Measurement of Monopoly Behavior: An Application to the Cigarette Industry Author(s): Daniel A. Sumner Reviewed work(s): Source: Journal of Political Economy, Vol. 89, No. 5 (Oct., 1981), pp. 1010-1019 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1830817 . Accessed: 18/01/2012 17:45 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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Measurement of Monopoly Behavior: An Applicationto the CigaretteIndustry

DanielA. Sumner NorthCarolina State University

A simple scheme is proposed to measure monopolypricingbehavior. The coefficientof the tax rate termin a price equation identifiesthe ratio of price to marginal cost. No direct measurement of costs is required,so a major problemforotherempiricalstudiesof monopoly is avoided. Empirical results for cross-sectiontime-seriesdata support rejection of atomistic competition but also provide evidence against the operation of an effectivecartel in the cigaretteindustry. The model representsan alternativeinterpretationof related results in a recentpaper by Barzel. Applicationof the methodologyto other marketsis feasible.

I.

Introduction

The cigarette industryis often used as an example of a less than perfectlycompetitiveindustry.For example, in the famous Tobacco Case of 1946, the major cigarette manufacturerswere accused of operatingan illegal cartel; though theywere convicted,the consensus was thatcompany behavior was not altered by the verdict.1This paper This is a revised version of "Interstate Cigarette Price Differentialsand the Measurementof Firm Level Demand Elasticities"(October 1979). I wish to thank Yoram Barzel, Robert Clark, James Easley, David Flath, Charles Knoeber, Michael Kusnic, Thomas MaCurdy, Michael McElroy,Ronald Schrimper,Michael Wohlgenant,and an unknown referee for theircomments.This paper is no. 6626 of the JournalSeries of the North Carolina AgriculturalResearch Service, Raleigh. 1 See Nicholls (1949), Bain (1968), or Tennant (1971) fordiscussion of the 1946 case and of the "structure,conduct and performance" of the cigarette industry.Stigler (1966, p. 244) presents a table of industrieswith high concentration;cigarettesrank fourthin the share of assets held by the "giant firms."Friedman (1953, p. 37) also [Journalof PoliticalEconomy,1981, vol. 89, no. 5] ( 1981 by The Universityof Chicago. 0022-3808/81/8905-0009$01.50 1010

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attemptsto investigatethe alleged market power of cigarette manufacturerswitha simple scheme for measuringthe weighted-average price elasticityof demand facing firmsin this industry. The empiricalexaminationof the pricingbehavior of the cigarette industryfindsan absence of evidence of an effectivecartel, but the hypothesisof atomisticcompetition is also rejected. The approach uses data on excise taxes, but it does not depend on measuring the cost of production.Since reliablecost data are not generallyavailable, this paper avoids an important weakness of directly measuring monopoly power by the ratio of product price to marginalcost. The model suggested here is also applicable to other industrieswithvariation in excise taxes or some other directlymeasurable componentsof marginal cost.2 II.

A Simple Model

The equilibrium output condition, that marginal revenue equals marginal cost, implies that Pi =

j + l)]Mj, [7n)jIn

(1)

where Pi is the product price,Mj is the marginalcost of production, and -qj is the price elasticityof the demand curve facingfirm. If the industryis purelymonopolistic,-qj is equal to the marketelasticity'rm; while if it is perfectlycompetitive,q j = -?o and is independent of -qm. Thus q j is a measure of the degree to which the firmis not strictlya price taker.3However, since good measurementsof Mj are difficultto find,equation (1) does not offera practicalsolutionto the problem of determiningpotential monopoly power. For a product like cigarettes,which has a per unit excise tax, the marginal cost term may be expanded as Mj=Xjf+Ej+R,

(2)

discusses potentialmonopoly power of cigarettefirms,predictingthatin an analysisof response to tax rate changes, "broadly correct results will be obtained by treating cigarette firmsas if they were producing an identical product and were in perfect competition." 2 The empirical model derived in this paper is similar to that used for a different purpose by Barzel (1976) (and also in a comment by Johnson [1978]). The present paper was well under way when the Barzel resultswere pointed out to me by Charles Knoeber. A paper by Manchester (1976) also presents (in an appendix) a regression related to those estimatedbelow. However, Manchesterdoes not interprethis tax rate coefficientsin that paper. 3For multiproductfirms,optimal pricing decisions require attentionto cross elasticitiesof demand. I will simplyignore this refinementand implicitlyassume that it is not empiricallyimportant.In what followsI use the term "firm"to mean the relevant pricingdecision maker for the given product.

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where Xjf representsthe set of observed factorsdeterminingmarginal costs, Ej represents unobserved factors, and R is the tax rate, which does not vary by firmor brand. Equations (1) and (2) may be combined to show that even withoutdirect measurement of Mj, the firm-levelelasticityof demand may be estimated as a function of the coefficientof the tax rate variable. Equations (1) and (2) apply to pricing decisions made by firms. However, since firm-leveldata on prices are generallynot available, some discussion of aggregation is in order. The observationsare on the average price of cigarettes,defined as

P -zSPj, whereJ is the number of firmsand Sj is the marketshare of thejth firm.Analogously define

M-

SMj9 i=l

n _

j9

Ein =l

and 0 i=l

J

where Oj = q}jl(-qj+ 1). From these definitionsit followsthat0 = q/(-q + 1) and P = OM + ZSj(Oj

-

0)(M, -M).

(3)

i=1

This resultshows the relationshipbetweenaggregate prices and costs that follow from the firm-leveltheory. From equation (3) there are three conditions under which the simple aggregate relationship,P = OM, approximatelyholds: (1) The variationin elasticityof demand across firmsis small,thatis, (0j - 0) is small on average; (2) the variation in marginal costs across firmsis small,thatis, (Mj - M) is small on average; and (3) thereis littlelinear relationship between the elasticityof demand and marginal costs across firms.The termafterthe plus sign in equation (3) is simplyan estimateof the covariance between 0j and Mj. In the empiricalmodel thistermis assumed to be negligible,so P = OM willbe fitto aggregate data. This is supported by the facts that retail cigaretteprices vary littleacross brands withinany market and that costs of production

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differencesacross brands are likely to be small since cigarettesare produced in a single region of the countrywitha standard technology. Finally, since firm-or brand-level data are not available, no adjustment for the potential covariance is empiricallypossible. A linear price equation for cross-sectiontime-seriesdata may be writtenas

Pit= Xitq + ORit+ Uit,

(4)

where i refersto states,t refersto years,and Uitis a random disturbance term.This says that as the tax per pack varies across statesand years, the price varies by a proportion equal to or greater than 1.0. For example, if the tax in Washingtonis 4 cents per pack higherthan the tax in Oregon then, ceteris paribus, if there is some monopoly power, the price in Washingtonwill be more than 4 cents higher.4 The model just presented notes that monopoly power would give cigarette manufacturersan incentive to charge differentprices in statesand years withdifferentexcise tax rates.5However, the observation of this behavior is limited by the extent of interstate(and interyear)arbitrage. A cigarettemerchantin a high-taxstate who is charged a higher price by the manufacturer(because 0 > 1) would want to buy in a low-taxstate,transportthe cigarettesback to his own state, and thus, by competition,eliminate price differentials. In fact,the legal institutionsregulatingthe distributionof cigarettes place strong restrictionson the potential for arbitrage. The federal tax is paid by manufacturerson all cigarettessold in the domestic marketwiththe tax stamp affixedat the factoryand so is unrelated to across-statearbitrage. Distributorsbuying these cigarettesfrom the manufacturersare required to have state licenses in the state where theyoperate; theymust pay the statetax and affixthe statetax stamp 4 For eq. (4) to be the pricingequation, the demand elasticity,7q, must be a constant withrespect to P so that q,and 6 are constantparameters. If the underlyingfirm-level demand curve does not have a constant elasticity,the price equation is nonlinear. Nonlinear variantsof (4) are developed below byallowing71to be an explicitfunctionof price. The methodologyof this paper is applicable under any functionalformfor the firm-level demand curve. There is also variationacross statesand yearsin sales tax rates applied to cigarettes.However, if the ratioof the sales tax rate to I q I is small,the effect of sales taxes on (4) is negligible.Since the sales tax rates range from0 to 0.06 and | is much larger (well above 1), I have ignored this complication in the sequel. 5 Wholesale prices forcigarettesare published bythe U.S. Departmentof Agriculture in its "Tobacco Situation" reports. These figuresshow that all brands and companies charge the same price. (There is a small price differencebetween regularcigarettesand long cigarettes.)Furthermore,these prices have remained the same over several years and move up togetherin periodic discretejumps. (The jumps have been more frequent recently,given the inflationof the last few years.) However, these published prices are of littleinteresthere. They do not necessarilyreflectthe price at which cigarettesare actually sold-only the "list" price. Thus discounts, promotional aids, and special considerationare not included. For the purposes of this paper, only actual transacted wholesale prices would be useful.

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withina fewdays of receivinga shipment.In some statesa distributor may receive shipmentsto be sold and taxed in another state,but that typicallyrequires a special permit from the state governmentwhich gives informationon the quantityof the shipmentand its finaldestination. Since distributorsmust be licensed to pay the state tax and hence to sell cigaretteslegallywithina state,manufacturershave available (frompublic records) a listof all wholesalersof theirproductsfor each state. Furthermore,since to resell cigarettesout of state takes a special permit,the manufacturercan easilyknow the finalstateof sale for cigaretteswhich they ship. Thus it would be very difficultfor cigarettedistributorsto arbitragelegallyacross statelines withoutthe knowledge of manufacturers.This allows the manufacturersto discriminateon the basis of tax rate in the state of final sale. Furthermore, profitablelegal interstatearbitragedepends on price differentials generated by the monopoly power in the marketand on the cost of shipping and handling. There is room for a differentialof several cents per pack before distributorswould be able to avoid manufacturers' sanctions profitablyor engage in illegal movements. Thus for implied differentialsin the range found below, the estimatesshould be relativelyfree of the influence of potential arbitrage. This issue mightwarrantfurtheranalysisiflarge differentialswere generated by monopoly power.6 Monopoly on the part of wholesalers or retailers could also influencethe relationshipbetweenPitand Ritand hence could bias the interpretationof q as revealing monopoly power of the manufacturing firms.My assumptionof a high degree of competitionat these two levels is supported by the large numbers of retailersin each market area as well as significantnumbers of distributorsand chain-store organizations at the wholesale level. (For data on the retail and wholesale tobacco distributionindustryand a summaryof laws, see the National Associationof Tobacco Distributors'Coordinator [1979].) 6 Two effects,related to illegal arbitrage("buttlegging"),may generate a relationship between tax rates and the average price net of taxes. First,in stateswithrelativelylow tax rates,a significantportionof cigarettessold may be sold in large lots fortransferto another state. The average transactioncost per pack on these sales will likelybe low, and thereforethe measured average price of cigarettessold will be low. This yields a positivecorrelationbetween the tax rate and the price net of taxes. Second, in states withrelativelyhigh tax ratesa significantportionof cigarettesconsumed maybe bought outside legal channels. Competition from the illegal market (which does not pay the state tax) will cause a lower average price among the legal dealers. The result is a negative correlation between tax rates and average price net of taxes. Putting these togetherimplies a concave relationshipbetween tax rates and price. (Very-low-taxand very-high-taxstates should lie below the regressionline.) Below, I test for the importance of smugglingin affectingthe relationshipbetween the retailprice and the excise tax across states. Note thatif smugglingwere dominant,all tax-relatedprice differentialswould collapse, and the coefficientbetween price and tax rate would be near zero. This has not taken place.

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Empirical Model

The empirical specificationof equation (4) requires a discussion of theXitvectorand the disturbancetermUit.The focus of thispaper is on the effectof excise taxes on pricing; therefore,the purpose of specifyingXit is to avoid bias in estimationof 0. The Xit vector is included to account for attributesof states and years that directly affectP and are correlatedwithR. In the estimation,several alternative sets of variables were used and compared. The most complete specificationuses a fullset of dummyvariables forstatesand years in Xit.Factorswhichvaryfromyear to year are accounted forby a set of DYt variables withone variable for each year in the sample (withone excluded to avoid singularity).Factors which varyfromstate to state are accounted for by a set of DS1 variables withone variable for each state in the sample (with one excluded to avoid singularity).In anotherspecification,the national consumer price index is used in place of theDYt variables. In each case the price variationremaining,which is representedby Uit,is assumed to be uncorrelatedwithRit.This Uit term either is treated as a single disturbance or is modeled in a variance-componentsframeworkwith separate random effectsfor the time-seriesand cross-sectionobservations.7 In this paper, tax rate variationis treated as exogenous. Research explaining the patternof cigarettetaxes would be interestingbut is not included in thispaper.8 Note thatwiththe whole set of individual statedummyvariablesincluded in the price equation, a stable pattern of state tax rates is accounted for by these interceptterms.For example, the location of the tobacco and cigarette industries has not changed over time,so the effectthattheirlocation has on stateprices Nonlinear models related to (4) were also applied. To allow for demand elasticities thatwere not constant,let [r/l(rq+ 1)] _(P) = yP(1l). Two plausible specificationsof the error term yield models which may be estimatedconvenientlyby nonlinear least squares. These are Pit=

[Xitiq+ yRit]lI"+ Vit

(4')

and Pit = [(Xittq+ yRit)lI]Vit.

(4")

In both cases X = 1 implies that 6 = y, and this parameter is a constant. 8 Some basic factsconcerningthe cigaretteexcise tax which mightguide a theoryof taxation are as follows:The federal tax rate has remained 8 cents per pack for more than 25 years.The median level of statetaxes has risenfrom3 cents per pack in 1954 to 12 cents per pack in 1978. This amounts to a fallin combined taxes in real termsand a fallfrom48.7 percentof retailprice in 1954 to 35.5 percentin 1978. In 1978 statetaxes ranged from 2 cents in North Carolina to 21 cents in Florida, Connecticut, and Massachusetts. The three states with a significantstake in production of cigarette tobacco and the manufactureof cigarettes(North Carolina, Virginia,and Kentucky)all have low tax rates. Variation across the restof the statescannot be explained by a local cigarette-producingindustry.

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is captured by statedummyvariablesand does not bias the coefficient of Rit. IV.

Empirical Results and Interpretations

The major empirical resultsof this studyare reported in table 1. In this section,these resultsare presented and interpreted.A potential alternativeinterpretationsuggested by Barzel (1976) is also considered. The estimatesreportedare based on annual tax ratesand price data for the years 1954-78 for 47 states and the Districtof Columbia. Alaska, Hawaii, and New Hampshire are excluded from the sample for the analysis reported in the table because of lack of data and peculiaritiesin theirtax laws. (See n. 11 below for more discussionof the New Hampshire case.) Informationon cigaretteprices and tax rates is collected and published by the Tobacco Tax Council. The "weighted-averageprice per package" published for each state and year uses national weightsfor typeof cigarette(regular, king, 100 mm) and for type of transaction (carton, single pack, machine). Wholesalers around the countryare asked to provide estimatesof the average retailprice in theirarea for each typeof cigaretteand typeof sale. These numbersare turnedinto state averages by the council. (This information is from correspondence withthe veryhelpful personnel at the Tobacco Tax Council.) Table 1 shows estimatesof the linear model of equation (4) under three alternativespecificationsof the Xitvector and the disturbance term.The table reportsthe estimated0 and, to aid in interpretation, the implied price elasticity,-R.In row 1, Xit consists of a dummy variable for each state and for each year. The tax rate effectin this row is 1.074, which says,for example, thata 10 cent differencein tax rates causes a 10.74 cent increase in price. The coefficient is above 1.0 (standard error = 0.013), whichis support for significantly rejecting the hypothesis of atomistic competition in this industry. However, the implied price elasticityis - 13.5, which indicates a rather flat demand curve. Row 2 replaces year dummies with the National Consumer Price Index and drops the statedummyvariables, while row 3 shows estimates from an application of a variancecomponentsmodel withthe price index as the onlyadditional explanatoryvariable. The estimatesof 0 for these rows are 1.029 and 1.069, and both are significantly above 1.0. Other specificationsofXitand Uit yielded estimatesof 0 similar to those reported. This basic model was also estimated separatelyfor each year using statesas the unit of observation.The estimatesof 0 were generallyin

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TABLE 1 ESTIMATES

OF THE

EFFECT

OF THE

SPECIFICATIONS

Estimated0 1.074 (.013) 1.029 (.011) 1.069 (.013)

PRICE TAX RATE ON CIGARETTE OF THE LINEAR MODEL (Eq. [4])

IN ALTERNATIVE

Implied Price Elasticity7v

Other Variables Included*

Method

-13.5

DYtDSi

OLS

-34.5

NCPI

OLS

-14.5

NCPI

VCt

NOTE.-The R2's in each of these models were high, those with dummy variables were about .99, and those withoutthe dummies were around .95. There were 1,200 observations (25 years for each of 48 states). SEs in parentheses. * DY, is a dummyvariable foreach year with 1978 excluded, DSj is a dummyvariable foreach statewithWyoming excluded, and NCPI is the national consumer price index for each year. t In thisequation a variance-component(VC) error scheme withan individual random effectfor each state and each year was used. See Fuller and Battese (1974) for a discussion.

the range reported in table 1 for the pooled model and were not differentfromone another. No trend in these estimates significantly was noted. Time-series changes in the industrydo not seem to have caused biases in the estimatesin table 1.9 Two furthercommentsshould be made in relationto these results. First,these estimatesare notconsistentwithan effectivecartel in the cigaretteindustry.The firm-levelelasticityestimatesare well below the range of the industrydemand elasticityestimatesusually found forcigarettes.(These are generallybetween -0.3 and -0.8.)10 Second, the effectof monopoly power as a source of price variation in the industryis small compared with tax rate differencesand other cost differencesover time and space. In fittingthe nonlinear specificationspresented in n. 7 above, the hypothesisthatX 1 is not rejected. For (4') X = 0.972 withSE = 0.027, and for(4") X = 0.981 withSE = 0.026. These testssupport the appropriatenessof the linear model resultspresented in table 1. The estimateof y from(4') is 1.029, and from(4") it is 1.062. These, together withthe X estimatesabove, implyvalues of 6 in the range of those in table 1 or slightly lower. This supports the hypothesisthatwhile perfectlycompetitivepricingbehavior is rejected,monopolypower is not a major factorin determiningcigaretteprice differentials. The hypothesisthat interstatesmuggling would imply that price is a concave functionof tax rate, as discussed in n. 6 above, is not supported by these results.As a furthernonlinear specification,a squared tax rate term was added to the separate yearlyprice equations. In most years the (R t)2 variable had an insignificanteffecton price. In only a few years out of 25 were the coefficientsfor Rit positive and (Rit)2 negative. 10In related work (Sumner 1979), using cross-sectiontime-seriesdata for the last 10 years,which attemptsto indirectlyquantifythe extent of interstatecigarettebootlegelasticityof demand forcigarettes ging ("buttlegging"),I findthe national industry-level to be approximately -0.40. This is in the range of other estimatesfrom time-series data. 9

=

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Barzel (1976) has suggested an alternativeinterpretationfor the coefficienton Ritin the pricingequation. He argues thata higher per unit tax on a good will induce a higher quality per unit to be sold. Since the relativeprice of quality is lower in high-taxareas, substitutionof qualityforquantitywilloccur. The after-taxprice per unit will be higher in a higher tax rate area to reflectthe higherqualityof the product. He also notes thatad valorem taxes fixedas a percentage of retail price (as was the practice in New Hampshire prior to 1975) would not have this effect. As Barzel points out, products actuallytraded are combinationsof many characteristics,most of which are extremelydifficultfor either the governmentor the empirical economist to measure. Thus, when Barzel argues that the quality of cigarettesvaries positivelywith the tax, no direct measurement of quality changes could reject that hypothesis. Barzel turnsinstead to price data on cigarettesacross years and states as published by the Tobacco Tax Council. The nature of these data is crucial. As noted above, the price data available for cigaretteshave the most obvious quality variations(type of sale and type of cigarette) held fixed across states. Furthermore,given centralized manufacturingand national distributionof brands, there is little scope for direct product-qualityvariation. This leads one to question the strengthof the expected Barzel effectin these data even if it were present in the real world. Hence it would appear that the "elasticityof demand" interpretationof 0 is a serious contender with Barzel's qualityshifterfor explaining a 0 coefficientgreaterthan 1.0. Finally,note thatthe Barzel effectwould cause an upward bias in the measurement of monopoly power so that there is an even stronger case for concluding that the cigarette industry does not act as a cartel.II 11 As furtherconsideration of the strengthof the Barzel effectin cigarettes,some estimationwas done which included data from New Hampshire with the other states. These resultswere essentiallyidenticalto those reported in the table. New Hampshire, whichhad an ad valorem cigarettetax until 1975, was found to have a stronglynegative statedummyvariable. However, it may be the case thatNew Hampshire has a low price of cigarettesnet of taxes not because its tax was ad valorem as suggested by Barzel but for the same reason thatthe per capita sales of cigarettesin New Hampshire are more than double the average of the other New England states.That is, residentsof nearby states buy a significantportion of their cigarettes in New Hampshire. Given size economies for sales transactions,a high proportionof thisinterstatetrade would tend to reduce the average price net of taxes in New Hampshire. Barzel's ad valorem tax hypothesisimplies thatthe special positionof New Hampshire would have evaporated after 1975 (when a fixedper unit tax replaced the ad valorem tax). The transactioncost hypothesis(among others) predictsthattherewillbe no effectof the 1975 law change. I found thatthe New Hampshire residuals fromthe linear model estimatedforeach year are just as negativeafter 1975 as before 1975, which indicates that the ad valorem tax was not the differentNew Hampshire characteristic.This is not to suggest that the Barzel effectis not theoreticallysound but, rather,that interstatecigaretteprices may not be useful to test the theory.

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The statisticalresultspresented in table 1 support rejection of the hypothesisof atomisticcompetition in the cigarette industry.The demand curves facingcigarettefirmsare not flatbut are close to it by most standards. Taking 0 = 1.05, a 1 percent rise in the price of a firm'sproductwould cause a 20 percentfallin the quantitysold. If the cigarette prices are above marginal cost by 5 percent, monopoly power adds approximately3 centsto the average price of a package of

cigarettes.

This paper has proposed and demonstratedthe applicabilityof a scheme for measuring monopoly behavior that may be relevant to several differentindustries. For example, application to the U.S. gasoline market is currentlybeing pursued. Data requirementsare informationon product price and some factor that has a directly measurable per unit cost. Variation over time or space or some other dimension is required for statisticalimplementation. References

Bain, Joe S. IndustrialOrganization.2d ed. New York: Wiley, 1968. Barzel, Yoram. "An AlternativeApproach to the Analysisof Taxation."J.P.E. 84, no. 6 (December 1976): 1177-97. Friedman, Milton. "The Methodology of Positive Economics." In Essays in PositiveEconomics.Chicago: Univ. Chicago Press, 1953. Fuller, Wayne A., and Battese, George E. "Estimationof Linear Models with Cross-ErrorStructure."J. Econometrics 2, no. 1 (May 1974): 67-78. Johnson,Terry R. "Additional Evidence on the Effectsof AlternativeTaxes on Cigarette Prices."J.P.E. 86, no. 1, pt. 1 (April 1978): 325-28. Manchester,Paul B. "InterstateCigaretteSmuggling."PublicFinanceQ. 4, no. 2 (April 1976): 225-38. National Associationof Tobacco Distributors.Coordinator. New York: NATD, 1979. Nicholls,WilliamH. "The Tobacco Case of 1946." A.E.R. Papersand Proc. 39, no. 3 (May 1949): 284-96. Stigler,George J. The TheoryofPrice. 3d ed. New York: Macmillan, 1966. Sumner, Daniel A. "Cigarette Smuggling and Estimates of the Demand to Consume and the Demand to Smuggle." Paper presentedat a workshopon agriculturaleconomics at North Carolina State Univ., Raleigh, November 1979. Tennant, Richard B. "The Cigarette Industry."In The Structure ofAmerican Industry, edited by Walter Adams. 4th ed. New York: Macmillan, 1971.