Structural Change and 

Competition in Seven U.S. 

Food Markets

A. J. Reed

J. S. Clark

Economic

Research 

Service

United States

Department of

Agriculture

Technical

Bulletin

Number 1881

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veal

pork

poultry

eggs

dairy

fresh fruit

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National Agricultural Library Cataloging Record:

Reed, A. J.

Structural change and competition in seven U.S. food markets.

(Technical bulletin; no. 1881)

1. Food industry and trade—Prices—United States.

2. Farm produce—Prices—United States. I. Clark, J. S.

II. United States. Dept. of Agriculture. Economic Research Service.

1 Ag84Te no.1881

HD9004
Structural Change and Competition in Seven U.S. Food Markets. By A. J. Reed

and J. S. Clark. Food and Rural Economics Division, Economic Research Service,

U.S. Department of Agriculture. Technical Bulletin No. 1881.

Abstract

Recent trends in mergers and acquisitions in the U.S. food sector – food manufacturers, wholesalers, and retailers – raise concerns about market power. In the presence of

market power, farmers may receive lower than competitive farm prices, and consumers may pay higher than competitive retail prices. This study presents empirical

tests of market power at the national level for seven food categories: beef, pork, poultry, eggs, dairy, fresh fruit, and fresh vegetables. At the national level, our tests provide evidence of competitive conduct in both the sale of final food products and the

purchase of farm ingredients.

Keywords: Retail food and farm prices, market power, structural change, cointegration.

Acknowledgments

Much of this research was accomplished while Clark was affiliated with the U.S.

Department of Agriculture, Economic Research Service, Food and Rural Economics

Division. The authors thank Mike Wohlgenant and Kuo Huang for helpful comments

on earlier drafts of this report.

A.J. Reed is an economist at the U.S. Department Agriculture, Economic Research

Service; J.S. Clark is an associate professor of agricultural economics at the Nova

Scotia Agricultural College. 

1800 M Street, NW

Washington, DC 20036-5831 February 2000
ii ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

Contents

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

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

The Economic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Structural Change, Cointegration, and Market Clearing . . . . . . . . . . . . . . . . . . . .7

Further Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

Consumer Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10

Tests of Competition and Constant Returns... . . . . . . . . . . . . . . . . . . . . . . . . .11

Oligopsony Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Longrun Industry Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Input Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

Full-Reduced-Form Price Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Summary

Recent trends in mergers and acquisitions in the U.S. food sector – food manufacturers, wholesalers, and retailers – raise concerns about market power. In the presence of

market power, farmers may receive lower than competitive farm prices, and consumers

may pay higher than competitive retail prices. This study presents empirical tests of

market power at the national level for seven food categories: beef, pork, poultry, eggs,

dairy, fresh fruit, and fresh vegetables. 

The procedures employed in this study account for three important features of food

markets. First, the procedures recognize that within a product category consumers prefer a variety of food items. Second, the procedures account for firm diversity by recognizing that different firms produce a variety of different products using different technologies. Firm and technological diversity seem to be particularly relevant to food

industries because mergers and acquisitions may be feasible only if firms and technologies are diverse. Third, the procedures recognize that structural changes in food

markets may be unpredictable. Some of the most significant impacts on food markets

may have been unpredictable. For example, it was probably difficult to predict trends

in consumer patterns following the entry of women into the labor force in the 1970’s

and 1980’s. Unpredictability of consumer behavior poses considerable risk to food

producers and can induce industrial reorganizations that spread this risk across stages

of food production. Failure to account for product diversity and uncertainty has been

shown to seriously affect tests of market power.

The empirical evidence presented in this bulletin is mostly consistent with competitive

conduct. At the national level, our tests provide evidence of competitive conduct in

both the sale of final food products and the purchase of farm ingredients. Also at the

national level, the tests suggest that food industries pay competitive prices for farm

commodities. The results do not rule out imperfectly competitive local markets, and

they cannot be used to address questions of relative market power between specific

stages of food production. Nevertheless, the broad implications of these results may be

that it is the unpredictable nature of trends in consumer demand, and not imperfect

competition, that may be responsible for observed trends in the industrialization and

concentration of the U.S. food sector. 

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ iii
Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 1

This bulletin presents empirical analyses of market

structure and competition for seven major U.S. food

markets: beef, pork, poultry, eggs, dairy, fresh fruit,

and fresh vegetables. The analyses account for structural change. Our work emerges from a theory first

developed by Heiner in which consumer demand and

input supply mesh with the output supply and the input

demands of nonidentical firms. While Chavas and Cox

have recently generalized this theory, Wohlgenant

(1989) and Wohlgenant and Haidacher (WH) were the

first to extend and apply it to food markets. This bulletin builds on the work of WH by accounting for

structural change. 

We appeal to the economic theory found in WH and

Wohlgenant (1989, 1996) to test for market power.

However, the market data that we use to implement the

tests appear to be driven by trends. In food markets,

we hear about trends in technical change among firms

(e.g., Clark and Youngblood), about trends in the

industrial reorganization of industries (e.g., Martinez

and Reed, MacDonald and Ollinger), and about trends

in food consumption (Kinsey and Senauer). In this

study, we define structural change as trends in market

variables and account for different types of trends in

tests of market power.

Unlike approaches that define structural change by

changes in a model’s parameters (e.g., Goodwin and

Brester), our approach allows us to capture a key feature of some types of structural change: its changing

trends are unpredictable. This view allows us to

describe and to test for unpredictably changing trends

in consumer and producer behavior. It allows us to

test for market-clearing and to estimate longrun structural relationships despite such unpredictability.

Finally, it allows us to test for market power in markets that may have undergone a series of permanent

changes over time.

Our work sheds light on policy concerns associated

with trends in the industrialization of food industries

and in consumer behavior. Economic theory suggests

such trends would be linked if markets clear (Engle

and Granger). A cointegrated model links trends

across variables and, in our case, provides a marketclearing representation. By failing to reject competition with a cointegrated model, our results suggest that

trends in concentration and industrialization may be

efficient solutions to unpredictable trends in consumer

demand for food (Paul). 

Structural Change and Competition in

Seven U.S. Food Markets

A.J. Reed and J.S. Clark

Introduction
Wohlgenant (1989) and WH introduced the agricultural economics profession to a market-clearing framework in which diverse firms demand farm and nonfarm

inputs to produce the product mix of a composite

industry. By relaxing the restriction of identical production functions across firms, they account for an

industry’s heterogeneous food items. They note that

even if each firm produces its items in fixed-input proportions, because proportions vary across the diverse

firms of a food industry, production of the entire

industry is variable proportions.1 The framework

equips analysts with a tool for studying market relationships that is more general than the models derived

from the traditional assumptions of fixed proportions

and identical firms. 

Market models of diverse firms generalize competitive

market relationships. In particular, they can be used to

reconcile the concept of competitive markets with the

observation that: (1) increases in consumer food prices

are not fully passed through to farmers (Wohlgenant,

1994); (2) nonfarm input prices and consumer food

prices may move in opposite directions; (3) consumers

may pay higher markups for higher priced products

(George and King); and (4) competitive food industries

may earn positive longrun rents (U.S. Department of

Agriculture, September 1996). Market models based

on fixed-proportions production must appeal to imperfect competition to explain these observations

(Wohlgenant, 1999).

Tests of market power using market-level data, then,

depend on assumptions concerning the nature of

industry production. Retail-to-farm price spreads that

exceed the marginal cost of transforming farm ingredients to final food products suggest market power,

but the formulas used to compute spreads depend on

the industry production function.2 Studies based on

fixed-proportions consistently reject the competitive

model (e.g., Schroeter, Schroeter and Azzam, Azzam,

Azzam and Park, and Koontz, Garcia, and Hudson),

whereas WH and Wohlgenant (1989, 1996) just as

consistently fail to reject the competitive model for

U.S. food industries.3

This section presents an overview of the theory used in

our empirical analyses. We refer readers unfamiliar

with this theory to the cited studies of WH and

Wohlgenant (1989, 1996) for a discussion that is more

complete than that presented in this section. Readers

familiar with the theory can skip to the next section. 

At the core of the WH model are a pair of quasireduced-form retail and farm price equations for each

market and a system of consumer-demand relationships linking the markets. Given a consumer demand

schedule, the underlying structural model consists of

two market-clearing conditions. The first states that the

sum of food supply across the firms of the industry

equals consumer demand for the industry output. The

second states that the sum of farm ingredient demand

across firms of the industry equals farm supply. The

critical feature of the WH model is that an industry’s

firms are not restricted to possessing identical production functions. Within this general setup, WH assume

that each industry faces an infinitely elastic supply of

nonfarm inputs (exogenous nonfarm input prices), and

a less-than-infinitely elastic supply of farm ingredients

(endogenous farm prices). To simplify the model structure and isolate analysis on retail and farm prices, WH

assume the food industry for a particular market consists of all the firms that manufacture, wholesale, and

retail the industry’s final food products. 

2 Retail-to-farm price spread formulas used by ERS/USDA

(Elitzak) are based on fixed-proportions production. Presumably,

formulas based on variable-proportions would yield different magnitudes.

2 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

1 Wohlgenant (1999) formally shows that if one analyzes a competitive industry producing a heterogeneous mix of final consumer

goods that we treat as a single composite (e.g., beef ), the observation that retail-to-farm price spreads widen with increases in consumer food prices (e.g., George and King) implies input substitution. To explain this observation with a fixed-proportions based

model for this heterogeneous industry, one must rule out the competitive model.

3 These results are predicted by the theoretical results presented in

Wohlgenant (1999). 

The Economic Model
Based on this structure4 and on market clearing for

farm ingredients and food output, Wohlgenant (1989,

1996) and WH derive the quasi-reduced-form 

lnPrj = Arf

(j) lnFj + Arw(j) lnW + Arz(j) lnZj + erj

(1)

lnPfj = Aff

(j) lnFj + Afw(j) lnW + Afz(j) lnZj + efj

j = 1,...,J

in which lnPrj represents the natural logarithm (log) of

the retail price in the jth market, lnPfj is the log of the

price of the farm ingredient used to produce output of

the jth market, lnFj is the log of the supply of the farm

ingredient used to produce output of the jth market. In

this study, lnFj captures changes in domestic supply,

and excludes changes in net exports and changes in

private and government stocks of farm commodities.

lnW is a vector of logged nonfarm input prices, and

lnZj is a consumer demand shifter to be defined below.

erj and efj are model errors on the retail and farm price

equations.5 These two retail and farm price equations

are central to this bulletin. 

In this framework, consumer demand defines the market, and the total consumer demand shift variable for

the jth market, lnZj represents the effect of all variables

that affect demand except the own-retail price for the

product. For this bulletin, lnZj is derived as follows.

Let 

ln(Qj /POP) = ejj lnPrj + ejy ln (Y/POP) 

+Sk1 j ejk lnPrk + uj

be a per capita consumer demand relationship for the

jth product in which ln(Qj

/POP) is the log of per capita consumer demand for the output of the jth industry,

lnPrj is the log of the own-retail price, ln(Y/POP) is

the log of per capita disposable income, lnPrk (k1j) is

the kth retail price of a gross substitute or complement

to product category j, and uj is an error term. Hence,

the ejj is the own-retail price elasticity of consumer

demand, ejk (k1j) is a set of cross-price elasticities of

demand, and ejy is the income elasticity of demand for

the jth good. Based on this relationship, the total

demand shifter for the jth market is 

(2) lnZj = ejy ln (Y/POP) +Sk1 j ejk lnPrk + lnPOP

in which lnPOP is the log of population. lnZj does not

capture shifts in consumer demand caused by changes

in the demand for food away from home, nor does it

capture shifts caused by changes in the composition of

the population. 

The equations 1 are “quasi” reduced because they

account for market-clearing in the jth market independent of market clearing in other markets.6 Theory

suggests four sets of expected signs on the quasireduced forms. 

First, Heiner proves that for an industry of diverse

firms, an increase (decrease) in the price of an input

decreases (increases) an industry’s demand for the

input. While this result is standard for an isolated firm

and for an industry comprised of identical firms,

Heiner’s proof applies to an industry comprised of

firms with different longrun average costs. Heiner’s

proof does not describe the negative slope of the sum

of competitive firms’ input demand schedules holding

output price constant. It describes instead the slope of

industry input demand schedule as the sum of firms’

supply moves along a downward-sloping consumer

demand schedule and, output price changes.7 Braulke

showed that Heiner’s proof applies to longrun equilibrium in which firms enter and exit the industry. In

equations 1, Aff

(j) is the own-price flexibility of an

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 3

4 A brief discussion of the relationship between the structural

model and the quasi-reduced form is provided in the Appendix.

The reader is referred to Wohlgenant (1989) or Wohlgenant and

Haidacher for a more complete discussion.

5 Constants and deterministic time trends are added to all of the

empirical specifications below except the system of consumer

demand relationships (Appendix). Only a constant term was added

to the consumer demand system.

6 The quasi-reduced-form equations derive from Heiner’s seminal

work and the extensions of this work by Wohlgenant (1989) and

WH. In the quasi-reduced-form representation, shifts in the market’s demand schedule are exogenous. 

7 For any single firm, Heiner found that the simultaneous change

in the output price caused by the change in input price may trace

out a positively sloped input demand for the firm. He found this

positive relationship disappears when summing over all firms.
industry’s demand for farm ingredients, and theory

suggests Aff < 0.8

Second, the industry’s longrun quantity of food supply

increases with its own-consumer food price. Heiner,

Braulke, Panzar and Willig, and WH show that even if

all input prices are exogenous to a competitive industry (flat input supplies), firm diversity implies that

positive shifts in consumer demand trace an upwardsloping longrun industry supply function. Theory

implies Arz > 0. 

Third, if firms are identical and farm ingredients are

normal factors of production, a decrease in the supply

of farm ingredients leads to a contraction of food supply and to an increase in consumer food prices. A normal factor of industry production is one in which the

industry uses more of the factor to produce more output, while an inferior factor is one in which the industry uses less of the input to produce more output. The

theory of diverse firms extends the neoclassical result

that an increase in farm prices leads to increases in

food prices only if farm ingredients are normal factors

of industry food production. Since we expect that the

aggregate farm ingredients specified here are normal,

we expect Arf < 0. 

Fourth, if farm ingredients are normal factors of industry production and firms are diverse, positive shifts in

consumer demand lead to longrun increases in farm

prices. For that reason we expect Afz > 0. 

The theory of diverse firms does not unambiguously

sign the response of consumer food prices to changes

in nonfarm input prices. The reason is that a marketing

input may be an inferior factor of production.9 An

increase in the price of an inferior factor raises a firm’s

average costs, but reduces its marginal costs. For a

competitive industry comprised of identical firms,

higher longrun average costs drive firms from the

industry, reduce industry supply, and drive up consumer prices. The results may be different if an industry’s firms are diverse. 

Inframarginal firms are bestowed with firm-specific

fixed assets that earn rent in the long run. Such firms

are bestowed with firm-specific entrepreneurial capacity (Friedman) or location that provides them with a

cost advantage over marginal firms (Panzar and

Willig). One could argue that the entrepreneurial

capacity of inframarginal pork-producing firms in the

Southeast United States exceeds that of marginal producers in the Midwest. The cost advantage of inframarginal firms allows them to remain in the industry

even as the longrun average cost of other firms is

above market price. It follows that even in competitive

markets, if the factor is inferior to inframarginal firms,

an increase in its prices allows inframarginal firms to

increase their supply even in the long run. The increase

places downward pressure on output price. On the

other hand, if the factor is inferior to marginal firms,

their longrun average cost rises above output price.

Marginal firms would exit the industry, thereby reducing industry supply and placing upward pressure on

the market’s average price of output. A negative sign

on an element of Arw suggests the associated factor is

inferior to industry production, and that the positive

supply response of inframarginal firms outweighs

the negative response of marginal firms10 (Panzar

and Willig). 

Theory provides a homogeneity condition. Since consumer demand is homogeneous of degree zero in

retail (food) prices and income, and output supply and

input demand are homogeneous of degree zero in

farm and nonfarm input prices, the market-clearing

price equations of (equations 1) are homogeneous of

degree zero in farm and nonfarm input prices, retail

prices, and income (e.g., WH, Wohlgenant [1989],

Chavas and Cox). 

The WH framework provides a test of the competitive

model. The test is based on the notion that if a firm is

4 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

8 Correspondingly, the retail price equation of (1) is a Heiner-type

of industry-level output supply schedule. 

9 The example given here would not hold for the special case of

only two inputs (e.g., one farm and one non-farm input). In this

two-input case both factors must be normal, and increases in the

price of either input raise the output price.

10 Because firm-level production functions are not identical, a factor of production can be normal for some firms and inferior for

others (e.g., older versus modern plants). Hence, a factor is normal

(inferior) for an industry if the industry uses more (less) of the factor as it increases output. The weighted sums of individual firmlevel elasticities determine whether a factor is normal or inferior

(WH).
a price taker in both its purchase of inputs and its

sales of output its profit function exists, and the symmetric second derivatives of its profit function define

reciprocal relationships between a firm’s output supply and input demands. Wohlgenant and WH derive an

analogous symmetry condition for the group of

diverse industry firms. Denoting Sf

(j)

as the cost share

of farm ingredients for the jth industry, and to the

coefficients in equations 1, WH show that symmetry

at the industry level implies

Arf

(j) = -Sf(j) Afz(j).

This condition states that if firms take farm and consumer prices as given, there exists a symmetric

response of consumer and farm-level prices. 

When studying retail and farm price relationships,

analysts are often interested in the elasticity of transmission of farm prices to retail food prices. The elasticity of price transmission is the percent change in a

retail food price induced by a 1-percent change in the

farm price (George and King). Estimates of this elasticity reduce to the farm share if the food industry is

competitive and if industry production exhibits constant returns with respect to farm ingredients. The

assumption of fixed-proportions production (at the

industry level) imposes constant returns with respect

to all inputs, and therefore ensures transmission elasticities equal to the farm share. The WH model

allows us to test whether the elasticity of price transmission equals the farm share within a variable-proportions framework. 

Wohlgenant and WH show that in terms of the coefficients of equations 1, the jth industry’s production displays constant returns with respect to the farm input if 

Arz

(j) = -Arf(j)

Afz

(j) = -Aff(j)

hold. Constant returns for an industry imply zero

industry profits in the long run. If both the symmetry

and the constant returns restrictions hold, the elasticity

of price transmission equals the farm share. 

The model provides refutable hypotheses concerning

oligopsony power. Policymakers often express concern that food producers exert market power when

acquiring raw agricultural commodities from farmers.

Some point out that captive supplies associated with

new marketing arrangements may have changed the

market structure so as to favor food producers and

keep farm prices below competitive levels (U.S.

Department of Agriculture, February 1996). Others

counter that such voluntary arrangements may reflect

the response to risk in a competitive market (Paul).

The WH framework provides a test of the null that

food producers acquire farm commodities competitively in national markets.

The test recognizes that if firms exert market power in

acquiring farm commodities, a gap would exist

between the farm price and the industry’s demand for

farm ingredients. Shifters on the farm supply function

would define this gap.

At the level of the firm, the arguments are as follows.

Let Pfj = Pfj (Fj

, Sj) denote the inverse supply function

for farm commodities facing the jth food industry,

where Sj denotes a vector of shifters to this supply

function. The first-order condition for profit maximization of a food-producing firm takes the form MVP =

Pfj + lf (MPfj /MF), where MVP is the marginal value

product or firm-level demand for the farm commodity,

and l is a market power parameter. l embodies the

firm’s conjecture about the effect its purchases of farm

ingredients will have on the market (Bresnahan, p.

102-104). Note that the term (MPf /MF) in the above

relationship is a function of Sj

. When l 1 0, the market

level demand shifters, Sj

, enter the firm’s optimization

rule and define a gap between the market’s farm price

and the value of the marginal product for a competitive

firm. Hence, when l 1 0, the marginal farm price – the

firm’s MVP – lies above the average farm price and

firms restrict their demand for farm commodities. If l

= 0, price-taking firms recognize that their purchases

impart no effect on the market, the farm price (or the

value of the marginal product) equals the MVP as the

industry level demand shifters (Sj,) do not enter firms’

optimization conditions. 

For a group of nonidentical firms of an industry, the

arguments are similar. By eliminating Fj from equations 1, the two equations reduce to 

(3) Prj = Bf

(j) Pfj + Bw(j) W + Bz(j) Zj + vr

.

Equation 3 is an industry-level relationship similar to

the first-order conditions of a price-taking firm. Under

the null of no oligopsony power, the vector of supply

shifters, Sj

, does not appear in equation 3. Under the

alternative, Sj explains the gap and 

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 5
(4) Prj = Bf

(j) Pfj + Bw(j) W + Bz(j) Zj + Bs(j)¢ Sj + vr

suggests the industry exerts oligopsony power in

acquiring farm inputs. Equations 3 and 4 suggest that

if industry j acquires farm commodities competitively,

Bs

(j)¢ = 0. 

This concludes the review of the theory used to interpret the empirical results presented in the remainder

of this report. Before we present these empirical

results, however, we review the way in which structural change enters our empirical analyses. 

6 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA
In the previous section, the retail and farm price equations of 1 derive from market-clearing conditions for

consumer food products and for farm ingredients (see

Appendix). However, questions concerning the specification of equations 1 arise if markets have undergone

structural change.

Regardless of the impact of structural change, market

clearing means that excess supply (demand) would be

of short duration and would equal zero on average.

Furthermore, the effects of unforeseen shocks to market clearing would die out over time. In time series jargon, excess supply (demand) would be stationary. It is

straightforward to show (using the market-clearing

conditions shown in the Appendix) that the error

terms, erj and efj , of equations 1 may represent excess

supply (demand) variables for food and farm products.

Stationary error terms imply market clearing, and market clearing would prevent the variables of equations 1

from moving too far apart. 

Associated with structural change are market trends.

Evidence of trends or changes in trends of market variables are often used as indicators of structural change.

In time series jargon, variables that are characterized

or generated by trends are non-stationary. However,

even if each of the variables of equations 1 displays

trends, the equations would still reflect market clearing

if the excess supply variables or error terms are stationary. If each of the time series variables used in a

model displays trends, and if model errors are stationary, the model is cointegrated (Engle and Granger).

Tests of cointegration are tests of whether the data support the theory. In a cointegrated regression, some

mechanism cancels or aligns the trends among the

variables, and in equations 1 the mechanism is market

clearing. 

If the trends driving the non-stationary variables of

equations 1 are not linked, excess supply would not

die out, and the regression would be spurious (Granger

and Newbold, p. 202-214, Hamilton p. 557-562). If the

price equations of (1) are spurious, inter-temporal

movements in one set of variables of equations 1 do

not explain inter-temporal movements in other variables. A finding of a spurious regression would not

support the theory.

In general, if market variables are driven by trends, the

trends can be deterministic, stochastic, or a combination

of both. A deterministic trend is a time trend defined in

the usual way. Trends in demographics or predictable

increases in real wages and productivity over the last

century may drive the deterministic portion of trends in

market variables. Market variables generated by deterministic trends pose few problems for statistical inference because with an infinite number of observations,

such variables can be forecast from past observations

with an arbitrary degree of accuracy. The second type of

trend is a stochastic trend. Variables driven by stochastic trends are referred to as unit root or integrated

series. For example, trends in real wages tied to unpredictable changes in the direction of inflation, unpredictable changes in the direction of consumer demand,

technology, or the continual process of industrial reorganization, may be generating stochastic trends in market variables.11 Unlike deterministic trends, stochastic

trends change direction unpredictably. Integrated market

variables pose special problems for statistical inference

because even in infinite samples, optimal forecasts of

these variables do not converge, but are continually

revised as new observations become available. 

More formally, the accuracy and reliability of forecasts

of market variables depend on whether the variable is

driven by a deterministic or a stochastic trend. As the

forecast horizon grows, the forecast of a series generated by a deterministic trend converges to a time trend,

and the mean squared error (MSE) of this forecast converges to the unconditional variance of the series

(Hamilton, p. 438-42). Population, real wages, and real

disposable income may be accurately and reliably forecast. On the other hand, tastes and preferences, technology, and the continual reorganization of an industry

may be stochastic trends because changes in any of

these may be impossible to predict. Unlike deterministically trending variables, the forecast of a unit root

variable diverges with the length of the forecast horizon, and the MSE of the forecast increases without

bound (Hamilton, p. 438-42). 

Associated with each type of trend is a type of cointegration. A model constructed from deterministically

trending variable series is deterministically cointegrated if the deterministic trends in the model’s variables are linked. In practice, a regression model is

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 7

11 That is, a series that is stationary around a deterministic trend.

Structural Change, Cointegration, and Market Clearing
deterministically cointegrated if a time trend variable

appended to the model is not statistically different

from zero. A model constructed from a set of stochastically trending series is stochastically cointegrated if the model errors are stationary. Just as market variables may reflect both a deterministic and a

stochastic trend, a model may be both deterministically and stochastically cointegrated.

Using annual time series from 1958-97, we computed

Dickey-Fuller and Phillips-Perron t-tests for the logged

and deflated variables used in the seven sets of retail

and farm price equations.12 Both sets of tests are

designed to refute the hypothesis that, conditioned on

an AR(1) representation, a single unit root net of an

intercept (or drift) or net of a deterministic time trend

governs the series. The tests differ in the way they

handle serial correlation of the error terms of the

AR(1) specification.13 Almost without exception, the

two sets of tests suggest that both a stochastic and a

deterministic trend drive most of the variable series

used in equations 1.14

Given evidence of trends in the variables, the question

is whether these equations are stochastically and deterministically cointegrated. The specification of equations 1 used throughout this report is as follows. The

deterministic regressors include an intercept and a

deterministic time trend. The stochastic regressors

include a vector of (logged) nonfarm input prices (ln

W), a (log) farm supply variable specific to market i

(ln Qi

), and the total demand shifters (ln Zi) for each of

the consumer demand equations.15 The vector ln W

consists of (logs of) wages, the price of packaging, the

price of transportation, and the price of energy. To satisfy homogeneity, all prices and income variables in

equations 1 and 2 are deflated by the price of other

nonfarm inputs (Elitzak). Hence, the tests for cointegration are based on a specification that includes six

stochastic regressors, a constant, and a deterministic

time trend for each retail and farm price equation. We

compute two sets of tests.16

The first is based on model residuals, and specifically

tests the null hypothesis of a spurious regression.

Again, a model is spurious (or not stochastically cointegrated) if the model errors follow a unit process.

Engle and Granger (1987) suggest applying DickeyFuller tests to model residuals. Phillips and Ouliaris

confirm that the Dickey-Fuller and Phillips-Perron statistics can be used to test for spurious regressions. They

find, however, that the critical values depend not on the

number of observations, but on the number of stochastic regressors used in model specification, and whether

the regression includes an intercept or a deterministic

time trend. 

Table 1 reports Dickey-Fuller and Phillips-Perron ttests designed to refute the null that the equations 1 are

spurious regressions. The statistics are based on

Ordinary Least Squares (OLS) residuals. The DickeyFuller results presented in table 1 fail to reject the null

of a spurious regression for each of the 14 equations,

while the Phillips-Perron results fail to reject the null

for 8 of the 14 equations. 

8 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

12 The sample series used to create the variables are discussed in

the Appendix. All price and income variables are deflated by the

price of other nonfarm inputs and logged prior to testing. The total

demand shifters are computed directly from the estimates of the

double-log level system of consumer demand equations. Prices and

income are also deflated by the price of other nonfarm inputs prior

to estimation. The test results were computed using Shazam.

13 Dickey and Fuller control for the serial correlation in the error

terms by adding lags to the AR(1) representation. Phillips and

Perron compute estimates of the covariogram of the errors of an

AR(1) process. For a concise comparison between the tests we

refer the reader to Hamilton (p. 504-518). The simulations presented in Phillips and Perron (1988) reveal that neither test is universally more powerful than the other. 

14 The Dickey-Fuller and Phillips-Perron results are available upon

request. Some results conflict. For example, the results suggest the

farm prices for poultry and eggs may be stationary around a time

trend (-3.95 and -4.49) but are unit root non-stationary around an

intercept. The results also suggest the farm supply for beef may be

stationary around a constant but non-stationary around a time

trend. When unit root tests conflict, Holden and Perman spell out a

multi-step procedure that may be useful in sorting out the results.

15 The seven-equation demand system was also found to be stochastically cointegrated, and seemingly unrelated canonical cointegrating regression estimates with an intercept and no time trend

and symmetry and homogeneity imposed are used to construct the

demand shift variables used in equations 1. 

16 Because we found that a linear deterministic time trend variable

was invariably statistically different from zero, we reject the null

of deterministic cointegration for each price equation and included

it in the model specifications for each industry. Hence, our tests of

cointegration are tests specifically for stochastic cointegration. 
The second set of tests is designed to examine the null

that the regressions are stochastically cointegrated. The

tests are based on the observation by Park (1990) that

appending a set of integrated series to a stochastically

cointegrated model yields a spurious regression. If the

additional variables add no explanatory power to the

regression, they are superfluous, and the original

model specification is cointegrated. The technical

problem of testing whether the variables are superfluous is that, in general, the model error terms are correlated with the first differences of the model’s regressors. This correlation destroys the asymptotic normality of parameter estimates, and hence destroys the reliability of the usual chi-square tests. Park (1990) derives

a transformation that accounts for this correlation, and

uses it to transform each of the variables of a model.

Chi-square tests based on the transformed regression

represent valid tests of the null that the additional variables are superfluous, and the original model is stochastically cointegrated. 

To employ the test, however, one is faced with choosing a set of integrated and potentially superfluous variables to append to the model. Here, theory provides no

clear guide. Hence, we follow Park’s suggestion by

appending higher order polynomials of deterministic

time trends to the retail and farm price equations. 

Table 2 reports chi-square estimates associated with

Park’s J1 test (1990) of the null that the coefficients of

the polynomial time trend terms (T2, T3 & T4) are

jointly zero (see table 2 for the specification of the

polynomial terms). The p-values (in parentheses) suggest that at the 0.05 level of rejection, all equations are

stochastically cointegrated except the retail price equation for poultry and the farm price equations for beef,

poultry, and dairy. 

The results in tables 1 and 2 provide somewhat mixed

results. The Dickey-Fuller tests (table 2) suggest each

of the 14 equations is spurious. The Phillips-Perron

tests suggest that, at reasonable levels of rejection, 8 of

the 14 price equations are cointegrated. Finally, Park’s

J1 test suggests that, at reasonable levels of rejection,

10 of the 14 equations are cointegrated. In combination, the Phillips-Perron and Park’s test results suggest

that only the retail price equation for poultry and the

farm price equation for beef and veal may be spurious.

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 9

Table 1  Residual-based tests of spurious

regressions

Dickey-Fuller Phillips-Perron

Retail price equations

Beef and veal -3.61 (1) -5.73** (1)

Pork -3.18 (3) -5.74** (3)

Poultry -4.65 (0) -4.44 (1)

Eggs -3.94 (4) -3.80 (1)

Dairy -4.84 (1) -7.52** (1)

Fresh fruit -4.20 (0) -4.12 (1)

Fresh vegetables -4.22 (2) -4.55 (2)

Farm prices (ln Pf)

Beef and veal -3.18 (0) -3.15 (1)

Pork -3.41 (0) -3.49 (1)

Poultry -3.41 (1) -5.21* 1)

Eggs -3.15 (1) -4.99 (1)

Dairy -3.72 (1) -6.00** (1)

Fresh fruit -4.02 (0) -3.92 (1)

Fresh vegetables -3.82 (1) -5.23* (1)

Values are t-tests associated with the coefficient of the lagged OLS

residuals in which the regression includes a constant and a time

trend. Values in parentheses indicate the number of lagged-first differences in the autoregression (Dickey-Fuller) or the number of lags

included in the error covariogram (Phillips-Perron). 

*Reject the null of a spurious regression at (approximately) the 0.10

level. The result is based on a critical value of approximately -5.2.

which is -0.5 plus -4.7. -4.7 is the critical value computed by Phillips

and Ouliaris for a demeaned (constant) and detrended (one deterministic time trend) regression with five stochastic regressors

(Phillips and Ouliaris, Table IIc). -0.5 is the increment associated

with adding the sixth stochastic regressor (Ng). 

**Reject the null of a spurious regression at (approximately) the

0.05 level. The result is based on a critical value of approximately 

-5.5 which is -0.5 plus -5.0. -5.0 is the critical value associated with

a demeaned and detrended regression with five stochastic regressors

and -0.5 is the increment associated with the sixth regressor (Ng).

Table 2  Variable-addition tests of cointegration

Industry Retail price equations Farm price equations

Beef and veal 6.83 9.52

(.08) (.02)

Pork 3.75 0.59

(.29) (.90)

Poultry 18.23 27.27

(.00) (.00)

Eggs 4.81 3.16

(.19) (.37)

Dairy 7.72 16.90

(.05) (.00)

Fresh fruit 1.28 6.83

(.73) (.08)

Fresh vegetables 0.31 2.92

(.96) (.40)

Entries are c2 with the restriction a1=a2=a3=0 in the general regression P=Xb + f(a,T) + e in which f(a,T) = 1T2 + a2T3 + a3T4 and in

which T = t/max(t) where P is either the logged and deflated retail or

farm price, X includes the intercept, the linear time trend, and the

six logged and deflated stochastic regressors. The values in parentheses are p-values, and represent the size of the rejection region

associated with the restriction. For example, values greater than

0.05 fail to reject the null of stochastic cointegration at the 0.05 level

of rejection. 
In the previous section, we argued that trends in market data reflect structural change, and found evidence

of both deterministic and stochastic trends in key variables associated with seven U.S. markets. In addition,

we found evidence that markets distribute these trends

across consumers and food producers. Despite the

claim that food markets may have undergone a

sequence of permanent changes over time, we show in

this section that market-clearing provides mostly stable

longrun retail and farm price relationships.

The stochastic trends embedded in the variables of

equations 1 require us to deviate from textbook estimation procedures. As stated above, such procedures fail

to account for a non-zero correlation (at any lag)

between the first difference of an explanatory variable

(i.e., the fundamental error terms of the variables) and

a cointegrated model’s stationary error terms. This correlation is present in all but the simplest class of cointegrated models. While it does not destroy the consistency of parameter estimates, the correlation does

destroy the asymptotic normality of the estimates and

renders textbook formulas for the c2, F, and t tests

invalid for inference. 

Park (1990, 1992) and Park and Ogaki transform variables of cointegrated regressions based on this correlation. Their transformations reduce general, cointegrated regressions to the simple (or canonical) class of

cointegrated regressions in which first differences of

explanatory variables are not correlated with regression errors. The procedure is to first transform the variables of a cointegrated regression and then to apply

textbook procedures to the transformed regressions.

The canonical cointegrating regression (CCR) estimator applies OLS to a transformed single equation (Park

1990). We used the CCR estimator in the previous section to compute Park’s variable addition test of the null

of cointegration (Park 1992). In this section we again

use the CCR estimator to compute a variable addition

test of oligopsony power. In addition, we apply the

seemingly unrelated regression (SUR) estimator to a

transformed, seven-equation consumer demand system, and to the cointegrated quasi-reduced-form retail

and farm price equations (i.e., equations 1) for each

industry. This two-step estimator, termed the seemingly unrelated canonical cointegrating regression estimator (SUCCR), provides us with unbiased estimates of

market structure and asymptotically-correct inference

on tests of market power and constant returns in multiple equation systems (Park and Ogaki). We refer interested readers to Park, and to Park and Ogaki for details

on the transformations that we use to compute the estimates presented in this section. 

Consumer Demand 

Kinsey and Senauer argue that changing trends in

consumer behavior lead to a changing structure of the

food sector. Cointegrated, market-clearing relationships would reflect the transmission of trends from

consumers. To capture trends in consumer demand,

we specify and estimate a consumer demand system

for the seven industries. In this section, we discuss

the specification of the seven-equation consumer

demand system. 

Appendix table 1 presents point estimates and t-values

of the seven-equation system of composite per-capita

demand. To construct the empirical consumer demand

model, we used logged data on per-capita consumer

disappearance as proxies for the seven dependent per

capita consumption variables, and deflated all prices

and income (explanatory variables) by the price of

other nonfarm inputs (to ensure homogeneity of the

market-clearing conditions). Based on Dickey-Fuller

and Phillips-Perron tests, we could not refute the null

that virtually all of the logged variables of the consumer demand system are unit root non-stationary

around a deterministic trend. In addition, we found

evidence that the individual consumer demand equations are cointegrated. Next, we imposed the symmetry

and homogeneity restrictions (e.g., Deaton and

Muellbauer, p. 43-46; Silberberg, p. 250-253) at the

mean of the sample, and report the restricted point

estimates in appendix table 1. The restricted estimates

were then used to construct the demand shifters, ln Zj

,

for each industry j (equation 2), and to compute full

reduced-form price responses reported below.17

10 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

Further Empirical Results

17 We are aware of the problem with incorporating the adding-up

condition on this double-log specification (Deaton and Muellbauer,

p. 17), and are aware of the conceptual problem of using farmlevel disappearance data as the dependent variable of the system

(WH). Our purpose here is to compute only approximate values of

the shifters on consumer demand. 
Tests of Competition and Constant Returns 

Table 3 reports the c2 and p-values associated with

symmetry, constant returns or zero profits for the

industry, and the joint restrictions of symmetry and

constant returns for the seven industries. Failure to

refute symmetry suggests food firms take both output

and farm ingredient prices as given. Failure to reject

constant returns for the industry suggests that free

entry and exit of diverse firms result in zero longrun

profits. Failure to refute the joint hypotheses of symmetry and constant returns suggests that, in the long

run, a 1-percent increase in the price of a farm commodity results in an increase in the price of a composite food category by a percentage equal to the cost

share of the farm commodity used in producing the

food category. 

The symmetry (only) and constant returns (only) test

results provide evidence of longrun competition. In

particular, the symmetry test fails to refute (at the 0.05

level) the longrun competitive model for the beef,

dairy, eggs, fresh fruit, and fresh vegetable industries.

The constant returns test fails to refute the longrun

competitive model for poultry, fresh fruit, and fresh

vegetables. It is worth repeating that this general finding of competitive markets takes into account the

many permanent changes that may have occurred in

these markets over time. 

Furthermore, our tests reject the joint restriction of

symmetry and constant returns for all industries except

fresh fruit and fresh vegetables. The results suggest

that estimates of elasticities of farm price transmission

to retail apply only to markets in which final products

undergo a minimal amount of food processing. 

The general finding of competitive markets is consistent with WH and Wohlgenant’s (1989, 1994, 1996)

findings. On the one hand, we expect our findings to

be similar because the model structures and data are

very much the same.18 On the other hand we expect

differences because of the different estimation procedures. While our approach exploits deterministic and

stochastic trends in market data, the cited works

remove stochastic trends through a first-difference

transformation prior to estimation. In comparing the

procedures using the same retail and farm price equations, Reed and Clark find that one fails to reject parametric restrictions more often using a first-difference

specification of an econometric model.19 The reason is

if the explanatory variables are integrated, a first-difference transformation removes the dominant, longrun

component of the variance of the variables. Hence, if

the variables are integrated, a first-difference filter

would inflate the variance of parameter estimates and

could reduce the likelihood of rejecting any parametric

restrictions. It is noteworthy that we reject both the

symmetry and the joint restriction of symmetry and

constant returns more often than the cited works.

Oligopsony Power

In a previous section, we reviewed the theory used to

test for oligopsony power. If food firms exert oligopsony power in acquiring farm ingredients, a gap would

exist between the farm price and the value of the marginal product of farm ingredients at the market level.

Shifters on the farm supply associated with the jth

market, Sj

, would explain this gap. Recall from above

that under the null hypothesis of food producers taking

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 11

Table 3  Tests of symmetry and constant returns

Symmetry Constant Symmetry and

only returns only constant returns

Beef and veal 0.4773 87.9159 97.2574

(.490) (0.00) (.000)

Pork 94.9740 34.3050 98.0828

(.000) (0.00) (.000)

Poultry 26.1533 4.0383 39.4573

(3E-7) (.133) (1E-8)

Eggs 0.0381 223.52 255.7759

(.845) (0.00) (0.00)

Dairy 0.9081 48.6256 49.1519

(.341) (0.00) (.000)

Fresh fruit 2.1428 4.7536 4.7871

(.143) (.093) (.188)

Fresh vegetables 1.7731 0.8505 6.0862

(.183) (.654) (.107)

Values are chi-square statistics. Values in parentheses are p-values,

or the size of the rejection region necessary to reject the null

hypothesis. 

18 We are aware that the model specifications for eight industries

in Wohlgenant (1989, 1994) include only a single nonfarm input

price. The model specification for beef and pork (only) used in his

1996 paper is similar to the specification used here, as it includes

the same four nonfarm input prices. Furthermore, our work uses a

different deflator to impose homogeneity.

19 The study controls for differences in the data and model 

specifications. 
farm prices as given, no gap exists and the retail-farm

price relationship is 

(3¢) Prj = Bf

(j) Pfj + Bw(j) W + Bz(j) Zj + vr .

Under the alternative of oligopsony power, the retailfarm price relationship is

(4¢) Prj = Bf

(j) Pfj + Bw(j) W + Bz(j) Zj + Bs(j)¢ Sj + vr .

A test of whether firms acquire farm commodities

competitively in national markets reduces to a test of

the restriction Bs

(j)¢=0. 

The usual chi-square tests of statistical significance of

the Sj variables would be reliable only if the variables

of equation 3¢ and the Sj would be stationary. Because

we found evidence that both sets of variables are integrated, we proceed as follows. Under the null hypothesis of price-taking, equation 3¢ is cointegrated and its

error terms are stationary, and the variables of equation

3¢ are transformed to account for the correlation

between first differences of explanatory variables and

the model error terms (Park 1990, 1992). Under the

null, the integrated (untransformed) Sj variables would

be independent of the stationary error terms of equation 3¢, and Bs

(j)¢=0. Under the alternative of oligopsony power, the error terms of equation 3¢ would be

integrated, and this price-taking relationship would be

spurious. In this case, the integrated Sj variables and

the integrated error terms of equation 3 would not be

independent and in general Bs

(j)¢1 0. Rather than testing for the statistical significance of Sj

, chi-square tests

of Bs

(j)¢=0 represent a test of whether the price taking

model is cointegrated or correctly specified against the

alternative that the oligopsony power relationship is

correctly specified (Park 1992).

Table 4 reports the chi-square and p-values computed

from the transformed regressions. The results report

the statistics associated with one integrated, industryspecific farm supply shifter (S1) and both integrated,

industry-specific farm supply shifters (S1 & S2).20 The

results are based on a specification that includes a constant and a deterministic time trend. At reasonable levels of rejection, we fail to reject the null that in national markets, the seven food industries acquire farm

ingredients competitively.

Longrun Industry Structure

Table 5 presents SUCCR estimates of the parameters

of equations 1 for the seven food markets. Although

they account for a negative own-price consumer

response, they are conditioned on shifters of consumer

demand (i.e., ln Z). Hence, the estimates would not

account for particular shifts in consumer demand

induced by endogenous changes in relative retail prices

among the seven composite markets. However, by controlling for such shifts, the ‘quasi’ reduced-form estimates of equations 1 provide information on industry

structure. Given evidence of permanent change and

cointegration presented above, the results in table 5

represent longrun estimates of industry structure. 

Theory predicts a negatively sloped, longrun industry

demand for farm ingredients. In terms of equations 1,

12 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

Table 4  Tests of competition in acquiring farm

commodities

S1 S1 & S2

Beef and veal 1.2377 1.3832 

(.266) (.501)

Pork 0.0443 2.4686

(.833) (.291)

Poultry 0.0538 0.2956

(.816) (.862)

Eggs** 0.1994

(.655)

Dairy 0.1294 0.2022

(.719) (.904)

Fresh fruit 2.5509

(.110)

Fresh vegetables 0.2176

(.641)

Entries are c2 values and values in parentheses are significance

levels. The sets of supply shifters on farm supply are as follows

(see Appendix for data series definitions): Beef: S1 is steers, S1 &

S2 are steers and corn price; Pork: S1 is hog inventories, S1 & S2

are hog inventories and corn price; Poultry: S1 is the price of soybean meal, S1 & S2 are the price of soybean meal and corn price;

Eggs: S1 is laying flock; Dairy: S1 is cow numbers and S1 & S2 are

cow numbers and price of soybean meal; Fresh fruit: S1 is farm

wages; Fresh vegetables: S1 is farm wages. 

**Sample interval is 1960-97.

20 The industry-specific shift variables on farm supply are defined

in the appendix. For the test to be meaningful, the variables must

be integrated. We could not refute the claim of integrated farm

supply shifters. Furthermore, because the null hypothesis is that

equation 3¢ (and not equation 4¢) is cointegrated, the Sj variables

are not transformed.
	
	
		 
					
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theory predicts Aff < 0. The negative estimates of Aff

for each of the seven markets are statistically different

from zero. The estimates describe downward sloping,

industry-level demand schedules for farm ingredients. 

The theory of diverse firms in a competitive market

predicts that positive shifts in the consumer demand

function trace an upward sloping, longrun industry

supply schedule. In terms of equations 1, theory predicts Arz > 0. The estimates of Arz are positive for all

seven markets, and except for fresh fruit and fresh vegetables, they are statistically different from zero at reasonable levels of rejection. 

The theory of competitive markets predicts that if farm

ingredients are normal factors of production, a contraction in farm supply raises consumer food prices. In

terms of equations 1, theory predicts Arf < 0. The estimates of Arf are negative for each of the seven industries, and are statistically different from zero. Theory

also predicts that if farm ingredients are normal, Afz >

0. The estimates of Afz are positive for all seven markets and are statistically different from zero. Negative

estimates of Arf and positive estimates of Afz suggest

the aggregate farm ingredients are normal factors of

industry production.

The estimates presented in table 5 suggest some marketing factors are inferior to a number of industries.

Negative signs on elements of Arw suggest the particular factor is inferior and that the supply response of

inframarginal firms exceeds that of marginal firms. For

example, the results suggest transportation is an inferior factor for the beef and pork industries. The estimates may indicate that for the U.S. pork industry,

changes in vertical coordination have allowed the

inframarginal firms in the Southeast United States to

economize on the transportation of hogs. The estimates

also suggest that labor is an inferior factor for the fresh

fruit and fresh vegetable industries.

The results presented in table 5 also point to some

nonfarm inputs that appear to be normal across industries. The positive signs on the Arw coefficients associated with the price of packaging suggest that packaging is a normal factor for all seven industries. This

may reflect the notion that consumers value the convenience associated with the packaging of food products,

and suggests that consumers would be willing to pay

more for packaging through higher food prices.

Furthermore, labor appears to be a normal factor of

production for four of the seven industries. 

Input Substitution

The variety of consumer products and diversity of

firms within a composite industry (e.g., fresh fruits)

provide evidence of variable-proportions at the market

level (e.g., WH, Wohlgenant [1999]). Refutation of

restrictions implied by fixed-proportions analyses provides additional evidence. 

The diversity of a composite industry’s products suggests that production processes vary across firms. Meat

products, for example, vary by the amount of processing. Manufacturers of processed meat products would,

for example, utilize higher proportions of nonfarm

ingredients (e.g., packaging, energy) than manufacturers of fresh meat products. An increase in the price of

nonfarm inputs relative to farm inputs would, therefore, raise longrun average and marginal costs for

manufacturers of processed products more than for

manufacturers of fresh products.21 In terms of meat

industry supply, the quantity of manufactured products

would fall relative to fresh products. In terms of input

demand, the reduction in the supply of manufactured

products relative to fresh products means that the ratio

of nonfarm inputs to farm inputs demanded by the

industry falls in response to an increase in the relative

price of nonfarm inputs.

WH (p. 21) formally show that if firms are diverse, an

industry’s input price response can be decomposed

into a substitution and an output effect in precisely the

same manner as one could decompose the response of

a single firm with a variable proportions production

technology. Wohlgenant (1999) illustrates the presence of input substitution directly for a composite

industry producing heterogeneous final food products.

All that is required is that production functions differ

across firms. These results imply that even if each

firm in an industry produces its specific product in

fixed-input proportions, if these proportions vary

across firms, variable-proportions relationships apply

at the market level. 

Test results presented in table 6 suggest that market

data do not follow the predictions of fixed proportions.

In particular, fixed proportions at the market level

imply that the own-price elasticity of an industry’s

14 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

21 The marginal costs could fall if nonfarm ingredients are inferior

factors of industry production. The discussion here assumes they

are normal factors.
demand for farm ingredients equals the product of the

own-price elasticity of consumer demand and the

industry’s cost share of farm ingredients (e.g., George

and King). Since Aff

(j) is the inverse of the industry j’s

demand elasticity with respect to the jth farm price

(from equations 1), ejj is the own-price elasticity of

consumer demand for the jth consumer product, and

Sf

(j) is the industry’s cost share of farm ingredients, the

restriction Aff

(j) = 1/(Sf(j)ejj ) would hold if an industry

produced its composite mix of products in fixed-factor proportions. Based on the t-values reported in

table 6, one can refute the null hypothesis of fixed

proportions at the industry level for reasonable levels

of rejection.22

Estimates of elasticities of input substitution can be

computed from model parameters (Wohlgenant 1996)

and used to measure the ease with which an industry

varies its factor proportions. Table 7 reports estimates

of Morishima elasticities of substitution (Blackorby

and Russell) between the farm and the four marketing inputs when (in this case) changes in the farm-tononfarm price ratio are caused specifically by a

change in the farm price.23 The larger the magnitude

of the estimate, the easier it is for an industry to vary

ratios of farm and marketing inputs. Positive estimates suggest the input pairs are substitutes (when

the farm price changes), and negative estimates suggest they are complements. For example, the results

in table 7 suggest that as farm prices rise, labor and

packaging substitute for the farm ingredient in all

seven industries. As in Wohlgenant (1996), the estimates suggest that significant substitution possibilities exist in U.S. food production. 

Full-Reduced-Form Price Responses

Table 8 reports full-reduced-form estimates of percent

changes in retail and farm prices induced by a 1-percent increase in the set of explanatory variables.

Unlike the quasi-reduced-form estimates (table 5), the

full-reduced-form estimates account for the effect of

endogenous shifts in consumer demand when relative

retail prices change. For example, increased wages

may increase the retail price of both beef and pork

products, but the magnitude of the responses would

differ in the markets. The results presented in table 8

capture the effect of consumer responses to changes in

relative retail prices on retail and farm prices.24

Table 7  Morishima elasticities of substitution

Industry Nonfarm inputs

Labor Packaging Transport Energy

Beef and veal 2.613 1.910 -3.084 -1.775

Pork 1.717 0.456 -1.470 -0.013

Poultry 4.356 1.146 -1.912 -1.220

Eggs 4.181 0.092 -10.45 2.807

Dairy 3.083 0.590 -2.193 -1.210

Fresh fruit 2.811 0.697 0.939 -1.227

Fresh vegetables 2.270 1.275 -0.218 -1.212

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 15

Table 6  Tests of fixed-proportions production

Industry t-values

Beef and veal 110.744

Pork 15.063

Poultry 25.204

Eggs 233.344

Dairy 4.806

Fresh fruit 51.317

Fresh vegetables -331.354

Values are Student t-values designed to test the restriction that the

parameter Aff equals the inverse of the demand for farm ingredients

implied by fixed proportions. Values approximately equal to 2 (in

magnitude) would reject the null of fixed proportions at the 0.05

level. The estimates of Aff are found in table 5, and the estimates of

the standard errors are the estimates used to compute the t-values

in table 5. Point estimates of the own-price elasticities of consumer

demand and the farm share for each market are found in appendix

tables 1 and 2.

22 The results are similar to those reported by Wohlgenant (1996).

The tests are preliminary because they treat the estimate of the

own-price elasticity of consumer demand as a parameter with no

variation. A simulation procedure suggested by Ng, or a bootstrap

procedure suggested by Li and Maddala may provide a more precise test. 

23 Since Morishima elasticities of substitution are not symmetric,

an estimate of response caused by a 1-percent change in the factor

price ratio induced by a change in the nonfarm input price would

differ from the estimates reported in table 7. 

24 The full-reduced-form estimates are computed using equations

19a and 19b (Wohlgenant 1991) or equations 30a and 30b (WH).

Whereas theory provides expected signs on the coefficients of the

quasi-reduced form, it does not provide expected signs on the

parameter estimates of the full-reduced form. Technically, the reason is that unlike a single consumer demand equation, a system of

consumer demand equations is not negative definite (Chavas and

Cox). This is essentially why the quasi-reduced form can provide

information on industry structure and the full-reduced form cannot.
❖ 	












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The effect of consumer substitution links the effects of

changes in farm supply on retail and farm prices

across the seven markets. For example, the first panel

of table 8 suggests that increases in cattle supply

depress both retail and farm prices for pork. Hence,

increased cattle supply will lower both cattle prices

(farm-level price) and consumer-level beef prices.

Because our estimates suggest that consumers treat

beef and pork as gross substitutes (appendix table 1),

lower relative beef prices imply a reduction in consumer demand for pork. Because hogs are a normal

factor of production in pork supply, hog prices (farm

level) also fall. In this particular example, it is important to recall that estimates presented in table 8

exclude the effects of imports and exports of farm

commodities.25

The column labeled “spread” summarizes the relative

responses of retail and farm prices associated with a

1-percent increase in a particular explanatory variable. In particular, the estimates, computed in this

double-log specification as the difference between the

percent change in the retail and the percent change in

the farm price, represent Gardner’s response estimates

of retail-to-farm price spreads. A positive (negative)

sign implies that the market’s retail price response

exceeds (is less than) the response of the market’s

farm price. Because the estimates account for the

response of a market’s farm price and not the retail

equivalent farm price based on variable proportions,

the “spread” estimates reported in table 8 represent

responses of spreads computed under the assumption

of fixed-factor proportions. 

Table 9 compares the own-price elasticities of consumer demand with the full-reduced form, own-price

elasticity of farm demand for farm ingredients for each

market. Fixed-proportions production implies that an

industry’s input demand would be less own-price elastic than the own-price elasticity of retail demand.

However, the results in table 9 suggest that for four of

the seven markets, the industry’s full-reduced-form

demand for farm ingredients is more own-price elastic

than consumer demand.26 Such results call into question the validity of market price analyses based on

fixed proportions. 

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 17

25 Attempts to interpret the results presented in this section are difficult because standard errors and t-tests are not computed. Such

estimates might be computed using the methods suggested in footnote 22. 

26 The derived demand for farm ingredients reported in table 9 is

as follows. If the full-reduced-form system (i.e., table 8) of farm

price equations is represented in matrix notation as Pf = b1 F + b2

X, where F is the vector of farm supplies, and X is the vector of all

other explanatory variables, the estimates in table 9 are b1

-1. The

own-price elasticities of derived demand for farm ingredients

(accounting for consumer substitution) are the diagonal elements

of b1

-1.

Table 9  Own-price elasticities of farm and consumer demand

Own-farm price elasticity Own-retail price

of industry demand elasticity of 

Market for farm ingredients consumer demand

Beef and veal -0.402 -0.065

Pork -0.514 -0.745

Poultry -1.074 -0.607

Eggs -0.472 -0.064

Dairy -0.627 -0.974

Fresh fruit -1.020 -0.208

Fresh vegetables -0.753 0.054
This report demonstrates that structural change can be

incorporated directly into a very general and powerful

set of market models. Early empirical findings of competitive U.S. food markets based on this general theory

stood in sharp contrast to findings of market power

based on the traditional and restrictive assumptions of

fixed-factor proportions. By accounting for structural

change, we have shown that food market data closely

support this general theory and result in further evidence of competitive U.S. food industries. 

In this report, we equate trends in market variables

with structural change. We found that the most intriguing type of trend is the type that changes direction

unexpectedly. Unpredictable changes in trends fit

Kinsey and Senauer’s description of structural change

in food consumption and Paul’s explanation of industry reorganization. Yet, it is precisely their unpredictability that poses obstacles to statistical inference.

A main motivation of this report is to provide inference on competition, and we have relied on recent

advances in econometrics to exploit such trends in

market variables and test whether seven U.S. food

industries operate competitively within an environment

of structural change.

Although market variables may be driven by unpredictable changes in trends, it is necessary that models

constructed from them do not. Our finding that retailand farm-price relationships derived from this general

theory are cointegrated supports the theory, as well as

the claim, that changing trends in food consumption

alter the structure of food industries. It also suggests

that such models can be used to test for market power

despite the many permanent changes in U.S. food markets that may have occurred over time. 

Our finding of mostly competitive U.S. food industries

offers important explanations of why concentrated

food industries may be competitive. Paul argues that

unexpected downward trends in consumer demand

motivate firms to specialize and seek vertical arrangements that serve to spread the risk of downward trends

in revenues. Our finding of cointegrated retail- and

farm-price relationships suggests that competitive

industries will reorganize to spread the risk of uncertain downward trends in consumer demand. 

18 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

Conclusions
Azzam, A.M. “Testing the Competitiveness of Food

Price Spreads.” J. Agr. Econ. 43 (May 1992): 248-256.

__, and T. Park, “Testing for Switching Market Conduct.”

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Blackorby, C., and R.R. Russell. “Will the Real Elasticity of

Substitution Please Stand Up? (A Comparison of the

Allen/Uzawa and Morishima Elasticities).” Amer. Econ.

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Braulke, M. “On the Comparative Statics of a Competitive

Industry.” Amer. Econ. Rev. 77 (June 1987): 479-485. 

Bresnahan, T.F. “The Oligopoly Solution Concept Is

Identified.” Economics Letters. 10 (1982): 87-92.

Chavas, J.P., and T. Cox. “On Market Equilibrium

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Dickey, D.A., and W.A. Fuller. “A Distribution of the

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Engle, R.F., and C.W.J. Granger. “Co-integration and Error

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Fuller, W.A. Introduction to Statistical Time Series. New

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Gardner, B.L. “The Farm-Retail Price Spread in a

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George, P.S., and G.A. King. “Consumer Demand for Food

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Goodwin, B.K., and G.W. Brester, “Structural Change in

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Granger, C.W.J., and P. Newbold. Forecasting Economic

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Hamilton, J.D. Time Series Analysis. Princeton: Princeton

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Heiner, R.A., “Theory of the Firm in ‘Short-Run’ Industry

Equilibrium.” Amer. Econ. Rev. 72 (June 1982): 555-562.

Holden, D., and R. Perman. “Unit Roots and Cointegration

for the Economist.” Cointegration for the Applied

Economist, B. Bhaskara Rao, ed., New York: St. Martin’s

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Huang, K.S. “An Inverse Demand for U.S. Composite

Foods,” Amer. J. Agr. Econ. 70 (November 1988): 902-909.

Kinsey, J. and B. Senauer. “Consumer Trends and Changing

Food Retailing Formats.” Amer. J. Agr. Econ. 78

(December 1996):1187-1191.

Koontz, S.R., P. Garcia, and M.A. Hudson. “Meatpacker

Conduct in Fed Cattle Pricing: An Investigation of

Oligopsony Power.” Amer. J. Agr. Econ. 75 (August

1993): 527-548.

Li, H., and G.S. Maddala. “Bootstrapping Cointegrated

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MacDonald, J.M., and M. Ollinger. “U.S. Meat Slaughter

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Martinez, S.W., and A.J. Reed. From Farmers to

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Martinez, S.W., K. Smith, and K. Zering. “Changing Pork

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May-August 1997, pp. 17-21.

Ng, S. “Testing for Homogeneity in Demand Systems When

the Regressors Are Nonstationary.” J. of Applied

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Panzar, J.C., and R.D. Willig. “On the Comparative Statics

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 19

References
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20 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA
Structure of the WH Model 

Underpinning the pair of quasi-reduced-form retail and

farm price equations in the text equations 1 for each

market is a general market-clearing condition for final

industry output and a general market-clearing condition for farm ingredients. They are general because,

within the same composite industry, firms’ farm

demand and firms’ output supply will vary across

firms. Within the same industry, one firm’s production

function may be different from other firms’ production

functions. Hence, the structure of this class of models

provides an analytical framework for price analyses of

market for which any one industry produces a variety

of different final products. The comparative static

results developed by Heiner, and extended by

Wohlgenant (1989), do not depend on the restriction of

identical firms. For a more detailed discussion of this

structure, see WH or Wohlgenant (1989). 

In the particular setup in the text, a food industry consists of all manufacturing, wholesaling, and retailing

firms associated with a composite final demand product (e.g., beef). Each industry faces a final, marketlevel consumer demand schedule for its products and a

market-level supply schedule for the farm ingredients.

For tractability, firms in the same industry face the

same composite market prices for output and all

inputs. 

In this setup, if i denotes an index associated with a

firm in the industry, market clearing for final consumer

goods could be generally written as

Si Sr

i (Pr , Pf , W) = Dr (Pr

, Z) (i)

where Sr

i is the supply of the ith firm, Pr the output

price, Pf the farm price, W a vector of non-farm input

prices, and Z is a consumer demand shifter. Condition

(i) states that the sum of firm-level supply equals final

consumer demand for the industry’s output. Market

clearing associated with farm ingredients is expressed

as

Si Df

i (Pr , Pf , W ) = F (ii)

in which F is farm supply, and Df

i is the ith firm’s

demand for farm ingredients. Condition (ii) states 

that the sum of firm-level demands for farm ingredients equals the market-level supply of farm ingredients. Equations i and ii represent a general form of 

the structural model for each market examined in 

this study. 

The structural parameters of equations i and ii define

the Ar and the Af of equations 1 in the text. The structural parameters of equations i and ii are found by

totally differentiating equations i and ii and expressing

the results in terms of partial elasticities of supply and

demand. Totally differentiating equations i and ii and

rearranging, gives

(err - e) d lnPr + erf d lnPf = ez d lnZ - erw d lnW

- efr d lnPr - eff d lnPf = efw d lnW - d ln F

where err, for example, is the weighted sum of the

elasticities of firm supply, i.e., err = Si err

i (Qri

/Qr).

Wohlgenant and WH solve the two-equation system

for d lnPr and d lnPf in terms of d lnZ, d lnW, and d

lnF and reveal the precise way in which the structural

parameters define the coefficients of the quasireduced-form flexibilities (the A coefficients) in the

text. The relationship between the structural parameters and the response coefficients are spelled out in the

cited articles, and define the comparative static results

discussed in the text.

Data

To the greatest extent possible, we followed the directions of Wohlgenant and Haidacher (WH) when constructing the economic variables used in this study. All

of the variables of equations 1-4 in the text were constructed from annual data from 1958 to 1997. All of

the potentially superfluous farm supply shift variables

except the laying flock (for eggs) were also constructed from annual data from 1958 to 1997. The laying

flock variable was constructed from 1960-97 data. 

The retail prices are constructed from annual average

Consumer Price Index (CPI) data, U.S. City Average,

Not Seasonally Adjusted. The particular series used to

construct retail prices are:

Beef and veal Beef and Veal, CPI, U.S. City

Average, Not Seasonally Adjusted

Pork Pork, CPI, U.S. City Average, Not

Seasonally Adjusted

Poultry Poultry, CPI, U.S. City Average,

Not Seasonally Adjusted

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 21

Appendix
Eggs Eggs, CPI, U.S. City Average, Not

Seasonally Adjusted

Dairy Dairy and Related Products, CPI,

U.S. City Average, Not Seasonally

Adjusted 

Fresh fruit Fresh Fruits, CPI, U.S. City

Average, Not Seasonally Adjusted

Fresh veg. Fresh Vegetables, CPI, U.S. City

Average, Not Seasonally Adjusted

Nonfood All Items Less Food, CPI, U.S. City

Average, Not Seasonally Adjusted

Beverages Non-Alcoholic Beverages and

Beverage Material, CPI, U.S. City

Average, Not Seasonally Adjusted

Sugar Sugar and Sweets, CPI, U.S. City

Average, Not Seasonally Adjusted

Cereal Cereals and Bakery Products, U.S.

City Average, Not Seasonally

Adjusted

Farm level prices are constructed from non-seasonally

adjusted annual Producer Price Index (PPI) data for

farm products. The series used to construct farm price

variables are:

Beef and veal Slaughter Cattle, PPI, Farm

Products, Not Seasonally Adjusted

Pork Slaughter Hogs, PPI, Farm

Products, Not Seasonally Adjusted

Poultry Slaughter Poultry, PPI, Farm

Products, Not Seasonally Adjusted 

Eggs Chicken Eggs, PPI, Farm Products,

Not Seasonally Adjusted

Dairy Fluid Milk, PPI, Farm Products,

Not Seasonally Adjusted

Fresh fruit Fresh Fruits and Melons, PPI, Farm

Products, Not Seasonally Adjusted

Fresh veg. Fresh Vegetables Except Potatoes,

PPI, Farm Products, Not Seasonally

Adjusted

The raw farm prices for beef and veal and pork (Pf*)

are adjusted (as in Wohlgenant and WH) to account for

the value of byproducts in the farm prices for slaughter

cattle and slaughter hogs. We use the 1982 levels of

the gross farm value (GFV) and the byproduct value

(BPV), and hence the net farm value (NFV = GFV -

BPV) for cattle and for hogs. These data are recorded

by USDA/ERS. Using the 1982 values, data on

byproduct allowances (Pb) for cattle and hogs are used

to adjust the raw PPI farm price series. In general, the

log of the adjusted farm price, ln Pf is computed as

ln Pf = (GFV82/ NFV82) ln Pf

* - (BPV82/ NFV82) ln Pb

In particular, the adjusted farm price formula for beef

is

ln Pf = (155.5/141.1) ln Pf

* - (14.4/ 141.1) ln Pb

and is

ln Pf = (94.3/87.0) ln Pf

* - (7.3/87.0) ln Pb

for pork.

All CPI and PPI price series were obtained from

Bureau of Labor Statistics (BLS) web sites, and the

GFV, BPV and byproduct allowances were obtained

from ERS data sets with help from Lawrence Duewer. 

The price of labor, packaging, transportation, energy,

and other inputs from 1968-1997 were obtained directly from published reports (Elitzak). The series was

extended back to 1958-1967 by overlapping the 1968-

97 data set with a consistent and similar data set covering the 1958-67 period. The data were provided by

Howard Elitzak. 

The series used to construct farm supply are computed

as the product of per capita food disappearance multiplied by U.S. Population, including armed services

(July 1). The particular per capita disappearance data

series used are:

Beef and veal Beef plus Veal, Food Disappearance

Per Capita, Carcass Weight (lbs)

Pork Pork, Food Disappearance Per

Capita, Carcass Weight (lbs)

Poultry Total Chicken Plus Turkey, Food

Disappearance Per Capita, Carcass

Weight (lbs)

22 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA
Eggs Eggs, Food Disappearance Per

Capita, Farm Weight (lbs) 

Dairy All Dairy Products, Food

Disappearance Commercial Sales

plus USDA donations (lbs of milk

equivalent, milkfat basis)

Fresh fruit Fresh Fruit (including melons),

Food Disappearance Per Capita,

Farm Weight (lbs) 

Fresh veg. Commercially Produced Fresh

Vegetables Excluding Potatoes and

Sweet Potatoes Minus Mushrooms,

Commercial Disappearance Per

Capita, Farm Weight (lbs) 

The farm supply variables for beef and pork were converted from carcass weight to live weight by dividing

the disappearance values (in carcass weight) by the

annual average ratio of the dressed to live weight

under federal inspection. The dressed and live weight

data are reported in Annual Livestock Slaughter, the

Agricultural Statistics Board, NASS, USDA, and were

made available by Lawrence Duewer. The dependent

variables used in the estimation of the system of consumer demand relationships were constructed using

the same food disappearance variables, except no

adjustment was made to convert the beef and pork disappearance data to live weight. 

The data to compute shifters on consumer demand

(other than prices) are:

Population U.S. Population, including armed

services, July 1

Income Per Capita Personal Disposable

Income, Current Dollars, multiplied

by Population

The data used to form nonfarm input prices were provided by Howard Elitzak. They are:

Packaging Food Marketing Cost Index 

(1982 = 100), packaging component

Transportation Food Marketing Cost Index 

(1982 = 100), transportation component

Energy Food Marketing Cost Index, energy

component

Other Food Marketing Cost Index, advertising, communications, rent maintenance and repair, business services,

supplies, property taxes, short-term

interest. This variable is used as the

deflator in this bulletin. 

Data to construct the shifters on the farm supply used

to test for oligopsony power tests are:

Beef & veal S1: Steers, 1 year and older, January 1

S2: Price of number 2 yellow corn,

Chicago 

Pork S1: U.S. hog inventory, all hogs and pigs

S2: Price of number 2 yellow corn,

Chicago 

Poultry S1: Price of soybean meal, 48 percent,

Decatur 

S2: Price of number 2 yellow corn,

Chicago

Eggs S1: Laying flock, average annual per

month

Dairy S1: Cows and heifers on farms, 2 years

and older, January 1

S2: Price of soybean meal, 48 percent,

Decatur

Fresh fruit S1: Average hourly wages paid to

all hired farm workers

Fresh vegetables S1: Average hourly wages paid to

all hired farm workers

Economic Research Service/USDA Structural Change and Competition in Seven U.S. Food Markets/TB-1881 ❖ 23
24 ❖ Structural Change and Competition in Seven U.S. Food Markets/TB-1881 Economic Research Service/USDA

Appendix table 1  System of consumer demand equations

Explanatory Per capita consumer demand equation for:

variable Beef Pork Poultry Eggs Dairy Fresh fruit Fresh vegetables

Beef -0.065 0.574 -0.333 0.191 0.089 -0.621 -0.481

price (-1.02) (15.3) (-3.20) (5.08) (2.37) (-6.5) (-7.3)

Pork 0.322 -0.745 -0.085 0.030 0.069 -0.083 -0.152

price (15.0) (-20.0) (-1.2) (.91) (2.23) (-1.3) (-3.04)

Poultry -0.078 0.029 0.607 0.091 0.112 0.335 0.207

price (-3.0) (-.95) (-6.0) (2.60) (3.36) (5.02) (3.70)

Egg 0.045 0.012 0.083 -0.064 0.030 -0.101 0.014

price (4.70) (.79) (2.31) (-2.18) (1.50) (-2.90) (.37)

Dairy 0.053 0.085 0.303 0.084 -0.974 -0.140 -0.035

price (1.87) (2.06) (3.01) (1.45) (-14.5) (-1.52) (-0.37)

Fresh fruit 0.148 -0.033 0.327 -0.089 -0.039 -0.208 0.135

price (-6.51) (-1.24) (4.90) (-2.77) (-1.37) (-2.50) (2.63)

Fresh vegetable 0.093 -0.050 0.157 0.015 -0.004 0.113 0.054

price (-7.22) (-2.89) (3.59) (.51) (-.17) (2.66) (.81)

Nonfood 0.210 0.139 -1.170 0.388 0.905 -0.008 -0.466

price (1.93) (2.00) (-6.67) (5.5) (13.8) (-.052) (-4.08)

Beverage -0.163 0.164 0.093 0.012 0.110 0.202 0.057

price (-3.74) (6.37) (1.36) (.47) (4.78) (3.12) (1.32)

Sugar 0.410 -0.367 -0.701 -0.195 -0.101 -0.455 -0.253

price (4.51) (-6.50) (-4.48) (-3.3) (-1.9) (-3.0) (-2.53)

Cereal -0.668 0.353 0.967 -0.129 0.235 0.801 0.564

price (-4.56) (3.57) (3.53) (-1.2) (2.51) (2.92) (3.19)

Income/ 0.175 -0.103 0.965 -0.335 -0.430 0.145 0.357

pop. (5.33) (-3.23) (12.2) (-9.0) (-13.8) (2.10) (5.66)

Intercept 1.005 -0.321 6.291 2.797 5.406 5.010 5.344

(14.0) (-4.51) (36.9) (34.3) (79.5) (33.0) (38.7)

Entries are elasticity estimates with symmetry and homogeneity imposed at the sample means. Values in parentheses are t-values. The 

shares of income used to impose the symmetry restriction at the point estimates are as follows: 0.316 (beef and veal), 0.0180 (pork), 

0.008 (poultry), 0.0082 (eggs), 0.0241 (dairy), 0.0075 (fresh fruit), and 0.0062 (fresh vegetables).

Appendix table 2  Factor shares for the seven industries

Industry Labor Packaging Transport Energy Other Farm

Beef & veal 0.1892 0.0731 0.0430 0.0215 0.1032 0.5700

Pork 0.2904 0.1122 0.0660 0.0330 0.1584 0.3400

Poultry 0.2156 0.0833 0.0490 0.0245 0.1176 0.5100

Eggs 0.1628 0.0629 0.0370 0.0185 0.0888 0.6300

Dairy 0.2244 0.0867 0.0510 0.0255 0.1224 0.4900

Fresh fruit 0.2948 0.1139 0.0670 0.0335 0.1608 0.3300

Fresh vegetables 0.2904 0.1122 0.0660 0.0330 0.1584 0.3400

Estimates of Consumer Demand and Factor Shares
United States Department of Agriculture

Economic Research Service

1800 M Street, NW

Washington, DC 20036-5831