Forecasting Consumer Price Indexes for Food: A Demand Model Approach.

By Kuo S. Huang, Food and Rural Economics Division, Economic Research

Service, U.S. Department of Agriculture. Technical Bulletin No. 1883.

Abstract

Forecasting food prices is an important component of the U.S. Department of

Agricultures short-term outlook and long-term baseline forecasting activities.

A food price-forecasting model is developed by applying an inverse demand

system, in which prices are functions of quantities of food use and income.

Therefore, these quantity and income variables can be used as explanatory variables for food price changes. The empirical model provides an effective instrument for forecasting consumer price indexes of 16 food categories. 

Keywords: Food price forecasts, inverse demand system, autoregressive model. 

Acknowledgments

The author thanks Mark Denbaly, Paul Westcott, Albert Reed, and Annette

Clauson for helpful review of the earlier drafts of this report, Martha Evans for

editorial advice, and Anne Pearl for text layout and cover design. 

1800 M Street, NW

Washington, DC 20036-3851 February 2000
Contents

Page

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

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

A Price-Forecasting Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Empirical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 

Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Appendix A: Graphic Comparison of Actual and Fitted Food Prices . . . . . . . 11

ii ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA
Summary

A food price-forecasting model is developed to provide information about how

changes in the quantities of food use affect consumer food prices. The model

specification explicitly recognizes that lags between farmers’ decisions on production and commodities marketed may predetermine quantities, with price

adjustments providing the market-clearing mechanism. This model, by incorporating economic rationale specification, is an alternative approach to the commonly used time series model for food price forecasts. The empirical model,

represented by a set of price equations with estimates expressed as price flexibilities, provides an effective instrument for forecasting consumer price indexes

of 16 food categories by using 6 aggregate food quantities as input information. 

According to the model estimates, for example, a marginal 1-percent increase in

the quantity of red meats would result in price decreases of 0.91 percent for

beef, 1.42 percent for pork, and 0.27 percent for other meats. On the other

hand, a marginal 1-percent increase in the quantity of poultry would result in a

price decrease of 0.84 percent for poultry. Regarding the cross-quantity effects,

an estimated cross-price flexibility between two food categories shows the percentage change in the amount consumers are willing to pay for one food when

the quantity of another food increases by 1 percent. For example, the crossprice flexibility of poultry with respect to the quantity change of red meats is 

-0.40 percent, and the cross-price flexibilities of beef, pork, and other meats

with respect to the quantity change of poultry are -0.15, -1.03, and -0.42 percent. The negative values of these cross-price flexibilities suggest that red meats

and poultry are substitutes. 

Regarding forecasting capability of the model, the estimates of goodness of fit

(R2) in each price equation are satisfactory. All estimates of R2 are higher than

0.91, and in 14 of 16 cases, R2 is higher than 0.95. Also, in the simulation over

the sample period, the measures of root-mean-square errors as a percent of sample mean are in a range between 0.37 and 1.98 percent, indicating that the conformity of the fitted prices with the sample observations appears reasonably

good. These statistical results suggest that the estimated inverse demand model

alone can be used for price forecasts.

Finally, a spreadsheet model for forecasting consumer food prices was developed that users can easily implement for timely outlook and market analysis.

For conducting forecasting, one may use the prior information on quantities of

food use and per capita income to forecast food prices. For program analysis,

one may assume various scenarios of changes in the prior information and then

conduct simulation experiments for evaluation of the program effects. The

accuracy of the forecasts of consumer food prices, however, depends on the reliability of prior information on quantities of food use and per capita income in

the future.

Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ iii
Introduction

Forecasting food prices is an important component of

the U.S. Department of Agriculture’s short-term outlook and long-term baseline forecasting activities. A

food price-forecasting model is needed to provide

information for use by agricultural policy decisionmakers to evaluate the effects of changes in farm products due to farm programs, economic conditions, and

weather on food prices. The objective of this report is

to develop a price-forecasting model that can be easily

implemented for timely outlook and situation analyses. 

Some food price-forecasting models use a time series

approach such as the Autoregressive Integrated

Moving-Average (ARIMA) model in Box and Jenkins

(1970). The time series model, which depicts the historical movement of time series data observations, is a

convenient approach because it uses mainly its own

price variable to predict food prices. Because none of

the time series models incorporates economic rationale, however, the models’ forecasts may be unreliable

when there is a change in economic conditions. 

To include economic reasoning in the food price forecasts, this study applies an inverse demand system, in

which prices are functions of quantities and income.

As indicated by Hicks (1956), the Marshallian

demands have two functions: one shows the amounts

consumers will take at given prices, and the other

shows the prices at which consumers will buy at given

quantities. The latter function, “quantity into price,” is

essentially what the inverse demand system expresses. 

The inverse demand system is theoretically sound and

has considerable appeal as applied to food price forecasting. It has been long recognized that lags between

farmers’ decisions on production and commodities

marketed may predetermine quantities, with price

adjustments providing the market-clearing mechanism.

Therefore, quantities of food production and use are

likely appropriate variables to use in food price forecasts. Hence, an inverse demand system for food price

forecasts is capable of capturing the economic

demand-pull factors, such as food use and income in

the food-price movements.

The materials of this report are presented in two parts.

At the beginning, the specification of a price-forecasting model is discussed. The major focus is on how to

apply an inverse demand system for forecasting food

prices. Then the empirical results of an estimated

inverse demand system are presented.

Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 1

Forecasting Consumer Price 

Indexes for Food

A Demand Model Approach

Kuo S. Huang
A Price-Forecasting Model

In this section, a price-forecasting model is developed

by applying an inverse demand system approach.

Assuming that there are n goods in a demand system,

let q denote an n-coordinate column vector of quantities demanded for a “representative” consumer, p an

n-coordinate vector of the corresponding prices for the

n goods, m = p¢q the consumer’s expenditure, and U(q)

the utility function, which is assumed nondecreasing

and quasi-concave in q. The primal function for maximizing consumer utility is the Lagrangian function:

By differentiating the Lagrangian function, the necessary conditions for optimums are

in which ui (q) is the marginal utility of the ith good.

In equation 2, l is known as the marginal utility of

income, showing the change in the maximized value of

utility as income changes. This equation represents an

equilibrium condition, in which each marginal utility

divided by its price is equal (constant at l) for all

goods. 

The inverse demand system can be obtained by eliminating the Lagrangian multiplier l from the necessary

conditions of equation 2. Multiplying both sides of

equation 2 by qi and summing over n goods to satisfy

the budget constraint of equation 3, the Lagrangian

multiplier is then obtained as 

Substituting equation 4 into equation 2 yields the

Hotelling-Wold identity, which defines the inverse

demand system from a differentiable direct utility

function as

in which pi / m is the normalized price of the ith commodity. 

Equation 5 represents an inverse demand system in

which the variation of price is a function of quantities

demanded and is proportional to a change in income.

For given quantities demanded, an increase in income

will cause each commodity’s price to increase at the

same rate. Therefore, all income flexibilities are

implicitly constrained to 1. This model has been

applied in Huang (1991) for a 40-equation demand

system consisting of 39 food categories and 1 nonfood

sector. 

On the choice of functional form for equation 5, the

loglinear approximation of the Hotelling-Wold identity

is used in this study for practical reasons. In addition

to the linear model for easy estimation, the parameters

of the loglinear form represent direct estimates of

demand flexibilities. An annual statistical model for

the ith price equation in terms of n quantities demanded is specified as follows:

where variables at time t are pi t (price of ith commodity), mt (per capita income), qj t (quantity demanded

for jth commodity); vi t’s are random disturbances. 

Furthermore, according to Houck (1966) and Huang

(1994), the price flexibilities of $i j’s should be constrained by the following theoretical relationships:

where wi is the expenditure share of the ith food category. 

As suggested by Muth (1961), there is little empirical

interest in assuming that the disturbance term in a

structural model is completely unpredictable, and it is

desirable to assume that part of the disturbance may be

predicted from past observations. Because the expected values of the disturbance could be related to economic conditions prevailing in the past years, the disturbance is assumed to be not independent over time

but to follow an autoregressive process. 

Following Muth’s suggestion, an autoregressive specification for the disturbance terms of the inverse

demand system in equation 6 is applied in this study to

enhance the price-forecasting capability. An autore2 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA

(1)

(2)

(3)

(4)

log ( pi t / mt ) = ai + 'j bi j log (qj t ) + vi t 

$i j = (wj / wi) $j i - wj (Sk $j k - Sk $i k) 

(5)

(7)

(6)

ui (q) = l pi i = 1, 2,..., n

l = 'j qj uj (q) / m j = 1, 2, .., n

pi / m = ui (q) / 'j qj uj (q) i, j = 1, 2, .., n

Maximize L = U(q) - l ( p¢q - m ).

p¢ q = m

i, j, k = 1, 2, .., n

i , j = 1, 2, .., n
gressive process of residuals lagged up to l years is

specified as follows:

where ei t’s are random disturbances in which ei t is

assumed to be identical normal and independently distributed as ei t ~ IN( 0, d2 I ), and vi t is assumed to be

serially correlated. 

In the following empirical application, a structural

component model of equation 6 is estimated. In addition, for an improvement in forecasting performance,

an autoregressive model is estimated by incorporating

the disturbance specification of equation 8. 

Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 3

vi t = 'h g i h vi t-h + ei t

i = 1, 2, .., n; h = 1, 2, .., l (8)
Empirical Application

Data Sources 

The model developed in the last section is used to formulate a price-forecasting model for the consumer

prices of 16 food categories as defined in the structure

of Consumer Price Indexes (CPI ). These food categories are (1) beef and veal, (2) pork, (3) other meats,

(4) poultry, (5) fish and seafood, (6) eggs, (7) dairy

products, (8) fats and oils, (9) fresh fruits, (10) fresh

vegetables, (11) processed fruits and vegetables, (12)

sugar and sweets, (13) cereals and bakery products,

(14) nonalcoholic beverages, (15) other prepared

foods, and (16) food away from home. The price data

for these food categories come from the annual

Consumer Price Index from 1980 to 1997 (U.S.

Department of Labor). Per capita total expenditures to

represent the income variable are computed by dividing the personal consumption expenditures (obtained

from the U.S. Department of Commerce) by the civilian population of 50 States on July 1 of each year. 

The quantity data are compiled from Food

Consumption, Prices, and Expenditures (Putnam and

Allshouse, 1999). Most of the food quantities are

measured in retail weight. For example, the quantities

of red meats are measured in retail cut equivalent. The

quantity of poultry is measured in boneless trimmed

equivalent. The quantities of dairy products are measured in milk equivalent on milkfat basis. Some quantity data of food categories cannot be constructed to

match the price indexes defined by the CPI. For

example, wheat food use was tried as a quantity proxy

in the equation for cereals and bakery products but was

not satisfactory in fitting the demand equation. One

reason is that wheat is only one farm-level ingredient

in cereals and bakery products, so the farm-level quantity is probably not representative of the retail quantity.

Another reason is that the farm value represented by

the wheat quantity measure is a small share of the

retail product value of cereals and bakery products. 

Given the difficulty of defining a pairwise price-quantity for individual food categories, the aggregated

quantities consisting of six food groups (red meats,

poultry, dairy, fruits and vegetables, starchy foods, and

other foods) are used as proxy explanatory variables

for each price equation. These aggregate quantities for

each food group are calculated as the Laspeyres indexes from a total of 143 individual food items. For

explaining price changes of those food categories

without explicitly defined quantities of own category

as an explanatory variable in the model, cross-quantity

effects and per capita income are considered major

determinants. For example, the price variations of the

other meats category are likely captured or represented

by per capita income and the cross-quantity effects

with red meats and poultry. Because the pairwise

price-quantity is lacking for some food categories, the

parametric constraints across demand equations (equation 7) cannot be applied, and each price equation of

the demand system has to be estimated separately.

Estimation Results

The estimation results by applying an autoregressive

procedure (equation 8) with a specification of residuals

lagged up to 2 years are contained in table 1. The

quantity variables of food groups, the lagged residuals,

and a constant term are listed across the top of the

table, and the normalized price variables defined as the

consumer prices deflated by the index of per capita

income are listed down the left-hand side. For each

pair of estimates, the upper part is the estimated price

flexibility of a particular food category in response to

the changes in group quantities, and the lower part is

the estimated standard error.

In table 1, the estimated price flexibilities in each column can be used to assess how a change in the quantity of a specific food group, while holding the quantities of other groups fixed, affects the changes of all

food prices. According to the estimates, for example,

a marginal 1-percent increase in the quantity of red

meats would reduce beef prices by 0.91 percent, pork

prices by 1.42 percent, and prices of other meats by

0.27 percent. On the other hand, a marginal 1-percent

increase in the quantity of poultry would reduce poultry prices by 0.84 percent. 

Regarding the cross-quantity effects, an estimated

cross-price flexibility between two food categories

shows the percentage change in the amount consumers

are willing to pay for one food when the quantity of

another food increases by 1 percent. A negative crossprice flexibility means substitution, while a positive

sign signals a complementary relationship between the

two goods. This is because a marginal increase of the

quantity of one good may have a substitution effect on

other goods, and the price of other goods should be

lower to induce consumers to purchase the same quantity of the other goods. For similar reasons, a positive

cross-price flexibility means a complementary relationship.

4 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA
Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 5

Table 1—Estimated price flexibilities, 1980-97

Food Quantity A(1) A(2) Const. R2 D.W

category R.meat Poultry Dairy Fru-veg Starch Other

Price 

Beef -0.9103 -0.1463 0.9731 -2.228 0.3930 -1.5542 -0.1730 0.8288 19.7644 0.98 2.25 

0.5804 0.3875 0.7832 0.5998 0.4629 0.6856 0.2282 0.1901 3.7322

Pork -1.4213 -1.0333 0.2833 -0.5971 0.4137 -0.2665 0.0083 0.7127 15.6813 0.98 2.19 

0.5191 0.3363 0.6111 0.4300 0.3796 0.5373 0.2854 0.2570 3.1171

O. meat -0.2662 -0.4173 0.2760 -1.5301 0.7003 -1.0070 0.2346 0.7306 14.0854 0.99 2.25 

0.4562 0.2646 0.4570 0.2948 0.2628 0.4266 0.2830 0.2495 2.5691

Poultry -0.3992 -0.8367 1.3397 0.3317 0.6789 -1.8243 0.0456 0.7690 6.9754 0.98 1.81 

0.6098 0.3930 0.7266 0.4974 0.4353 0.6241 0.2672 0.1976 3.5818

Fish 0.4006 -0.9340 3.6906 1.4430 1.7932 -3.8765 0.9194 0.5765 -7.7412 0.96 2.41 

0.4645 0.2361 0.4219 0.2293 0.2171 0.4154 0.2796 0.2835 2.6863

Eggs -1.6583 0.4597 -4.6023 -0.9403 -1.8582 0.8445 0.2614 0.4717 38.7187 0.95 2.05 

1.5750 0.8698 1.6411 1.0972 0.8885 1.6114 0.3579 0.3622 9.3285

Dairy -0.1783 -0.0538 -0.8482 -1.5566 -0.1226 -0.3093 0.8725 0.6772 17.7182 0.99 2.24

0.5139 0.2434 0.5009 0.2309 0.2180 0.4824 0.3404 0.3819 3.1305

Fat-oil -0.2304 -0.0820 0.4172 -1.1413 -0.4135 -0.6658 0.2503 0.9355 13.3481 0.99 1.77

0.2740 0.1571 0.2823 0.1854 0.1603 0.2579 0.1550 0.0782 1.5532

Fruits -1.9234 -0.6129 -0.4895 -1.0900 0.8372 0.8228 0.1439 0.7708 14.6914 0.91 1.84 

0.6464 0.3728 0.6130 0.4234 0.3618 0.6043 0.2185 0.2307 3.5118

Veget. 0.8952 0.7380 -1.8528 0.0539 -0.0475 -0.8965 1.0257 0.8455 8.3168 0.94 1.53

0.3616 0.1752 0.3180 0.1641 0.1536 0.3221 0.1930 0.1727 2.0949

Pro. F&V -0.5765 0.0285 0.3798 -0.0196 -0.8083 -1.3045 0.8989 0.5559 14.0099 0.99 2.57 

0.3625 0.1837 0.3714 0.1880 0.1791 0.3426 0.2909 0.3090 2.1740

Sugar 0.1189 -0.3436 0.6003 -1.0903 0.2854 -0.8623 -0.0094 0.8353 9.6658 0.99 2.20 

0.3157 0.1978 0.3910 0.2766 0.2256 0.3394 0.2610 0.2039 1.9273

Cereal 0.6012 0.4581 -1.2757 -1.2137 -0.1140 0.0186 0.5964 0.4646 10.4283 0.98 2.11 

0.4674 0.2260 0.3329 0.1852 0.1704 0.3677 0.3855 0.4477 2.5367

Beverage 0.1991 -1.3034 -0.0354 -0.4102 0.9869 -0.2275 0.7213 0.6979 7.4882 0.99 2.03 

0.3253 0.1644 0.2756 0.1587 0.1412 0.2909 0.2574 0.2801 1.8378

Pre. food -0.1502 -0.2142 -0.1900 -0.4653 -0.0003 -0.5002 - 0.3165 0.1613 10.4945 0.99 2.11 

0.2832 0.1817 0.4107 0.2908 0.2388 0.3686 0.3595 0.3671 2.1118

Food away -0.1099 -0.2759 0.5666 -0.5129 -0.1798 -0.3626 -0.6332 0.5804 7.5716 0.99 2.37 

0.1854 0.1759 0.3012 0.3203 0.2185 0.3318 0.3317 0.3343 1.5418

Note: For each pair of estimates: the upper part is flexibility, and the lower part is standard error.

The notations are R. meat (red meats), Fru-veg (fruits and vegetables), Starch (starchy foods ), Const.(constant), O. meat (other meats), Veget.

(fresh vegetables ), Pro. F&V (processed fruits and vegetables ), and Pre. food (prepared foods). A(1) and A(2) represent the autoregressive

residuals lagged by 1 and 2 years, respectively, and D.W. represents Durbin-Watson statistics.
According to the estimates in table 1, for example, the

cross-price flexibility of poultry with respect to the

quantity change of red meats is -0.40 percent, and the

cross-price flexibilities of beef, pork, and other meats

with respect to the quantity change of poultry are

-0.15, -1.03, and -0.42 percent. The negative values of

these cross-price flexibilities suggest that red meats

and poultry are substitutes. Many of the estimated

cross-price flexibilities, however, are not statistically

significant. This is probably because even though

some individual foods either substitute or complement,

aggregating different food items into a food category

mitigates these cross-quantity effects. Also, annual

data aggregates over seasons may contribute to the

lack of statistical significance in some estimated crossprice flexibilities. 

In addition, the residuals of the demand system are

further specified as a second-order autoregressive

process as suggested in equation 8. The estimation

results are presented in the table under the columns of

A(1) and A(2), which are estimated coefficients of

autoregressive residuals lagged by 1 and 2 years,

respectively. The estimates of goodness of fit (R2) in

each price equation are satisfactory. All estimates of

R2 are higher than 0.91, and in 14 of 16 cases the R2

is higher than 0.95. The Durbin-Watson (D.W.) statistics shown in the last column of the table suggest that

the errors of each price equation are not serial correlated, and the estimated standard error is unbiased for use

in a significant test of estimated price flexibilities.

To examine the possibility of improving forecasting

performance by applying the autoregressive procedure

(AUTO) rather than ordinary least squares (OLS), two

indicators of performance are presented in table 2; one

is R2 and the other is the root-mean-square percent

error (RMSE). The RMSE of the ex post simulation is

calculated as

where pt and pt* are respectively the actual and fitted

normalized price levels for a sample period T years,

and p is an average of actual normalized price levels.

The RMSE expressed as a percent error of sample

mean can be used for comparison across the price

equations, because each RMSE is independent of the

magnitude of each price index series, which ranged

from 130 percent for nonalcoholic beverages to 236

percent for fresh fruits in 1997. 

According to the estimated indicators in table 2, the

estimates of R2 in the AUTO case are uniformly higher

than those of OLS, especially for cases like fresh

fruits, which increased from 0.81 to 0.91, and fresh

vegetables, which increased from 0.74 to 0.94.

Regarding estimated RMSEs, most of the estimates of

AUTO are smaller than those of OLS, except for cereal and other prepared food categories with slightly

higher estimates. The measures of RMSE for the

AUTO model range between 0.37 and 1.98 percent,

while the measures for the OLS model range between

0.38 and 2.03 percent. 

On the basis of estimated R2 and RMSE, as expected,

the application of an autoregressive model yields significant improvement in forecasting performance. The

conformity of the fitted prices with the sample observations by using the AUTO model appears reasonably

good. These results provide evidence that the estimated parameters adequately reflect food price responses

to changes in quantity and income over the sample

period. Therefore, for the purpose of price forecasting,

the estimates of the autoregression model contained in

table 1 should be used. 

To clarify the forecasting results over the sample period, the fitted normalized prices from the estimated

model are further transformed into Consumer Price

Indexes. To get a close look at the accuracy of fitted

prices, a comparison of actual and fitted food prices

over the years 1995, 1996, and 1997 are presented in

table 3. The errors of prediction are within 5 percent

for most cases; in particular, all the errors of prediction

in 1997 are within 3 percent. In addition, the turningpoint errors over the whole sample period 1980-97 are

listed in the last column of the table. The number of

turning-point errors among 17 observed changes is

equal to 5 errors or less in 13 cases out of 16 price

forecasts. Graphic comparisons of actual and fitted

results are presented in appendix A. This graphic presentation provides additional information about forecasting performance.

To facilitate the application of the price-forecasting

model, a spreadsheet model was developed for an

automated simulation of food prices. Users are

required to provide input data about the concerned per

capita quantity of food consumption and per capita

income. The simulation results expressed in logs of

normalized prices that is log( pi t / mt ) at year t, are

generated first. Then all forecasts of normalized prices

are transformed into price index levels. 

6 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA

RMSE = [ St (pt - pt

* )2 / T ] 1⁄2 / p  ́ 100 

t = 1,2,..,T (9)
Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 7

Table 2—Comparison of autoregressive and ordinary least square results

Food category R2 RMSE

AUTO OLS AUTO OLS

Beef and veal 0.98 0.97 0.99 1.31

Pork 0.98 0.98 0.76 0.80

Other meats 0.99 0.99 0.60 0.73

Poultry 0.98 0.96 0.90 1.08

Fish and seafood 0.96 0.94 0.63 0.72

Eggs 0.95 0.94 1.98 2.03

Dairy products 0.99 0.99 0.65 0.78

Fats and oils 0.99 0.99 0.40 0.76

Fresh fruits 0.91 0.81 0.74 0.97

Fresh vegetables 0.94 0.74 0.50 0.92

Pro. fruit & veget. 0.99 0.98 0.52 0.69

Sugar and sweets 0.99 0.99 0.49 0.66

Cereals and bakery 0.98 0.98 0.42 0.40

Beverages 0.99 0.99 0.41 0.52

Prepared foods 0.99 0.99 0.43 0.40

Food away from home 0.99 0.99 0.37 0.38

Note: The notations are R2 (R-squared), RMSE (root-mean-square

percent error), AUTO (autoregressive procedure), and OLS (ordinary

least squares).
8 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA

Table 3—Forecasting performance

Food 1995 1996 1997 Turning

category Actual Predict Error Actual Predict Error Actual Predict Error point

(1) (2) percent (1) (2) percent (1) (2) percent error

Beef 134.9 133.0 -1.39 134.5 140.1 4.15 136.8 137.6 0.56 3

Pork 134.8 140.1 3.90 148.2 145.7 -1.70 155.9 155.4 -0.31 1

O. meat 139.0 140.5 1.06 144.0 145.3 0.94 148.1 146.1 -1.36 2

Poultry 143.5 142.8 -0.46 152.4 150.9 -0.98 156.6 157.2 0.36 7

Fish 171.6 159.9 -6.83 173.1 181.2 4.70 177.1 176.6 -0.28 4

Eggs 120.5 131.7 9.31 142.1 127.2 -10.46 140.0 144.1 2.92 4

Dairy 132.8 138.2 4.04 142.1 138.8 -2.31 145.5 144.3 -0.80 6

Fat-oil 137.3 138.5 0.89 140.5 140.5 -0.02 141.7 140.5 -0.81 4

Fruits 219.0 223.1 1.88 234.4 232.3 -0.88 236.3 234.9 -0.60 1

Veget. 193.1 185.6 -3.87 189.2 194.7 2.93 194.6 193.3 -0.65 5

Pro. F&V 137.5 139.9 1.76 144.4 142.7 -1.17 147.9 148.7 0.54 7

Sugar 137.5 138.9 1.00 143.7 144.7 0.70 147.8 146.0 -1.19 3

Cereal 167.5 170.8 1.95 174.0 171.6 -1.36 177.6 177.7 0.06 0

Beverage 131.7 130.8 -0.65 128.6 131.2 2.02 133.4 130.6 -2.12 5

Pre. food 151.1 151.3 0.13 156.2 155.8 -0.29 161.2 162.1 0.57 1

Food away 149.0 149.5 0.31 152.7 155.6 1.88 157.0 159.5 1.57 1

Note: The notations are O. meat (other meats), Veget. (fresh vegetables ), Pro. F&V (processed fruits and 

vegetables ), and Pre. food (prepared foods). Error percent is calculated as [(2) - (1)] / (1) x 100.
Concluding Remarks 

In this study, an inverse demand system approach

is applied to specify a price-forecasting model.

Six aggregate food quantities and per capita

income are used as explanatory variables for forecasting consumer price indexes of 16 food categories. To enhance the forecasting capacity of the

model, the disturbance terms of each price equation are specified as a second-order autoregressive

process. The forecasting performance of the

model is satisfactory. 

This price-forecasting model is useful in capturing

economic demand-pull factors such as food use

and income in the food price changes. The

model, however, has its limitations and should be

used in conjunction with some other food priceforecasting models. First, the accuracy of food

price forecasts in this model is conditional on the

prior information of aggregate food quantities and

per capita income, while reliable prior information

for these input data may be difficult to obtain.

Second, the price-forecasting model developed

here is an annual model, and some research is

needed to extend the model for providing monthly

or quarterly short-term price forecasts. 

Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 9
References

Box, G.E.P., and G.M. Jenkins. Time Series

Analysis: Forecasting and Control. San Francisco:

Holden-Day, Inc., 1970. 

Hicks, J.R. A Revision of Demand Theory.

Oxford: Oxford Univ. Press, 1956.

Houck, J.P. A Look at Flexibilities and

Elasticities. J. Farm Econ., Vol. 48, May 1966, 

pp. 225-232.

Huang, K.S. U.S. Demand for Food: A Complete

System of Quantity Effects on Prices, Technical

Bulletin No. 1795, U.S. Dept. Agr., Econ. Res.

Serv., July 1991.

Huang, K.S. A Further Look at Flexibilities and

Elasticities. Amer. J. Agr. Econ., Vol. 76, May

1994, pp. 313-317.

Muth, J.F. Rational Expectations and Theory of

Price Movements, Econometrica, Vol. 29, 1961,

pp. 315-335.

Putnam, J.J., and J.E. Allshouse. Food

Consumption, Prices, and Expenditures, 1970-97.

Statistical Bulletin No. 965. U.S. Dept. Agr.,

Econ. Res. Serv., April 1999.

U.S. Department of Commerce, Personal

Consumption Expenditures, various issues.

U.S. Department of Labor, Consumer Price Index,

various issues.

10 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA
Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 11

1980 1985 1990 1995 2000

Percent

A-1: Consumer Price Index: Beef and veal

1982-84 = 100

Appendix A: Graphic comparison of actual and fitted food prices

1980 1985 1990 1995 2000

Percent

1982-84 = 100

1980 1985 1990 1995 2000

Percent

1982-84 = 100

90

100

110

120

130

140

150

70

80

90

100

110

120

130

140

150

160

80

90

100

110

120

130

140

150

160

170

Actual

A-2: Consumer Price Index: Pork

A-3: Consumer Price Index: Other meats A-4: Consumer Price Index: Poultry

1982-82 = 100

160

150

130

140

90

100

110

120

80

1980 1985 1990 1995 2000

Percent

Actual Fitted

Actual Fitted Actual Fitted

Fitted
12 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA

1980 1985 1990 1995 2000

Percent

1980 1985 1990 1995 2000

Percent

1980 1985 1990 1995 2000

1982-84 = 100

Percent

A-7: Consumer Price Index: Dairy products

80

100

120

140

160

180

200

Actual Fitted

80

90

100

110

120

130

140

150

Actual Fitted

80

90

100

110

120

130

140

150

Actual Fitted

Percent

1980 1985 1990 1995 2000

80

90

100

110

120

130

140

150

Actual Fitted

1982-84 = 100

A-8: Consumer Price Index: Fats and oils

A-5: Consumer Price Index: Fish and seafood

 1982-84 = 100

A-6: Consumer Price Index: Eggs

 1982-84 = 100
Economic Research Service/USDA Forecasting Consumer Price Indexes for Food / TB-1883 ✥ 13

1980 1985 1990 1995 2000

Percent

A-9: Consumer Price Index: Fresh fruits

1982-84 = 100

Actual Fitted

1980 1985 1990 1995 2000

Percent

Actual Fitted

1980 1985 1990 1995 2000

Percent

1982-84 = 100

1980 1985 1990 1995 2000

Percent

1982-84 = 100

50

100

150

200

250

60

80

100

120

140

160

180

200

220

70

80

90

100

110

120

130

140

150

160

80

90

100

110

120

130

140

150

160

Actual Fitted Actual Fitted

A-11: Consumer Price Index: Processed fruits and vegetables A-12: Consumer Price Index: Sugar and sweets

A-10: Consumer Price Index: Fresh vegetables

1982-84 = 100
14 ✥ Forecasting Consumer Price Indexes for Food / TB-1883 Economic Research Service/USDA

1982-84 = 100

1982-84 = 100 1982-84 = 100

1980 1985 1990 1995 2000

Percent

1982-84 = 100

1980 1985 1990 1995 2000

Percent

Actual Fitted Actual Fitted

1980 1985 1990 1995 2000

Percent

1980 1985 1990 1995 2000

Percent

Actual Fitted Actual Fitted

60

80

100

120

140

160

180

200

80

90

100

110

120

130

140

70

80

90

100

110

120

130

140

150

160

170

70

80

90

100

110

120

130

140

150

160

170

A-13: Consumer Price Index: Cereal and bakery Products A-14: Consumer Price Index: Non-alcoholic beverages

A-15: Consumer Price Index: Other prepared foods A-16: Consumer Price Index: Food away from home