

2.0

2

1.5

3

1.75

1

1.25

4

3.5

Avg. CPI ∆ 0.59 0.96 1.48 1.00 0.91 1.22 1.08 1.64 1.66 1.16 1.10

Cereals and 

bakery 

products

Revisions

Change

2

0.5

1

0.5

1

1.0

1

0.5

2

1.5

6

6.5

1

0.5

4

2.5

3

1.75

3

0.25

4

2.0

Avg. CPI ∆ 0.68 0.52 0.68 0.77 1.17 2.28 0.62 0.46 1.28 0.81 0.57

Avg. wholesale PPI ∆ 2.10 2.38 1.35 3.78 7.90 15.22 5.19 5.31 7.73 4.56 4.42

Avg. farm 

PPI ∆ 6.08 3.99 3.81 5.35 14.03 23.83 8.63 7.85 14.46 6.41 5.37

continued—
36

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table A.1

Total number of forecast revisions, magnitudes of forecast changes, and volatility, 

by year and CPI category, 2003 to 2013—continued

CPI category 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Nonalcoholic 

beverages

Revisions

Change

2

0.0

2

1.5

3

2.0

1

0.5

6

3.5

5

1.5

2

1.0

2

2.5

2

2.25

1

0.25

2

3.25

Avg. CPI ∆ 0.92 0.61 0.64 0.65 1.09 1.17 0.87 0.83 0.97 0.59 0.73

Other foods Revisions

Change

3

0.5

3

1.5

1

0.5

1

0.5

4

1.0

5

3.0

1

1.0

3

2.5

2

0.25

2

1.5

4

2.0

Avg. CPI ∆ 0.78 0.79 0.98 0.68 0.78 1.30 0.76 0.46 1.03 0.71 0.68

Sum Revisions 72 100 58 66 101 95 86 73 77 68 69

Mean Revisions

Change

3.27

1.81

4.54

2.75

2.63

1.5

3.0

1.29

4.59

2.71

4.31

3.59

3.90

5.03

3.31

2.18

3.5

3.09

3.09

1.42

3.14

1.71

Min Revisions 0 1 0 0 1 1 1 1 1 1 1

Max Revisions 7 9 10 9 8 11 7 7 7 6 5

Notes: ∆ = change. The Wholesale Producer Price Index (PPI) and/or Farm PPI is not included in this analysis for some food categories 

as they use a farm to retail or wholesale to retail model. Change is the percent difference between the initial forecast made in July of the 

previous year and the final forecast made in December of the listed year. This is calculated as the absolute value of the difference between 

the midpoints of the two forecasts. For 2003, forecasts were not made in the previous year, meaning comparisons with the remaining years 

are not entirely applicable. The change in the forecast is based on the comparison between the January and December forecasts. 

CPI = Consumer Price Index.

Source: USDA, Economic Research Service calculations using ERS Food Price Outlook forecast data.
37

How USDA Forecasts Retail Food Price Inflation, TB-1940

Economic Research Service/USDA

Table A.2

Forecast revisions, by month and Consumer Price Index (CPI) category

Months of forecasted data

CPI category 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 

All food - 1 - 1 - 5 1 3 2 3 2 2 3 1 1 1 3

 Food away from home - - - 1 - 1 2 - 1 1 1 1 2 - - 1 2

 Food at home - 1 - 2 1 4 2 4 2 3 3 4 2 2 2 2 4

 Meats, poultry, and fish 1 1 - 1 1 3 2 2 4 2 2 3 4 4 2 3 4

 Meats 1 1 1 1 1 3 3 2 3 4 2 6 2 4 4 4 3

 Beef and veal 1 1 - 2 2 4 2 2 4 3 3 5 4 3 3 4 5

 Pork 2 1 - 2 2 5 1 2 2 2 4 6 3 4 3 2 5

 Other meats - 1 - - 1 4 3 2 4 3 2 2 1 1 1 3 4

 Poultry - 1 - 1 2 1 5 2 4 1 4 3 3 3 2 5 2

 Fish and seafood - 2 1 1 1 5 2 2 2 2 4 3 3 2 2 2 3

 Eggs 1 3 2 2 3 4 5 6 7 3 6 5 4 4 4 2 6

 Dairy products - 2 2 2 3 2 2 3 3 4 5 4 3 4 1 1 1

 Fats and oils 2 3 3 2 - 3 5 4 5 3 5 5 3 5 1 - 4

 Fruits and vegetables 1 1 - 3 - 1 3 1 3 4 3 5 5 2 4 2 5

 Fresh fruits and 

 vegetables 1 3 1 3 1 2 3 1 4 2 3 4 6 3 4 3 5

 Fresh fruits 1 1 1 1 1 1 4 2 3 2 5 5 6 2 2 2 4

 Fresh vegetables 2 2 - 3 3 2 3 3 3 5 3 3 7 5 4 5 4

 Processed fruits and 

 vegetables - 1 2 2 1 1 4 1 2 1 6 4 3 - 3 1 2

 Sugar and sweets - - - 2 - 2 1 3 5 3 4 3 1 1 - - 3

 Cereals and bakery

 products

1 1 - 3 2 1 1 2 4 - 3 6 1 - - 2 3

 Nonalcoholic beverages - 1 2 2 2 - 2 - 2 1 3 3 3 2 2 1 2

 Other foods - 1 1 1 1 1 1 1 2 2 3 5 3 1 - 2 4

Total Changes 14 29 16 38 28 55 57 48 71 54 76 87 72 53 45 48 78

Notes: A dash signifies no change was made in that month for the specified food category.

Each year’s forecast is initially published in July of the previous year. At this point, there are 18 months of data to be forecasted, but the 

initial forecast is not counted as a revision. The final forecast for each year is made in December when CPI data for November are released, 

meaning there is 1 month of data to be forecast. 

Source: USDA, Economic Research Service calculations using ERS Food Price Outlook forecast data.