Label Confusion: The Groucho Effect of Uncertain Standards. Rick Harbaugh, John W. Maxwell, and Beatrice Roussillon.

Transcription

1 Label Confuion: The Groucho Effect of Uncertain Standard Rick Harbaugh, John W. Maxwell, and Beatrice Rouillon November 15, 21 Abtract Label certify that a product meet ome tandard for quality, but often conumer are unure of the exact tandard that the label repreent. Focuing on the cae of eco-label for environmental quality, we how how even mall amount of uncertainty can create conumer confuion that reduce or eliminate the value to firm of adopting voluntary label. Firt, conumer are mot upiciou of the tandard for a label when a product with a bad reputation ha it, o label are often unperuaive at howing that a eemingly bad product i actually good. Second, label proliferation multiplie the effect of uncertainty, cauing the informativene of label to decreae rather than increae. Third, uncertainty make labeling and non-labeling equilibria more likely to coexit a the number of label increae, o conumer face greater trategic uncertainty over how to interpret the preence or abence of a label. Finally, a label can be either legitimitized or poiled for ue by other product when a product with a good or bad reputation diplay it, o firm have an incentive to adopt label trategically to manipulate uch information pillover, which further exacerbate label confuion. Manager can reduce label confuion by upporting mandatory labeling or by undertaking invetment to make certain label focal. JEL Claification Categorie: L15, L21, D82 Key Word: Eco-label, quality label, dicloure, certification, peruaion, tandard proliferation, elf-regulation For their helpful comment we thank Mike Baye, Oliver Board, Harrion Cheng, Michael Fihman, Ivan Patine, and eminar and conference participant at the Federal Trade Commiion, the Self-Regulation Conference at Harvard Univerity, the Informing Green Market Conference at the Univerity of Michigan, the International Indutrial Organization Conference, the Mid-Wet Theory Conference, the Univeritie of Toronto, Michigan, Wetern Ontario, and Lauanne, the Frontier in Environmental Economic and Natural Reource Management Meeting of the French Economic Aociation at the Touloue School of Economic, and the Conference on Public Economic at the Univerity of the Mediterranean. Thi paper ha alo circulated under the title The Groucho Effect of Uncertain Standard. Harbaugh, Maxwell: Kelley School of Buine, Indiana Univerity; Rouillon: Department of Economic, Univerity of Mancheter.

2 1 Introduction When product quality i unobervable, quality label are an important mechanim for firm to prove their quality to conumer. However, conumer are often unure of the exact quality tandard that a label repreent i it a relatively eay or diffi cult tandard? Thi i particularly important for eco-label for certifying environmental quality ince environmental impact i often a credence good that conumer cannot directly oberve and ince there ha been a proliferation of numerou different label for firm to chooe from. 1 Depite attempt by government, indutry group, and NGO to clarify label tandard, confuion by conumer i widely blamed for undermining the credibility of eco-label, thereby reducing the incentive for their adoption by firm. 2 We examine thi iue of how conumer uncertainty about label tandard affect the managerial deciion to certify a product of given environmental quality with an eco-label. When label tandard are uncertain, conumer face a joint etimation problem. If they ee a label on a product they mut etimate whether the label i more indicative of a high quality product, or of an undemanding tandard for the label. For intance, when a car buyer ee a Low Emiion Vehicle label, he will update both her etimate of the car environmental quality and of the meaning of the Low Emiion Vehicle label. If the car i a large SUV then the updating on both dimenion i likely to be very different than if the car i a mall hybrid. Jut a an employer mut jointly etimate the ability of a job applicant and the value of hi degree, or a tourit mut jointly etimate the quality of a hotel and the toughne of the local rating ytem, a conumer cannot rely on the mere preence of an eco-label to determine a product environmental quality. We invetigate how thi joint etimation problem affect the power of label to reduce information aymmetrie about product quality. We find that concern over the effect of uncertain labeling tandard i well founded. In addition to the direct information lo due to the uncertainty, the optimal repone of conumer and firm lead to further information loe that can greatly undermine the value of voluntary labeling. Firt, labeling i mot valuable when conumer think that a product i likely to be bad but in fact it i certifiably good. But when tandard are uncertain, if a product i expected to be low quality then there i a Groucho effect in which conumer infer that the labeling tandard i probably weak if uch a product can meet it. Jut a Groucho Marx famouly joked that he did not want to join a club with tandard o low a to accept him a a member, a firm with a bad reputation gain little from labeling. Therefore the incentive for labeling i undermined when the problem of information aymmetry, and hence the potential gain from labeling, i greatet. 1 Ecolabelling.org lit over 3 eco-label in ue. Many of thee apply to multiple product categorie and ue varying tandard for the categorie, e.g., only 11% of light fixture are eligible for the U.S. EnergyStar Label for energy aving while 89% of televiion are eligible for the ame label (Wahington Pot, February 22, 21). 2 A a report prepared for the World Bank noted, The diverity of ecolabel (which reflect the multitude of certification cheme) can be confuing to conumer and weaken the credibility of all label, (Ficher et al., 25). See alo What do label really tell you? A eco-label proliferate, o do doubt, Wall Street Journal, April 2, 29. The impact of label confuion on adoption incentive i een for the E.U. Flower label where no product by major manufacture have been certified for ome product categorie (ee European Eco-label Catalogue at and urvey indicate that undertanding of the label i far lower than of other regional and national eco-label (Sto and Strandbakken, 25). 1

3 Second, the preence of multiple label with different tandard hould create more opportunity for firm of different quality level to certify themelve and thereby reduce information aymmetrie. But when tandard are uncertain, the proliferation of label ha the oppoite impact. Since conumer do not know which tandard are eay and which are diffi cult, a label only prove that a firm ha met the eaiet of the different tandard, even if the firm ha met a higher tandard. Thi both reduce the informativene of labeling and alo reduce the incentive to be certified. A the number of different tandard rie, we find that the informativene of labeling goe to zero and that a non-labeling equilibrium alway exit for a uffi ciently high number of tandard. Third, uncertain tandard aggravate the problem of trategic uncertainty due to the coexitence of labeling and non-labeling equilibria. Multiple equilibria can arie with voluntary labeling becaue if conumer expect a firm to have a label then lack of one i particularly damaging to the firm etimated quality, but if labeling i not expected then the firm loe le from not having a label and can ave on certification cot. When tandard are known, thi multiplicity of equilibria diappear under a regularity condition a the number of tandard increae. But with uncertain tandard we find intead that the multiple equilibrium problem i aggravated by more label and that labeling and non-labeling equilibria alway coexit for a uffi ciently large number of label unle certification cot are o high that only non-labeling i an equilibrium. Finally, we find that uncertainty over tandard generate information externalitie between firm that can lead to trategic behavior that further reduce the informativene of label. A firm can legitimize or poil a label for ue by other firm depending on whether the firm ha a good or bad reputation. Conequently direputable firm have an incentive to adopt the ame label a reputable firm, while reputable firm intead have an incentive to avoid label adopted by direputable firm. Such managerial trategizing make it diffi cult for conumer to rely on the exiting reputation of firm a a imple way to learn about different tandard, and give certifier an incentive to promote early adoption among firm of recognized high quality. 3 A key factor in conumer uncertainty over labeling tandard i that the ource of a label or certificate i often unclear. For intance, the imilar-appearing FSC and SFI label are two of the main eco-label for foret product, but one i controlled by an environmental NGO and the other by an indutry-backed NGO. The potential for uch confuion i widepread of the 363 different labeling cheme tracked by ecolabelling.org, 29 are run by NGO, 59 are run by indutry group, 53 are run by government, and 42 are run by for-profit firm. Moreover, even when the ource of a label i clear, the objective of certifier, and hence the likely diffi culty of their tandard, are often unclear. 4 To capture thee uncertaintie, we model conumer a having a prior ditribution of the labeling tandard() that can be arbitrarily precie or diffue, and arbitrarily kewed toward higher or lower 3 An E.U. report on the diffi culty of getting the E.U. Flower Label etablihed in the laundry detergent market tate, Moreover, a real break-through call for one or more of the multinational to apply for the eco-label on their main product... it will probably have a nowball effect on the market. (Maden et al., 22). 4 Shaked and Sutton (1981) dicu the varying objective of indutry group, and Maxwell (21) dicue the unclear objective of NGO. 2

4 level. For intance, conumer might believe that an eco-label tandard i likely to be eay or diffi cult, but be unure of exactly how eay or diffi cult, or they might be completely uncertain of the diffi culty. Thi ditinguihe our approach from mot of the literature in which the labeling tandard are aumed to be common knowledge. Our model i mot appropriate for conumer product market where buyer are unlikely to be well-informed, rather than for market for raw material or intermediary product where buyer have trong incentive to acquire exact information on the ource and meaning of different tandard. Since label confuion reduce the value of labeling a a trategy to inform conumer about product quality, firm with high environmental quality might want to take variou managerial action to reduce label confuion. Mot directly, invetment in clarifying label tandard can enhance both the informativene and likelihood of labeling, thereby allowing conumer to make more informed deciion. 5 Indutry group, government, for-profit labeler, or NGO intereted in promoting label adoption can alo try to make a particular tandard focal in the ene of publicizing it and making conumer expect that firm will adopt the tandard if they meet it. Thi can reduce or eliminate the information loe caued by label proliferation and by trategic uncertainty over which equilibria are being played by firm. For intance, look for the label campaign can be interpreted a encouraging conumer to focu on particular label among the multiplicity of poible label. Government and indutry attempt to reduce the number of label or harmonize or tandardize different voluntary tandard alo have thi effect. 6 Thee reult on label confuion add to the literature on verifiable meage peruaion or dicloure game (ee the urvey by Dranove and Jin, 21), 7 and in particular to the debate on mandatory v. voluntary dicloure. The claic unravelling reult find that mandatory dicloure i unneceary ince even thoe with bad information have an incentive to prove they do not have wore information. 8 However, a recognized early on, voluntary dicloure might be inuffi cient if 5 Additional gain can arie from a quality repone to label a found by Jin and Lelie (23), but we take quality a exogenou in our model and focu on the certification deciion. Lerner and Tirole (26) allow firm to adjut their quality in repone to tandard. 6 In repone to Canadian regulation enforcing a ingle definition for organic, a pokeperon for the Organic Trade Aociation tated: It a conumer dream. When they ee an organic claim out in the marketplace, it ha a very trict definition, the government i behind it, and everybody i meeting the ame tandard. (Montreal Gazette, February 17, 29). More generally, the EU ha been attempting to harmonize eco-label acro countrie in the Propoal for a Regulation of the European Parliament and of the Council on a Community Ecolabel Scheme, SEC(28) 2118 and SEC(28) Regarding private effort, the ISEAL Alliance of certifier ha tried to make tandard for eco-label more tranparent in order to reduce conumer confuion ( Of coure, not all firm prefer harmonization and tranparency. Firm who cannot meet labeling tandard or who prefer not to pay the cot can potentially benefit from more label confuion due to label proliferation. 7 The retriction of meage to certain type, e.g., a firm cannot how a label it i not qualified for, ditinguihe thi literature from cheap talk game. Communication i till poible through pure cheap talk if there are multiple dimenion of quality (Chakraborty and Harbaugh, 21), but in thi paper we follow the tandard aumption of a ingle dimenion. 8 Mandatory dicloure i ditinct from the impoition of minimum quality tandard that can exclude firm from the market (Leland, 1979). The application to environmental quality tandard i conidered by Arora and Gangopadhyay (1995) and Lutz, Lyon, and Maxwell (2), and the application to eco-labeling i analyzed by Amacher, Kokela, and Ollikainen (24) and Mattoo and Singh (1994). 3

5 dicloure i cotly (Vicui, 1978; Jovanovic, 1982; Verrecchia, 1983). Our analyi contribute to thi debate by howing that the combination of cotly dicloure and uncertainty i particularly diruptive to voluntary dicloure, and that the effect are exacerbated when there are multiple label. The idea that the imperfect nature of label can have an important effect on dicloure trategie appear in other paper that differ from our in other key repect. Sinclair-Degagne and Gozlan (23) conider binary tet of environmental quality that are known by conumer to vary in accuracy and allow firm to chooe whether to take the more accurate or le accurate tet. Lerner and Tirole (26) and Farhi, Lerner, and Tirole (28) conider tandard that are known to be of differing diffi culty and aume the firm i uncertain of it own quality, o that from the firm perpective there i uncertainty over whether a particular tandard will turn out to be too diffi cult. Thee paper focu on how firm can bet how off their quality by chooing tandard that are known to be either more or le diffi cult, and find that multiple tandard increae the ability of firm to provide information about their quality. But for eco-label we believe that our aumption that conumer are unaware of the underlying tandard embodied in a certification label i more appropriate. Becaue of thi difference in aumption, other paper have not addreed the main iue that we examine, including confuion due to label proliferation, legitimizing and poiling of label, and the role for mandatory dicloure or focal equilibria in reducing confuion. A dicued later, the exception i Fihman and Hagerty (199) who conider cotle dicloure of one of multiple noiy ignal of high or low quality and whoe reult are cloely related to our finding regarding focal equilibria. Our analyi i for the cae where label certify that a tandard ha been met and provide no more detailed information. Voluntary label typically take thi pa-fail form in which a certificate or label i awarded or not, even in cae where more detailed information could be provided. For intance, of the 1 non-government eco-label for carbon emiion lited at the ecolabelling.org webite, all but one provide a imple label of approval without more detailed information about the product carbon footprint. The prevalence of imple label could reflect the need to reduce information proceing by conumer. Or, conitent with the theoretical literature, it could reflect the incentive of certification intermediarie to withhold more detailed information when labeling i voluntary (Lizzeri, 1999). Given the prevalence of the pa-fail form and the multiple reaon for it, we take the form a given in our analyi. We dicu our reult in the context of eco-labeling, but they apply to any certification or labeling cheme about which uncertainty over a pa-fail tandard exit. More broadly, the iue we invetigate arie in any ituation in which oberver mut jointly update their belief about an agent quality and an uncertain quality tandard. For intance, conitent with Groucho Marx concern, our analyi how that a direputable individual might indeed find little benefit from joining a club becaue the very fact of hi memberhip downgrade the perceived tandard of the club. The paper proceed a follow. In Section 2 we develop the baic model with one tandard, define the condition for the exitence of both labeling and non-labeling equilibria, how the exitence of 4

6 the Groucho effect and analyze it impact on informativene. In Section 3 we analyze the multitandard cae, howing that the qualitative reult of Section 2 continue to hold, and that the impact of the Groucho effect i worened. In Section 4 we conider trategic interaction between firm when there are multiple tandard and information pillover. In Section 5 we preent our concluion. 2 Bae Model We conider a firm deciion to have it product certified that it meet a quality tandard for a eco-label. The product exogenouly given (environmental) quality Q i ditributed according to ditribution F with full upport on [, 1] and with correponding denity function f. 9 The firm know the realized value q of Q, but conumer only know it ditribution F. There exit a label with tandard S which i ditributed according to the ditribution G with full upport on [, 1] and with correponding denity function g. The firm know the realized value of S. If conumer alo know the realized value we ay the tandard i certain and if they only know the ditribution G we ay the tandard i uncertain. For implicity we aume Q and S are independent. In thi ection we aume that there i only one label. If q the firm ha a choice to obtain a label or not, i.e., a firm that meet the labeling tandard need not chooe to be certified for the label. If q < the firm doe not meet the tandard o it ha no choice. Certification ha a fixed cot c > that i independent of q or 1 and capture any fee to the certifier and any other cot, e.g., the expene of documenting quality control procee, auditing and teting cot by the certifier, and the opportunity cot of providing pace on the product packaging for the label. 11 We aume the payoff to the firm i the expected quality of it product a etimated by conumer le the certification cot if it chooe to certify. Since we allow for general F, all of the reult hold a long a the firm payoff i a trictly increaing function of quality a etimated by conumer. Conumer concern for environmental quality could capture direct financial gain to the conumer, e.g., aving from lower energy ue, or internalized ocial benefit, e.g., knowing that foret are protected. 9 The exogeneity aumption applie bet to quality feature that are not o eential to conumer that the firm will immediately change it product in repone to a label tandard. While eco-labeling organization typically hope for product change over time, uch hope depend on the ucceful initial adoption of the eco-label for exiting product. Our model i focued on thi label adoption deciion. 1 Since quality q i exogenou thi cot i purely a certification cot rather than a cot to improve the product. We aume the certification cot i alo independent of the tandard but in ome cae the teting component of certification cot might be more expenive when the tandard i tougher. Thi would trengthen our reult that conumer are upiciou that a label repreent a low tandard and aggravate the negative effect of tandard uncertainty on labeling incentive. 11 The cot of certification for eco-label can be a ubtantial fraction of total cot (Vitali, 22). The main aociation of mall and medium buinee in the E.U. lit it primary requeted reviion in eco-label policy a, An overall reduction of the cot, in particular the cot of the technical tet required in order to how the repect of the criteria. (See UEAPME Poition on the Reviion of the Eco-label Regulation, UEAPME, November, 28). Note that we are not differentiating between whether the manufacturer or retailer i paying the certification cot (Guo, 29). 5

7 The expected quality of a product conditional on quality Q exceeding the tandard S, where the value of S i ditributed according to G, i E[Q Q S] = qdf (q)dg(), (1) df (q)dg() and imilarly the expected quality conditional on not meeting the tandard i E[Q Q < S] = qdf (q)dg(). (2) df (q)dg() When i known thee conditional expectation reduce to E[Q Q ] = qdf (q)/ df (q) and E[Q Q < ] = qdf (q)/ df (q). Before analyzing the equilibrium behavior of firm, firt conider the effect of uncertainty about the tandard on conumer information uppoing that all firm meeting the tandard obtain a label. Becaue the label provide information about both Q and S, it provide le information about Q alone than when S i known. For intance, for the cae of uniform F and G, the expected meanquared-error of conumer etimate of Q fall from 1/12 to 1/24 when S i certain but fall only to 1/18 when S i uncertain. A the following propoition confirm, thi pattern hold for general F and G. For particular realization of S, e.g., for very high or low, certain tandard can be le informative than uncertain tandard, but on average a certain tandard i more informative. Propoition 1 Suppoe all eligible firm are labeled. The expected informativene of the label i lower if the tandard i uncertain than if it i certain. Proof. All proof are in the Appendix. Clearly, if the objective of firm in affi xing a label to their product i to convey information about quality to conumer, it i deirable that conumer undertand the meaning of the label. Our objective in the preent paper i to explore how the equilibrium labeling deciion of firm aggravate the uncertainty problem to create further confuion among conumer. Our equilibrium concept i perfect Bayeian equilibrium ubject to a belief-refinement introduced below. In a labeling equilibrium a firm whoe product meet or exceed the labeling tandard alway obtain a label, o the lack of a label implie failure to meet the tandard. Conumer belief ued to update product quality are conitent with thi firm trategy in equilibrium, o the equilibrium condition i imply that the benefit from labeling i higher than the cot, 12 E[Q Q S] E[Q Q < S] c. (3) Since E[Q Q S] > E[Q Q < S] uch an equilibrium exit for c uffi ciently mall and doe not exit for c uffi ciently large. In a non-labeling equilibrium a firm doe not certify product quality 12 If a labeling equilibrium exit a continuum of equilibria alo exit where only type in ome ubet X [S, 1] obtain a label with the knife-edge reult that E[Q Q X] E[Q Q / X] = c. We do not analyze thee equilibria in which all type are indifferent between labeling and non-labeling. 6

8 even if it can, o lack of a label repreent no new at all, implying the prior etimate E[Q] i unchanged. Labeling in the non-labeling equilibrium i an unexpected, out of equilibrium action. We refine the perfect Bayeian equilibrium et by auming that conumer believe that uch an action i equally likely to have been by any type that meet the tandard, o an unexpected label i good new that generate the updated etimate E[Q Q S]. 13 Therefore the equilibrium condition for the non-labeling equilibrium i E[Q Q S] E[Q] c. (4) Since E[Q Q S] > E[Q] uch an equilibrium doe not exit for c uffi ciently mall and doe exit for c uffi ciently large. Comparing the two condition, ince E[Q Q < S] < E[Q] the left hand ide of (3) i greater than the left hand ide of (4), implying for any given c one or the other of thee two equilibria exit. Both condition are atified imultaneouly, indicating the exitence of multiple equilibria, when E[Q Q S] E[Q] c E[Q Q S] E[Q Q < S], (5) which i poible again by the fact that E[Q Q < S] < E[Q]. Regarding when one of the equilibria i unique, the labeling condition (3) cannot be atified for c uffi ciently large and the non-labeling condition (4) cannot be atified for c uffi ciently mall. We tate thee reult a the following propoition where the proof verifie the inequalitie tated above. Propoition 2 With certain or uncertain labeling tandard, there exit c < c 1 uch that a non-labeling equilibrium exit iff c > c, a labeling equilibrium exit iff c < c, and both equilibria exit iff c [c, c]. To ee the differential effect of certainty and uncertainty, firt conider Figure 1(a) where F and G are uniform o that the prior are (E[S], E[Q]) = (1/2, 1/2). The updated expectation of S and Q for Q S and Q < S are given by the center of ma of the upper and lower triangle repectively, o E[Q Q S] = 2/3 and E[S Q S] = 1/3, while E[Q Q < S] = 1/3 and E[S Q < S] = 2/3. Therefore meeting the tandard i good new about Q and bad new about S, while failing to meet the tandard i the oppoite. We term the downward adjutment of the etimate of S due to a label the Groucho effect achieving the goal diminihe the goal itelf. And we term the upward adjutment to the etimate of S due to lack of a label the revere Groucho effect failing to meet the goal enhance the goal itelf. Thee adjutment lead to a moderating effect on the etimate of Q where conumer are both le impreed by a label and le dicouraged by lack of a label. Thi can be een by comparion with Figure 1(b) where F and G are till uniform and the realized value of the tandard i known to conumer. The updated quality etimate baed on meeting the tandard or not, E[Q Q ] = (1 + )/2 and E[Q Q < ] = /2, are given repectively by the upper and lower line in the figure. Integrating thee etimate of Q over the different value of we get the 13 There i no variation in the incentive of different type to certify o, a dicued by Bank and Sobel (1987), tandard forward-induction argument do not indicate that one type or another i a more plauible ource of the unexpected action. 7

9 Figure 1: Updated Quality and Standard Etimate ex ante expected qualitie for a certain tandard of E[E[Q Q ]] = 3/4 and E[E[Q Q < ]] = 1/4. Thee are the average expected qualitie for the certain tandard cae where i known, and they are the expected qualitie that would reult for the uncertain tandard cae if the conditional ditribution of S did not become le favorable when Q S and more favorable when Q < S. Comparing thee expectation with thoe in Figure 1(a), the example illutrate the general rule, verified in the proof of the following propoition, that E[E[Q Q < ]] < E[Q Q < S] < E[Q] < E[Q Q S] < E[E[Q Q ]], (6) o meeting the labeling tandard i better new on average if the tandard i known for ure than if it i uncertain, and not meeting it i wore new on average if the tandard i known for ure than if it i uncertain. The relationhip in (6) implie that condition (3) for a labeling equilibrium i more trict with an uncertain tandard than it i on average for a certain tandard, and that condition (4) for a non-labeling equilibrium i le trict with an uncertain tandard than it i on average for a certain tandard. Thu, the Groucho effect make the condition for the labeling equilibrium harder to meet, and the revere Groucho effect make the condition for the non-labeling equilibrium eaier to meet. Propoition 3 The expected range of certification cot upporting a labeling (non-labeling) equilibrium i maller (larger) if the tandard i uncertain rather than certain. To gain further inight into thee difference, conider Figure 2 where G i uniform and F follow the Beta ditribution B(q; a, b). For the figure we retrict either a = 1 and b 1, or a 1 and b = 1, 8

10 Figure 2: Labeling (L) and Non-Labeling (N) Equilibrium Region o that the ditribution i repectively concave (a bad reputation firm with low expected quality) or convex (a good reputation firm with high expected quality) and i uniquely determined by it mean E[Q] = a/(a + b). 14 Figure 2(a) how the cot cutoff c = E[Q Q S] E[Q Q < S] for the boundary of the labeling region (L) from the equilibrium condition (3), and the cot cutoff c = E[Q Q S] E[Q] for the boundary of the non-labeling region (N) from the equilibrium condition (4). Figure 2(d) how the certain tandard cae where the correponding region are determined by the expected value E[c] = E[E[Q Q ]] E[E[Q Q < ]] and E[c] = E[E[Q Q ]] E[Q] baed on averaging out the exact value for different realization of S =. The figure illutrate the reult from Propoition 2 that uncertainty over the tandard make label adoption le likely in that, relative to the cae of certain tandard, the equilibrium range for the labeling equilibrium i alway maller and the equilibrium range for the non-labeling equilibrium i alway larger. Conider the effect of prior expectation about firm quality on labeling incentive. The Groucho effect i tronget for firm with bad reputation becaue conumer are upiciou of any tandard that uch a firm can meet, and imilarly the revere Groucho effect i tronget for firm with good 14 For intance, for integer value of a and b, if a = 1 and b 1 then f(q) = b(1 q) b 1 and if the oppoite then f(q) = aq a 1. Therefore the Beta ditribution reduce to the uniform ditribution for a = b = 1, a falling triangle ditribution for a = 1 and b = 2, and a riing triangle ditribution for a = 2 and b = 1. 9

11 reputation ince conumer infer that failure to obtain a label implie that the tandard for the label wa very diffi cult. Therefore the incentive to obtain a label i undermined the mot for both good and bad reputation firm. Since the Groucho and revere Groucho effect are weaket for intermediate firm whoe quality i mot uncertain, the impact of certification on expected quality i the tronget, and uch firm have the mot incentive to obtain a label. 15 Thi i een in Figure 2(a) where the labeling region i at a minimum and the non-labeling region i at a maximum for E[Q] approaching or 1. When tandard are certain there i no joint updating about both quality and tandard o bad reputation firm who are actually of high quality can effectively certify their quality, and good reputation firm who fail to certify their quality when expected to can be heavily penalized by conumer. Therefore, a een in Figure 2(d) the labeling equilibrium region i comparably large for all firm. The non-labeling region i mallet for bad reputation firm becaue they have a trong incentive to certify their quality even when not expected to, while good reputation firm can rely on their good reputation and ave the certification cot. Thee reult on the role of prior expectation imply that firm with bad reputation for environmental quality that can in fact meet relatively tringent tandard have the mot to gain from more tranparent labeling tandard. A will be een in the following ection, and a illutrated in the remaining panel of Figure 2, the divergence in labeling incentive between the certain and uncertain cae, and the differential effect on incentive baed on prior expectation, become increaingly tark a the number of tandard increae. 3 Multiple Label We now conider how label confuion i affected by the availability of multiple label with different tandard. A noted in the introduction, the proliferation of different label for ome product i quite extreme. For intance, the webite ecolabelling.org lit over 3 different label for foret product, over 4 different label for textile, and over 1 different label for food product. It might eem that more option hould offer firm more way to how off their quality, o that label uage increae. But the proliferation of tandard i often blamed for creating confuion among conumer that weaken the credibility of all label and reduce label adoption (Ficher et al., 25). Thi ugget that an increae in label can aggravate the underlying problem of uncertain tandard. To gain inight into how the proliferation of label interact with tandard uncertainty, we now aume that there are n 1 label with different tandard drawn independently from the ame ditribution G with the ame cot c. Following tandard notation for order tatitic we denote the random variable repreenting the ith lowet realized tandard by S i:n and it ditribution by G i:n, o that G 1:n repreent the ditribution of the wort tandard and G n:n repreent the ditribution 15 The functional form of F in the figure implie that F i mot diffue for E[Q] = 1/2. Regarding mean-preerving pread in F, for the cae of uniform G it can be hown that they increae the incentive to dicloe both for certain and uncertain tandard. From a ociological perpective, Phillip and Zuckerman (21) find that middle tatu type have the mot incentive to meet ocial norm given the uncertainty of their tatu. 1

12 of the bet tandard. The firm quality and the realized diffi cultie of the different tandard are only known by the firm, while F, G, c, and n are alo known by conumer. For implicity we aume that if a firm meet the tandard for multiple different label it can only adopt one of them. A long a attaining and diplaying extra label i cotly, thi aumption doe not affect our main qualitative reult. 16 We alo retrict attention initially to a ymmetric labeling trategy where the firm adopt the toughet label that it meet independent of any arbitrary propertie of the ex ante identical tandard. Any other equilibrium trategy that i imilarly ymmetric, uch a alway adopting the econd toughet tandard when poible, provide equivalent information about firm quality to conumer. For now we do not conider focal equilibrium trategie where it i aumed that a particular label will alway be adopted if the tandard for it i met. Since conumer do not know which of the label ha a more diffi cult tandard, a label under a ymmetric labeling trategy only prove that a firm ha met the eaiet tandard, even if the firm ha in fact met the bet tandard. Hence the incentive to obtain a label or not are exactly the ame a in the previou ection, with the only exception that we replace the random variable S with the random variable S 1:n repreenting the weaket of the n tandard. Therefore, following condition (3) and (4), for uncertain tandard a ymmetric labeling equilibrium exit if and only if and a non-labeling equilibrium exit if and only if E[Q Q S 1:n ] E[Q Q < S 1:n ] c (7) E[Q Q S 1:n ] E[Q] c. (8) For certain tandard the condition are quite different becaue conumer know the diffi culty of the tandard that wa met, and alo know the diffi culty of tandard that were not met. We define a labeling equilibrium for certain tandard a an equilibrium in which any of the different label are adopted. For intance, a firm might find a label with a high tandard worth the certification cot, but not a label with a lower tandard (e.g., Vicui, 1978; Jovanovic, 1982). A labeling equilibrium exit if and only if ome firm type find it more profitable to pay the certification cot and prove that they meet a particular tandard (and none higher) than to be thought of a coming from the whole range below that tandard, 17 i.e., if and only if max {E[Q i:n Q i+1:n ] E[Q Q < i:n ]} c, (9) i=1,..,n 16 The retriction to diplaying one label doe not affect the condition for exitence of labeling and non-labeling equilibria if there are contant or diminihing return to label. Thi hold, for intance, for uniform F and G. But if return are increaing over ome range, then it might be worthwhile to be certified by multiple label even if it would not be worthwhile to be certified by one label, e.g., a retaurant might diplay multiple label in it window. Since the marginal value of any label goe to a the number of label increae, the limiting reult of thi ection are unaffected by the poibility of howing multiple label. 17 Given that firm meeting the label with tandard i adopt it, firm meeting a label with an even higher certain tandard will alo want to adopt that label, o the binding contraint i for the label with tandard i. 11

13 where we define n+1:n = 1. The condition for a non-labeling equilibrium i impler ince lack of a label alway give a payoff of E[Q], implying that the incentive to unexpectedly adopt a label i alway highet for thoe meeting the highet tandard. In particular, under our belief refinement a non-labeling equilibrium exit if and only if E[Q Q n:n ] E[Q] c. (1) A hown in Figure 2, thee condition imply that behavior with uncertain tandard diverge dramatically from that with certain tandard. A the number of label n increae conumer become increaingly upiciou of the value of a label and the expected quality conditional on having a label E[Q Q S 1:n ] fall. Therefore, comparing panel (a) with panel (b) and (c), a n increae the non-labeling equilibrium region baed on equation (8) expand. In the limit condition (8) converge to E[Q] E[Q] c o a non-labeling equilibrium alway exit for c >, which i particularly damaging to bad reputation firm who loe the opportunity to diprove conumer expectation. Regarding the labeling equilibrium, if conumer expect a firm to obtain a label and the firm doe not, then the expected quality conditional on not having any label E[Q Q < S 1:n ] alo fall a the number of label increae. Since both E[Q Q S 1:n ] and E[Q Q < S 1:n ] are decreaing in n, the labeling equilibrium region baed on (7) can expand or contract, and a een in the figure in thi example the region expand. In the limit condition (7) converge to E[Q] c, o a labeling equilibrium only exit if firm reputation are uffi ciently good. 18 Thi labeling equilibrium provide almot no information on firm, but good reputation firm till feel compelled to obtain a label to avoid being thought of a very low quality. In contrat, comparing panel (d) with panel (e) and (f), for certain tandard a n increae the labeling incentive for bad reputation firm become increaingly trong, while the labeling incentive for good reputation firm diappear. The following propoition how that thee pattern hold generally for uncertain tandard and, following Lizzeri (1999, Theorem 1), hold for certain tandard a long a the ditribution of F i log-concave. 19 Propoition 4 Suppoe there are n label with i.i.d. tandard. If tandard are uncertain, (i) the upport of a non-labeling equilibrium i increaing in n, and, in the limit a n increae: (ii) non-labeling i an equilibrium for all c >, (iii) ymmetric labeling i an equilibrium if and only if E[Q] c, and (iv) the ymmetric labeling equilibrium i uninformative. If tandard are certain, in the limit a n increae: (v) non-labeling i almot urely an equilibrium if and only if E[Q] 1 c, and (vi) for F log-concave, labeling i almot urely an equilibrium if and only if E[Q] 1 c. 18 Note that at E[Q] = 1 the firm quality i perfectly revealed and the incentive to label diappear, but our analyi aume Q ha full upport on [, 1] o the analytic reult and the figure are for the range E[Q] (, 1). 19 A a tep in a more general analyi, Lizzeri (1999) analyze the cae where certification cot are given and each quality level can be certified. In our cae in the limit a the number of label increae there i eentially a different label for every quality level, o the problem converge to that analyzed by Lizzeri. Note that logconcavity i equivalent to a decreaing revere hazard rate and i atified by mot commonly ued ditribution including the Normal, Uniform and Beta ditribution (Bagnoli and Bergtrom, 25). 12

14 Recall that Propoition 1 howed that certification i alway le informative when tandard are uncertain. Propoition 4(iv) how that for large n thi reult i even tronger in that, even though labeling can till be an equilibrium for large n, the informativene of a label when tandard are uncertain goe to zero, i.e., etimate of Q are no better than the prior etimate without a label. Manager find themelve in a labeling paradox. Labeling i completely wateful ince in equilibrium the firm prove that it i not of the lowet type, but the firm doe not benefit relative to prior expectation and conumer do not learn any information ince the firm being of the lowet type i a zero probability event anyway. Thi contrat with the reult for certain tandard where a n increae a label become highly informative and the only reidual uncertainty arie from firm who do not have a label becaue of the certification cot. Thi ugget that a the number of labeling organization expand organization intereted in promoting eco-label hould try to limit the number of label or better educate conumer about label tandard. That labeling provide no new information a n increae i related to the finding by Lizzeri (1999) that a certification intermediary who i intereted in maximizing profit from certification will often chooe the lowet poible tandard with the reult that there i no net gain in information to conumer. Since a firm that doe not meet the tandard will be thought of a extremely low quality, firm are willing to pay a high cot for the certificate, and ince the certificate i o eay, almot all of them are able to pay for the certificate and receive it. Therefore a profit-maximizing certification intermediary unintereted in informing conumer benefit the mot from a low tandard. Our model differ in the aumption that there are multiple exogenou labeling tandard rather than an endogenou tandard choen by a profit-maximizing certification intermediary, and that there i a fixed cot to certification rather than a profit-maximizing price et by the intermediary. Neverthele we find the ame reult that a the number of label grow conumer learn little from certification even a firm feel forced to expend ubtantial reource on it. With multiple tandard one tandard i ometime focal or alient in that conumer expect firm to adopt the tandard if they are able to, even if they alo meet another potentially more demanding tandard. For intance, in many European countrie regional or national eco-label appear to be focal relative to the E.U. Flower Label, e.g., the Nordic Swan label and German Blue Angel label are more widely adopted for almot all product categorie. Given the focality of thee label and that conumer do not know which labeling tandard are tougher, conumer might infer that a firm which diplayed the E.U. Flower label wa only able to attain it and not the focal label. It might eem that information flow will decreae if firm are expected to chooe a focal tandard rather than the one they know to be toughet. To ee how a focal tandard can increae rather than decreae information flow, we now conider focal labeling trategie baed on arbitrary propertie of the label that are unrelated to their diffi culty. In uch a trategy there i one label, ay label X, that a firm i expected to adopt if it can. If the firm adopt another label, ay label Y, then it i aumed that it could not meet label X and that label Y wa the bet of the other label it did meet. For certain tandard, a firm will clearly certify whichever label i toughet o any equilibrium baed on focal trategie will break down. But for uncertain tandard, conumer do not know which label i tougher o uch a focal labeling equilibrium i poible. Such an equilibrium i more informative 13

15 than a ymmetric labeling equilibrium a the following propoition how. 2 Propoition 5 Suppoe there are n label with i.i.d. tandard. (i) If tandard are uncertain and c i uffi ciently low there exit a focal labeling equilibrium that i more informative than the ymmetric labeling equilibrium. ii) If tandard are certain a focal labeling equilibrium cannot exit. The focality of a tandard eliminate the problem caued by multiplicity of voluntary tandard. The reult i then imilar to the n = 1 cae in that there i no degradation of the expected diffi culty of the tandard, but it i actually better ince firm who do not meet the focal tandard can till provide information to conumer by meeting a different tandard. A dicued in the introduction, thi reult provide a role for indutry group, government, and NGO in not jut etting and clarifying tandard, but in attempting to make particular tandard focal. Look for the label campaign can help induce an equilibrium where conumer expect a particular tandard to be ued, and look le favorably on adoption of other label. The key i not necearily that the focal label ha a higher tandard, or that the tandard be certain, but imply that there i a ingle tandard which conumer expect firm to try to attain. Thi reult ha important implication for the debate over the role of indutry-ponored label aimed at environmental and or ocial apect of product quality. It i common for NGO to criticize the introduction of indutry-ponored label, often citing them a embodying lower quality tandard than exiting NGO label. However, if the indutry label are introduced a a repone to label proliferation, and if the indutry ucceed in making it label focal, then there can be a gain in information to conumer. Therefore it might be trategic for NGO to ettle for le demanding label that have a greater chance of becoming focal. Our reult on focal certification equilibria i cloely related to a finding by Fihman and Hagerty (199) who analyze a peruaion game with cotle dicloure where there are multiple noiy ignal about whether an invetment project i profitable or not, and aume that a firm can only reveal one of them. Similar to our reult they find that a lexicographic equilibrium i mot informative in which a firm releae the firt ignal that i favorable in accordance with a et order that i anticipated by receiver, o that releaing another favorable ignal i therefore evidence that the firt ignal wa not favorable. 21 An alternative to the ue of campaign to etablih focal tandard i to imply make it mandatory for a firm to dicloe whether it meet a particular tandard. In thi cae bad new regarding thi 2 The following propoition look at the cae where cot are uffi ciently low that a firm will adopt another label if it cannot meet the tandard for the focal label. It can alo be an equilibrium for a firm to adopt the focal label if it can and otherwie not adopt any label. For uffi ciently many tandard uch a trategy i alo more informative than the ymmetric dicloure equilibrium, but for low cot the firm ha an incentive to deviate to the equilibrium trategy we examine. Note alo that in a focal equilibrium fewer firm pay the certification cot than in a ymmetric equilibrium. 21 For more than two ignal the lexicographic equilibrium they conider differ from our focal equilibrium becaue there i a backup econd focal label, then a third, etc. Becaue our etup i complicated by allowing for a continuum of firm type and labeling tandard, and becaue uch a full degree of coordination appear unlikely for product label, we do not evaluate uch a lexicographic trategy. 14

16 mandatory dicloure on one tandard can till be upplemented with good new on other tandard, o the reult i eentially the ame a in the focal equilibrium if the certification cot for the mandatory tandard are taken a unk cot. Therefore the informativene reult of Propoition 5 alo provide an argument for mandatory certification of a particular label, even if conumer do not know the exact tandard for the label, and ugget that firm may benefit from partnering with government or dominant NGO to promote a pecific label a a marketing trategy. 4 Multiple Firm We now conider how the preence of multiple firm affect label confuion. It might eem that, by oberving which firm obtain which label, conumer hould be able to learn about different labeling tandard, and thereby reduce the information problem analyzed above. Indeed, if there i only one label and all firm that can meet the label tandard adopt it, then a the number of firm increae, the fraction of the firm obtaining the label i an increaingly precie etimate of the label tandard. However, we find that two factor limit uch learning. Firt, the non-labeling equilibrium i unaffected by an increae in the number of firm, o the potential for no learning, and alo the potential for trategic uncertainty about how to interpret lack of a label, remain. Second, in the realitic cae where there are both multiple firm and alo multiple label, we find that firm have an incentive to chooe tandard trategically in a way that interfere with conumer learning. Firt conider the impler cae where m firm with i.i.d. qualitie Q 1,..., Q m imultaneouly chooe whether to adopt a ingle label with tandard S. Aume that firm know the realized value of their own and each other qualitie q 1,..., q m and the realized diffi culty of the tandard, but that conumer only know F, G, c, and m. The firt part of the following propoition ue a tandard Law of Large Number reult to confirm that the fraction of firm obtaining the label can be an aymptotically precie etimate of the tandard, o the ituation for each firm i equivalent to that of a ingle firm facing a certain tandard a examined in Section 2. The econd part how that thi logic doe not extend to the non-labeling equilibrium ince the gain from deviating by a ingle firm i E[Q i Q i S] E[Q i ], o the condition for a nondicloure equilibrium remain exactly the ame a that of a ingle firm facing an uncertain tandard. The third part confirm that for a certain tandard the number of firm ha no effect on the upport of either equilibrium. Propoition 6 Suppoe m i.i.d. firm face a ingle label. If the label tandard i uncertain: (i) the expected upport of a labeling equilibrium converge to that of a ingle firm facing a certain tandard a m increae, while (ii) the expected upport of a non-labeling equilibrium i the ame a for m = 1. (iii) If the label tandard i certain the expected upport of either equilibrium i the ame a for m = 1. Looking back at Figure 2, thi Propoition implie that the region where the labeling and nonlabeling equilibria coexit expand from the L,N area in the eparate panel of (a) and (d) to encompa the area above c in panel (a) and underneath E[c] in panel (d). Therefore even though 15