MANAGEMENT SCIENCEArticles in Advance, pp. 1–16issn 0025-1909 �eissn 1526-5501 doi 10.1287/mnsc.1110.1412

© 2011 INFORMS

Label Confusion: The Groucho Effect ofUncertain Standards

Rick Harbaugh, John W. MaxwellKelley School of Business, Indiana University, Bloomington, Indiana 47405

{riharbau@indiana.edu, jwmax@indiana.edu}

Beatrice RoussillonGrenoble Applied Economic Laboratory, University of Grenoble, F-38000 Grenoble, France,

beatrice.roussillon@upmf-grenoble.fr

Labels certify that a product meets some standard for quality, but often consumers are unsure of the exactstandard that the label represents. Focusing on the case of ecolabels for environmental quality, we show how

even small amounts of uncertainty can create consumer confusion that reduces or eliminates the value to firms ofadopting voluntary labels. First, consumers are most suspicious of a label when a product with a bad reputationhas it, so labels are often unpersuasive at showing that a seemingly bad product is actually good. Second, labelproliferation aggravates the effect of uncertainty, causing the informativeness of labels to decrease rather thanincrease. Third, uncertainty makes labeling and nonlabeling equilibria more likely to coexist as the number oflabels increases, so consumers face greater strategic uncertainty over how to interpret the presence or absenceof a label. Finally, a label can be legitimitized or spoiled for other products when a product with a good or badreputation displays it, so firms may adopt labels strategically to manipulate such information spillovers, whichfurther exacerbates label confusion. Managers can reduce label confusion by supporting mandatory labeling orby undertaking investments to make certain labels “focal.”

Key words : marketing; communications; information theory; environmentHistory : Received February 26, 2010; accepted May 16, 2011, by Pradeep Chintagunta and Preyas Desai,

special issue editors. Published online in Articles in Advance.

1. IntroductionWhen product quality is unobservable, quality labelsare an important mechanism for firms to prove theirquality to consumers. However, consumers are oftenunsure of the exact quality standard that a label rep-resents—is it a relatively easy or difficult standard?This is particularly important for “ecolabels” thatcertify environmental quality, because environmentalimpact is often a credence good that consumers can-not observe directly and because there has been aproliferation of different labels by different organi-zations. Despite attempts by governments, industrygroups, and nongovernmental organizations (NGOs)to clarify label standards, confusion by consumersis widely blamed for undermining the credibility ofecolabels, thereby reducing the incentive for firmsto adopt them.1 We examine this issue of how con-

1 The website Ecolabelling.org lists more than 300 different eco-labels in use, many with widely different standards for differentproducts. As a report prepared for the World Bank noted, “Thediversity of ecolabels (which reflect the multitude of certificationschemes) can be confusing to consumers and weaken the credibil-ity of all labels” (Fischer et al. 2005). The impact of label confu-sion on adoption incentives is seen for the European Union (EU)

sumer uncertainty about label standards affects themanagerial decision to have a product of given envi-ronmental quality certified with an ecolabel.

When label standards are uncertain, consumers facea joint estimation problem. If they see a label on aproduct, they must estimate whether the label is moreindicative of a high-quality product or of an unde-manding standard for the label. For instance, when acar buyer sees a Low Emission Vehicle ecolabel, shewill update both her estimate of the car’s environ-mental quality and of the meaning of the ecolabel. Ifthe car is a large sports utility vehicle, then the updat-ing on both dimensions is likely to be very differentthan if the car is a small hybrid. Just as an employermust jointly estimate the ability of a job applicant andthe value of his degree, or a tourist must jointly esti-mate the quality of a hotel and the toughness of thelocal rating system, a consumer cannot rely on the

Flower label, where for some product categories none of the majormanufacturers have certified their products (see European Eco-labelCatalogue at http://www.eco-label.com) and surveys indicate thatunderstanding of the label is far lower than of other regional andnational ecolabels (Sto and Strandbakken 2005).

1

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Published online ahead of print August 4, 2011

Harbaugh, Maxwell, and Roussillon: Label Confusion2 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

mere presence of an ecolabel to determine a product’senvironmental quality.

We investigate how this joint estimation problemaffects the power of labels to reduce informationasymmetries about product quality. We find that con-cern over the effects of uncertain labeling standardsis well founded. In addition to the direct informa-tion loss due to the uncertainty, the optimal responsesof consumers and firms lead to further informationlosses that can greatly undermine the value of volun-tary labeling. First, labeling should be most valuablewhen consumers expect a product to be bad but infact it is certifiably good. However, when standardsare uncertain, if a product is expected to be of lowquality, then there is a “Groucho effect” in which con-sumers infer that the labeling standard is probablyweak if such a product can meet it. Just as GrouchoMarx famously joked that he did not want to joina club with standards so low as to accept him as amember, a firm with a bad reputation gains little fromlabeling. Therefore, the incentive for labeling is under-mined when the problem of information asymmetry,and hence the potential gain from labeling, is greatest.

Second, the presence of multiple labels with dif-ferent standards should create more opportunity forfirms of different quality levels to certify themselvesand thereby reduce information asymmetries. Butwhen standards are uncertain, the proliferation oflabels has the opposite impact. Because consumers donot know which standards are easy and which are dif-ficult, a label only proves that a firm has met the easi-est of the different standards, even if the firm has meta higher standard. This reduces the informativenessof labeling and also reduces the incentive to be cer-tified. As the number of different standards rises, wefind that the informativeness of labeling goes to zeroand that a “nonlabeling” equilibrium always exists fora sufficiently high number of standards.

Third, uncertain standards aggravate the problemof strategic uncertainty because of the coexistence oflabeling and nonlabeling equilibria. Multiple equilib-ria can arise with voluntary labeling because if con-sumers expect a firm to have a label, then lack ofone is particularly damaging to the firm’s estimatedquality, whereas if labeling is not expected, then thefirm loses less from not having a label and can saveon certification costs. When standards are known, thismultiplicity of equilibria disappears under a regular-ity condition as the number of standards increases.But with uncertain standards we find instead that themultiple equilibrium problem is aggravated by morelabels and that labeling and nonlabeling equilibriaalways coexist for a sufficiently large number of labelsunless certification costs are so high that only nonla-beling is an equilibrium.

Finally, we find that uncertainty over standardsgenerates information externalities between firms thatcan lead to strategic behavior that further reduces theinformativeness of labels. A firm can “legitimize” or“spoil” a label for use by other firms depending onwhether the firm has a good or bad reputation. There-fore, disreputable firms have an incentive to adoptthe same label as reputable firms, but reputable firmsinstead have an incentive to avoid labels adoptedby disreputable firms. Such managerial strategizingmakes it difficult for consumers to rely on the existingreputations of firms as a simple way to learn aboutdifferent standards and gives certifiers an incentive topromote early adoption among firms of recognizedhigh quality.

A key factor in consumer uncertainty over labelingstandards is that the source of a label or certificateis often unclear. For instance, the similar-appearing“FSC” and “SFI” labels are two of the main eco-labels for forest products, but one is controlled by anenvironmental NGO and the other by an industry-backed NGO. The potential for such confusion iswidespread—of the 363 different labeling schemestracked by ecolabelling.org, 209 are run by NGOs,59 are run by industry groups, 53 are run by govern-ments, and 42 are run by for-profit firms. Moreover,even when the source of a label is clear, the objec-tives of certifiers, and hence the likely difficulty oftheir standards, are often unclear (see, e.g., Shakedand Sutton 1981, Maxwell 2010).

To capture these uncertainties, we model con-sumers as having a prior distribution of the labelingstandard(s) that can be arbitrarily precise or diffuseand arbitrarily skewed toward higher or lower lev-els. For instance, consumers might believe that anecolabel standard is likely to be easy or difficult butbe unsure of exactly how easy or difficult, or theymight be completely uncertain of the difficulty. Thisdistinguishes our approach from most of the litera-ture in which the labeling standards are assumed tobe common knowledge. Our model is most appro-priate for consumer product markets, where buyersare unlikely to be well informed, rather than formarkets for raw materials or intermediary products,where buyers have strong incentives to acquire exactinformation on the source and meaning of differentstandards.

Because label confusion reduces the value of label-ing as a strategy to inform consumers about prod-uct quality, investments in clarifying label standardscan enhance both the informativeness and likelihoodof labeling, thereby allowing consumers to makemore informed decisions. For instance, the ISEALAlliance of certifiers has tried to make standardsfor ecolabels more transparent to reduce consumerconfusion (http://isealalliance.org). Industry groups,

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 3

governments, for-profit labelers, or NGOs interestedin promoting label adoption can also try to makea particular standard “focal” in the sense of pub-licizing it and making consumers expect that firmswill adopt the standard if they meet it. This canreduce or eliminate the information losses caused bylabel proliferation and by strategic uncertainty overwhich equilibria are being played by firms. “Look forthe label” campaigns can be interpreted as encour-aging consumers to focus on particular labels amongthe multiplicity of possible labels. Government andindustry attempts to reduce the number of labels or“harmonize” or standardize different voluntary stan-dards also have this effect. Of course, not all firmsbenefit from stronger incentives to label due to har-monization and transparency. Firms that cannot meetlabeling standards clearly benefit from more labelconfusion. And even firms that can meet the stan-dards are sometimes better off in a nonlabeling equi-librium from saving labeling costs.

These results on label confusion add to the liter-ature on verifiable message “persuasion” or “disclo-sure” games (see the survey by Dranove and Jin 2010),and in particular to the debate on mandatory ver-sus voluntary disclosure. The classic “unravelling”result finds that mandatory disclosure is unnecessarybecause even those with bad information have anincentive to prove they do not have worse informa-tion.2 However, as recognized early on, voluntary dis-closure might be insufficient if disclosure is costly(Viscusi 1978, Jovanovic 1982, Verrecchia 1983). Ouranalysis contributes to this debate by showing thatthe combination of costly disclosure and uncertaintyis particularly disruptive to voluntary disclosure, andthat the effects are exacerbated when there are multi-ple labels.

The idea that the imperfect nature of labels canhave an important effect on disclosure strategiesappears in other papers that differ from ours in otherkey respects. Sinclair-Desgagne and Gozlan (2003)consider binary tests of environmental quality that areknown by consumers to vary in accuracy and allowfirms to choose whether to take the more accurate orless accurate test. Lerner and Tirole (2006) and Farhiet al. (2008) consider standards that are known to beof differing difficulty and assume the firm is uncertainof its own quality, so that from the firm’s perspectivethere is uncertainty over whether a particular stan-dard will turn out to be too difficult. These papers

2 Mandatory disclosure is distinct from the imposition of minimumquality standards that can exclude firms from the market (Leland1979). The application to environmental quality standards is con-sidered by Arora and Gangopadhyay (1995) and Lutz et al. (2000),and the application to ecolabeling is analyzed by Amacher et al.(2004) and Mattoo and Singh (1994).

focus on how firms can best “show off” their qual-ity by choosing standards that are known to be eithermore or less difficult and find that multiple stan-dards increase the ability of firms to provide informa-tion about their quality. But for ecolabels we believethat our assumption that consumers are unaware ofthe underlying standard embodied in a certificationlabel is more appropriate. Because of this differencein assumptions, other papers have not addressed themain issues that we examine, including confusioncaused by label proliferation, legitimizing and spoil-ing of labels, and the role for mandatory disclosure or“focal” equilibria in reducing confusion. As discussedlater, the exception is Fishman and Hagerty (1990),who consider costless disclosure of one of multiplenoisy signals of “high” or “low” quality and whoseresults are closely related to our findings regardingfocal equilibria.

Our analysis is for the case where labels certifythat a standard has been met and provide no moredetailed information. Voluntary labels typically takethis “pass-fail” form, in which a certificate or label isawarded or not, even in cases where more detailedinformation could be provided. For instance, of the10 nongovernment ecolabels for carbon emissionslisted at the ecolabelling.org website, all but one pro-vide a simple label of approval without more detailedinformation about the product’s carbon footprint. Theprevalence of simple labels could reflect the need toreduce information processing by consumers. Or, con-sistent with the theoretical literature, it could reflectthe incentive of certification intermediaries to with-hold more detailed information when labeling is vol-untary (Lizzeri 1999). Given the prevalence of thepass-fail form and the multiple reasons for it, we takethe form as given in our analysis.

We discuss our results in the context of ecolabel-ing, but they apply to any certification or labelingscheme about which uncertainty over a pass-fail stan-dard exists. More broadly, the issues we investigatearise in any situation in which observers must jointlyupdate their beliefs about an agent’s quality and anuncertain quality standard. For instance, consistentwith Groucho Marx’s concerns, our analysis showsthat a disreputable individual might indeed find littlebenefit from joining a club because the very fact ofhis membership downgrades the perceived standardsof the club.

This paper proceeds as follows. In §2 we developthe basic model with one standard, define theconditions for the existence of both labeling and non-labeling equilibria, show the existence of the Grouchoeffect, and analyze its impact on informativeness.In §3 we analyze the multistandard case, showingthat the qualitative results of §2 continue to hold andthat the impact of the Groucho effect is worsened.

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Harbaugh, Maxwell, and Roussillon: Label Confusion4 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

In §4 we consider strategic interactions between firmswhen there are multiple standards and informationspillovers. In §5 we present our conclusions.

2. Base ModelWe consider a firm’s decision to have its product cer-tified that it meets a quality standard for an ecola-bel. The product’s exogenously given (environmental)quality Q is distributed according to distribution Fwith full support on 60117 and with correspond-ing density function f . The firm knows the realizedvalue q of Q, but consumers only know its distribu-tion F . There exists a label with standard S, whichis distributed according to the distribution G withfull support on 60117 and with corresponding densityfunction g. The firm knows the realized value s of S.If consumers also know the realized value s, we saythe standard is “certain,” and if they only know thedistribution G, we say the standard is “uncertain.”For simplicity we assume Q and S are independent.In this section we assume that there is only one label.

If q ≥ s, the firm has a choice to obtain a label ornot; i.e., a firm that meets the labeling standard neednot choose to be certified for the label. If q < s, thefirm does not meet the standard so it has no choice.Certification has a fixed cost c > 0 that is indepen-dent of q or s and captures any fees to the certifierand any other costs, e.g., the expense of documentingquality control processes, auditing and testing costsby the certifier, and the opportunity cost of provid-ing space on the product packaging for the label.3 Weassume the payoff to the firm is the expected qual-ity of its product as estimated by consumers less thecertification cost if it chooses to certify. Because weallow for general F , all the results hold as long as thefirm’s payoff is a strictly increasing function of qual-ity as estimated by consumers. Consumer concern forenvironmental quality could capture direct financialgains to the consumer, e.g., savings from lower energyuse, or internalized social benefits, e.g., knowing thatforests are protected.

3 Because quality q is exogenous, we are not considering costs toimprove the product. Vitalis (2002) notes that certification costs canbe a substantial fraction of total costs. These costs may be paidby a manufacturer or a retailer (Guo 2009). We assume that c isthe same for any s, but in some cases the testing component ofcertification costs might be more expensive when the standard istougher. As long as any such variation in c is not known by theconsumer and therefore cannot be used to infer the difficulty of astandard, consumers will have even more reason to be suspiciousthat a label represents a low standard, and the negative effect ofstandard uncertainty on labeling incentives will be aggravated.

The expected quality of a product conditional onquality Q exceeding the standard S, where the valueof S is distributed according to G, is

E6Q �Q ≥ S7=

∫ 10

∫ 1sq dF 4q5dG4s5

∫ 10

∫ 1sdF 4q5dG4s5

1 (1)

and similarly the expected quality conditional on notmeeting the standard is

E6Q �Q< S7=

∫ 10

∫ s

0 q dF 4q5dG4s5∫ 1

0

∫ s

0 dF 4q5dG4s50 (2)

When s is known, these conditional expectationsreduce to E6Q �Q ≥ s7=

∫ 1sq dF 4q5/

∫ 1sdF 4q5 and E6Q �

Q< s7=∫ s

0 q dF 4q5/∫ s

0 dF 4q5.Before analyzing the equilibrium behavior of firms,

first consider the effect of uncertainty about the stan-dard on consumer information, supposing that allfirms meeting the standard obtain a label. Becausethe label provides information about both Q and S, itprovides less information about Q alone than whenS is known. For instance, for the case of uniform Fand G, the expected mean-squared-error of consumerestimates of Q falls from 1/12 to 1/24 when S is cer-tain but falls only to 1/18 when S is uncertain. As thefollowing proposition confirms, this pattern holds forgeneral F and G. For particular realizations s of S, e.g.,for very high or low s, certain standards can be lessinformative than uncertain standards, but on averagea certain standard is more informative.

Proposition 1. Suppose all eligible firms are labeled.The expected informativeness of the label is lower if thestandard is uncertain than if it is certain.

Proof. All proofs are in the appendix. �As expected, uncertainty over the meaning of a

label reduces the ability of the label to convey infor-mation about quality to consumers. Our objective inthis paper is to explore how the equilibrium labelingdecisions of firms aggravate the uncertainty problemto create further confusion among consumers.

Our equilibrium concept is perfect Bayesian equi-librium subject to a belief-refinement introducedbelow. In a labeling equilibrium a firm whose productmeets or exceeds the labeling standard always obtainsa label, so the lack of a label implies failure to meetthe standard. Consumer beliefs used to update prod-uct quality are consistent with this firm strategy inequilibrium, so the equilibrium condition is simplythat the benefit from labeling is higher than the cost,4

E6Q �Q ≥ S7−E6Q �Q< S7≥ c0 (3)

4 If a labeling equilibrium exists, a continuum of equilibria also existwhere only types in some subset X ⊂ 6S117 obtain a label, with theknife-edge result that E6Q � Q ∈ X7 − E6Q � Q y X7 = c. We do notanalyze these equilibria in which all types are indifferent betweenlabeling and nonlabeling.

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 5

Figure 1 Updated Quality and Standard Estimates

Q = S Q = s(E[S |Q ≥ S], E[Q |Q ≥ S])

(E[S], E[E[Q |Q ≥ s]])

(E[S], E[E[Q |Q < s]])

(E[S |Q < S], E[Q |Q < S])

E[Q |Q ≥ s]

E[Q |Q < s]

(E[S], E[Q]) (E[S], E[Q])Q Q

1 1

0 1

(a) Uncertain standard S (b) Certain standard S = s

S 0 1s

Because E6Q � Q ≥ S7 > E6Q � Q < S7 such an equi-librium exists for c sufficiently small and does notexist for c sufficiently large. In a nonlabeling equilib-rium a firm does not certify product quality even ifit can, so lack of a label represents no news at all,implying the prior estimate E6Q7 is unchanged. Label-ing in the nonlabeling equilibrium is an unexpected,out-of-equilibrium action. As discussed by Banks andSobel (1987), there is no variation in the incentives oftypes to certify, so standard forward induction argu-ments do not indicate one type or another is a moreplausible source of the unexpected action. We refinethe perfect Bayesian equilibrium set by assuming thatconsumers believe that such an action is equally likelyto have been by any type that meets the standard, soan unexpected label is good news that generates theupdated estimate E6Q �Q ≥ S7. Therefore, the equilib-rium condition for the nonlabeling equilibrium is

E6Q �Q ≥ S7−E6Q7≤ c0 (4)

Because E6Q � Q ≥ S7 > E6Q7, such an equilibriumdoes not exist for c sufficiently small and does existfor c sufficiently large. Comparing the two conditions,because E6Q �Q< S7 < E6Q7 the left-hand side of (3) isgreater than the left-hand side of (4), implying for anygiven c one or the other of these two equilibria exists.Both conditions are satisfied simultaneously, indicat-ing the existence of multiple equilibria, when

E6Q �Q ≥ S7−E6Q7

≤ c ≤ E6Q �Q ≥ S7−E6Q �Q< S71 (5)

which is possible again by the fact that E6Q �Q< S7 <E6Q7. Regarding when one of the equilibria is unique,the labeling condition (3) cannot be satisfied for c suf-ficiently large and the nonlabeling condition (4) can-not be satisfied for c sufficiently small. We state theseresults as the following proposition, where the proofverifies the inequalities stated above.

Proposition 2. With certain or uncertain labelingstandards, there exists 0 ≤ c < c̄ ≤ 1 such that a non-labeling equilibrium exists iff c > c, a labeling equilibriumexists iff c < c̄, and both equilibria exist iff c ∈ 6c1 c̄7.

To see the differential effects of certainty and uncer-tainty, first consider Figure 1(a), where F and Gare uniform so that the priors are 4E6S71E6Q75 =

41/211/25. The updated expectations of S and Q forQ ≥ S and Q< S are given by the centers of mass ofthe upper and lower triangles, respectively, so E6Q �

Q ≥ S7 = 2/3 and E6S � Q ≥ S7 = 1/3, and E6Q � Q <S7 = 1/3 and E6S � Q < S7 = 2/3. Therefore, meet-ing the standard is good news about Q and badnews about S, and failing to meet the standard is theopposite. We term the downward adjustment of theestimate of S due to a label the “Groucho effect”—achieving the goal diminishes the goal itself. And weterm the upward adjustment to the estimate of S dueto lack of a label the “reverse Groucho effect”—failingto meet the goal enhances the goal itself. These adjust-ments lead to a moderating effect on the estimatesof Q, where consumers are both less impressed by alabel and less discouraged by lack of a label.

This can be seen by comparison with Figure 1(b),where F and G are still uniform and the realizedvalue s of the standard is known to consumers. Theupdated quality estimates based on meeting the stan-dard or not, E6Q �Q ≥ s7= 41+ s5/2 and E6Q �Q< s7=s/2, are given respectively by the upper and lowerlines in the figure. Integrating these estimates of Qover the different values of s we get the ex anteexpected qualities for a certain standard of E6E6Q �

Q ≥ s77 = 3/4 and E6E6Q � Q < s77 = 1/4. These arethe average expected qualities for the certain standardcase where s is known, and they are the expectedqualities that would result for the uncertain stan-dard case if the conditional distribution of S didnot become less favorable when Q ≥ S and more

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Harbaugh, Maxwell, and Roussillon: Label Confusion6 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

favorable when Q< S. Comparing these expectationswith those in Figure 1(a), the example illustrates thegeneral rule, verified in the proof of the followingproposition, that

E6E6Q �Q< s77 < E6Q �Q< S7 < E6Q7 < E6Q �Q ≥ S7

< E6E6Q �Q ≥ s771 (6)

so meeting the labeling standard is better news onaverage if the standard is known for sure than if it isuncertain, and not meeting it is worse news on aver-age if the standard is known for sure than if it isuncertain.

The relationship in (6) implies that condition (3) fora labeling equilibrium is more strict with an uncertainstandard than it is on average for a certain standard,and that condition (4) for a nonlabeling equilibriumis less strict with an uncertain standard than it ison average for a certain standard. Thus, the Grouchoeffect makes the condition for the labeling equilibriumharder to meet, and the reverse Groucho effect makesthe condition for the nonlabeling equilibrium easierto meet.

Proposition 3. The expected range of certificationcosts supporting a labeling (nonlabeling) equilibrium issmaller (larger) if the standard is uncertain rather thancertain.

To gain further insight into these differences, con-sider Figure 2, where G is uniform and F follows theBeta distribution B4q3a1 b5. For the figure we restricteither a = 1 and b ≥ 1, or a ≥ 1 and b = 1, so thatthe distribution is respectively for a “bad reputationfirm” with low expected quality or for a “good repu-tation firm” with high expected quality and the dis-tribution is uniquely determined by its mean E6Q7 =

a/4a + b5. Figure 2(a) shows the cost cutoff c̄ = E6Q �

Q ≥ S7 − E6Q � Q < S7 for the boundary of the label-ing region (L) from the equilibrium condition (3), thecost cutoff c = E6Q � Q ≥ S7 − E6Q7 for the boundaryof the nonlabeling region (N) from the equilibriumcondition (4), and the resulting multiple equilibriumregion (LN). Figure 2(d) shows the certain standardcase where the corresponding regions are determinedby the expected values E6c̄7 = E6E6Q � Q ≥ s77 −

E6E6Q � Q < s77 and E6c7 = E6E6Q � Q ≥ s77 − E6Q7based on averaging out the exact values for differentrealizations of S = s. The figures illustrate the resultfrom Proposition 2 that uncertainty over the standardmakes label adoption less likely in that, relative tothe case of certain standards, the equilibrium rangefor the labeling equilibrium is always smaller and the

equilibrium range for the nonlabeling equilibrium isalways larger.5

Consider the effect of prior expectations about firmquality on labeling incentives. The Groucho effect isstrongest for firms with bad reputations because con-sumers are suspicious of any standard that such afirm can meet; similarly, the reverse Groucho effectis strongest for firms with good reputations, becauseconsumers infer that failure to obtain a label impliesthat the standard for the label was very difficult.Because the Groucho and reverse Groucho effectsare weakest for intermediate firms whose quality ismost uncertain, the impact of certification on expectedquality is the strongest, and such firms have themost incentive to obtain a label.6 This is seen in Fig-ure 2(a), where the labeling region is at a minimumand the nonlabeling region is at a maximum for E6Q7approaching 0 or 1.

When standards are certain there is no jointupdating about both quality and standards, so badreputation firms that are actually of high quality caneffectively certify their quality, and good reputationfirms that fail to certify their quality when expected tocan be heavily penalized by consumers. Therefore, asseen in Figure 2(d), the labeling equilibrium region iscomparably large for all firms. The nonlabeling regionis smallest for bad reputation firms because they havea strong incentive to certify their quality even whennot expected to, whereas good reputation firms canrely on their good reputations and save the certifica-tion costs.

These results on the role of prior expectations implythat firms with bad reputations for environmentalquality that can in fact meet relatively stringent stan-dards have the most to gain from more transparentlabeling standards. As will be seen in the follow-ing section, and as illustrated in the remaining pan-els of Figure 2, the divergence in labeling incentivesbetween the certain and uncertain cases, and the dif-ferential effect on incentives based on prior expecta-tions, becomes increasingly stark as the number ofstandards increases.

5 The effects of intermediate degrees of uncertainty over the stan-dard G are also interesting. If F is uniform, then higher vari-ance in G reduces labeling incentives, but in general the relation-ship between variance in G and labeling incentives need not bemonotonic.6 The functional form of F in the figure implies that F is most dif-fuse for E6Q7 = 1/2. Regarding mean-preserving spreads in F , forthe case of uniform G it can be shown that they increase the incen-tive to disclose both for certain and uncertain standards. From asociological perspective, Phillips and Zuckerman (2001) find thatmiddle status types have the most incentive to meet social norms,given the uncertainty of their status.

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 7

Figure 2 Labeling (L) and Nonlabeling (N) Equilibrium Regions

0 01

11 1

1 1

N

NN N

N

N

L N

L NL N

L NL N

L

LL

L

L

E[Q]

0 1E[Q] 0 1E[Q] 0 1E[Q]

E[Q] E[Q]

c

c c c

c

c

c

1 1

0

c

1(a) n = 1 Uncertain standard

(d) n = 1 Certain standard (e) n = 4 Certain standards (f) n = ∞ Certain standards

(b) n = 4 Uncertain standards (c) n = ∞ Uncertain standards

– c–c–

–

E[c]–

E[c]–

E[c]–

E[c]–

E[c]–

c–

3. Multiple LabelsWe now consider how label confusion is affected bythe availability of multiple labels with different stan-dards. As noted in the introduction, the proliferationof different labels for some products is quite extreme.For instance, the website ecolabelling.org lists morethan 30 different labels for forest products, more than40 different labels for textiles, and more than 100 dif-ferent labels for food products. It might seem thatmore options should offer firms more ways to showoff their quality, so that label usage increases. But theproliferation of standards is often blamed for creatingconfusion among consumers that weakens the credi-bility of all labels and reduces label adoption (Fischeret al. 2005). This suggests that an increase in labelscan aggravate the underlying problem of uncertainstandards.

To gain insight into how the proliferation of labelsinteracts with standard uncertainty, we now assumethat there are n ≥ 1 labels with different standardsdrawn independently from the same distribution Gwith the same cost c. Following standard notation fororder statistics we denote the random variable repre-senting the ith lowest realized standard by Si2n andits distribution by Gi2n, so that G12n represents the dis-tribution of the worst standard and Gn2n the distribu-tion of the best standard. The firm’s quality and therealized difficulties of the different standards are onlyknown by the firm, but F , G, c, and n are also knownby consumers.

For simplicity we assume that if a firm meets thestandards for multiple labels it can only adopt one ofthem. As long as attaining and displaying extra labelsis costly, this assumption does not affect our mainqualitative results.7 We also restrict attention initiallyto a “symmetric” labeling strategy, where the firmadopts the toughest label that it meets independentof any arbitrary properties of the ex ante identicalstandards. Any other equilibrium strategy that is sim-ilarly symmetric, such as always adopting the secondtoughest standard when possible, provides equiva-lent information about firm quality to consumers. Fornow we do not consider “focal” equilibrium strate-gies where it is assumed that a particular label willalways be adopted if the standard for it is met.

Because consumers do not know which of the labelshas a more difficult standard, a label under a sym-metric labeling strategy only proves that a firm hasmet the easiest standard, even if the firm has in factmet the best standard. Hence the incentives to obtain

7 The restriction of displaying one label does not affect the condi-tions for existence of labeling and nonlabeling equilibria if there areconstant or diminishing returns to labels. This holds, for instance,for uniform F and G. But if returns are increasing over some range,then it might be worthwhile to be certified by multiple labels, evenif it would not be worthwhile to be certified by one label; e.g.,a restaurant might display multiple labels in its window. Becausethe marginal value of any label goes to 0 as the number of labelsincreases, the limiting results of this section are unaffected by thepossibility of showing multiple labels.

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Harbaugh, Maxwell, and Roussillon: Label Confusion8 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

a label or not are exactly the same as in the previoussection, with the only exception being that we replacethe random variable S with the random variable S12n,representing the weakest of the n standards. There-fore, following conditions (3) and (4), for uncertainstandards a symmetric labeling equilibrium exists if andonly if

E6Q �Q ≥ S12n7−E6Q �Q< S12n7≥ c1 (7)

and a nonlabeling equilibrium exists if and only if

E6Q �Q ≥ S12n7−E6Q7≤ c0 (8)

For certain standards the conditions are quite dif-ferent because consumers know the difficulty of thestandard that was met and the difficulty of standardsthat were not met. We define a labeling equilibriumfor certain standards as an equilibrium in which anyof the different labels are adopted. For instance, a firmmight find a label with a high standard worth the cer-tification cost, but not a label with a lower standard(e.g., Viscusi 1978, Jovanovic 1982). A labeling equi-librium exists if and only if some firm types find itmore profitable to pay the certification cost and provethat they meet a particular standard (and none higher)than to be thought of as coming from the whole rangebelow that standard, i.e., if and only if

maxi=110001n

8E6Q � si2n ≤Q ≤ si+12n7−E6Q �Q< si2n79≥ c1 (9)

where we define sn+12n = 1.The condition for a nonlabeling equilibrium is sim-

pler because lack of a label always gives a payoffof E6Q7, implying that the incentive to unexpectedlyadopt a label is always highest for those meetingthe highest standard. In particular, under our beliefrefinement a nonlabeling equilibrium exists if andonly if

E6Q �Q ≥ sn2n7−E6Q7≤ c0 (10)

As shown in Figure 2, these conditions imply thatbehavior with uncertain standards diverges dramati-cally from that with certain standards. As the numberof labels n increases, consumers become increasinglysuspicious of the value of a label and the expectedquality conditional on having a label E6Q � Q ≥ S12n7falls. Therefore, comparing panel (a) with panels (b)and (c), as n increases the nonlabeling equilibriumregion based on Equation (8) expands. In the limitcondition (8) converges to E6Q7− E6Q7 ≤ c so a non-labeling equilibrium always exists for c > 0, which isparticularly damaging to bad reputation firms, whichlose the opportunity to disprove consumer expec-tations. Regarding the labeling equilibrium, if con-sumers expect a firm to obtain a label and the firmdoes not, then the expected quality conditional on not

having any label E6Q �Q< S12n7 also falls as the num-ber of labels increases. Because both E6Q � Q ≥ S12n7and E6Q � Q < S12n7 are decreasing in n, the labelingequilibrium region based on (7) can expand or con-tract, and as seen in the figure in this example theregion expands. In the limit condition (7) convergesto E6Q7− 0 ≥ c, so a labeling equilibrium only existsif firm reputations are sufficiently good.8 This label-ing equilibrium provides almost no information onfirms, but good reputation firms still feel compelledto obtain a label to avoid being thought of as very lowquality. In contrast, comparing panel (d) with panels(e) and (f), for certain standards as n increases thelabeling incentive for bad reputation firms becomesincreasingly strong because of the absence of theGroucho effect and the greater availability of differ-ent standards. At the same time, the labeling incentivefor good reputation firms decreases, because they canrest on their reputations and save the labeling costs.

The following proposition shows that these pat-terns hold generally for uncertain standards and, fol-lowing Lizzeri (1999, Theorem 1), hold for certainstandards as long as the distribution of F is log-concave.9

Proposition 4. Suppose there are n labels with i.i.d.standards. If standards are uncertain, (i) the support ofa nonlabeling equilibrium is increasing in n; and in thelimit as n increases, (ii) nonlabeling is an equilibrium forall c > 0, (iii) symmetric labeling is an equilibrium if andonly if E6Q7 ≥ c, and (iv) the symmetric labeling equi-librium is uninformative. If standards are certain, in thelimit as n increases, (v) nonlabeling is almost surely anequilibrium if and only if E6Q7 ≥ 1 − c, and (vi) for Flog-concave, labeling is almost surely an equilibrium if andonly if E6Q7≤ 1 − c.

Recall that Proposition 1 showed that certificationis always less informative when standards are uncer-tain. Proposition 4(iv) shows that for large n thisresult is even stronger in that, even though labelingcan still be an equilibrium for large n, the informa-tiveness of a label when standards are uncertain goesto zero; i.e., estimates of Q are no better than the priorestimates without a label. Managers find themselves

8 Note that at E6Q7 = 1 the firm’s quality is perfectly revealed andthe incentive to label disappears, but our analysis assumes Q hasfull support on 60117 so the analytic results and the figure are forthe range E6Q7 ∈ 40115.9 As a step in a more general analysis, Lizzeri (1999) analyzesthe case where certification costs are given and each quality levelcan be certified. In our case in the limit as the number of labelsincreases there is essentially a different label for every quality level,so the problem converges to that analyzed by Lizzeri. Note that log-concavity is equivalent to a decreasing reversed hazard rate and issatisfied by most commonly used distributions, including the Nor-mal, Uniform, and Beta distributions (Bagnoli and Bergstrom 2005).

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 9

in a labeling paradox. Labeling is completely waste-ful because in equilibrium the firm proves that it isnot of the lowest type, but the firm does not benefitrelative to prior expectations, and consumers do notlearn any information because the firm being of thelowest type is a zero probability event anyway. Thiscontrasts with the result for certain standards, whereas n increases a label becomes highly informative andthe only residual uncertainty arises from firms that donot have a label because of the certification costs. Thissuggests that as the number of labeling organizationsexpands, organizations interested in promoting ecola-bels should try to limit the number of labels or bettereducate consumers about label standards.

That labeling provides no new information asn increases is related to the finding by Lizzeri (1999)that a certification intermediary that is interested inmaximizing profits from certification will often choosethe lowest possible standard, with the result that thereis no net gain in information to consumers. Because afirm that does not meet the standard will be thoughtof as extremely low quality, firms are willing to paya high cost for the certificate; because the certificateis so easy to earn, almost all of them are able topay for the certificate and receive it. Therefore, aprofit-maximizing certification intermediary uninter-ested in informing consumers benefits the most froma low standard. Our model differs in the assump-tion that there are multiple exogenous labeling stan-dards rather than an endogenous standard chosenby a profit-maximizing certification intermediary, andthat there is a fixed cost to certification rather than aprofit-maximizing price set by the intermediary. Nev-ertheless, we find the same result that as the numberof labels grows, consumers learn little from certifica-tion even as firms feel forced to expend substantialresources on it.

With multiple standards, one standard is sometimes“focal” or “salient” in that consumers expect firmsto adopt the standard if they are able to, even ifthey also meet another potentially more demandingstandard. For instance, in many European countries,regional or national ecolabels appear to be focal rel-ative to the EU Flower label; e.g., the Nordic Swanlabel and German Blue Angel labels are more widelyadopted for almost all product categories. Given thefocality of these labels and the fact that consumers donot know which labeling standards are tougher, con-sumers might infer that a firm that displayed the EUFlower label was only able to attain it and not thefocal label.

It might seem that information flows will decreaseif firms are expected to choose a focal standard ratherthan the one they know to be toughest. To see how afocal standard can increase rather than decrease infor-mation flows, we now consider focal labeling strate-gies based on arbitrary properties of the labels that are

unrelated to their difficulty. In such a strategy there isone label, say label X, that a firm is expected to adoptif it can. If the firm adopts another label, say labelY , then it is assumed that it could not meet label Xand that label Y was the best of the other labels it didmeet. For certain standards, a firm will clearly certifywhichever label is toughest so any equilibrium basedon focal strategies will break down. But for uncer-tain standards, consumers do not know which labelis tougher so such a focal labeling equilibrium is pos-sible. Such an equilibrium can be more informativethan a symmetric labeling equilibrium, as the follow-ing proposition shows.10

Proposition 5. Suppose there are n labels with i.i.d.standards. (i) If standards are uncertain and c is suffi-ciently low, there exists a focal labeling equilibrium that ismore informative than the symmetric labeling equilibrium.(ii) If standards are certain, a focal labeling equilibriumcannot exist.

The focality of a standard eliminates the problemscaused by multiplicity of voluntary standards. Theresult is then similar to the n= 1 case in that there isno degradation of the expected difficulty of the stan-dard, but it is actually better because firms that donot meet the focal standard can still provide infor-mation to consumers by meeting a different standard.As discussed in the introduction, this result providesa role for industry groups, governments, and NGOsin not just setting and clarifying standards, but inattempting to make particular standards focal. “Lookfor the label” campaigns can help induce an equilib-rium where consumers expect a particular standardto be used and look less favorably on adoption ofother labels. The key is not necessarily that the focallabel has a higher standard, or that the standard becertain, but simply that there is a single standard thatconsumers expect firms to try to attain.

This result has important implications for thedebate over the role of industry-sponsored labelsaimed at environmental and/or social aspects ofproduct quality. It is common for NGOs to criticizethe introduction of industry-sponsored labels, oftenciting them as embodying lower-quality standardsthan existing NGO labels. However, if the industrylabels are introduced as a response to label prolifera-tion, and if the industry succeeds in making its label

10 Proposition 5 looks at the case where c is sufficiently low that itis an equilibrium for the firm to adopt another label if it cannotmeet the standard for the focal label. It can also be an equilibriumfor a firm to adopt the focal label if it can and otherwise not adoptany label. For sufficiently many standards such a strategy is alsomore informative than the symmetric disclosure equilibrium, butfor low costs the firm has an incentive to deviate to the equilibriumstrategy we examine.

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Harbaugh, Maxwell, and Roussillon: Label Confusion10 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

focal, then there can be a gain in information to con-sumers. Therefore, it might be strategic for NGOs tosettle for less-demanding labels that have a greaterchance of becoming focal.

Our result on focal certification equilibria is closelyrelated to a finding by Fishman and Hagerty (1990),who analyze a persuasion game with costless dis-closure where there are multiple noisy signals aboutwhether an investment project is profitable andassume that a firm can only reveal one of them. Sim-ilar to our result, they find that a “lexicographic”equilibrium is most informative; a firm releases thefirst signal that is favorable in accordance with a setorder that is anticipated by receivers, so that releasinganother favorable signal is therefore evidence that thefirst signal was not favorable.

An alternative to the use of campaigns to establishfocal standards is to simply make it mandatory fora firm to disclose whether it meets a particular stan-dard. In this case bad news regarding this mandatorydisclosure on one standard can still be supplementedwith good news on other standards, so the result isessentially the same as in the focal equilibrium if thecertification costs for the mandatory standards aretaken as sunk costs. Therefore, the informativenessresult of Proposition 5 also provides an argument formandatory certification of a particular label, even ifconsumers do not know the exact standard for thelabel, and suggests that firms may benefit from part-nering with government or dominant NGOs to pro-mote a specific label as a marketing strategy.

4. Multiple FirmsWe now consider how the presence of multiple firmsaffects label confusion. It might seem that, by observ-ing which firms obtain which labels, consumersshould be able to learn about different labeling stan-dards and thereby reduce the information problemsanalyzed above. Indeed, if there is only one label andall firms that can meet the label standard adopt it,then as the number of firms increases, the fraction ofthe firms obtaining the label is an increasingly pre-cise estimate of the label standard. However, we findthat two factors limit such learning. First, the non-labeling equilibrium is unaffected by an increase inthe number of firms, so the potential for no learning,and also the potential for strategic uncertainty abouthow to interpret lack of a label, remains. Second, inthe realistic case where there are both multiple firmsand also multiple labels, we find that firms have anincentive to choose standards strategically in a waythat interferes with consumer learning.

First consider the simpler case where m firmswith i.i.d. qualities Q11 0 0 0 1Qm simultaneously choosewhether to adopt a single label with standard S. As

discussed at the end of this section, we do not modelproduct market competition between firms; we justassume that each firm wants to be perceived as higherquality rather than lower quality. Each firm knowsthe realized value of its own quality and each other’squalities q11 0 0 0 1 qm and the realized difficulty of thestandard s, but consumers only know F , G, c, and m.The first part of the following proposition uses a stan-dard Law of Large Numbers result to confirm that thefraction of firms obtaining the label can be an asymp-totically precise estimate of the standard, so the sit-uation for each firm is equivalent to that of a singlefirm facing a certain standard, as examined in §2. Thesecond part shows that this logic does not extend tothe nonlabeling equilibrium, because the gain fromdeviating by a single firm is E6Qi �Qi ≥ S7− E6Qi7, sothe condition for a nondisclosure equilibrium remainsexactly the same as that of a single firm facing anuncertain standard. The third part confirms that for acertain standard the number of firms has no effect onthe support of either equilibrium.

Proposition 6. Suppose m i.i.d. firms face a singlelabel. If the label standard is uncertain, (i) the expectedsupport of a labeling equilibrium converges to that of asingle firm facing a certain standard as m increases, and(ii) the expected support of a nonlabeling equilibrium is thesame as for m= 1. (iii) If the label standard is certain, theexpected support of either equilibrium is the same as form= 1.

Looking back at Figure 2, this proposition impliesthat with uncertain standards a large number of firmsexpands the region where labeling and nonlabelingequilibria coexist from the “L1N” areas in the sepa-rate panels of (a) and (d) to encompass the area abovec in panel (a) and underneath E6c̄7 in panel (d). There-fore, even though the presence of multiple firms canpotentially reduce uncertainty over the standard bythe first part of the proposition, it need not do so bythe second part, and the combination of these resultsimplies that there is increased strategic uncertaintyfrom the larger range of c that supports multiple equi-libria.11 Therefore, this result reinforces the argumentthat firms and organizations interested in promotingecolabel adoption need to consider how to promoteecolabels in an environment where both labeling andnonlabeling are equilibria. Similarly, it supports a rolefor mandatory labeling to avoid the multiple equilib-rium problem.

11 This is seen for the EU Flower label, which has different stan-dards for different product categories, and where label adoptionrates for the categories vary greatly. For instance, consumers couldinterpret the absence of adoption by any major laundry detergentproducts either as reflecting a nonlabeling equilibrium or as strongevidence that the labeling standard for detergents is very strict. Inthis case the former interpretation appears to be correct (Rubik andFrankl 2005).

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 11

Figure 3 Strategic Choice of Labels

0

1

0 11

1

E[Qi] E[Q1] – E[Q2]

E[Qi |Same]

E[Qi |Same]

E[Q1|Same]

E[Q2|Same]

E[Q1|Different]

E[Q2|Different]

E[Qi |Different]

E[Qi |Different]

(a) Two i.i.d. firms (b) Good and bad reputation firms

Now considering the case where there are both mul-tiple firms and multiple labels, learning about labelstandards is more difficult because adoption of onelabel by a firm creates an information externality orspillover that can affect the incentives for other firmsto certify. If a firm follows the strategy of adoptingthe toughest label that it meets, and if the firm is agood reputation firm, then adoption of a label mightbe good news about the label standard, which counter-acts the Groucho effect. Because of this selection effect,a good reputation firm can “legitimize” a standard andmake it more attractive to other firms, but because ofthe Groucho effect, a bad reputation firm can “spoil”a standard and make it less attractive to other firms.Firms therefore have an incentive to choose standardsstrategically in a way that interferes with consumerlearning.

To gain insight into this incentive, first suppose thereare two labels with i.i.d. standards and two i.i.d. firms.If one firm follows the strategy of adopting the tough-est label it meets and the prior F is very favorable,then the label that it adopts is likely to be the betterone. This gives the other firm an incentive to adoptthe same label, regardless of whether the label is reallythe toughest. Conversely, if the prior F is very unfa-vorable, then the label that is adopted is still likely tobe the worse one. This gives the other firm an incen-tive to adopt the opposite label, regardless of whetherit really is the toughest. Therefore, in both cases firmshave an incentive to deviate from the symmetric certifi-cation strategy of adopting the label with the tougheststandard.12

12 Jovanovic (1982) notes in passing that the disclosure incentives ofone firm can be affected by those of another if firm quality is corre-lated. Here firm quality is independent, but conditional correlationis generated by the same uncertain standards being available toeach firm.

This is seen in Figure 3(a) for two firms with i.i.d.quality given by the Beta distribution as before andfor two standards with i.i.d. uniform distribution.Define E6Qi � Same7 as the expected quality of firm i’sproduct when the toughest standard that each firmmeets is the same,

E6Qi � S122 ≤Q11Q2 < S222 ∪ S122 < S222 ≤Q11Q271 (11)

and E6Qi �Different7 as the expected quality of firm i’sproduct when one firm meets a higher standard:

E6Qi � S122 ≤Q1 < S222 ≤Q2 ∪ S122 ≤Q2 < S222 ≤Q170 (12)

Because the firms are i.i.d., E6Q1 � Same7= E6Q2 � Same7and E6Q1 � Different7 = E6Q2 � Different7, so if (11) >(12), both firms will prefer to adopt the same stan-dard even if one meets a higher standard, and if(11) < (12), both firms will prefer to adopt a differentstandard even if they both meet the higher standard.Only in the knife-edge case where (11) equals (12) andthe firms are just indifferent is it an equilibrium forfirms to always follow the symmetric labeling strat-egy. This is seen in the figure where, unless E6Qi7 =

1/2, firms have an incentive to either pool with eachother or separate from each other by choosing stan-dards strategically. Such strategic behavior aggravateslabel confusion and makes it more difficult for a firmwith a bad reputation to prove itself to be good.

Now consider more generally m firms with i.i.d.qualities choosing simultaneously whether to adoptone of n labels with i.i.d. standards, where againthe realized qualities and standards are known bythe firms but only F , G, c, m, and n are known toconsumers. Let a = 4a11 0 0 0 1 am5, where aj equals thelabel 1 to n adopted by firm j with 0 representing nolabel. Then in a candidate symmetric labeling equilib-rium E6Qi � a7 is expected quality conditional on the

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Harbaugh, Maxwell, and Roussillon: Label Confusion12 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

observed a and on the equilibrium strategy of adopt-ing the toughest label attainable. If E6Qi � a7 is constantfor all a that are attainable for a given realization of4Q11 0 0 0 1Qm5, then no firm has an incentive to devi-ate. But if this knife-edge condition does not hold, asin the two-firm and two-label example above, at leastone firm has an incentive to deviate by adopting alower standard.

This problem does not arise for a focal equilibrium.Suppose that there is a particular label that each firmis expected to adopt or not if it meets the standardfor it. Then the incentive to adopt the label is exactlythe same as if there was only one label,13 includ-ing the result from Proposition 6, that with manyfirms consumers will become increasingly certain ofthe standard for the focal label. Therefore, the focalequilibrium can approximate the case of a mandatorylabel, allowing consumers to learn about the meaningof the standard for the label from their experienceswith different products. Again this result supports arole for marketing efforts aimed at the developmentor adoption of a focal labeling standard.

The proof of the following proposition followsdirectly from the above arguments.

Proposition 7. Suppose m > 1 i.i.d. firms chooseamong n > 1 labels with i.i.d. standards. (i) If the labelstandards are uncertain, then a symmetric labeling equilib-rium does not exist generically, but a focal labeling equilib-rium always exists under the same condition as for n= 1.(ii) If the label standards are certain, then the support ofany equilibrium is the same as for m= 1.

This incentive to choose standards strategically canbe aggravated if consumers have different prior dis-tributions about the different firms’ products. Fig-ure 3(b) shows the case where “good reputation”firm 1 has convex Beta distribution parameterized by4�115 and “bad reputation” firm 2 has the symmetricconcave independent Beta distribution parameterizedby 411 �5, so E6Q17 − E6Q27 = 4� − 15/4� + 15. When� = 1, both firms have uniformly distributed quality(E6Q17 = E6Q27 = 1/2 in the figure) and there is noincentive to be strategic, but as soon as a gap emerges,the good reputation firm always wants to choosea different label than the bad reputation firm, andthe bad reputation firm always wants to choose thesame label as the good reputation firm. If both firmsadopt the same label, it is likely that only the weakerstandard was met, which is bad news for the good

13 If firms that do not meet the standard for the focal label adoptanother label, this is good news that the firm at least meets theeasiest standard. Which of the other labels firms choose dependson the same coordination issues regarding the symmetric labelingequilibrium, so generically there will be a mixed-strategy equilib-rium for the other labels. But this does not affect the incentive toadopt the focal label.

reputation firm but still good news for the bad rep-utation firm. If both firms adopt different labels, it islikely that the good reputation firm met the tougherstandard and the bad reputation firm met the weakerstandard, so the good reputation firm gains and thebad reputation firm loses. Hence there cannot be anequilibrium in which each firm always adopts thetoughest label it meets. Instead, if both firms meetboth standards, there must be a mixed-strategy equi-librium where the bad reputation firm tries to choosethe same label as the good reputation firm and thegood reputation firm tries to avoid such an outcome.

The above analysis assumes that the choice of stan-dards is simultaneous, but the analysis can also beapplied to the case of sequential adoption. In thesequential case, a “labeling cascade” can emerge inwhich firms choose the same label strategically. Forinstance, in the two-firm and two-label example inFigure 3(a), if both firms have good reputations sothat E6Qi � Same7 > E6Qi � Different7, then the secondfirm raises its expected quality by herding with thefirst firm and adopting the same label, even if itmeets an even tougher standard for another label.Similarly, if both firms have bad reputations, so thatE6Qi � Same7 < E6Qi � Different7, then antiherding canarise, in which the second firm chooses a differentlabel than the first firm. These effects are amplified ifthe firms have different reputations, as in the examplein Figure 3(b), in which case herding will arise if thegood reputation firm goes first and antiherding willarise if the bad reputation firm goes first. In each case,the uncertainty of standards creates interdependencein the perceived quality of products that leads to astrategic choice of labels.14

As mentioned in the introduction, a common strat-egy when introducing a new ecolabel is to try toinduce the most reputable companies to adopt thelabel with the hope that other companies will thenadopt it. Similar strategies occur in many other con-texts; e.g., new journals try to start with articles byrespected authors. The above analysis implies thatinformation spillovers may be one reason for thisstrategy. If a good reputation firm moves first, thenthe bad reputation firm can always choose the samelabel if it is capable of doing so. Therefore, thegood reputation firm has no incentive to deliberatelychoose an easier label, and if it faces any uncertaintyat all over whether the bad reputation firm will meetthe tougher label, it has a strict incentive to choose

14 This discussion applies to choices between different labels, ratherthan the choice to obtain a label at all. If choices are sequential and afirm unexpectedly deviates from the nonlabeling equilibrium, thenconsumer beliefs might reasonably change and other firms mightface pressure to also deviate. Our belief refinement does not applyin this case.

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 13

the tougher label. However, because there is a second-mover advantage, a good firm needs to be given someincentive to move first.

We have assumed that firms do not care directly howother firms are regarded by consumers, but only careif the label itself is diminished or enhanced because ofthe actions of other firms. In many situations firms willbe in the same industry and therefore have a compet-itive incentive to look good relative to other firms byundermining their competitors’ perceived quality. Theabove analysis shows that, even without such prod-uct market externalities, firms need to worry about thestrategic effects of labeling decisions.15

5. ConclusionThe literature on ecolabels and other quality certifi-cation schemes has long recognized that consumerconfusion is a major hurdle to their adoption andeffective use. Our analysis provides a theoretical basisfor such concerns when consumers have even slightuncertainty about the difficulty of labeling standards.Because consumers must jointly update the estimatedquality of the product and the estimated difficultyof the standard, there are not only direct informa-tion losses but also substantial indirect losses as firmsdecide whether it is worthwhile to be certified and,if so, which of multiple labels to adopt. We find thata “Groucho effect” due to uncertainty discourageslabeling when it is most beneficial to consumers andfirms, that the effects of uncertainty are aggravatedby the proliferation of labels with different standards,that strategic uncertainty from multiple equilibriabecomes particularly problematic as the number oflabels increases, and that information spillovers givefirms an incentive to choose strategically among dif-ferent labels to make learning about labeling stan-dards more difficult for consumers.

Mandatory adoption of ecolabels can also sufferfrom direct information losses due to uncertaintyover certification standards, but it precludes the addi-tional indirect losses due to firm labeling decisionsand can also facilitate consumer learning about stan-dards. Therefore, these results provide an additionalconsideration in the debate over voluntary versusmandatory disclosure of product quality. We find thatactions aimed at making one standard “focal” can alsoreduce the indirect information losses. “Look for thelabel” promotional campaigns that induce consumersand firms to focus on a particular label, even if thestandard for it remains uncertain, can increase cer-

15 Note that competition does not always lead to more disclosure.Guo and Zhao (2009) show that there is less disclosure in a com-petitive than in a monopolistic environment and that the amountof disclosure depends on whether it is sequential or simultaneous.See also Hotz and Xiao (2011), Board (2009), and Levin et al. (2009)for the effect of competition on disclosure.

tification incentives, reduce the problem of strategicuncertainty due to multiple equilibria, and improveconsumer learning by eliminating firm incentives tochoose among labels strategically.

Our results assume that consumers are unsure ofboth the absolute and relative difficulty of differentstandards, but sometimes the relative difficulty of dif-ferent standards is known even when the exact stan-dards are not. For instance, consumers might knowthat one ecolabel is an industry label while anotheris an NGO label and infer that the latter representsa more difficult standard. Clearly, such relative infor-mation can reduce some of the problems identifiedin this paper. Therefore, another strategy for orga-nizations to reduce label confusion is to focus onproviding a clear ranking of different labels, evenif the exact standards remain difficult to communi-cate to consumers. One option is for a single certi-fier to provide multiple labels representing differentranked standards, e.g., gold, silver, and bronze labelsfor LEED certification of buildings. However, as dis-cussed in the introduction, the vast majority of eco-labels take the simple pass-fail form analyzed in thispaper, so better understanding of why certifiers donot provide richer information to consumers is animportant area of future research.

If ecolabels can help consumers successfully iden-tify more environmentally friendly products, theymay also be able to induce firms to improve theenvironmental quality of products over time. In thecontext of restaurant hygiene labels, Jin and Leslie(2003) show that restaurants improve their hygienein response to public disclosure of hygiene ratings.We assume for our analysis that quality is fixed, sothe issue of endogenous quality response to labelswith uncertain standards remains open for furtherresearch. Given that consumers do not know the dif-ficulty of labeling standards, it seems that firms havean incentive to save costs by only attaining the qual-ity needed to meet the easiest standard. We conjecturethat this makes attainment of a particular standard aneven worse signal of the standard’s likely difficulty,thereby strengthening the Groucho effect and aggra-vating the problem of label confusion.

AcknowledgmentsFor helpful comments, the authors thank Mike Baye, OliverBoard, Harrison Cheng, Michael Fishman, Ivan Pastine, andseminar and conference participants at the Federal TradeCommission, the Self-Regulation Conference at HarvardUniversity, the Informing Green Markets Conference at theUniversity of Michigan, the Allied Social Science Associ-ation Annual Meetings, the International Industrial Orga-nization Conference, the Mid-West Theory Conference, theFrontiers in Environmental Economics and Natural Resource

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Harbaugh, Maxwell, and Roussillon: Label Confusion14 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

Management Meeting of the French Economic Association atthe Toulouse School of Economics, the Conference on Pub-lic Economics at the University of the Mediterranean, theUniversity of Guelph, the University of Lausanne, the Uni-versity of Michigan, the University of Toronto, and the Uni-versity of Western Ontario.

Appendix

Proof of Proposition 1. Let q = E6Q � Q < S7 and q̄ =

E6Q �Q ≥ S7, and for the realized value S = s, let q4s5= E6Q �

Q< s7 and q̄4s5= E6Q �Q ≥ s7. Then the mean-squared error(MSE) for the uncertain case is

∫ 1

0

(

∫ s

04q − q52 dF 4q5+

∫ 1

s4q − q̄52 dF 4q5

)

dG4s5

=

∫ 1

0

(

∫ s

04q2

− 2qq + q25 dF 4q5

+

∫ 1

s4q2

− 2qq̄ + q̄25 dF 4q5

)

dG4s5

= E6Q27+∫ 1

04F 4s54q2

− 2qq4s55

+ 41 − F 4s554q̄2− 2q̄q̄4s555 dG4s51 (13)

and the expected MSE for the certain case is∫ 1

0

(

∫ s

04q − q4s552 dF 4q5+

∫ 1

s4q − q̄4s552 dF 4q5

)

dG4s5

= E6Q27+∫ 1

04F 4s54q4s52

− 2q4s525

+ 41 − F 4s554q̄4s52− 2q̄4s5255 dG4s5

= E6Q27−∫ 1

04F 4s5q4s52

+ 41 − F 4s55q̄4s525 dG4s50 (14)

Comparing, (13) minus (14) equals∫ 1

0F 4s54q2

− 2qq4s55+ 41 − F 4s554q̄2− 2q̄q̄4s55 dG4s5

+

∫ 1

0F 4s5q4s52

+ 41 − F 4s55q̄4s52 dG4s5

=

∫ 1

0F 4s54q2

− 2qq4s5+ q4s525

+ 41 − F 4s554q̄2− 2q̄q̄4s5+ q̄4s525 dG4s5

=

∫ 1

0F 4s54q − q4s552

+ 41 − F 4s554q̄ − q̄4s552 dG4s5 > 01 (15)

so the MSE is larger for the uncertain case. �

Proof of Proposition 2. Given that the support of q isrestricted to 60117, we just need to verify for the uncertaincase that E6Q � Q ≥ S7 > E6Q < S7, E6Q � Q ≥ S7 > E6Q7, andE6Q � Q< S7 < E6Q7, and for the certain case that E6Q � Q ≥

s7 > E6Q < s7, E6Q � Q ≥ s7 ≥ E6Q7, and E6Q � Q < s7 ≤ E6Q7for all s. The last group of inequalities is standard for condi-tional expectations. Checking the first group of inequalities,note that E6Q �Q ≥ S7−E6Q7 is proportional to

∫ 1

0

∫ 1

sq dF 4q5dG4s5−E6Q7

∫ 1

0

∫ 1

sdF 4q5dG4s5

=

∫ 1

0

(

∫ 1

sq dF 4q5−

∫ 1

sdF 4q5E6Q7

)

dG4s5

∝∫ 1

04E6Q �Q ≥ s7−E6Q75dG4s5 > 01 (16)

where the inequality follows because E6Q �Q ≥ s7≥ E6Q7 forall s with strict inequality for s > 0. By similar calculations,E6Q � Q < S7 < E6Q7 also holds. Thus, combining the twoinequalities, E6Q �Q ≥ S7 > E6Q< S7. �

Proof of Proposition 3. Substituting (1) and (2) into (3),for the labeling equilibrium we need to show that

∫ 10

∫ 1s q dF 4q5dG4s5

∫ 10

∫ 1s dF 4q5dG4s5

−

∫ 10

∫ s

0 q dF 4q5dG4s5∫ 1

0

∫ s

0 dF 4q5dG4s5

≤

∫ 1

0

∫ 1s q dF 4q5∫ 1s dF 4q5

dG4s5−∫ 1

0

∫ s

0 q dF 4q5∫ s

0 dF 4q5dG4s51 (17)

and substituting (1) and (2) into (4), for the nonlabelingequilibrium we need to show that

∫ 10

∫ 1s q dF 4q5dG4s5

∫ 10

∫ 1s dF 4q5dG4s5

≤

∫ 1

0

∫ 1s q dF 4q5∫ 1s dF 4q5

dG4s50 (18)

Considering the nonlabeling equilibrium first, (18) is equiv-alent to

∫ 1

0

(

∫ 1s q dF 4q5

∫ 10 4∫ 1t dF 4q55 dG4t5

−

∫ 1s q dF 4q5∫ 1s dF 4q5

)

dG4s5≤ 0

⇐⇒

∫ 1

0

(

∫ 1

sq dF 4q5

)(

∫ 10 F 4t5dG4t5−F 4s5

41−∫ 1

0 F 4t5dG4t5541−F 4s55

)

dG4s5≤0

⇐⇒

∫ 1

0E6Q �Q ≥ s7

(

∫ 1

0F 4t5dG4t5− F 4s5

)

dG4s5≤ 0

⇐⇒

∫ 1

0E6Q �Q ≥ s7

(

1 −F 4s5

∫ 10 F 4t5 dG4t5

)

dG4s5≤ 00 (19)

Letting P4s5 =∫ s

0 F 4t5 dG4t5/4∫ 1

0 F 4t5 dG4t55, then (19) isequivalent to

∫ 10 E6Q � Q ≥ s7 dP4s5 ≥

∫ 10 E6Q � Q ≥ s7 dG4s5,

or integrating by parts, −∫ 1

0 44d/ds5E6Q � Q ≥ s754P4s5 −

G4s55 ds ≥ 00 Therefore, because 4d/ds5E6Q � Q ≥ s7 > 0, theinequality holds if G4s5 ≥ P4s5 for all s, i.e., if P �FOSD

G. Note that G4s5 ≥ P4s5 is equivalent to∫ 1

0 F 4t5 dG4t5 ≥

4∫ s

0 F 4t5 dG4t55/G4s5. The right-hand side is an increasingfunction of s and the inequality holds weakly for s = 1, sothe inequality holds for all s.

Now considering the labeling equilibrium, given that (18)holds, (17) holds if

∫ 10

∫ s

0 q dF 4q5dG4s5∫ 1

0

∫ s

0 dF 4q5dG4s5≥

∫ 1

0

∫ s

0 q dF 4q5∫ s

0 dF 4q5dG4s51 (20)

which always holds by the same arguments as above. �

Proof of Proposition 4. (i) We first want to show thatG12n �MLR G12n+1, i.e., for all x < y,

g12n4x5

g12n+14x5≤

g12n4y5

g12n+14y50 (21)

Noting that

gk2n4x5=n!

4k− 15!4n− k5!G4x5k−141 −G4x55n−kg4x51 (22)

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Harbaugh, Maxwell, and Roussillon: Label ConfusionManagement Science, Articles in Advance, pp. 1–16, © 2011 INFORMS 15

(21) simplifies to G4x5 ≤ G4y5, which holds for all x < y.Now we want to show that if G �MLR H for any two dis-tributions G and H , then it is better news when the firmmeets a standard with distribution G than H . So we needto prove that

∫ 10

∫ 1s q dF 4q5dG4s5

∫ 10

∫ 1s dF 4q5dG4s5

≥

∫ 10

∫ 1s q dF 4q5dH4s5

∫ 10

∫ 1s dF 4q5dH4s5

1 (23)

which can be rewritten as∫ 1

0 E6q �q≥s741−F 4s55g4s5ds∫ 1

0 41−F 4s55g4s5ds≥

∫ 10 E6q �q≥s741−F 4s55h4s5ds

∫ 10 41−F 4s55h4s5ds

0

(24)Define the densities p4s5 = 41 − F 4s55g4s5/

∫ 10 41 − F 4t55g4t5 dt

and q4s5= 41 − F 4s55h4s5/∫ 1

0 41 − F 4t55h4t5 dt and let P4s5 andQ4s5 represent the respective distributions. Because E6q � q ≥

s7 is increasing in s, the above condition holds if P �FOSD Q.By the assumption that G�MLR H , for all x < y,

g4x5

g4y5≤

h4x5

h4y5

⇐⇒41 − F 4x55g4x5

41 − F 4y55g4y5≤

41 − F 4x55h4x5

41 − F 4y55h4y5

=⇒

∫ y

0 41 − F 4x55g4x5dx

41 − F 4y55g4y5≤

∫ y

0 41 − F 4x55h4x5dx

41 − F 4y55h4y5

⇐⇒

∫ y

0 41 − F 4x55g4x5dx

p4y5∫ 1

0 41 − F 4x55g4x5dx≤

∫ y

0 41 − F 4x55h4x5dx

q4y5∫ 1

0 41 − F 4x55h4x5dx

⇐⇒

∫ y

0 p4x5dx

p4y5≤

∫ y

0 q4x5dx

q4y5

⇐⇒P4y5

p4y5≤

Q4y5

q4y51 (25)

so P reverse hazard rate dominates Q, which impliesP �FOSD Q and hence (23) holds. Letting G = G12N and H =

G12n+1, this establishes that E6Q �Q ≥ S12n7≥ E6Q �Q ≥ S12n+17.Therefore, from (8), the support of a nonlabeling equilib-rium is increasing in n.

(ii) By the Glivenko-Cantelli theorem, the empirical dis-tribution Gn4s5 of n standards converges uniformly to thetheoretical distribution G as n goes to infinity, implying thatfor any � > 0, the minimum of these standards is almostsurely less than � in the limit. Hence the expected qualityfrom unexpected labeling converges to E6Q7 in the limit,and the necessary and sufficient condition (8) for a nonla-beling equilibrium reduces to E6Q7−E6Q7≤ c or c ≥ 0.

(iii) By the same argument as in (ii), the expected qual-ity from nonlabeling converges to 0 and from labeling con-verges to E6Q7 in the limit as n increases, so the necessaryand sufficient condition (7) for a symmetric labeling equi-librium reduces to E6Q7− 0 ≥ c.

(iv) By the same argument as in (ii), in the limit as nincreases a firm meets the worst of the n standards almostsurely and expected quality conditional on meeting thestandard equals E6Q7, so the expected MSE in the labelingequilibrium just equals the variance of F .

(v) For any firm of type q, consider the largest realizedstandard s such that q ≥ s and the smallest realized stan-dard s̄ such that s̄ ≥ q. Given s and s̄, in a nonlabeling equi-librium, if the firm certifies, then it has expected quality

E6Q � s ≤ Q < s̄7 and if it does not certify, then it still hasexpected quality E6Q7, so nonlabeling is an equilibrium ifand only if E6Q � s ≤ Q < s̄7 − E6Q7 ≤ c. By the Glivenko-Cantelli theorem, the empirical distribution Gn4s5 of n stan-dards converges uniformly to the theoretical distribution Gas n goes to infinity, so for any � > 0, for any q, max8q −

s1 s̄− q9 < � for sufficiently large n. Therefore, because E6Q �

s ≤ Q < s̄7 ∈ 6s1 s̄7, for any firm of type q, in the limit E6Q �

s ≤ Q < s̄7 = q almost surely. So the condition for a nonla-beling equilibrium is q −E6Q7≤ c for all q, or 1 −E6Q7≤ c.

(vi) Following the same argument as in (v), the conditionfor a symmetric labeling equilibrium is E6Q � s ≤ Q < s̄7 −

E6Q � q ≤ s7≥ c for some q, which converges to q−E6Q �Q ≤

q7≥ c almost surely. Following Lizzeri (1999, Theorem 1), theleft-hand side is increasing in q if F is logconcave (Bagnoliand Bergstrom 2005), so this condition is met for some q ifand only if it holds for q = 1, or 1 −E6Q7≥ c. �

Proof of Proposition 5. (i) Consider a focal labelingequilibrium in which a firm that does not meet the focalstandard instead adopts the highest other standard it meets.The estimation of the focal standard is not affected by thenumber of standards present on the market, so such a focallabeling equilibrium exists if

E6Q �Q ≥ S7−E6Q �Q< S12n7≥ c (26)

andE6Q � S12n ≤Q< S7−E6Q �Q< S12n7≥ c0 (27)

The latter condition is clearly binding and holds for suffi-ciently low c. In such an equilibrium consumers learn thatthe firm did not meet even the lowest standard, Q < S12n,or that the firm met the lowest standard but not the focalstandard, S12n ≤ Q < S, or that the firm met the focal stan-dard, Q ≥ S. In a symmetric labeling equilibrium they learnonly that the firm met or did not meet the lowest standard,Q< S12n or Q ≥ S12n. The former partition is finer so it revealsmore information.

(ii) Suppose the firm is following a focal certificationstrategy of always adopting a standard X even if standardY is tougher. Because consumers know which standard istougher, this is only possible if consumer beliefs “punish”the firm for choosing Y out of equilibrium. But under ourbelief refinement, we assume that any type is equally likelyto have deviated, so the expected quality of adopting Y ishigher and the proposed strategy is not an equilibrium. �

Proof of Proposition 6. (i) Suppose each firm followsthe labeling equilibrium strategy of certifying when possibleand that k of m firms meet the standard and m− k do not.From the Glivenko-Cantelli theorem, the empirical distribu-tion Fm4q5 of m firm qualities converges uniformly to the the-oretical distribution F so limm−→� Q�qm�2m = F −14q5 for any q,where �x� denotes the smallest integer at least as large as x.Hence, the expected value conditional on being in the groupof k firms that certify converges to the expected value condi-tional on having quality Qi ≥ s, limm−→�

∑mj=m−k+1 Qj2m/k =

limm−→�

∫ 1s Q�qm�2m dq/41 − F 4s55 =

∫ 1s F −14q5 dq/41 − F 4s55 =

∫ 1s q dF 4q5/41 − F 4s55 = E6Qi � Qi ≥ s7 for any s. Similarly, the

expected value conditional on being in the group of m − kfirms that do not certify converges to the expected value

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Harbaugh, Maxwell, and Roussillon: Label Confusion16 Management Science, Articles in Advance, pp. 1–16, © 2011 INFORMS

conditional on having quality q < s, limm−→�

∑m−kj=1 Qj2m/

4m− k5= E6Qi �Qi < s7 for any s. Noting that a single devia-tion from the equilibrium strategy has vanishing impact onthe expected value of either group, the limiting condition foreach firm to follow the labeling strategy is E6Qi � Qi ≥ s7 −

E6Qi � Qi < s7 ≥ c for any s. The expected support for theequilibrium over the distribution of possible standards isthen c < E6c̄7, where

E6c̄7= E6E6Qi �Qi ≥ s77−E6E6Qi �Qi < s771 (28)

which is the same as that for a single firm facing a certainstandard.

(ii) Suppose each firm follows a strategy of not labeling.The expected payoff for a single firm is just E6Qi7. If a sin-gle firm deviates, then as discussed our belief refinement isthat the label is treated as good news that concentrates theposterior distribution of Qi on 6s117, where s is distributedaccording to G. Therefore, the payoff to a single firm fromdeviating is E6Qi � Qi ≥ S7− c, so the equilibrium conditionfor nonlabeling is

E6Qi �Qi ≥ S7−E6Qi7 < c1 (29)

which is the same as that for a single firm facing an uncer-tain standard.

(iii) If the standard is certain then consumers by defini-tion learn nothing about the distribution of standards fromwhich firms adopt which labels. Hence, the equilibriumconditions are the same as in the case of a single firm. �

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