risk reduction and umbrella branding

8/4/2019 Risk Reduction and Umbrella Branding

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Risk Reduction and Umbrella Branding

Cynthia A. Montgomery; Birger Wernerfelt

The Journal of Business, Vol. 65, No. 1. (Jan., 1992), pp. 31-50.

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Cynthia A. MontgomeryHarvard Universi ty

Birger Werne rfeltMassachuse t t s Ins t i tu te o f Technology

Risk Reduction and UmbrellaBranding*

I. IntroductionDespite the fact that branding is a very commonand resource-consuming pract ice , there a re fewtheor ies abou t i t s economic funct ions . Th e bulkof exta nt theo ry (Klein and Leffler 1981; Mil-grom an d R obe rts 1986; W ernerfelt 1988) looksat branding as a guarantee of quali ty. A problemwith these theories is that they do not explainthe s imul taneous exis tence of branded and un-branded p roducts . ' W e here extend the model ofKlein and Leffler (1981) by allowing consumersto be asymmetrically inform ed. In such a model,both type s of products ex is t , and, in d i rec t con-trast to the exist ing li terature, branded productswill have lower average quali ty than unbrandedproducts . H ow ever , th is lower average is coun-terbalanced by a lower variance in quali ty. In afurther develop me nt of the mo del, we allow firmsto offer several products. By using the samebrand name on these p roducts , a pract ice here incalled umbrella branding, firms post repeat

* Comments from an anonymous referee, Tim Bollerslev,Peter Pashigian, and seminar audiences at Carnegie-Mellon,Cornell, Stanford, and the University of Texas are gratefullyacknowledged. We thank Robert Sartain for commendableresearch assistance. All errors are ours.I . Wiggins and Lane (1983) is an exception to this, buttheir model has the unfortunate property that prices are exog-enous.(Journa l o f Bus ines s , 1992, vol. 6 5 , no. I ) O 1992 by The University of Chicago. All rights reserved. 0021-93981921650 1-0002$01.50

In the context of com-petitive markets withasymmetric informa-t ion, we develop amodel of firms' brand-ing decisions. In equi-l ibrium, both bra ndedand unbranded p rod-uc ts ex is t, and w echaracterize price-quality relationshipsbe tween them. In con-t ras t to o th er adver t i s -ing models, we predictthat branded productswill have l o w e r average(price-adjusted) qual-i ty than unbrandedproducts . This loweraverage is counterbal-anced by lower vari-anc e in product qual-ity, giving branding arisk-reducing ratherthan a quality-guaranteeing func t ion.We descr ibe indus t riesin which these relation-ships are l ikely to b es t ronger and tes t thepredictions using C o n -s ~ c r n e rR e p o r t s d a t a o nquality and price.


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purchases of all produc ts a s bonds for the quality of each prod uct. Inthis conte xt, umbrella branding lowers the cost of r isk reduction.The article is organized as follows. In Section I1 we present thetheory outlined above and describe equilibrium price-quality relation-ships. In particular, we demonstrate the risk-reduction effect of um-brella branding and show that this effect will be stronger in marketswith higher prices. In the remaind er of the article we test these resultson a sample of 3,335 individual products. These da ta and the measuresemployed are described in Section 111. In Section IV we present theresults. Consistent with expectations, umbrella branded products arefound to be low-value, low-risk offerings. Further, as expected, thisrisk-reduction effect is stronger for higher-priced products. We con-clude with a discussion in Section V .

11. The ModelA unit m ass of identical consum ers eac h buys on e unit of a product inperiods t = 1 , 2 , . . . . They have income, y, which can be spent onthe produ ct in que stion , and a num eraire goo d, z. I t is not possible totransfer products between periods. If a product of quality q sells forprice p( q) , we ca n su bsti tute the budget con straint into the util ity func-tion U(Z , q) to get the partially indirect utility function W (p , q) = U (y- p , q) . Under s tandard assum ptions , W is decreasing in p , increasingin q , and concave in both arguments . The product is to some extentan exper ience good (Nelson 1970), such tha t only a frac tion, a , of thecon sum ers can tell quality on sight. Th e remaining 1 - a consumersmust rely on price signals to evaluate current quality, although theywill learn about past quality by word of mouth. All consumers knowthe s t ructure of the game.There is free entry in each period, and a measure n firms choose toparticipate by selecting a quality level and posting prices. Prices andqualit ies can be changed each period. In the period before each entry ,these f i rms incur a one- t ime sunk cost s , and af ter entry they faceaverage salvageable costs c(x, q) = C,(q) /x + C,(x), wh ere x is quan-tity sold. We assu m e that c is U-shaped in x and increasing and co nve xin q . Fo r a given interest rate r > 0, we can define c(q) = min,[c(x, q)+ ~ ~ 1 x 1 .e as su m e th at c is increasing and convex.A . F u l l InformationSuppose first that a = 1. Th at is , all con sum ers ca n tell quality onsight.

C L A IM1. In equilib rium , n * firms produce a price, qu ality, quantitytriple p * , q* , x* such that


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(zero profits),

(the marginal value of quality equals its marginal cost), and

(all dem and is met-recall that dema nd is standardized to unity ).W e take the l iberty of omitt ing a proof.B. Asy mm etric InformationThe more interesting si tuation occurs when a E [0, 1). Suppose thatprior to purchase the 1 - a uninformed consumers can identifywhether current quali ty is below q or not but cannot make furtherdist inctions. In addit ion, let us al low the f irms to spend a mo unts b o nconspicuo us expen diture, such a s advertising, in the period beforeentr y . All consu me rs observe these expend i tures a s well a s the pas tqualities of each firm. We finally assume that the out-of-equilibriumbeliefs ar e that a ny price or an y b , different from those in equil ibrium,signals that current quality is q.A s illustrated in figure 1 below , fou r type s of strategies thu s need tobe considered: (a) n* firms that offer (p*, q*) and sell at least to theinformed; (b) n firms th at o ffer q at p = c( q) , such that the uninformedcan eliminate all risk; (c) no firms th at will offer - a t p* , hop ing to r ipoff the uninformed who gamble by buying at p*; and (d) E firms thatwill pursue the solution offered by Klein and Leffler: sink & into con-sp icuous consumpt ion and then o ffe r ( p , q ) where p , q , and & are givenby

(z er o profits-this is eq . [7] in Klein and Leffler 1981);

(minimum average costs) ;

(no cheating-if a firm chea ts without changing price, it will sell F;ifi t changes price, we assume that consumers infer a low quali ty); and

(the marginal value of quality equals its total marginal costs).Since all consu me rs are identical , the uninformed will prefer ( p , 7 )o ve r ( p , q ) if W -= W(p, g ) > W (p, q ) . T o make the m odel interes ting,we will assume that this is the case. We further define W* = W ( p * ,q*) and WO = W ( p * , -) .


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Our final assumption has to do with the rip-off strategy ( p * , q ) .Firm s following this strategy will be penalized by the consum ers suchthat they will find it profitable to produce in only 1 period. In orderfor this strategy to be individually rational, there has to exist a salesvolume suc h that thes e firms can reco up their entry cost (plus interest)in 1 period. That is, i t is necessary thatmax,[p* - c(x ,q ) ] xr s(l + r). (8)

If (8 ) is violated, the ( p * , q ) strategy is not viable and all sales at p*will be fo r q*. con sequ ent ly , the demand for ( p ,q)will disap pear also .T o focus on the ca se wh ere branding occurs , we therefore assum e that(8)holds. Further, we define x" a s the smallest quantity

( 1 + r)s = [p* - c(xO,q)]xO. (9 )W e ca n now prove the following. C L A I M . T he strateg ies described below constitute an equilibrium. If a < (x* - xO)(W- WO ) (a)xO(W*- W")+ (x* - xO)(W- w")'

then a fract ion, 1 - u , of the uninformed buy at p, whereAll other consu m ers buy at p*, where- [ ( I - a)(x* - xn)(W- W")- axn(W*- W")]n = >X(x* - xO)(W- W O )and

a(W* - W )no = (x* - xO)(W- WO) T h e ( p ,q ) firms remain the same each period, while the (p* , q ) firmsexit after 1 period. At the beginning of each pe riod, nof irms en ter , andthese, together with the n* firms who offered ( p * , q *) last period,randomize between offering ( p * ,-) and (p*, q*) for the new period.Ifx* - xo (x* - xO)(W- WO)

x * > a > xO(W*- W")+ (x* - xO)(W- w")' (b)then all cons um ers buy at p*, where


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and( 1 - a ) x * - x O

n o = ( x * - x O ) x O *T he ( p * , q ) firms exit after 1 period, and n o new entrants replacethem. At thebeg inning of each period, the new entrants and the incum-bents randomize between offering ( p * , -) and ( p * , q * ) for the newperiod.Ifthen all trad e takes place at ( p * , q * ) , and the firms ar e infinitely lived.Proof . F o r free-entry equilibrium we need ( 1 ) zer o profit, ( 2 )profitmaximization, ( 3 ) consum er m aximizat ion, and ( 4 ) fulfilled demand ateach price-quantity pair.

1 . This is assured by the definitions of the ( p , q , x , 6 ) vectors .2 . Dev iations in p o r b are inoptimal by the postulated beliefs. Devi-ations in q are not a n issue for ( p * ,-) f irms. Fo r ( p * , q * ) firms, suchdeviat ions merely change them to ( p * ,-) firms. F inally, (6) checks thetemptat ion to cheat for ( p , q) firms.Consider finally the randomization rules. If a firm offers ( p * , q ) , it

receives a one-tim e cas h flow of s . If a firm offers ( p * , q * ) , its periodcash flow is r s , and it can o pt to offer ( p * , q ) next period, giving it ( 1+ r ) s . The net present value of this would be rs + ( 1 + r ) s ( l + r ) - '= ( 1 + r ) ~ ,he same as the value of offering ( p * , q ) a t once . S o thefirms are indeed indifferent between ( p * , q * ) and (p*, q ) . Note thatthis assu m es that i t is costless t o change quality. W e will discuss thisassumption below.3 . Su pp ose that all three ty pes of firms ex ist . Given the firm random-ization, the only useful historical information is w hether a firm sp entb . To sustain consumer randomizat ion, the uninformed have to beindifferent between W a n d a convex combinat ion of W * and W O .T h u s ,we need

4 . Fulfilled demand at ( p * , q * ) means thatn*x* = a + ( 1 - a ) u n * ( n * + n o ) - ' . ( 1 1 )

At ( p * ,-) we needn O x O= ( 1 - a ) u n O ( n *+ n o ) - ' . ( 1 2 )And at ( p ,g) we need -x = ( 1 - a ) ( 1 - u). (1 3 )


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By solving (10) - (13) for v , E , n * , and n o , one gets ( a ) of the claim.At

v = 1 , and we get (b) .Note that we then only need

andn O x O= ( 1 - a ) n O ( n *+ n o ) - ' . ( 1 2 ' )

At a = ( x * - x O ) / x " ,n o = 0 , and we have ( c ) . Q . E . D .Note that the equilibrium is well-behaved in the sense that it is acontinuous function of a that specializes to the full-information out-

come (E = n o = 0 ) or the Klein-Leffler (1981) outcome ( n o = n* =0 ) a s a = 1 o r 0, respectively. Part ( a ) of the claim is illustrated infigure 1, where the location of x O reflects that the ( p " , - ) firms haveto recoup their entry fee in 1 period.To discuss the robustness of this equil ibrium, we focus on two is-sues . F i rs t , the assumption that cos ts , c ( x , q ) , are independent acrossperiods and, second, the homogeneity of preferences.

I I I II I I I

wX 0 _X x* --X

FIG.1.-Market equilibria


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The independence assumption is s tandard in Arrow-Debreu theoryand has been used in most dynamic models of imperfect competit ion,including that of Klein and Leffler (1981). The usual defense invokesthe presum ption that "small" levels of dyna mic interdep enden cewould lead to "small" chan ges in equilibria. Howe ver, in mixed-strategy equilibria such as that presented above or by Varian (1980),things are especially complicated.T o analyze robu stness , let us informally consider a s imple examp leof intertemporal externalit ies. Specifically, assume that f irms incur afixed, posit ive cost 6 every t ime they change their quality levels. Thishas two effects on equilibrium. First , the bond b , posted by the ( p , q )firms, can be s ma ller. T he rea son is that the gains from cheating for afirm that has produced q earlier have been reduced by 6. (This argu-ment do es not apply in t h e first period, s o there will be som e nonsta-tionarity in the payoffs.) Seco ndly, the uninformed custom ers can nowdistinguish between three types of f irms: (p,q) f i rms, p* f i rms whooffered q* las t t ime, and new p" firms. The last group of f irms canoffer q without incurring 6, so the volume sold by these firms shouldyield profits of rs from q" and (1 + r)s from q . S imilarly, the "old"firms should each sell enough to make r(s + 6) f rom q* and (1 + r)(s + 6) from c. T o see that these re turns would support randomizat ionby the f irms, com pare the profi ts f rom (entry , q) to those f rom (entry ,q " , q) . In the former case , the f irm makes -s-+ (1 + r ) s ( l + r ) - ' =0, and in the la t ter case i t makesS o while intertem poral externa lit ies change the equilibrium, they neednot change it drastically, nor make it unravel.Let us now assume that the firms each sell m different products tothe same consumers .C . Mult ip roduc t F i rmsW e divide each period into m p arts , using the notation (T, T) for the 7thpart of the Tth p eriod. T he idea now is that the parties trade product 1in part 1 of each period, p roduc t 2 in part 2 , and so on . Information ishere revealed after each part of each pe riod, s o a firm that supplies qf q " o r q # ij in any (T, T) will bear the conse quen ces from (T, T +1) on . Assuming that the preferen ces and the c ost functions are identi-cal acros s pro ducts , the analogues of (6) and (9) are

and[ p * - c (xO , ) ]xO / ( l+ r) = m s. (15)

Compared to the s ingle-product case , these dif fer only because the


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38 Journal of Businessright sides are m ultiplied by the num ber of prod ucts. Intuitively , the(p , q ) firms post the su nk co sts in all products as bonds t o guaranteequality of each p roduc t. Similarly, the ( p * , q) firms forgo future profitsin all prod ucts in return for "cheating" profits in one product.' Weclaim without proof that the structure of equilibrium is the same as insect ion B .A property of the equilibrium is that higher values of m make forche ape r quality as sur an ce (14) and lowe r risk of ripoffs in the se nse of(15). To see this, we first assume that the analog of (8) holds:such that the heterogeneous equilibrium exists. In this case the exce ssprofits per product to the (p ,q) firms a re, by (4) and (14),S o b is smaller for larger m.D. ImplicationsWe can derive three testable implications of the m odel.PRICEPR EM IUM Th e avera ge relative price for brand edYPOTHESIS.products is higher than that for unbranded products.Proof. Define the isoutil ity curv es, Q (p) , by W (p, q) = constant.Because of the assumptions on U ( . ) , the isoutility cu rves Q (p ) ar eincreasing and concave. Further, lower curves have steeper slopes.S o if Q *(p) and a ( p ) correspond to W* and W ,respectively, thendQ*ldp < dQ ldp (see fig. 2).Since the net cost of signaling is positive (counting q and b), theright-hand side of (7) is larger than that of (2). This implies thatdQ *(p* ) ldp > d Q (p )l dp , s o p > p * . Q . E . D .RISK-REDUCTION Branded products have lower meanYPOTHESIS.value and low er variance in value than un branded p roducts.Proof. Since the variance result is trivial, we conc entrate onshowing

Given that p > p * , (16) will hold if dQ (p )ld q < ql p. The la tter inequal-i ty in turn follows from the con cavity of Q. Q . E . D .According to this hypothesis, the role of branding is to reduce therisk of getting "lem ons." Th is is illustrated in figure 3.Th e inequality (16) is in dire ct contra diction to the existing literatureon branding an d advertising (e .g., Klein and Leffler 1981;Milgrom an d2 . Sullivan (1990) has measured effects of this type .


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Quality

FIG.2.-Isoutility curves

Ro berts 1986; W ernerfelt 1988). It predicts a lower average (price-adjusted) quali ty of branded products. In further contrast to the ex-ist ing l i terature, our model al lows branded and unbranded products t ocoexist in equil ibrium, even when tastes are homogeneous.Assuming that th e production function and the information structu reis unaffected by unit price gives us the following.PRICE EFFECTSHYPO THESIS. he expected value d iscount forbranded products goes up with industry price level .Proof. Assume that (a)holds such that branded p roducts exist . Wecan then write (16) as

Since the hypothesis involves varying product category prices, thequestion is how increasing price levels deform C and U . There is no


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MeanValue

. Unbranded ProductsBranded Products

Variance of q / pFIG.3.-Mean value and variance of q /p

reason to believe that the produ ction function or the information struc-ture should vary systematically with unit price, while we have en-dowed U with r isk aversion. T o compare across two categories , nor-malize such that q * / p * and W* are the same in both. Given riskaversion, the higher-priced category will have a lower WO,a lower q/P (by eq. [7]), and a lower W .Now denote the left-hand side of (17)by L. Clearly dLld(g1p)< 0. By equation (10) and claim 2 , we c an findthe change in W as a f ract ion (W* - W)(W* - wO)-'f the change


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in WO.By direct computat ion, dLldWO+ (W * - W ) ( W * - w " ) - ' ~ L /aw = 0. S o the net effect of high prices is to increase L . Q.E.D.

111. Data and MeasuresA. DataT o tes t our hypo thesis we n eeded object ive quali ty and pr ice m easureson a large sample of products. Consum er Repor t s , published by theConsum ers U nion, is a unique s ource of such data . Fo r this s tudy weused their 1972 and 1977 Buying Guides . These issues provided dataon 3,335 individual products . Fo r each product , we recorded i ts pr ice ,i ts quality rank w ithin i ts produ ct ca tegory (ind ustry), i ts brand n am e,and the name of i ts parent corporat ion.T o attest to the integrity of the da ta, i t should be noted that Con sum -er s Un ion is an indep enden t, nonprofit org anization, which is not all iedwith any firm whose products i t evaluates. The ratings themselves arebased on laboratory- tes t , control led-use exper iments , and/or exper tjudgments of purchased samples and are general ly regarded to be ofhigh quality (Thorelli and Thorelli 1977).As in our model , Consumers Union assumes homogeneous tas tesand publishes unidimensional quality measures. While this procedureinvolves a loss of information, i t can be defended o n several groun ds.Firs t , product categories are def ined qui te narrowly. For example,canis ter and upr ight vacuum cleaners are evaluated separate ly . Sec-on d, in a surv ey of 385 studies, Cu rry and F aulds (1986) show ed thatoverall quality rankings are insensitive to weights given to individualproduct dimensions. This result is due to the fact that scores on indi-vidual dimensions tend to be posit ively correlated. Third, unidimen-sional measures of quality permit comparisons across product catego-r ies . Fourth , our theory assumes homogeneous ut i l i ty funct ions .However, having noted these points, noise will be introduced intothe data to the extent that real tas tes are heterogeneous or poorlyapproximated by the Consum er Repor t s rankings.Two addi t ional proper t ies of the data deserve ment ion. The intentof Consum er Repor t s is to meet demand for product information.He nce the product categories are not chosen randomly. In par t icular ,inexpensive, nondurable search goods, while not missing from thedat a , are underrepresented. Fur th er , the pr ices quoted in most productcategories are manufacturers ' recommended l is t pr ices ( t ransact ionprices are given in a few grocery categories) . I f markups, coupons,and sales differ across products, additional noise will be introduced.On balance, however , g iven the large sample s ize , these issues areunlikely to ca use ser ious problems.


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B. MeasuresWithin the theo ry, a brand ed produ ct is one that has been t ied to som elevel of conspicuous exp end iture, such as advertising. Th e theory fur-ther suggests that ther e are eco nom ies of scope in branding such thatall brand names should be placed on several products. However, dueto factors not included in this model, for example, problems with thetransferability of a particular brand name, or issues relating to thescop e of the f irm, we do not alway s obs erve m ultiple-product branding.In practice, branding represents a continuum, on one end boundedby products that lack any kind of credible support , and on the otherend bounded by products with extensive commitments, often madethrough long periods of t ime and shared across multiple products.Therefore, to distinguish betw een "branded" and "unbranded" prod-ucts is very difficult. Given th e impossibility of getting co mp lete histor-ical records of dedicated expenditure (e.g., the amount that has beenspent in building the GE brand name), we elected to dist inguish be-tween branded and unbranded products based on the use of sharednam es. T hat is , we are implicit ly assuming that there is a relat ionshipbetween the size of the bond posted and i ts association with multipleprod ucts. Although this is not a perfect co rrelat ion, there should be areasonable correspondence between the two.A key operationalization in the study, then, is the measure of multi-ple branding, herein called umbrella branding. Following the theory,we need to identify prod ucts that are sold to the sam e group of consum -ers (o r , more genera l ly , to the group of people to w hom these consum-ers talk). This should exclude some instances of shared names; how-eve r, in practice, ho w mu ch to exclud e is a difficult question. I t seem sfair to include instances wh ere a brand nam e is used on several prod-ucts within the same product category (Sappington and Wernerfelt1985). In con tras t , the extent to w hich the theory applies across prod-uct categories would seem to de pend o n the relationship among indi-vidual categories. For example, bicycle locks and bicycles appear tobe a logical f i t , as do sleeping bags and tents. However, one wouldguess that w om en's clothing and battery ch argers rarely are bought bythe sam e people .In order to develop a robust analysis of these issues, we decidedto use three hierarchical measures of umbrella branding. Our narrowm easu re, UBO, adm its only shared nam es if they are used both w ithinthe same product category and in other product categories as well .Ou r medium me asure , U B I, adm its a ll shared names used w i thin thesame product catego ry. (So UB1 captures al l "l ine-extensions".) Fi-nal ly , our broad measure , UB2, admits a l l shared names wi thin thesample . That i s , U B2 admits names if they are shared wi thin o r acrossproduct categories. S o the set of products for which UBO is on e is a


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subset of the set for which U B 1 is one , and th e latter is again a subsetof the set of products for which U B 2 is one. Within individual productcategories , sample representat ion is reasonably comp lete . For exam -ple, the 1977 Buying Guide l ists 7 typ es of bicycle locks, with 22, 13,6 , 9 , 1 1, 14 , and 9 products of each type. We can thu s be confident thatwe have a re l iab le measure o f umbre l la b randing wi th in ca tegor ie~ .~However , g iven the fact that all consumer products are not in thesample, umbrella branding will be underestimated when a firm hasmore than o ne product sharing a brand name bu t has only one productin the sample . For this reason, we prefer the middle measure in ourhierarchy, U B 1 .Th e following variables were c onstructe d for all produ cts. L et t de-note a product and i i ts product category.

UBO, = narrow dum my for umbrel la branding, se t equal to on e ifthe f irm uses the sam e name o n at leas t one other productin the sam e product category and at least on e other prod-uct in another product category. Otherwise i t is set equalto zero. Of the 3,335 produc ts , 1,248 (37%) were umbrellabranded in this sense.UB1, = medium dum my for umbrella branding, se t equal to on e ifthe f irm uses the sa m e name on at least one other productin the same product category. Otherwise i t is set equal tozero. I t should be noted that U B 1 contains UBO, in thatwhenever UBO is se t equal to one , U B 1 will also be setto one . Of the 3,335 produc ts , 2,223 (67%) were umbrellabranded in this sense.UB2, = broad dummy for umbrella branding, set equal to one ifthe f irm uses the same nam e on a t leas t one othe r productin an y product category. O therwise it i s se t equal to ze ro.I t should be noted that U B 2 contains U B 1 , in that when-eve r U B I is se t to one , U B 2 will also be set to on e. Ofthe 3,335 products , 2,775 (83%) were umbrella branded inthis sense.

Q , = relative quality of t in i ts product category. If productsare ranked in groups with g , , gZ,. . . , g,, members and tis in group j, then

3. Within-category umbrella branding will be underrepresented to the extent thatsmall-volume regional products are not included and to the extent that an umbrellaidentifier, different from a product's brand name, is associated with a product.


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-- -- - - - ---


P, = relative price of t in its product category. If there are Nifirms in the categ ory, with prices p , , . . . , p , , . . . , p , ,then

V, = value of t. It is set equal to Q,lP,. 0, = average price in t 's product category i . It is defined as

AV = average value of branded products, minus average valueof unbranded products.A a = stand ard devia tion of V, for branded pro du cts , minusstandard deviation of V, for unbranded products.

A P = average relative price of branded products, minus averagerelative price of unbranded products.Th e data are descr ibed in table 1 .Th e pr ice premium hypothesis predicts that A P is positive.The risk-reduction hypothesis, that values of branded productshaver lower mean and var iance than values of unbranded products ,predicts that AV and Au are negative.Moving to th e price effects hyp othe sis, it is useful to recall that valueis normalized betw een industries suc h that a larger value discount forbranded products is reflected in a smaller (more negative) correlationbetween UB, and V,. We can therefore test the hypothesis, thatbranded products have a larger value discount in higher-priced productcategories, through the regression

The price effects hypothesis predicts that P I will be less than zero.Th e regression also provides an alternative test of the m eans compo-nent of the risk-reduction hypothesis, specifically that P2 + 62.4 P I


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45isk Reduction

Th e three tes ts descr ibed a bov e are formulated a t the product level.Tha t is , each of ou r 3,335 produ cts co nsti tutes a data point. I t is tempt-ing to also test a t the m arket level to s ee if the m ajority of the ma rketsconform to the theory. There are two problems with this idea. Firs t ,we can only es t imate A V and A P for approximately 100 ma rkets (Aufor fewer) . Secondly, s ince most of these es t imates have very largevariance, our sample would be small and noisy. The logical approachwould be to weigh the d at a points according to their precision , a proce-dure that ult imately would lead back toward our product-level test .IV . ResultsThe tes ts of the pr ice premium hypothesis are reported in table 2 . Ascan be se en, the results point exactly opposite the predicted direc tion,and q uite strongly s o.4 W e will com e back and disc uss this after re-porting the other test results.The aggregate results of our tests of the risk-reduction hypothesisare given in table 3 . N ot all means and standard deviations ar e signifi-cantly different in the expected directions, but four out of six resultsar e significant, in particular those for the m edium m easure of umb rellabranding (UB 1). Collectively these results sup port the view that bran d-ing serves a risk-reducing function.

The regression analyses are reported in table 4. Two things are im-portant. First , there is strong and consistent support for the price ef-fects hypothe sis, that the value discount for branded produ cts is largerfor higher prices. Second, as can be seen from the l ine labeled P, +62.4 P , , the results for the risk-reduction hypothesis are in l ine withthose in table 3 . That is , the results are significant in the expecteddirect ion for UB 1 and U B2.Given that the dat a support only two of ou r three hy potheses , i t isimperat ive to evaluate other explanat ions of the coexis tence ofbranded and unbranded products. Note that heterogeneity in sellers t ra tegies (other than mixing) requires heterogeneous buyers . In thepresent model , b uyers a re informational ly heterogeneous. H eterogene-ity in p reference s is the oth er vehicle for generating equilibria in whichboth branded and unbranded products exis t . In such a model , brandsignaling would follow the lines of the price signaling described by

4. An alternative cut at this may be to look at four classes of products. Those with noumbrella branding within or between categories, those with umbrella branding betweencategories but not within, those with umbrella branding within categories but not be-tween, and those with umbrella branding both within and between. The average relativeprices for these are 1.03, 1.025, 100, and .97, respectively. From a business perspective,we have a hard time understanding umbrella branding between categories but not withinas a conscious strategy (552 products fall in this class), so we will stay with the hierarchi-cal classification UBO, UBI, and U B 2.


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46 Journal of BusinessTABLE 2 Average Relative Prices

UBO UBI UB2-- --- . .....-.-

mbrella branded .97 1.OO 1.OONo t umbrella brande d 1.02 1.01 1.03t - 3.76 - 1.06 - 2.06Sign .OO .29 .04

Wolinsky (1983). In the present notation, some consumers would pre-fer the branded p roduct (p,q ) ,while othe rs would buy the unbrandedproduct (p , -). Such an equilibrium is consistent with the price pre-mium hypothesis and the price effects hypothesis, but not with therisk-reduction hypothesis, nor with the results reported here.However , a s imple combinat ion of the two models could explainthe data. Assume that there is heterogeneity in both information andpreferen ces, such that the informed custom ers place a higher premiumon qual i ty than the uninformed. This is a qui te natural assumptionbecause customers who care the most about qual i ty should use moreinformation sources (including any outside the model). Specifically,denote the indirect uti l i ty functions of the informed and uninformed

TABLE 3 Means and Standard Deviations in Product ValueN Mean Va lue S t anda rd D ev ~ a t ~ o n

UBO *Um brella brand ed 1,248 574 362Not umbrella brande d 2,087 560 534t - 83F 2 17S ~ g n 41 00UB1 I.Um brella brande d 2,223 552 359No t umbrella brande d 1,112 592 65 1t 2 29F 3 30S ~ g n 02 00UB2 tUmb rella brand ed 2,775 558 474No t umbrella brand ed 560 60 1 49 1t 1 93F 1 07Slgn 05 26-* UB O I S a dum my v ar ~a b lese t equal to one when the b rand name I S used both on another productIn the sa me category and on ano ther product In anoth er categoryt UB l 1s a dumm y v ar~ ab lese t equal to one when the b rand nam e IS used on anoth er product Inthe sam e ca tegory$ UB2 1s a dum my va r~ ab lese t equal to one when the b rand name I S used on another product Inthe same ca tegory o r ano ther p roduct ca tegory


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-- - --47is k Reduction

TABLE 4 Regressions on ValueUBO UB 1 UB2

Intercept ,560(53.7)Umbrella branding x price - ,0004(-2.68)Um brella branding ,037(1.94)

NOTE-N = t - s t a t ~ s t ~ c s,335 are In parentheses

cons umer s V and W, respectively. We can still find ( p , q ) by (4)-(7),while (p * , q*) a re g iven by ( I ) , (3), and the analogue of (2):This also gives (p " , q* ) , and we can descr ibe the equil ibrium as before.Suppo se now that p * f rom (18) is greater than p. With this assumption ,the resul ts a re cons is tent wi th the resul ts in table 2 . At the sam e time,the r isk-reduction hypothesis and the price effects hypothesis wouldcontinue to hold. This is illustrated in figure 4.In extens ive conversat ions wi th col leagues , we have found thatmany expect the r isk-reduction effect to be stronger when fewer con-sumers are informed an d w hen purchase f requen cy is lower . The intu-i t ion behind this view appears to be that such ci rcumstances wouldprovide less market discipline and thus leave consumers worse off .Our theory , h owev er , does n ot suppor t th i s v iew. T o look a t the effec tof a , the n um ber of informed c on sum ers, it is suff icient to no te that (17)is indep ende nt of a . Th e ef fect of r, the inverse p urchase f req uen cy, ismore diff icult to assess. However, higher values of r will have twoeffects in (17): increase the p 's ( in part icular , p) and decrease the W's(in particular, W).Without fur ther assum pt ions on c( ) and W( ), itis not possible to predict the n et effect .T o test these "predictions," we classified produ cts into expe rienceand search goods using Nelson 's (1970) ~ r i t e r i o n . ~e further dividedthe sample into durables and nondu rables in orde r to get a proxy forpurchase frequency. These classif icat ions give us

E , = dummy for an experience good. This is I i f the product is anexper ience good , 0 otherwise. Fif ty-four percent of the prod-ucts were exper ience goods .5. To do this, we used the nonmerchandise receipts from the 1977 Census of RetailTrade .


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Journal of Business

FIG.4.-Heterogeneous tastes

D , = dumm y for durable good. This is 1 if the product is durable,0 o th e rwi s e. E ig ht y pe rc e nt of t h e p r od u ct s we r e d ~ r a b l e . ~

In table 5 we report regressions which control for the interactionterms U B , E , and UB , D,. Consistent with the theory, the value dis-count for branded produc ts is not influenced by E , and D,.Another intuit ive conjecture is that the quali ty variance of non-branded products should decrease as the proportion of informed buy-ers increases. Unfortunately, the model does not unambiguously sup-port this conjecture ei ther. Consider case (b)of claim 2 , in which valueand quality ar e proportional. T he ratio n O ln* s decreasing in a , butmay be larger than one (if a < (x* - xO)l(x*+ xO)) .The re is , how ever , so me indirec t evidence to suppor t the conjecture .

6. The correlation between El and 0, is .31, and the correlation between Dl and 6,s. 26 . This level of correlat ion subsets suggests that multicollinearity is not a seriousproblem.


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49isk Reduction

TABLE 5 Regressions on Value with Control VariablesUBO UB 1 UB 2

-- .~ ... .-.. .. . ...- .-- - . . .--. .-nterc ept ,560 ,592 ,601

(53.7) (41.5) (29.9)Umbrella branding x experien ce ,036 ,002 ,024(1.16) (.09) (1.11)Umbrella branding x durables ,001 - ,009 - ,006(.03) ( - .29) ( - .22)Umbrella branding x price - ,0004 - ,0004 - ,0003(-2 .80) ( -2 .77) ( -2 .71)Um brella brandin g ,024 - ,014 - ,032( 5 3 ) ( - .40) ( - .91)$ ,0016 ,0036 ,0028~ ~ ~-

OTE.-N = 3,335. [-statistics are in parentheses.

Specifically, Tellis and Wernerfelt (1987) show that the price qualitycorrelation is larger in markets for unpackaged products. In our sam-ple, table 6 com pares th e stand ard deviations in value for various typ esof unbranded products when El = 1 versus when El = 0. As can beseen, the results are roughly consistent with the conjecture.Sum marizing, the emp irical results provide s uppo rt for a model withheterogeneity in both preferences and information. Most important,the data are consistent with the view of branding as serving the func-tion of risk reduction.V. ConclusionWhile previous l i terature looks at branding as a guarantee of quality,we developed and tested a theory portraying branding as a means ofrisk reduction. The empirical results are consistent with the theory,indicating that umbrella branding serves a risk-reducing function andthat this effect is strongest when the product is expensive.Two addi t ional contr ibut ions are worth not ing. Firs t , our theoryexplains the s im ultaneous exis tence of branded and un branded p rod-ucts . S econ d, we hope to h ave dem onstra ted the usefulness of a directapproach to the measurem ent of product qual ity . While such measuresTABLE 6 Sta nda rd D eviations in Value

UnbrandedUBO UB I UB2 All

Experience good .60 (1,258) .74 (727) ,466 (352) ,536 (1,814) Search good .42 (829) .45 (385) ,530 (208) ,395 (1,521) F 2.07 2.69 1.29 1.85 Sign .OO .OO .0 4 .OO

NOT E.-N is in oaren theses.


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have a long history in the m arketing l i terature, economists have tradi-tionally preferred more indirect measures.Concerning fu rther res earch , i t seem s pertinent, but difficult, to lookat the model in the context of oligopoly. Another potentially fruitfulline of research would be to introduce some noise in consumers' prod-uct evaluations. Such an effect might reduce the incentives to applyan umbrella brand to an infinite number of products and give moreappealing, intermediate, results.In a broader perspective, our argument suggests the existence ofreputational economies of scope. Since reputations are examples ofproductive fa ctors that ar e difficult t o trade in the open market (Mon t-gomery and Wernerfelt 1988), they may provide a natural reason forthe existence of multiproduct firms.ReferencesCurry, D. J., and Faulds, D. J. 1986. Indexing product quality: Issues, theory andresults. Journal of C onsum er Research 13 (September): 134-45.Klein, B., and Leffler, K . 1981. The role of mark et forces in assuring contractual perfor-mance. Journal of Political Economy 89 (A ugus t): 615-41.Milgrom, P. , and Rob erts , J. 1986. Price and advertising signals of new produc t quality.Journal of Political Economy 94 (August): 796-821.Montg omery , C . A ., and W ernerfelt, B. 1988. Diversification, Ricardian re nts, andTobin 's q . Rand Journal of Economics 19 (W inter ): 623-32.Nelson, P . 1970. Inform ation and consumer behav ior. Journal of Political Economy 78(Mar chiApril): 41 1-29.Sappington, D. , and Wernerfelt, B . 1985. To brand or not to brand? A theoretical andempirical question. Journal of Business 58 ( July) : 279-93.Sullivan, M. 1990. Measuring image spillovers in umbrella-branded products. Journalof Business 63 (October): 309-29.Tellis, G. J., and Wernerfelt, B. 1987. Competitive price and quality under asymmetricinformation. Marketing Science 6 ( Sum me r): 240-53.Thorelli, H . B ., and Thorelli, S. V. 1977. Consumer Information Systems and ConsumerPolicy. Cambridge, Mass.: Ballinger.U.S . Department of Commerce. 1977. Census of Retail Trade. Washington, D.C .: U.S.Government Printing Office.Varian, H . R . 1980. A m odel of sales. American Economic Review 70 (September):

65 1-59.Wern erfelt, B . 1988. Umbrella branding as a signal of new product quality: An exampleof signalling by posting a bond. Rand Journal of Economics 19 (Au tum n): 458-66.Wiggins, S. N., and Lane, W. J . 1983. Qii?lity uncertainty, search, and advertising.American Economic Review 73 (D ecem ber) : 881-94.Wolin sky, A. 1983. Prices as signals of product quality. Review of Economic Studies 50(Octo ber): 647-58.

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