THE SOUND OF SILENCE IN ONLINE FEEDBACK: ESTIMATING TRADING RISKS IN THE PRESENCE OF REPORTING BIAS

Transcription

1 THE SOUND OF SILENCE IN ONLINE FEEDBACK: ESTIMATING TRADING RISKS IN THE PRESENCE OF REPORTING BIAS CHRYSANTHOS DELLAROCAS CHARLES A. WOOD Atract. Mot online feedack mechanim rely on voluntary reporting of privately oerved outcome. Thi introduce the potential for reporting ia, a ituation where trader exhiit different propenitie to report different outcome type to the ytem. Unle properly accounted for, reporting ia may everely ditort the ditriution of pulic feedack relative to the underlying ditriution of private tranaction outcome and, thu, hamper the reliaility of feedack mechanim. Thi tudy offer a method that allow uer of feedack mechanim where oth partner of a ilateral exchange are allowed to report their atifaction to ee through the ditortion introduced y reporting ia and derive uniaed etimate of the underlying ditriution of privately oerved outcome. A key apect of our method lie in extracting information from the numer of tranaction where one or oth trading partner chooe to remain ilent. We apply our method to a large data et of ebay feedack. Our reult confirm the widepread elief that ebay trader are more likely to pot feedack when atified than when diatified. Furthermore, we provide rigorou evidence for the preence of poitive and negative reciprocation among ebay trader. Mot importantly, our analyi derive uniaed etimate of the rik that are aociated with trading on ebay that, we elieve, are more realitic than thoe uggeted y a naïve interpretation of the unuually high (> 99%) level of poitive feedack currently found on that ytem. 1. Introduction Online feedack mechanim have ecome an important component of electronic uine, helping to elicit good ehavior and cooperation among looely connected and geographically dipered economic agent (Dellaroca 2003). For example, ebay feedack mechanim i the primary mean through which ebay elicit honet ehavior and, thu, facilitate tranaction among tranger over the Internet (Renick and Zeckhauer 2002). Since mot detail of commercial tranaction are privately oerved y the partie involved, the majority of online feedack mechanim rely on voluntary elf-reporting of tranaction outcome. A a conequence, not every tranaction receive feedack. More importantly, elf-reporting open Date: January 2006; Revied: June 2006, Octoer

2 the door to everal form of reporting ia: trader may electively chooe to report certain type of outcome and not other. If reporting ia i evere enough, pulic feedack provide a ditorted view of the rik that are aociated with trading in a given market. It uefulne, oth in deterring fraud and in informing uyer, then ecome everely diminihed. There are important indication that reporting ia i preent in online feedack: Feedack in mot ytem i overwhelmingly poitive. For example, more than 99% of all feedack poted on ebay i poitive (Renick and Zeckhauer, 2002; Kauffman and Wood, 2005). A naïve reading of thi empirical fact may lead one to conclude that more than 99% of ebay tranaction reult in atifactory outcome. Such a concluion run againt widepread report of conumer fraud in online auction. For example, Internet Auction accounted for 16% of all conumer fraud complaint received y the Federal Trade Commiion in 2004, the highet level of fraud of any Internet tranaction type (ee One poile explanation for thi dicrepancy i that, wherea atified trader generally report their atifaction online, diatified trader often prefer to remain ilent. The reciprocal nature of auction feedack i conidered y many a the main reaon ehind uch reporting ia. Specifically, it i widely elieved (though, o far, not rigorouly proven) that many trader chooe to remain ilent ecaue they are afraid that, if they report their negative experience, their partner will retaliate y poting negative feedack for them a well. The preence of reporting ia in online feedack mechanim ha een mentioned y everal author (Reichling 2004; Klein et al. 2005; Hu et al. 2006). However, o far there ha not een an attempt to quantify the degree to which it i preent in a given ytem or an aement of the extent to which it ditort the ditriution of pulihed feedack relative to the underlying ditriution of tranaction outcome that trader privately experience. We fill thi gap y offering what we elieve i the firt quantitative method that can ae and repair the impact of reporting ia on feedack mechanim. Given a ufficiently large ample of online feedack our method derive quantitative etimate of uer propenitie to report variou type of outcome to the ytem. Baed on thee etimate, the method then derive uniaed etimate of the ditriution of private tranaction outcome that i mot likely to have produced the target ample of pulic online feedack. Our approach, thu, enale trader to ee through potentially iaed online feedack and, thu, to otain a more reliale picture of the rik aociated with tranacting in a given pace. The method i fairly general and applie to a wide variety 2

3 of idirectional feedack mechanim, that i, mechanim that allow oth partner of a ilateral exchange to rate each other. We apply our method to a large data et of online feedack otained from ebay. Our reult provide rigorou evidence upporting the fact that ebay trader are more likely to report atifactory outcome than mildly unatifactory outcome. (Reporting proailitie go up again when trader are very diatified.) Furthermore, we how that a trader propenity to pot feedack i highly enitive to her partner reporting action. In addition to confirming that unfavorale feedack increae the other trader propenity to pot unfavorale feedack in return, we how that favorale feedack increae the other trader propenity to pot favorale feedack in return (when atified) and to withhold poting unfavorale feedack (when mildly diatified). Overall, our reult indicate that reciprocity i an important driver of reporting ehavior on ebay. Our method i ale to dientangle a trader reporting ehavior from the tranaction outcome he ha oerved and, thu, to derive etimate of the ditriution of private outcome that i mot likely to have produced the pulic feedack pattern oerved in our data et. Our mot detailed model etimate that, on average, ebay uyer walk away from a tranaction atified 78.9% of the time, mildly diatified 20.4% of the time and very diatified 0.7% of the time. The correponding etimate for eller are 85.7%, 13.7% and 0.6% repectively. Thee, we elieve, are more realitic etimate of trader atifaction rate than the 99% rate uggeted y a naïve interpretation of the percentage of poitive feedack currently found on ebay. An important element of our method conit in extracting information from the temporal order of uyer and eller feedack umiion, a well a from the fraction of tranaction where one or oth trader chooe to remain ilent. Our work, therefore, demontrate that a trader choice to not pot feedack provide important information that can e exploited to ee through the ditortion introduced y reporting ia. ebay currently doe not pulih any information on the numer of a trader tranaction where the partner did not provide feedack. We argue that thi omiion make it difficult for ebay trader to accurately ae the rik that are inherent in trading online and diminihe the effectivene of it feedack mechanim. We elieve that thi work contriute on everal front. Firt, we offer a general methodology that can e applied to ae the preence of reporting ia and the ditriution of privately oerved tranaction outcome in a wide variety of idirectional feedack mechanim. Second, our analyi i the firt to derive quantitative etimate of average trader atifaction and feedack reporting 3

4 ehavior on ebay. Third, our reult ugget that the impact of reciprocity in people online reporting ehavior i more complex than previouly thought: Wherea we confirm prior conjecture uggeting that the fear of retaliation might dicourage ome trader from reporting ad outcome, we alo find evidence uggeting that the expectation of poitive reciprocation may e partly reponile for the high level of feedack contriution on ebay. Lat, ut not leat, we demontrate how one can extract ueful information from a trader deciion to not pot feedack and argue that the numer of ilent tranaction (i.e., tranaction for which no feedack wa poted) hould ecome a tandard part of a trader feedack profile on ebay and other feedack mechanim. The ret of the paper i tructured a follow. Section 2 decrie our data et. Section 3 introduce a family of model that draw inference from the relative frequency of different type of feedack oerved in a ufficiently large ample of tranaction. Section 4 extend our aeline model to take into conideration the temporal order of feedack umiion; we how that thi extenion allow the analyt to derive more precie etimate of reporting ia, including etimate of how one partner feedack affect the other partner uequent reporting action. Section 5 further extend our modeling technology to derive tranaction-pecific etimate of trader atifaction and reporting ehavior. Finally, Section 6 dicue the managerial implication of thi work and lit opportunitie for future reearch. 2. Data Set Our data et conit of 51,062 rare coin auction that took place from April 24, 2002 to Septemer 11, 2002 on ebay. Thee auction include item from 6,242 ditinct eller and 16,405 ditinct uyer. We only conider auction that reulted in a tranaction (i.e., auction that received at leat one id and where the ecret reerve price, if it exit, wa met). Our data et include auction information (auction id, item decription, ending time, elling price, numer of id), eller information (ebay id, eller feedack profile information), and winning idder information (ebay id, uyer feedack profile information). In addition, our data et contain full information (date and time of feedack, auction id, rater ebay id, feedack type: poitive, neutral, or negative, aociated text comment) related to feedack poted for thee auction y oth uyer and eller within a 90-day window following the cloing time of the correponding auction. 1 1 ebay encourage trader to leave feedack within 90 day after the termination of an auction and doe not guarantee that trader will e ale to leave feedack after that period. Empirical evidence ugget that feedack left after 90 day i extremely rare. 4

5 Total numer of auction 51,062 Ditinct uyer 16,045 Ditinct eller 6,242 Min Mean Median Max Buyer feedack core Seller feedack core Bid per auction Auction cloing price $0.01 $52.98 $15.50 $16,500 Numer of Auction % of Total Auction where eller left comment 39, % Auction where uyer left comment 34, % Auction where oth left comment 29, % Auction where none left comment 6, % Auction where eller commented firt 30, % Auction where uyer commented firt 14, % Tale 1. Key decriptive tatitic of our data et. Numer of Auction % of Total Auction where eller left comment 39,561 poitive 39, % neutral % negative % Auction where uyer left comment 34,614 poitive 34, % neutral % negative % Tale 2. Breakdown of poted feedack into poitive, neutral, and negative. Tale 1 ummarize ome key decriptive tatitic of our data et. All metric of feedack core refer to the tandard ebay feedack core. 2 We oerve that feedack contriution i utantial: 77% of auction receive a comment from the eller and 67% of auction a comment from the uyer. Seller pot the firt comment almot twice a often a uyer, reflecting the fact that the outcome (good/ad) of a tranaction typically ecome clear to the eller ooner than to the uyer. 3 Tale 2 reak down poted feedack into poitive, neutral, and negative comment. The reakdown i conitent with that reported y mot other tudie, exhiiting an overwhelming (99%) preponderance of poitive feedack. Our data et can e further divided into feedack pattern 2 The tandard ebay feedack core i equal to the um of poitive rating minu the um of negative rating poted on ehalf of a trader y ditinct partner over the coure of that trader entire career on ebay. In the event that a trader receive multiple rating from the ame partner, all of them count a one. See Renick and Zeckhauer (2002) for a detailed decription of ebay feedack mechanim. 3 In mot cae, a tranaction i ettled for the eller a oon a he receive money from the uyer. The uyer, on the other hand, mut receive and examine the good efore he can determine her level of atifaction. 5

6 Buyer Comment Type Seller Comment Type Who comment firt? Numer of auction % of Total % % % % % % % % % % % % % % % Legend % % Comment Type % + Poitive feedack + S % 0 Neutral feedack 0 S % - Negative feedack - S % S No feedack (ilence) S % S % Who comment firt? S % Buyer S S % Seller Total % Tale 3. Conideration of the type and relative order of comment poted y the uyer and eller for a given tranaction give rie to 25 ditinct feedack pattern. according to the type and temporal order of feedack poted y uyer and eller in their repective auction. For example, one pattern conit of auction where the eller pot poitive feedack firt, and the uyer repond with poitive feedack. Another pattern conit of auction where the uyer pot poitive feedack and the eller remain ilent. If we conider all poile comination of each trader feedack ehavior (poitive, neutral, negative feedack plu ilence) and all poile temporal ordering of comment (uyer rate firt, eller rate firt) we otain 25 mutually dijoint feedack pattern, including a pattern that contain auction where oth the uyer and the eller remain ilent. Tale 3 lit all 25 feedack pattern and their relative incidence in our data et. Our uequent analyi of reporting ia and private tranaction outcome i heavily aed on the extraction of information from the relative incidence of thee 25 pattern in online feedack data. Figure 1 plot the empirical ditriution of feedack poting time relative to the correponding auction cloing time. We oerve that poitive feedack i poted relatively oon and that uyer feedack lag eller feedack y 3-4 day. Thi lag i intuitive, ince eller are typically in a poition to pot poitive feedack for a uyer a oon a they receive payment, wherea uyer 6

7 Daily numer of rating poted Day elaped ince auction cloing Seller Buyer (a) Poitive feedack 16 Daily numer of rating poted \ Day elaped ince auction cloing Seller Buyer Trendline (Seller) Trendline (Buyer) () Neutral and negative feedack Figure 1. Empirical ditriution of feedack poting time relative to the correponding auction cloing time. need to receive and examine the good efore they determine their level of atifaction. We alo oerve that oth the eller and uyer feedack ditriution are imodal; furthermore the location of the correponding mode are highly correlated. We hypotheize that thi imodality i a imple conequence of the variety of payment type upported y ebay: ome uyer pay y credit card and Paypal, and can, therefore immediately communicate their payment to the eller. Other ue check that take a while to reach the eller. The eller, typically will not pot feedack until payment i received and confirmed. We, therefore, hypotheize that the econd mode in eller feedack correpond to tranaction where payment i y check. Furthermore, the eller will only hip the good after he confirm receipt of payment. Thi lead to a correponding delay in uyer feedack for uch tranaction. Since unfavorale (negative or neutral) feedack i far le common, the hape of the correponding empirical ditriution (dotted line) are le regular; we, therefore, upplement them y 7

8 ixth-degree polynomial trendline (olid line). We oerve that unfavorale feedack i poted later than poitive feedack. Thi make ene ince prolematic tranaction are uually aociated with payment and/or hipment delay and additional communication etween uyer and eller efore trader give up on each other and pot unfavorale feedack. We conclude thi ection with a rief look at the text comment aociated with ebay feedack. We read all text comment in our data et eeking inight related to the type of trading rik that are preent on ebay. We found that the majority of poitive comment do not contain very ueful information for our purpoe. 4 Neutral and negative comment, on the other hand, were quite inightful, a they point to a numer of different ource of trader diatifaction. Tale 4 group neutral and negative comment found in our data et into a numer of prolem area. According to our reult, the mot common ource of uyer complaint were tranaction where the promied item were never received (40% of negative; 7% of neutral), followed y item whoe quality wa inferior to what wa expected (35% of negative; 50% of neutral). Slow hipping or other pot-ale communication prolem with the eller accounted for around 20% of complaint. Interetingly, aout 5% of uyer complaint referred to ituation where the eller acked out of the tranaction after the auction completion. Finally, a few uyer complain ecaue they found the hipping charge to e too high relative to the actual potage paid y the eller. The majority (81%) of negative eller comment relate to idder who ack out of their commitment to uy the item they won. Poor communication and unreaonale pot-ale uyer demand accounted for another 13% of eller complaint. Finally, 2.6% of eller complaint refer to uyer who are low in ending payment to the eller. The difference in the ditriution of neutral and negative comment among prolem area ugget that, in line with ebay uggeted guideline, trader are more likely to pot neutral feedack when prolem are mild (e.g. unhappy with item quality, poor communication), reerving negative feedack for ituation where prolem are evere (e.g. item not received, uyer never ent payment). 3. Baeline model Our aeline model draw inference from the relative frequencie of different type of feedack oerved in a ufficiently large ample of tranaction. We how that, if we can aume the aence of 4 It i cutomary for ebay trader poting poitive comment to ue exceive praie and colorful language. The mot common text comment aociated with poitive feedack read omething like Great tranaction - A+++. More colorful comment, like Fater than a cheetah chaing an antelope on an african plain!!!, referring to one of the author very prompt payment for an auction he once won, are not uncommon. 8

9 Buyer Comment Negative Comment Neutral Comment Numer % Numer % Item not received % % Unhappy with item quality % % Slow hipping, poor communication % % Seller acked out of tranaction % % Shipping charge deemed exceive % % Other * % % Total unfavorale comment: % % Seller comment Negative Comment Neutral Comment Numer % Numer % Buyer never ent payment % % Poor communication, unreaonale uyer % % Slow payment % % Other * % % Total unfavorale comment: % % * No clear reaon given. Tale 4. Summary of tranaction prolem aociated with neutral and negative comment in our data et. trategic mireporting, uch model are alway identifiale in mechanim that allow oth partner to rate one another Baic concept and identifiaility reult. We refer to feedack mechanim that allow oth partner of a tranaction to rate each other a idirectional feedack mechanim. Conider a idirectional feedack mechanim that allow trader to elf-report privately oerved tranaction outcome. Aume that each tranaction can reult in one out of N 2 ditinct outcome type (good, average, ad, etc.) for each partner. A tranaction outcome need not e identical for oth partner. For example, a tranaction where the uyer promptly end payment and the eller hip ack damaged item would leave the eller atified ut the uyer diatified. When oth partner atifaction level are taken into conideration, each tranaction can, thu, have N 2 ditinct outcome. Each of the two partner i given the option to report her level of atifaction y poting one out of M 1 availale feedack type (e.g. integer etween 1 and 5) on a pulic weite. Each partner alo ha the right to remain ilent. In the ret of the ection it will e convenient to treat ilence a an additional feedack type. If we treat ilence a feedack, our mechanim upport M + 1 ditinct feedack type per partner. When oth partner rate thi give rie to (M + 1) 2 ditinct feedack pattern per tranaction, including pattern where one or oth trader pot no feedack. 9

10 The pulic weite aggregate poted feedack and pulihe the relative frequencie of all ditinct feedack pattern. An important ojective of thi paper i to explore under what condition one can etimate the incidence proailitie of the N 2 private tranaction outcome from the relative frequencie of the (M + 1) 2 pulic feedack pattern. The prolem can e cat a a latent variale prolem (Bollen 1989). Let i, i {1,..., N} denote the outcome experienced y a tranaction uyer and eller repectively. Similarly, let j, j {1,.., M + 1} denote the type of feedack poted y each partner (including no feedack). Let π i i denote the proailitie of the N 2 private tranaction outcome and let ρ k j k i k denote the proaility that trader k (k = (uyer) or (eller)) report feedack type j k conditional on having oerved outcome i k. The following ytem of polynomial equation then relate the proaility F j j of oerving feedack pattern j j to the unknown proailitie π i i and ρ k j k i k : (1) F j j = N i =1 i =1 N π i i ρ j i ρ j i j, j {1,.., M + 1} Recall (Bollen 1989) that a imultaneou equation model i identifiale if and only if it atifie the order condition (numer of independent equation numer of independent unknown) and the rank condition (rank of Jacoian matrix equal to numer of independent unknown). The aove model ha (M +1) 2 1 independent equation (ytem (1) conit of (M +1) 2 equation that atify M+1 M+1 j =1 j F =1 j j = 1). Unknown include N 2 1 independent private outcome proailitie (there are N 2 unknown outcome proailitie π i i that mut atify N i =1 N i =1 π i i = 1) and M N independent reporting proailitie for each of the two partner (for each partner k and each of the N poile outcome, there are M + 1 unknown reporting proailitie ρ k j i that mut atify M+1 j=1 ρk j i = 1). The total numer of independent unknown i, thu, N MN. Unle M i utantially larger than N, elementary algera how that the numer of unknown i greater than the numer of equation. However, even when M i ufficiently large o that the order condition hold, the following propoition how that model (1) fail to uniquely identify the unknown outcome and reporting proailitie. Propoition 1. Model (1) i not identifiale for any M 1, N 2. Thing get etter if we can draw upon domain knowledge to reduce the numer of unknown reporting proailitie ρ k j i. For example, uppoe that we can aume that ome reporting proailitie are equal to zero (ecaue, for example, we know that trader never pot unfavorale 10

11 feedack when happy or favorale feedack when unhappy). A pecial cae of practical interet i one where we can aume that: (A1) (A2) there i a one-to-one mapping etween tranaction outcome and report type trader either truthfully report the tranaction outcome they oerve or remain ilent. The following reult then hold: Propoition 2. Under aumption (A1) and (A2) model (1) i identifiale for all N Application to ebay. Thi ection applie the previou reult in the context of our ebay data et. Recall that ebay feedack mechanim upport three ditinct feedack type (poitive, neutral, negative). To take advantage of Propoition 2 we develop a model where: each tranaction ha three poile outcome (good, mediocre, ad) for each trader: good outcome imply that the trader expectation were met or urpaed, mediocre outcome imply mild diatifaction and ad outcome imply evere diatifaction. there i a one-to-one mapping etween tranaction outcome and feedack type (good poitive, mediocre neutral, ad negative) each trader either truthfully report the feedack type that correpond to the outcome he oerved, or tay ilent The aumption that ebay trader are generally honet when poting feedack can e jutified y the preponderance of one-time tranaction in large-cale electronic market. If a trader i unlikely to tranact with the ame partner again in the future, elementary game theory predict that he i indifferent etween truthful and untruthful reporting (Dellaroca 2005). Therefore, although we do not preclude iolated incident of fale reporting, we aume that ytematic trategic mireporting doe not take place at the population level. Appendix I lit the equation derived from pecializing model (1) to the context of the aove domain (M = N = 3). In the ret of the paper we will refer to thi model a Model A. The model ha (M + 1) 2 = 16 equation and N 2 + 2M = 15 unknown. The notation F j j denote the proaility of oerving an ebay tranaction where the uyer pot feedack j {+, 0,, S} and the eller pot feedack j {+, 0,, S}. Symol +, 0, denote poitive, neutral and negative feedack repectively; S denote ilence. For example, F +S denote the proaility of oerving a tranaction where the uyer pot poitive feedack wherea the eller remain ilent. The 15 unknown model parameter are alo lited in Appendix I. Outcome proailitie are denoted π i i : 11

12 the firt ucript denote the outcome i {G, M, B} privately oerved y the uyer and the econd the outcome i {G, M, B} privately oerved y the eller. Symol G, M, B denote a Good, M ediocre and Bad outcome repectively. Since we have aumed honet reporting and a oneto-one mapping etween outcome and feedack type, reporting proailitie are imply denoted ρ k i ; k indicate the type of trader (uyer or eller) and i {G, M, B} indicate the outcome oerved y that trader (the type of feedack poted i implied y the type of outcome oerved). For example, ρ G denote the proaility that a uyer who oerved a good outcome will pot (poitive) feedack; accordingly, 1 ρ G i the proaility that a uyer who oerved a good outcome will remain ilent. The key to undertanding the form of our model equation i the oervation that, given our aumption of truthful reporting, feedack pattern where oth partner pot feedack reveal the underlying latent outcome experienced y oth partner. In contrat, feedack pattern where one of the partner tay ilent only reveal the latent outcome experienced y the vocal partner. All 16 Model A equation are traightforward conequence of thi oervation. Model A parameter can e etimated uing the maximum likelihood method. Specifically, we can treat the manifet feedack pattern j j of each tranaction a a random variale that follow a multinomial ditriution with 16 poile outcome, whoe repective occurrence proailitie F j j are given y the model equation. The unknown parameter etimate π i i, ρ k i then are the one that maximize the correponding log-likelihood function: (2) L = N j j log (F j j ) uject to the contraint: j,j {+,0,,S} (3) π i i, ρ k i [0, 1] and i,i π i i = 1 N j j F j j denote the numer of tranaction in our data where we oerve feedack pattern j j and i the right hand ide of the correponding Model A equation. It i known (ee, for example, Greene 2002, p. 127) that, for ufficiently large ample, the maximum likelihood method lead to (aymptotically) conitent, minimum variance uniaed etimator. 12

13 Parameter G GG GM GB M MG MM MB B BG BM BB G GG MG BG M GM MM BM B GB MB BB G M B G M B ML Etimate Mean Std. Error Confidence Interval 2.50% Median 97.50% π = π + π + π π = π + π + π π = π + π + π π = π + π + π π = π + π + π π = π + π + π ρ ρ ρ ρ ρ ρ Tale 5. Maximum likelikood etimate of Model A parameter. Tale 5 lit the parameter etimate that olve the aove contrained maximization prolem. To facilitate the interpretation of the reult we do not how the etimate of all nine joint outcome proailitie π i i ut intead lit the etimate of the marginal trader atifaction proailitie π i = j π ij π i = j π ji i.e. the marginal proailitie that the uyer and eller will oerve a good, mediocre and ad outcome repectively. The ret of the ection dicue the inight provided y the aove reult. Trader atifaction. The reult of Tale 5 imply that, on average, ebay tranaction leave uyer atified 81.5% of the time, mildly diatified 17.4% of the time and very diatified 1.1% of the time. The correponding figure for eller are 88.6%, 10.4% and 1% repectively. Thee figure are in line with common ene and more credile than the 99% atifaction rate that i tacitly implied y the percentage of poitive feedack on ebay. Note that a uyer atifaction rate of 81.5% doe not imply that ebay eller ehave adly 18.5% of the time. A dicued in Section 2, uyer diatifaction ha many ource, ome of which are aed on the uyer own miundertanding of the way ebay work. A imilar diclaimer applie to eller diatifaction. Note, alo, that the confidence interval of our trader atifaction proaility etimate π G, π G 13 are relatively road

14 (78% to 84% for uyer; 86% to 90% for eller). A we will how in the next ection, tighter interval can e otained y conidering the timing of feedack umiion. Reporting ehavior. Our reult how that atified ebay trader exhiit a relatively high propenity to pot poitive feedack (82% for uyer; 87% for eller). Mildly diatified trader, intead, prefer to remain ilent, poting neutral feedack only aout 1% of the time. The reporting proailitie of very diatified trader are utantially higher (41% for uyer; 47% for eller), ut till lower than thoe of atified trader. Notice that the confidence interval of ρ B and ρ B are very road, uggeting that our data doe not contain ufficient information to allow precie inference with repect to the reporting ehavior of very diatified trader. Importantly, however, the 95% confidence interval of ρ k G, ρk M and ρk B are mutually dijoint (for oth uyer and eller). Thi allow u to conclude (with 95% confidence) that, on average, ebay trader are more likely to report good outcome than ad outcome and more likely to report ad outcome than mediocre outcome. 4. Feedack Timing and Reciprocity Our aeline model (Model A) offer valuale initial inight into the trading rik and feedack reporting ehavior of ebay trader. On the poitive ide, the model i eay to undertand and relatively traightforward to etimate. On the negative ide, Model A ignore important apect of the ebay domain. Specifically, our model aume that each trader reporting ehavior i independent of hi partner reporting ehavior. Such an aumption might e plauile in feedack mechanim that imultaneouly pulih oth trader rating for each other; it i le plauile on ebay, where trader pot feedack aynchronouly and where poted feedack i immediately viile to the other trader. In uch a etting it i very likely that the feedack poted y the trader who report firt will have an impact on the uequent reporting ehavior of the other trader. A long literature in pychology and ehavioral economic offer powerful evidence for the importance of reciprocity in human interaction (Fehr and Gachter 2000). Reciprocal ehavior i the pattern of ehavior where people repond to friendly or hotile action with imilar action. In the context of thi work, reciprocity argument ugget that receipt of poitive feedack from a tranaction partner might make a trader (who ha not yet poted any feedack) more likely to report a good outcome and to withhold reporting a mediocre or ad outcome (poitive reciprocation). Similarly, receipt of neutral or negative feedack might make the ame trader more likely to report a mediocre or ad outcome and to withhold reporting a good outcome (negative reciprocation). 14

15 Undertanding the extent to which reciprocity affect trader online reporting ehavior i an intereting quetion in it own right. It complement our undertanding of reporting ia in feedack mechanim and ha important implication for their deign (ee Section 6). At the ame time, failure to recognize that the firt mover feedack might affect the other trader reporting ehavior could lead to inaccurate etimate of the underlying private outcome proailitie. 5 Motivated y the preceding argument thi ection extend our aeline model to capture the potential for reciprocity-driven change in the econd mover reporting ehavior A model with feedack timing. Attempt to incorporate the impact of reciprocity into our aeline model quickly run into identifiaility prolem. The firt tep toward uilding uch a model i to refine the pattern of oervale feedack that drive our original model to pecify not only the type of feedack poted y each trader ut alo which trader (uyer, eller) pot the firt feedack. Thi increae the numer of ditinct oervale pattern from 16 to 25 (ee Tale 3). The econd tep i to, imilarly, refine the equation of Model A, replacing each of the firt 9 equation (that decrie pattern where oth trader pot feedack) with two equation, one where the uyer rate firt and one where the eller rate firt. The third tep i to condition the econd mover reporting proailitie on the type of rating j poted y hi trading partner. Given 3 poile outcome i, 3 poile partner rating j and 2 trader type k, thi tep introduce 18 additional model parameter ρ k i j. We end with a model that ha 25 independent equation and 33 unknown (the original 15 unknown plu the 18 conditional reporting proailitie). In the ret of the paper, we will refer to thi model a Model B. Model B equation and unknown parameter are lited in Appendix II. Model B fail to atify the order condition and, thu, i not identifiale. However, it erve a a tepping tone for contructing an identifiale model. A we will how, identification can e otained if we extend Model B to take into conideration the time at which each trader pot her repective feedack (relative to the eginning of the correponding tranaction). The aic aumption that underlie our new model i that a trader time-to-feedack correlate with the type of private outcome oerved y that trader. Thi aumption can e jutified if trader pot feedack oon after they determine the outcome of a tranaction and if the time it take to determine a tranaction outcome correlate with the outcome type. The lat aumption i plauile on ebay ince good outcome are likely to e determined ooner than mediocre or ad 5 The term firt mover and econd mover refer to the relative order of feedack umiion. 15

16 outcome. A good outcome i one where the uyer promptly end payment to the eller and the eller promtly hip the promied good to the uyer. Mediocre and ad outcome, in contrat, are characterized y payment and/or hipment delay, unatifactory good that are often returned to the eller and additional communication etween uyer and eller a they try to reolve the dipute. The wore the final outcome, the longer it uually take efore the ituation ettle. We now develop expreion that model the proaility of oerving a randomly choen trader pot feedack of a given type at a given point in time. Our expreion aim to capture the reulting population-level ehavior and are independent of whether any or all trader ehave trategically or not. We ditinguih etween the cae where a trader rate efore hi partner and the cae where a trader rate after hi partner. Trader rate efore partner. A long a the partner ha not yet poted feedack, we aume that a trader time-to-feedack (conditional on the trader having decided to leave feedack) i governed y a failure time ditriution zi k(t) z(t; θk i ) that depend on the type of trader k (uyer, eller) and the type of outcome i oerved y that trader; z( ; θi k ) denote a uitale parametric family (e.g. Lognormal, Weiull, Gamma, etc.) whoe parameter vector θ k i i a function of the privately oerved outcome i and the trader type k; Z( ; θi k ) denote the correponding CDF. Since trader might decide to tay ilent, the denity function ri k(t) (CDF Rk i (t)) that characterize the proaility of oerving a trader of type k who ha experienced outcome i pot feedack (efore hi partner) at time t, mut alo include the trader reporting proaility ρ k i : (4) r k i (t) = ρ k i z(t; θ k i ) R k i (t) = ρ k i Z(t; θ k i ) Trader rate after partner. If a partner pot feedack at time t 0, her action i likely to affect the trader uequent conditional proaility of poting feedack for the ame tranaction, given that he han t done o already. At the population level the latter quantity i imply the hazard rate of r k i (t). Accordingly, we model the impact of partner feedack on the trader uequent propenity to rate y auming that the partner action multiplie the hazard rate of the trader denity function ri k(t) y a factor αk i j for all t t 0. Factor αi j k ha the following interpretation: If αk i j i greater than 1, thi implie that on average partner feedack j increae trader k uequent propenity to report outcome i. If, on the other hand, factor αi j k i le than 1, then partner feedack j decreae trader k uequent propenity to report outcome i. 16

17 The following propoition provide the analytic form of a failure time ditriution whoe original hazard rate get multiplied y a contant factor α at all time t t 0 : Propoition 3. Let f(t), F (t) denote a failure time denity and it CDF repectively. At time t 0, an external hock multiplie the hazard rate of f(t) y a factor α for all t t 0. The proaility f(t t 0 ) (CDF F (t t 0 )) of oerving the pertinent event occurring at time t t 0 i then given y: ( ) 1 F (t) α 1 ( ) 1 F (t) α (5) f(t t0 ) = αf(t) F (t t0 ) = 1 (1 F (t 0 )) 1 F (t 0 ) 1 F (t 0 ) The denity function r k i j (t t 0) (CDF R k i j (t t 0)) that characterize the proaility of oerving a trader pot feedack after hi partner i an immediate corollary of Propoition 3. Corollary 1. Let ri k(t) (Rk i (t)) denote the proaility (CDF) of oerving a randomly choen trader of type k who ha experienced outcome i pot feedack at time t if hi trading partner ha not yet poted feedack. Aume that the partner pot feedack j at time t 0. The pdf (CDF) that decrie the proaility of oerving a randomly choen trader k pot feedack at time t t 0 i then equal to: ( ) 1 R (6) r i j k (t t 0) = αi j k k α k rk i (t) i (t) i j 1 1 Ri k(t 0) ( ) 1 R R i j k (t t 0) = 1 (1 Ri k k α k (t 0 )) i (t) i j 1 Ri k(t 0) We have now derived expreion of the proaility of oerving a randomly-choen trader pot feedack at time t conditional on hi type, oerved outcome and hi partner reporting action up to that point. Going ack to our (underidentified) Model B, if we replace all ρ k i with ri k (t) and all ρ k i j with rk i j (t t 0), we otain a new model that incorporate the time of feedack umiion. We will refer to thi new model a Model C (ee Appendix III). Each of Model C 25 equation decrie the denity function fj k j (t, t ) of oerving a feedack pattern where trader k pot feedack firt, the uyer pot j at time t and the eller pot j at time t. For the mot part, Model C equation are traightforward extenion of the correponding equation of Model B. The only area where ome explanation i needed are equation that involve ilent trader (the model lat 7 equation). Model C aume the exitence of a data et that contain oervation of feedack poted from the eginning of each tranaction up until ome cutoff time T (T = 90 day in the cae of our data). The proaility that a trader will pot feedack firt (econd) within the time window [0, T ] i imply Ri k(t ) ( R i j k (T t 0) repectively), i.e. the relevant CDF evaluated at time 17

18 T. Accordingly, the proaility that we will oerve no feedack within [0, T ] i imply 1 Ri k(t ) (1 R i j k (T t 0) rep.). Model C ha 25 equation and P unknown, where P denote the numer of parameter of each failure time ditriution z(t; ). Unknown parameter include Model A original 15 parameter, 18 newly introduced hazard rate multiplier α k i j and 6 parameter vector θk i (i = G, M, B, k =, ) of failure time ditriution z(t; θ k i ). The ize P of vector θk i depend on the parametric family choen. In contrat to Model A and B, which were finite-dimenional ytem of imultaneou equation, the equation of Model C collectively define a continuou proaility ditriution f(i i, t, t ) (i.e. an an infinite-dimenional mathematical oject) where i i i the feedack pattern oerved and t, t are the uyer and eller feedack umiion time repectively. 6 Intuitively, an infinitedimenional model ha a unique pecification in term of any finite numer of calar parameter, provided that thee parameter are ufficiently independent from one another. Thi pecific notion of independence i formally captured y the rank of the Fiher information matrix. Specifically, Rothenerg (1971) and Bowden (1973) have hown that the (local) identifiaility of a parameter vector θ in the context of a tochatic model f(x; θ) can e etalihed y teting that the Fiher information matrix (7) H(θ) = [h ij (θ)] = E x [ logf θ i ] logf θ j i non-ingular at the parameter etimate ˆθ. Since the Fiher matrix uually doe not have a cloedform repreentation, in practice uch a tet i performed ex-pot, that i, after an etimate ha een derived uing ome tatitically ound etimation method. Etimation i, in principle, feaile if the numer of ditinct oervation i greater than the numer of parameter. Since Model C take into account the time of feedack umiion in each individual auction, etimation make ue of the full et of 51,062 ditinct oervation in our data Model etimation and reult. Each of the 51,062 auction in our data et can e equivalently expreed a a tuple (k, j, j, t, t ), where k {,, 0} denote the trader who pot the firt rating (0 indicate that no trader pot feedack), j, j {+,, 0, S} denote the type of rating poted y the uyer and eller repectively (S indicate ilence), and t, t [0, T ] denote the time 6 It i traightforward (though tediou) to verify that the 25 equation of Model C um to one and that for any feedack pattern (i, i ) {+, 0,, S} 2 and any pair of umiion time (t, t ) ([0, T ] ) 2 (where denote no feedack) there i exactly one model equation that provide the correponding oervation proaility. 18

19 of each trader feedack relative to the cloing time of the correponding auction (a value of 0 indicate that the correponding trader did not pot feedack). Since our data et only include rating poted up until 90 day after the auction cloing, T = 90. We model time-to-feedack denitie z(t; θi k ) uing lognormal ditriution. Lognormal ditriution are commonly ued to model a wide range of failure time ditriution (Limpert et al. 2001); for appropriate parameter range uch ditriution can approximate very well the empirical ditriution of feedack poting time in our data (Figure 1). A lognormal ditriution i fully defined y a parameter vector that include two component: a location parameter µ R and a cale parameter ς R +. Since our model aume that time-to-feedack denitie are conditional on the type of trader and the type of outcome, thi tep introduce = 12 additional parameter to our model. The final model, thu, ha 45 unknown parameter: 9 joint outcome proaility parameter π i i 6 firt mover reporting proailitie ρ k i (proailitie of reporting feedack conditional on the partner not having poted a rating) 18 hazard rate multiplier α k i j indicating how the partner feedack modifie a trader uequent propenity to rate 6 lognormal ditriution location parameter µ k i (one parameter per trader type and outcome type) 6 lognormal ditriution cale parameter ς k i (one parameter per trader type and outcome type) Etimate of all parameter can e otained y maximizing the log-likelihood function: (8) L = 51,062 n=1 ( ) log f k(n) j (n)j (t (n) (n), t (n) T = 90) where each f k j j ( ) i the right-hand ide of the correponding Model C equation. Parameter etimate mut atify the contraint: (9) π i i, ρ k i [0, 1], α k i j R+, µ k i R, ς k i R + and i,i π i i = 1 Tale 6 ummarize the propertie of the parameter etimate that olve the aove contrained maximization prolem. Identifiaility wa etalihed y numerically verifying that the Fiher 19

20 information matrix (7) ha a non-zero determinant at the parameter etimate. A efore, to facilitate the interpretation of our reult, Tale 6 lit the etimate of the marginal proailitie of trader atifaction π k i in lieu of the joint outcome proailitie π i i. We alo omit the etimate of the 12 parameter µ k i, ςk i ince their interet i econdary to the purpoe of thi tudy. In the ret of thi ection we dicu the mot important inight provided y thee reult. Trader atifaction and firt mover reporting proailitie. Trader atifaction proailitie etimated y Model C are in line with thoe etimated y Model A. Model C etimate that, on average, uyer oerve good outcome 78.9% of the time, mediocre outcome 20.4% of the time and ad outcome only 0.7% of the time. The correponding figure for eller are 85.7%, 13.7% and 0.6% repectively. Oerve that the etimate of oth good and ad outcome are a little lower than the repective etimate of Model A for oth uyer and eller. We attriute the difference in Model C aility to more accurately etimate a trader reporting proailitie efore and after receiving a rating from hi partner. Note, alo, that ince Model C i making ue of finer-grained data, it allow u to otain tighter confidence interval than Model A. In term of firt mover reporting proailitie, the mot notale feature of Tale 6 are the trikingly high etimate of very diatified trader propenitie to report negative feedack (ρ B, ρ B ). The correponding 95% confidence interval are till quite road, o comparion with the correponding propenitie to report atifactory outcome i tatitically amiguou. Oerve, however, that the lower ound of thee interval (51.5% for uyer; 68.2% for eller) allude to utantial reporting level of very ad outcome. Second mover reporting proailitie. The principal new feature of Model C i that it allow u to ae how partner feedack modifie a trader uequent reporting ehavior. Specifically, our model aume that a partner rating action j multiplie trader k uequent hazard rate of reporting i y an unknown factor αi j k, which i to e etimated together with all other model parameter. Tale 6 lit the ML etimate of all 18 hazard rate multiplier α k i j defined in thi manner. The interpretation of thee etimate i aed on the following reaoning: If the 95% confidence interval of a given α k i j fall entirely aove (elow) 1 then our model provide tatitical evidence (at the 95% level) that umiion of feedack j y the partner increae (decreae) trader k uequent propenity to report outcome i. In contrat, if the correponding 95% confidence interval contain 20

21 Parameter G GG GM GB M MG MM MB B BG BM BB G GG MG BG M GM MM BM B GB MB BB G M B G M B ML Etimate Mean Std. Error Confidence Interval 2.50% Median 97.50% π = π + π + π π = π + π + π π = π + π + π π = π + π + π π = π + π + π π = π + π + π ρ ρ ρ ρ ρ ρ α G M B G 0 M 0 B 0 G M B G M B G 0 M 0 B 0 G M B α α α α α α α α α α α α α α α α α Tale 6. Maximum likelihood etimate of Model C parameter. Boldface indicate hazard rate multiplier αi j k that were found to e ignificantly different than one. 1 then we do not find tatitically ignificant evidence that umiion of feedack j affect the trader uequent reporting ehavior. Tale 6 lit in oldface all hazard rate multiplier α k i j that were found to e ignificantly different than one according to thi definition. The following paragraph dicu what thee reult mean. 21

22 Impact of eller feedack on uyer ehavior. Receipt of poitive feedack from a eller appear to utantially increae the average uyer propenity to report good and ad outcome and to decreae her propenity to report mediocre outcome. Buyer, thu, appear to return the favor of poitive feedack y poting poitive feedack for the eller with increaed proaility (when atified) and y withholding the reporting of neutral feedack (when mildly diatified). On the other hand, poitive feedack doe not appear to e enough to appeae a uyer who ha experienced a ad outcome. Intead, the removal of the threat of retaliation (the eller can only pot feedack once) appear to emolden diatified uyer who are, then, more likely to pot negative feedack for the eller. Receipt of neutral feedack from the eller appear to decreae the average uyer propenity to report good outcome. Buyer who receive neutral feedack, thu, exhiit a form of negative reciprocation, withholding a poitive rating that they would otherwie e likely to pot for the eller. Interetingly, receipt of negative feedack doe not have any tatitically ignificant impact on the average uyer uequent reporting ehavior. In ummary, we find trong evidence of poitive reciprocation ut only mild evidence of negative reciprocation on the part of ebay uyer. Buyer alo appear to e enitive to the poiility of eller retaliation, and thu, more likely to report ad outcome after the eller ha poted feedack. Impact of uyer feedack on eller ehavior. Receipt of poitive feedack from a uyer appear to utantially increae the average eller propenity to report good outcome and to decreae hi propenity to report mediocre and ad outcome. Seller ehavior, thu, exhiit trong poitive reciprocation. In addition, eller appear to e willing to forgive delinquent (i.e. late-paying or non-paying) uyer in exchange for a poitive rating. Receipt of neutral feedack from a uyer decreae the eller propenity to report good outcome and increae hi propenity to report mediocre and ad outcome. Seller ehavior, thu, exhiit trong negative reciprocation to neutral feedack. Finally, receipt of a negative rating utantially increae the eller propenity to report ad outcome ut doe not appear to have a tatitically ignificant impact on hi propenity to report poitive and mediocre outcome. In ummary, evidence of reciprocal ehavior i even tronger in the cae of ebay eller. Like uyer, ebay eller appear to repond poitively to poitive feedack. Furthermore, ebay eller appear to e more enitive to unfavorale feedack than ebay uyer. The latter finding i intuitive: the advere impact of negative feedack i more evere for eller than it i for uyer. Seller, 22