Journal of Agricultural and Applied Economics, 31, l(April 1999): 1-130 1999 Southern Agricultural Economics Association

Estimating Market Power and PricingConduct in a Product-DifferentiatedOligopoly: The Case of the DomesticSpaghetti Sauce Industry

Steven S. Vickner and Stephen P. Davies

ABSTRACT

This paper develops a simultaneous-equations panel data econometric model to obtain pointestimates of market power and pricing conduct in a representative product-differentiated,oligopolistic food market. The importance of this class of markets is recognized given itsprevalence in the food and fiber system, especially for final consumer food products. The$1.3 billion domestic spaghetti sauce industry is featured. Although the results indicatefirms exert limited market power, a portion of this power is derived from tacit price col-lusion. A higher degree of price collusion was found among brands within a market seg-ment than between segments.

Key Words: market power, oligopoly, pricing conduct, product differentiation.

In the empirical marketing literature, research-ers have relied heavily on the assumption ofproduct homogeneity. The assumption hasbeen incorporated in both temporal and spatialanalyses of market power and firm conduct inoutput and input markets. Representative pa-pers for various agricultural industries includemeat processing (Schroeter; Koontz, Garcia,and Hudson; Azzam and Schroeder), fruit andvegetable processing (Warm and Sexton),dairy (Liu, Sun, and Kaiser), general food pro-cessing (Holloway), and tobacco (Appel-baum). There are several explanations for thecontinued emphasis on homogeneous product

Steven Vickner is assistant professor in the Depart-ment of Agricultural Economics at the University ofKentucky. Stephen Davies is professor in the De-partment of Agricultural and Resource Economics atColorado State University. The authors thank DanaHoag, Norman Dalsted, and Harvey Cutler for theircomments.

models in this realm of research. First, the as-

sumption appears to be consistent with prod-uct characteristics in the markets investigated.A second reason stems from theoretical ele-gance, as these models are more parsimoniousand allow for the direct estimation of a marketpower parameter (Varian). Finally, aggregatecommodity data are typically available in sec-ondar y sources.

A broad class of imperfectly competitivemarkets, product-differentiated oligopolies,has been under-represented in the literature de-spite its prevalence in the food and fiber sys-tem especially for final consumer food prod-ucts. The Connor et al. study is commonlycited as evidence that diversified food manu-facturers depart from marginal cost pricing.However, many of the SIC codes in that studyrepresent the aggregation of structural oligop-olies in which firms sell differentiated prod-

ucts to consumers. For example, SIC code

2 Journal of Agricultural and Applied Economics, Apri11999

20860 represents carbonated soft drinks andcontains nine brands and numerous associatedproducts in the regular (e.g., non-diet) segmentalone (Cotterill). The aggregation inherent infive-digit SIC codes falsely leaves the impres-sion that the product homogeneity assumptionis appropriate for every food market.

Our understanding of empirical marketpower and firm conduct in differentiated oli-gopolies is clearly in its infancy. Current an-alyses lag theoretical developments in this area(Tirole), and the empirical work is neither asextensive nor refined as homogeneous productindustry research. Business strategists and an-titrust policymakers would benefit from abroader base of empirical evidence. Thus, theempirical objective of this paper is to measuremarket power and pricing conduct at the brandlevel in a representative oligopolistic outputmarket.

The domestic spaghetti sauce industry waschosen as an intriguing and representative pro-cessed agricultural product to study for vari-ous reasons. The industry is worth $1.3 billionannually and so is an important component ofthe food and fiber system. It is a structuraloligopoly in which products, highly differen-tiated by brand, flavor, and size, are manufac-tured and sold. 1 Also, several features of thismarket may lead to heightened consumer pricesensitivity. Spaghetti sauce is a durable goodsince its shelf life exceeds the time period be-tween price changes (Tirole). Thus, a productbecomes an intertemporal substitute for itselfbecause consumers can stockpile when it is onsale. The products are sold in a common storelocation because they are substitutes in use, soconsumers can make comparisons across prod-ucts and brands. Another dimension of this in-dustry is the role of transportation costs inpricing decisions. These products are relative-ly heavy and need to be transported from re-mote manufacturing locations to spatially dis-persed selling markets.

This paper builds on several previous stud-ies addressing this class of markets to enlargethe pool of empirical knowledge. Contribu-

1Due to data and model size limitations, the anal-ysis is restricted to brand differentiation.

tions are made to the literature in terms ofmodel specification, where we control for mer-chandising, use a weekly time series, and em-pirically disentangle pricing conduct associat-ed with rivalrous behavior from pricingconduct related to a firm’s shipping costs.More generally, this New Empirical IndustrialOrganization (NEIO) study departs from thetraditional NEIO paradigm as it identifies, inpart, the source of market power and tracks asingle industry through both time and space(Bresnahan). Finally, in the process of obtain-ing feasible error-components three-stageleast-squares (EC3SLS) estimators of marketpower and pricing conduct with methods de-veloped by Kinal and Lahiri, several errors inthe econometrics literature were identified andcorrected (Vickner and Davies).

Related Literature

Examples of empirical market power researchrelaxing the assumption of product homoge-neity are relatively sparse. Baker and Bresna-han pioneered the use of residual demandanalysis, applying it to the brewing industry.Their study was one of the seminal NEIO pa-pers to model the attributes of a product-dif-ferentiated market, where each firm faces itsown demand curve rather than an industry de-mand curve. Moreover, prices in these demandsystems are not only endogenous but are alsointerdependent (Shapiro). Their practical ap-proach to market delineation had several un-desirable features. First, the estimated conductparameter, the residual demand elasticity, wasa composite of the price elasticity of demandand the conjectural variation elasticity, so in-dividual effects could not be identified. Sec-ond, as discussed by Froeb and Werden, theability to quantify the dynamic behavior ofboth consumers and purveyors is limited bythe use of temporally aggregated time series.

Liang investigated the ready-to-eat break-fast cereal industry using a different modelformulation to separately estimate both com-ponents of the residual demand elasticity. Sheused a linear demand system and correspond-ing set of linear price reaction functions to en-dogenize prices and quantify pricing conduct

Vickner and Davies: Market Power and Pricing Conduct in a Product-Dz~erentiated Oligopoly 3

at the firm level. A restrictive pairwise com-parison of firms and aggregate data limited theresults of the study.

More recently, Cotterill analyzed the car-bonated soft drink industry using an alterna-tive NEIO model. A theoretically consistent,linear approximate Almost Ideal Demand Sys-tem (LA/AIDS) model was used to representthe demand-side of the market (Deaton andMuellbauer). Consistent with the approachtaken by Liang, the first-order conditions of ageneral price conjectural variations modelwere to endogenize price and quantify strate-gic interaction among the firms. Cotterill’sstudy, while a generalization and extension ofprevious approaches, is not without problems.First, merchandising (e.g., in-store or point-of-purchase advertising) was not controlled forproperly, possibly due to data availability is-sues. Three mutually exclusive merchandisingmeasures were used to characterize the sellingconditions: (a) the product was highlighted ina feature ad or newsprint flier, (b) the productwas put on some form of display, and (c) theproduct was simultaneously placed in a featuread and on a display. Scanner data supplierssuch as Information Resources, Inc. (IRI),A.C. Nielsen, and Efficient Market Servicesmeasure both the percent of brand’s sales andthe percent of all commodity volume (ACV)made on a given merchandising condition.Cotterill used the former. Because the ACVmeasure quantifies the percent of stores in a

geographic market maintaining one of thethree merchandising conditions, we consider ita more appropriate demand shift variable.z

Cotterill also treated real expenditure as anexogenous variable in the model when it isclearly a function of the endogenous variables.Finally, data aggregation was an issue in thestudy. Quarterly time series observations wereused because a less aggregate series was notavailable. However, both consumer and stra-tegic behavior is affected on a weekly basis,

as pricing and merchandising activities aremanaged in that short time frame (Kinsey andSenauer). Because twelve weeks of data were

2Becausestores vary in size, the stores used in themeasure are weighted by sales or ACV.

averaged into one quarterly observation, theability to accurately measure consumer behav-ior, firm conduct, and, hence, market power,was diminished.

Model Development

Departures from the product homogeneity as-sumption result in several knotty modeling is-sues. First, industry output Q (e.g., ~!. 1 q, =Q jim jirms i = 1, . . . . n) and an overall in-dustry demand curve do not exist as the outputof each firm is measured in incommensurateunits. The convenient closed form expressionsfor market power based on Q are immediatelyrendered invalid and, instead, each firm facesan individual demand curve for its own prod-uct. Demand is then a function of its ownprice, prices of imperfect substitutes, expen-diture, and demand shift variables. Firm leveldemands must necessarily be obtained in asystems context to be used subsequently in thecalculation of market power.

Consistent with the approach taken by Cot-terill, the demand-side of the econometricmodel is based on the LA/AIDS model. Usingthe AIDS model is appropriate as it utilizesdollar market shares, thus measuring demandsin commensurate units across brands. The lin-ear approximation of the AIDS model appearsto be reasonable as well in that Stone’s linearprice index performs well relative to compet-ing price indexes, especially under conditionsof price multicollinearity (Alston, Foster, andGreen). The latter issue is important in mar-kets where price collusion or fellowship ispresent. Since the panel data model in thisstudy is used in part to explain pricing spa-tially and temporally, Moschini’s transforma-tion of the price series is inappropriate.3 Thedemand system is given by

()(1) s,,, = ~,+ : %,% p,,, + PJ% $

If

where

~MOs~hini’stransformation requires each price se-ries to be a price index, thus eliminating the price levelacross the selling markets.

4

(2) log P: = g Sk,,log Pkl,

(3) S%=1 $Pk=o

(4) jyk, =o Vk

(5) y,[ = y~~ vk- #1.

Journal of Agricultural and Applied Economics, April 1999

Equation (1) represents the share equationsfor each of the five brands included in the spa-ghetti sauce market, For example, brand 1’smarket share (ski,) equation is a function ofown price (log p, ,t), competitive prices (log

P2tr* . . . * logp,,,), real expenditure (log(xlp~)),

and miscellaneous shift variables relevant to

brand 1 (~&Dl 5@n~;,), such as own merchan-dising, competitive merchandising, timetrends, seasonality, and holiday effects (e.g.,the set D1). Each of the k share equations isstochastic and has two error components. Thefirst is the random unobservable individual ef-fect (q~l) that only varies spatially across mar-kets in the study. The second is the usual sto-chastic error (u~)) that varies over both timeand space. The subscript k and superscript sindicate the error components term for brandk’s share equation. Brands k = 1, . . . . 5 rep-resent, respectively, Ragu, Prego, Hunt’s,Classico, and Healthy Choice. The cross-sec-tional unit subscript i runs from selling mar-kets 1 to 10, while the time-series subscript truns from weeks 1 to 104. Equation (2) isStone’s linear price index. Equations (3) to (5)represent the usual adding-up,4 homogeneity,and symmetry restrictions, respectively. Sincethe term x in Stone’s price index representsexpenditure in the spaghetti sauce market, notincome, it is treated as endogenous. It is spec-ified in the system as an identity. Thus, realexpenditure in the spaghetti sauce market is

4In our model, the expenditure shares do not sumexactly to one as the i3~~parameters are not restrictedto sum to zero, hence preventing the covariance matrixfrom becoming singular.The usual remedy of droppinga share equation in the estimation to ensure the adding-up Property holds is not possible here as it would notpreserve the entire specification of endogenizing theshares and prices. We are unaware of a fully consistentprocedure to achieve this.

endogenous and is replaced by an instrumentin the estimation.

The second problem associated with relax-ing the assumption of product homogeneity isthat prices in the demand system are not onlyendogenous to the system, but are also inter-dependent given the strategic interactionamong purveyors in the industry. FollowingLiang and Cotterill, consistent parameter es-timates are recovered through the constructionof a price reaction function for each price pre-sent in the demand system. These are given by

(6) @ P,,, = w, + ~ fhb p,,, + Aklw c,,

+ ~ ek,vr,, + Tf# + Z&) ‘d k.,eRL

For example, brand 1‘s price (log p,,,) is afunction of competitive prices (log pz,,, . . . .

log p~,,), observable transportation costs (logc1,), and miscellaneous shift variables relevantto brand 1 (2,,., 8,, v,,,), such as time trends,seasonality, and holiday effects (e.g., the setRI). Because data for firm-specific manufac-turing costs are not available, the intercept p,~is used to capture its effect. Each price reac-tion function has two error components similarto the demand system equations, where thesubscript k and superscript p indicate thatthese are error components for brand k’s pricereaction equation.

Unlike the Liang and Cotterill models, thisspecification of the price reaction function dis-entangles pricing conduct associated with ri-valrous behavior of competing firms frompricing conduct related to each firm’s shippingcosts. Factors influencing the former are cap-tured by the term ~1~~$~1 log pli, where thesum captures all rivals’ pricing conduct. Theprice reaction elasticities, +~1,quantify the per-centage change in brand k’s price given a 1YO

increase in brand 1’s price. A positive pricereaction elasticity implies tacit price collusionand an upward sloping price reaction function.The latter is a necessary condition for a Nashequilibria in a static game of differentiatedBertrand competition (Shapiro).

The transportation cost term log c~, is theproduct of the time invariant shipping distance

Vickner and Davies: Market Power and Pricing Conduct in a Producl-lhfererrtiated Oligopoly 5

(e.g., distance from the brand’s manufacturing

location to a given selling market) and amonthly spot market fuel price. Cotterill did

not encounter this issue as local bottlers ser-

viced each selling market in his model. Thetime subscript t is omitted in log c~, because

the cost series does not vary weekly; however,

the series is not quite time-invariant as it

changes with monthly fuel costs. Since it

could be argued that firms do not purchasefuel in a spot market, the spatial component

of pricing is also measured as shipping dis-tance only in a second specification of the

model. The results of both models are com-

pared in the Results section. The h~ parame-ters, or transportation cost elasticities, quantify

the percent change in brand k’s price given a

1% increase in the cost of transportation. For

example, a positive transportation cost elastic-

ity may imply basing-point pricing conduct

(Greenhut, Norman, and Hung).

Data Description

The market level panel data set, assembled by

IRI, was collected for 104 weeks from May15, 1994 to May 5, 1996 for 10 selling mar-

kets spatially dispersed throughout the United

States. For each brand, week, and market, datawere collected for six separate measures—unitsales, average price per unit, expenditure, and

three in-store merchandising variables. Themerchandising measures control for the effectof feature ads and displays individually and

jointly on a brand’s market share. Given the

availability of the data, the relevant product

market was narrowly defined and so excludes

information regarding complementary prod-

ucts such as pasta, Parmesan cheese, or bread-

sticks. Other demand shift variables, such as

the seven calendar holiday dummies, threeseasonality dummies, and time trends, were

used to augment the brand data. Data on mediaadvertising were not available in this analysis.Demographic variables were tested in the

model, but were found to be statistically in-

significant.5 The distance, measured in miles,between a brand’s manufacturing location andeach selling market was estimated using the1997 Rand McNally Road Atlas mileage chart.The average national retail gasoline price se-ries measured in cents per gallon was takenfrom Standard and Poor’s Current Statisticspublication. A summary of the descriptive sta-tistics for selected continuous variables in theeconometric model is given in Table 1.

Empirical Results

Given the characteristics of the model pre-sented in equations (1) to (6) and the need togeneralize the results to other selling marketsnot present in the study, an EC3SLS estimatorwas chosen (Comwell, Schmidt, and Wy -howski). With respect to the latter rationale,the 10 markets represent a sample of sellingmarkets so an error-components model is re-quired to make inferences about the popula-tion. The results from the EC3SLS estimatorare also compared to a one-way fixed-effectsthree-stage least-squares (FE3SLS) estimator.The system is identified with respect to orderand rank conditions (Bhargava).G The matrixof instruments was constructed according toHausman and Taylor and maintains Baltagi’serogeneity properties; parameter estimateswere obtained using generalized least-squares(Kinal and Lahiri). In the process of obtainingfeasible EC3SLS estimators of market powerand pricing conduct with computational meth-ods developed by Kinal and Lahiri, several er-rors in the econometrics literature were iden-tified and corrected (Vickner and Davies). Thesystem weighted R2 value for the FE3SLS

5This result is not unexpected. The firm are astutemarketers and have designed marketing plans withthese demographic factors in mind. In the currentmod-el specification, the between version of the firms’ mar-keting control variables captures the demographic ef-fects sufficiently across selling markets, removing theirexplanatory power (Cornwell, Schmidt, and Wyhow-Ski).

c In the EC3SLS model, the instrumentset contains15 merchandising variables, a linear time trend, andfive transportation cost series. In the FE3SLS model,the instrument set contains the 15 merchandising var-iables, a linear time trend, and the fixed effects.

6 Journal of Agricultural and Applied Economics, April 1999

Table 1. Descrimive Statistics of Selected Continuous Variables in Econometric Model’

Standard CoefficientVariable Mean Deviation of Variation Minimum Maximum

Market Share:b

RaguPregoHunt’sClassicoHealthy Choice

Price:’

RaguPregoHunt’sClassicoHealthy Choice

Log of Real Expenditure

Feature Merchandising:d

RaguPregoHunt’sClassicoHealthy Choice

Display Merchandising:d

RaguPregoHunt’sClassicoHealthy Choice

Feature & Display Merchandising:d

RaguPregoHunt’sClassicoHealthy Choice

Fuel Price:’

35.6235.58

5.5416.946.32

1,861.971.072.481.98

12.20

22.7717.524.68

10.068.15

20.0811.993.283.562.54

13.338.301.352.971.33

115.07

9,128.732.528.552.19

0.200.190.090.160.16

0.73

21.5918.779.39

16.0116.01

13.8910.454.645.154.98

16.1811.883.957.594.32

4.24

25.6124.5545.5350.4934.70

10.959.628.306.398.32

6.01

94.78107.13200.78159.11196.52

69.1487.15

141.38144.60196.48

121.32143.08293.52255.35324.27

3.68

15.5213.000,352.052.24

1.231.350.551.711,52

10.70

0.000.000.000.000.00

0.000.000.000.000.00

0.000.000.000.000,00

108.00

71.9064.4519.0043.5220.83

2.472.491.352.922.51

13.89

93.2892.0368.44

100.00100.00

79.6459.7339.7137.8431.39

85.4263.0941.4362.6042.65

132.30

“ Calculationsbased on 1,040 observations in the panel data set.bDollar marketshare(percent).CDollars per 28-ounce equivalentunit.dPercentof all commodity volume (ACV).cCents per gallon.

model was 73.5 1%. Given the estimation tech- symrnetry restrictions in both estimators. Innique used for the EC3SLS model, a fit statis- the FE3SLS model, we failed to reject the fivetic is not available. homogeneity restrictions and the ten symme-

try restrictions. In the EC3SLS model, weHomogeneity and Symmetry Restrictions failed to reject homogeneity in the Ragu, Pre-

go, and Healthy Choice demand equations.A standard F-statistic was employed to exe- Also in the error-components model, we failedcute the tests of the linear homogeneity and to reject four of the 10 symmetry restrictions.

Vickner and Davies: Market Power and Pricing Conduct in a Product-D&erentiated Oligopoly 7

Table 2. Point Estimates of Uncom~ensated Price Elasticities’

HealthyRagu Prego Hunt’s Classico Choice

FE3SLS Model

Ragu –3,84*** 1.35*** 0.24*** 0.86*** 0.39***Prego 1.38*** –3.41*** 0.12*** 0.72*** 0.25***Hunt’s 1.52*** 0.76*** –5.59*** 1.84*** 0.47***Classico 1.78*** 1.47*** 0.60*** –-5,74*** 0.82***Healthy Choice 2.16*** 1.36*** 0.40*** 2.20*** ..-7,26 ***

EC3SLS Model

Ragu _3,92*** 1.17*** –0.27** 1.12*** 0.80***Prego 1.28*** –-3.16*** 0.38*** 0.85*** –0.15*Hunt’s 0.90*** 0.36 –6.43*** 0.28 0.94***Classico 2.31*** 1.62*** 1.24*** –-550*** 0.12Healthy Choice 2.32*** 0.90*** 0.81*** 0.73*** –.5.84***

nElasticitiesare read from left to right. The uncompensatedprice elasticities are given by e~l= —A~,+ ( l/sJ(-y~,—(3,s,),The Kroneckerdelta A,, equals one fork = 1and zero otherwise. Average shares are used in the calculation.

Note: *** 19. significance level; ** 5% significance; * 10% significance level,

The four respective pairs of prices are Pregoand Ragu, Classico and Ragu, Classico andPrego, and Healthy Choice and Hunt’s, Thoserestrictions that we failed to reject were im-posed on the model. This produced savings indegrees of freedom. Throughout the remainderof this section the results are reported with therespective restrictions imposed.

Price Elasticities

For the class of markets under investigation,calculations used to obtain measures of marketpower and pricing conduct require demandelasticities for each brand. Table 2 summarizesthe point estimates of the uncompensatedown-price and cross-price elasticities for thefive estimated demand equations. The priceelasticities for the LA/AIDS model are calcu-lated using average shares (sJ and, for eachdemand equation, are read from left to rightin the table. The uncompensated elasticity for-mula employs Chalfant’s assumption (e.g., dlog P*/il log pl = SI) and is given by e~l =–Ak[ + l/s~(y~{ – ~Nl). The Kronecker deltaA~l equals one for k = 1 and zero otherwise.Alston, Foster, and Green found this elasticitymeasure to perform well relative to alterna-tives in Monte Carlo experiments.

The own-price elasticities are found along

the diagonal in both sections of Table 2. Theyare statistically significant (p < 0.01) and neg-ative and, not surprisingly, the demand foreach brand is elastic. For example, in the caseof the FE3SLS estimator, a 1?toincrease in theprice of Ragu leads to a 3.84$Z0decrease in thequantity sold of Ragu. There are several ex-planations for the elastic demands. As notedabove, a jar of spaghetti sauce is a durablegood because its storable life exceeds the timebetween price changes, which implies thateach product is an intertemporal substitute foritself (Tirole). Hence, consumers can stockpilesauce when it is on sale and avoid purchasesat the regular price. The end result is a height-ened state of consumer price sensitivity. Thisfinding is entirely consistent with marketingresearch literature examining the adverse ef-fects of frequent price discounting (Papatlaand Krishnamurthi).

Another explanation for the magnitude ofown-price elasticities stems from the disaggre-gate data used in this study. Many empiricaldemand studies for food use yearly, quarterly,or monthly data for broad groups of relatedproducts. Because of the long-run nature ofthe data and the masking effect induced bybrand and market aggregation, own-price elas-ticities obtained in these studies are usuallyfound to be inelastic. In the present study,

8 Journal of Agricultural and Applied Economics, April 1999

Table3. Point Estiamtes of Price Reaction Elasticitiesa

HealthyRagu Prego Hunt’s Classico Choice

FE3SLS Model

RaguPregoHunt’sClassicoHealthy Choice

EC3SLS Model

RaguPregoHunt’sClassicoHealthy Choice

—

0.45***

0.33***

0.32***

0.27***

—

0.32***0.14***0.58***0.47***

0.47***—

0.16***

0.26***

0.17***

0.48***—

0.050.37***0.09***

0.08***0.05**

—

O.11***0.06*

–O,1O*0.08*

—

0.25***0.30***

0,30***0.25***0.40***

—

0.39***

0.23***0.26***0.04

0,23***

0.14***0.03O.1O**0.22***

—

0.33***0.08*0.21***0.09

—

“ Elasticities are read from left to right.

Note: *** 1% significance level; ** 5q0 significance; * 1O% significance level.

weekly brand-level scanner data was used tomeasure the consumer response to pricechanges in a narrowly defined market. Resultsof other studies based on this micro-level datacorroborate this finding (Guadagni and Little;Capps and Nayga; Cotterill; Seo and Capps).For example, despite being biased and incon-sistent, the average uncompensated own-priceelasticities of demand in the Seo and Cappsstudy are similar to those in Table 2 for Prego,Ragu, Classico, and Hunt’s sauces for the 10IRI markets used in this study.’

The cross-price elasticities are found offthe diagonal in both sections of Table 2. Forthe FE3SLS estimator, all cross-price elastici-ties are statistically significant (p < 0.01) and,consistent with a-prior expectations, positive.Thus, the brands represent economic substi-tutes and constitute a well-defined, relevantproduct market. For example, a 1% increasein the price of Prego leads to a 1.3590 increase

~The Seo and Capps study actually used store-level

data for a sample of 1,500 spatially dispersed stores.The authors then aggregated the data by store into 40“markets.” These data should not be confused with thestandard IRI Infoscan market-level data used in ourstudy. This data includes not only the 1,500 stores, butalso the other stores scanned in each market (e.g., itincludes the entirepopulation of scanned stores in eachmarket). Hence, the IRI market-level data is more com-prehensive and appropriate for the empirical objectiveof this paper (Cotterill).

in the quantity sold of Ragu. In the case of theEC3SLS estimator, all but five of 20 cross-price elasticities are statistically significant(p < ().()1)and positive. There are two nega-

tive cross-price elasticities, albeit at marginallevels of statistical significance, and three pos-itive but statistically insignificant cross-priceelasticities. The common store location of thismarket facilitates price comparisons and logi-cally leads to the general finding of economicsubstitutes. For similar studies reporting cross-price elasticities, the products were generallyfound to be economic substitutes (Cotterill;Seo and Capps).

Price Reaction Elasticities

The calculations used to obtain measures ofmarket power and pricing conduct also requireinformation regarding a firm’s price reaction,or response, to rivals’ pricing decisions. Table3 summarizes this information regarding thestrategic interaction among the firms. Readfrom left to right, the table presents the pointestimates of the price reaction elasticities foreach of the five price reaction equations in theeconometric system. Given the double logspecification, the price-reaction elasticities, or~{f, are given by the estimated +~, parametersfrom equation (6).

The empirical results are consistent with

Vickner and Davies: Market Power and Pricing Conduct in a Product-Dl~erentiated Oligopoly 9

Table 4. Point Estimates of Measures of Market Power and Pricing Conduct

Non- FullyFollowship Observed Collusive Rothschild O ChamberlainElasticity’ Elasticityb Elasticityc Index Index Quotient

Brands (i) (ii) (iii) (iii)/(i) (iii)/(ii) I-(ii)/(i)

FE3SLS Model

Ragu –3.84 –2.’77 –1.00 0.26 0.36 0.28Prego –3.41 –2.51 –0.94 0.28 0.37 0.27Hunt’s –5.59 –5.19 –1.01 0.18 0.19 0.07Classico –5.74 –4.28 –1.07 0,19 0.25 0.25Healthy Choice –7.26 –6.41 –1.14 0.16 0.18 0.12

EC3SLS Model

Ragu –3.92 –2.57 –1.10 0.28 0.43 0.35Prego –3.16 –2.24 –0.80 0.25 0.36 0.29Hunt’s –6.43 –6.14 –3.96 0.62 0.64 0.05Classico –5.50 –4.46 –0.20 0.04 0.05 0.19Healthy Choice –5.84 –4.76 – 1.08 0.19 0.23 0.19

“ Uncompensated own price elasticities, or ●k, for k = 1, from Table 2.

b Observed elasticity is given by 61 = ~kk + Z,Ak ~k,eff, where efl are the price reaction elasticities from Table 3.

‘ Fully collusive elasticity is gwen by tzf = Z, ek,,

theory, as the estimated price reaction func-tions are generally upward-sloping (Shapiro).For example, under the FE3SLS estimator, theRagu price reaction function (in the row la-beled Ragu) shows that a 1!ZOincrease in theprice of Prego results in a 0.47% increase inthe price of Ragu. Nineteen of the 20 pricereaction elasticities for the FE3SLS estimatorare statistically significant (p < 0. 10) and,consistent with a-priori expectations, positive.Only one price reaction elasticity is positiveand statistically insignificant. Sixteen of the 20price reaction elasticities for the EC3SLS es-timator are statistically significant (p <0. 10)and positive. Three price reaction elasticitiesare positive and statistically insignificant. Inthe Ragu price reaction function, the elasticityfor the price of Hunt’s sauce is negative andmarginally significant (p <0. 10).

Cotterill found similar results in the direc-tion, magnitude, and statistical significance forleading brands in the carbonated soft drink in-dustry (e.g., the Pepsi price reaction elasticityin the Coke empirical price reaction functionwas 0.51, while the Coke price reaction elas-ticity in the Pepsi empirical price reactionfunction was 0.56). Both estimates were sta-tistically significant (p < 0.01). Consistent

with Liang, price coordination appears to bemore common within a market segment thanbetween segments. For example, in theEC3SLS model, the respective pairs of pricereaction elasticities are greater in magnitudefor Ragu and Prego (within the traditional seg-ment) than for either Hunt’s and Prego (be-tween the canned and traditional segments) orHealthy Choice and Classico (between thehealth-conscious and premium segments).

Measures of Market Power and PricingConduct

Combining the results from Tables 2 and 3yields the various measures of market powerand pricing conduct that address the empiricalobjective of this paper. Table 4 summarizesthese point estimates. The market power for-mulas are restated in the footnotes to the tablefor convenience. The second column in Table4 contains the non-fellowship elasticities (USDOJ and FTC Horizontal Merger Guidelines).These are simply the uncompensated own-price elasticities from Table 2. As the nameimplies, this elasticity measures the sensitivityin quantity sold that a firm faces when it raisesprice but no rivals follow. For this reason, the

10 Journal of Agricultural and Applied Economics, April 1999

non-fellowship elasticity represents a unilat-eral measure of market power. The findingsare very similar across both estimators. Raguand Prego, the two largest brands in the mar-

ket, maintain the greatest degree of unilateralmarket power relative to the other competing

brands. However, in an absolute sense, none

of the brands in this market maintains muchunilateral market power as each has a sensitivenon-fellowship elasticity. The average non-followship elasticity in the Cotterill study of– 1.53 is much less elastic than those obtainedfor the brands in this study.

The third column in Table 4 contains theobserved elasticities. These are derived fol-lowing Baker and Bresnahan and are given by

Eg = ~~~+ ~1~~~~1ey. Following Cotterill, the

elasticities of demand (e.g., •~~and e~l) are tak-en from Table 2 and the empirical price re-action elasticities (e.g., eg)x are taken from Ta-

ble 3. In the presence of imperfect tacit pricecollusion (e.g., O < ●fl < 1), the observed

elasticities will be smaller in absolute valuethan the non-fellowship elasticities. In somecases, the observed elasticities are a full per-centage point lower in absolute value than thenon-fellowship elasticities. This is further ev-idence of tacit price collusion in the spaghettisauce market and the pattern persists acrossboth estimators. Based on the observed elas-ticities, Ragu and Prego again, in a relativesense, maintain the greatest degree of market

power. As was the case for the non-fellowshipelasticities, in an absolute sense, none of thebrands maintain much market power based onthe observed elasticities. The average ob-served elasticity in the Cotterill study of

– 1.45 is much less elastic than those obtainedfor the brands in this study.

The fourth column in Table 4 contains thefully collusive elasticities. These are given by● = ~1 6,,. In the presence of imperfect tacitprice collusion, the fully collusive elasticitieswill be smaller in absolute value than the ob-

8 The subscripts on the price reaction elasticity are

intentionally reversed to indicate the appropriate coC-

umn of data from Table 3.

served elasticities.g With the exception ofHunt’s and Classico in the EC3SLS model, thefully collusive elasticities are within one-fifthof a percentage point of being unitary elastic. 10Thus, the brands in the market acting in con-cert have the potential to substantially reducethe elasticity of their own respective demandcurves. In this scenario, each firm in the mar-ket exercises a high degree of absolute marketpower. The average fully collusive elasticity inthe Cotterill study of –0.94 is fairly close tothose obtained for the brands in this study.

The fifth and sixth columns in Table 4 con-tain two indexes of market power. The Roths-child index (RZ) measures the existence ofmarket power as the ratio of the fully collusiveelasticity to the non-fellowship elasticity(Greer). Under perfect competition, the latterelasticity converges to negative infinity, driv-ing the ratio to zero. Under monopoly, the twoelasticities coincide, resulting in an index val-ue of one. The closer the index is to one thegreater the degree of market power, and it isbounded as O s Rl 5 1.

The O index (01), introduced by Cotterill,also measures the existence of market power.The OZ is given by the ratio of the fully col-lusive elasticity. Similar to the RZ, it is bound-ed as O 5 OZ < 1. Again, the closer the indexis to one the greater the degree of market pow-er. The relationship between the two indexesis O s RZ s OZ = 1. In a relative sense, Raguand Prego tend to exercise more market powerthan the other brands. One exception to this isHunt’s in the EC3SLS model. In an absolutesense, comparing each index value to its max-imum possible value of unity shows that nofirm in the market exercises much marketpower. Additionally, the average RZ and OZvalues in the Cotterill study of 0.67 and 0.72,respectively, exceed those obtained for thebrands in this study. Again, this indicates less

gThe relationshipsamong the three elasticitiesinTable4 are as follows:

c; = q.. for ~{ = O and

•~ = ●kk for q = O.

10If preferences were homothetic (e.g., ~~ = OVk),the fully collusive elasticities would be exactly equalto unity with homogeneity imposed on the model.

Wckner and Davies: Market Power and Pricing Conduct in a Product-D@erentiated Oligopoly 11

market power exists in the spaghetti saucemarket than in the carbonated soft drink mar-ket.

The last column in Table 4 contains thevalues of the Chamberlain quotient (CQ). TheCQ, introduced by Cotterill, is given by oneless the ratio of the observed elasticity to thenon-fellowship elasticity. Thus, it quantifiesthe fraction of market power, as measured bythe observed elasticity, derived from tacitprice collusion. It is bounded as O s CQ 5 1,where higher CQ values indicate higher levelsof tacit price collusion. Under both estimatorsthe pattern of results is similar. Ragu and Pre-go each derive roughly 30% of their marketpower from tacit price collusion. Classico andHealthy Choice derive less market power fromtacit price collusion than the two leadingbrands, while Hunt’s derives the least. Juxta-posing this result with those based on the RIand 01, Hunt’s appears to possess market pow-er due to its positioning in a niche segment,not collusion. This result is consistent with thebrewing industry (Baker and Bresnahan),where the three largest players were found toexercise market power in the absence of pricecollusion. Finally, the average CQ value forthe two leading brands in the Cotterill study(e.g., Coke and Pepsi) of 0.15 is less than mostof those obtained for the brands in this study,indicating more tacit price collusion exists inthe spaghetti sauce market than in the regularcarbonated soft drink market.

Transportation Costs

In the FE3SLS model, the Xk parameters arenot estimable as the transportation costs, orlog c~i variables, do not vary by week and,hence, are correlated with the fixed-effects forthe markets. Given the generality of theEC3SLS framework (Cornwell, Schmidt, andWyhowski), it was possible to include time-invariant effects in the design matrix of themodel. Consequently, transportation costswere built into each price reaction function toempirically separate their effect on a firm’sprice from that of rivalrous pricing conduct.Table 5 summarizes the point estimates of thetransportation cost elasticities for the five

Table 5. Point Estimates of TransportationCost Elasticities’

FE3SLS EC3SLS EC3SLSModel Version 1 Version 2

Ragu — 0.02*** 0.02***Prego — –0.11*** –0.13***

Hunt’s — –001*** _o.ol***

Classico — 0.003 0.004*HealthyChoice — –0.01** –0.01**

“Transportationcostsaredefinedto be theproductof dis-tanceand fuel price in Version 1 and distance only in

Version 2,

Note: *** 1‘%osignificance level; ** 5% significance; * 10%

significance level.

brands represented in the econometric system.The first version of the EC3SLS model as-sumes transportation costs are defined to bethe product of shipping distance and ‘fuelprice, while the second version of the EC3SLSmodel uses shipping distance only.

The results for both versions of theEC3SLS model are similar. The Ragu trans-portation cost elasticity across both models isstatistically significant (p < 0.01) and positive.Thus, a 19Z0increase in the transportation costleads to a 0.0290 increase in the price of Ragu.The elasticity for Classico is also positive forboth models, but is statistically significant (p< 0. 10) in the second version only. The pos-

itive coefficient is evidence that the firms may

be practicing basing-point pricing (Greenhut,

Norman, and Hung). Across both models, the

transportation cost elasticities for Prego,

Hunt’s, and Healthy Choice are statistically

significant (p < 0.05) and negative. However,

the elasticities are very small in magnitude in

the case of Hunt’s and Healthy Choice. Based

on these parameter estimates and the relation-

ship among the firms in the industry, it may

be conjectured that Prego is more concerned

with being obedient to avoid a punishment

strategy administered by Ragu than to price its

products according to transportation costs.

Summary

Point estimates of measures of market power

and pricing conduct were obtained at the brand

level in a representative product-differentiated,

12 Journal of Agricultural and Applied Economics, April 1999

oligopolistic output market using a simulta-

neous-equations panel data model. The $1.3

billion domestic spaghetti sauce industry was

chosen as the case study for this paper. The

empirical model builds on Baker and Bresna-

han and Liang, and extends the approach taken

by Cotterill. The empirical findings augment

the existing pool of information available to

business strategists and antitrust policy makers

for this class of markets. Evidence of market

power was found in the domestic spaghetti

sauce industry, albeit to a lesser extent than in

the carbonated soft drink industry. However, a

higher percentage of market power was de-

rived from tacit price collusion in the former

than in the latter. Like the ready-to-eat break-

fast cereal industry, a higher degree of tacit

price collusion was found among brands with-

in a specific market segment than between

market segments. Similar to the three largest

firms in the brewing industry, one firm in this

study was able to maintain market power in

the absence of tacit price collusion, likely due

to its positioning in a niche segment of the

market.

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