Multidimensional Quality Sorting Between Online and Offline Auctions: The Role of Attribute Transparency *

Transcription

1 Multidimensional Quality Sorting Between Online and Offline Auctions: The Role of Attribute Transarency * Jafar Olimov Brian E. Roe May 8, 2013 Abstract We analyze how sellers of used construction equiment sort roducts between online and offline auctions based on the quality and transarency of different machine attributes. Mechanics collect attribute-secific quality data from a random samle of machines offered in both online and offline auctions within a single regional market. Sellers are more likely to offer machines online if quality is high for attributes whose integrity can be measured via hoto (e.g., general aearance) and are more likely to offer machines offline if quality is high for attributes whose integrity is more reliably evaluated in erson (e.g., engine). Quality averaged across all attributes is unrelated to auction choice, meaning standard tests of adverse selection can mask the subtle but significant effects of asymmetric information in this market. These findings corresond with redictions from our novel model of latform choice, which builds from standard signaling models and accommodates multile quality dimensions with auction-secific quality transarency. We confirm several additional redictions from this model for our samle market. * Ohio State University (roe.30@osu.edu and olimov.1@osu.edu). The authors acknowledge suort from the ational Institute of ood & Agriculture (grant# ), the Ohio Agricultural Research and Develoment Center, and the McCormick Program in Agricultural Marketing and Policy, Ohio State University. The authors thank John Kagel, Jim Peck, Ian Sheldon for reading early versions of this manuscrit, and Maryam Saeedi, Javier Donna, P.J. ealy and other seminar articiants at Michigan State University and Ohio State University for useful comments that imroved this work.

2 1. Introduction Consumers urchase goods from a variety of outlets, ranging from in-erson venues that allow for detailed roduct insection to online latforms in which roduct insection must rely uon hotos or other noisy quality signals. In markets where quality is heterogeneous, like used cars, one might imagine an Akerlof-style sorting result with sellers directing lower quality goods online where consumers find quality verification difficult. owever, the ersistence of online sales of used cars, equiment and other goods of heterogeneous quality suggests that, rather than comletely unraveling due to adverse selection, consumers are willing to risk lower quality and interret noisy quality signals in order to enjoy enhanced search efficiencies, lower transactions costs and the other conveniences offered by online latforms. In this aer, we ask the following question: for multi-attribute roducts where detailed hotograhy makes some asects of quality transarent in both online and offline latforms, will equilibrium outcomes necessarily result in lower quality roducts being sorted online? or examle, for used cars, a seller can ost hotos online to cature the aearance of a car s interior and exterior in detail similar to that available to the in-erson buyer. Of course, detailing the condition of an engine or transmission to online audiences in such a credible fashion is not ossible, leaving one to wonder whether the symmetry of information concerning the car s general aearance across latforms can offset the asymmetry of information about other systems and reverse lemons-style sorting result across latforms. In our emirical investigation, we analyze how sellers of used skid steer loaders, comlex machines used in construction and farming, sort roducts between online and traditional offline auctions based on the quality and transarency of different machine attributes. Mechanics assess attribute-secific quality through detailed insection of a random samle of machines offered for sale in a single regional market. We then estimate the robability that a machine is offered online rather than offline as a function of machine attributes requiring simle verification (e.g., age, size) and attributes requiring comlex assessment of vertical quality (e.g., general aearance, engine). Sellers are more likely to offer machines online if quality is high for systems whose integrity can measured via hoto (e.g., general aearance) and are more likely to offer machines offline if quality is high for systems whose integrity is more reliably evaluated in erson (e.g., engine). The seller s choice of auction is unrelated to quality averaged across all systems, meaning tests of adverse selection based uon global quality measures mask the subtle but significant effects of asymmetric information in this market. The findings corresond to redictions from our novel model of a seller s choice of auction latform. Sellers have a good with two attributes where the transarent attribute has quality that is observed regardless of the latform (e.g., general aearance) while the oaque attribute has quality that is oaque to online bidders but transarent to offline bidders (e.g., engine). Sellers offer the good in either an online or offline auction, where the offline auction charges a higher 1

3 sales commission that reflects the greater search and transactions costs of in-erson trade. We model the seller s sorting decision as an informative signal that bidders use to udate beliefs about item quality, and then derive equilibrium quality and rice by latform. Our model differs from revious quality sorting models by incororating multile quality dimensions with auctionsecific quality transarency and by modeling seller latform choice as a signal of roduct quality, both of which are relevant to canonical examles of goods in markets that suffer adverse selection such as used cars. Modest assumtions regarding bidder valuation and exectations lead to exected results for one-dimensional goods: so long as quality is oaque to online bidders and it is less costly to sell online, low quality is offered exclusively online. Bidders realize this, and in equilibrium, high quality goods suffer a rice discount when sold online, which may drive some or all high quality goods to an offline market. As a result, the quality online is never better than quality offline. In a model with two quality dimensions, where the second dimension is transarent to offline and online bidders, the unambiguous quality comarison between online and offline markets no longer holds. In articular, many goods with high transarent quality may be listed online because the transarent quality is accurately observed by bidders. Quality transarency reduces the online rice discount for goods with high transarent quality. In resonse sellers of items with high transarent quality are now temted to avoid the higher offline sales fees and list these items online. While sellers of items with low quality oaque attributes still list all such items online, the listing of some items with high transarent and high oaque quality online breaks down the quality sorting result from the one-dimensional model and leaves the comarison of the global quality of online versus offline items as an emirical question. Past emirical work on roduct quality in online auctions builds from Akerlof's (1970) lemons argument and suggests that adverse selection will sillover to online markets due to limited quality transarency in online settings (e.g., Adams, osken and ewberry (2011), Banker, Mitra and Sambamurthy (2011), Dewan and su (2004), Jin and Kato (2007), ewis (2011), Overby and Ja (2009), Wolf and Muhanna (2005)). In contrast, we analyze the quality sorting between online and offline auctions in the sirit of Sence s (1973) signaling model. Our emirical results are novel because we directly measure and comare multile vertically differentiated quality comonents of comlex goods listed in online and offline markets rather than relying uon indirect measures of quality (e.g., car mileage, Adams, osken and ewberry (2011)) or focusing on goods with a single quality dimension (e.g., baseball cards, Jin and Kato (2007)). Our finding that online and offline offerings feature similar global quality does not necessarily contradict other emirical studies, which find evidence of adverse selection to online markets (e.g., Banker, Mitra and Sambamurthy (2011), Dewan and su (2004), Jin and Kato (2007) and Wolf and Muhanna (2005)). or examle, the evidence of adverse selection online in Jin and Kato (2007) is consistent with our theoretical and emirical results because Jin and Kato (2007) study a market of baseball cards, i.e., goods whose vertical quality can be succinctly reresented by a single quality measure. We also find emirical evidence of conditional adverse 2

4 selection, i.e., adverse selection when we fix the quality level of transarent attributes and measure differences in quality for oaque attributes. The evidence of severe adverse selection in an online automobile market in Wolf and Muhanna (2005) may be driven by their imerfect quality indicators (age and mileage), which may not fully reresent overall quality. Our emirical findings are consistent with other studies that find little evidence of adverse selection in online latforms. or examle, Garicano and Kalan (2001) and Adams, osken and ewberry (2011) find little evidence of ronounced adverse selection online versus offline in markets for used cars. Our theoretical model is related to several strands in the literature. The first strand includes models of asymmetric information: screening models (e.g. Mussa and Rosen (1978), Maskin and Riley (1984)) and signaling models (e.g. Sence (1973)). We build from a signaling model for our analysis. The second strand is the literature on the otimality of latform fees in two-sided latforms (e.g. Rochet and Tirole (2003), Anderson and Coate (2005), Armstrong (2006)). In our model we introduce only one latform fee: the commission that the seller ays for using the offline latform. owever, by introducing differentiated listing fees on sellers and buyers we can easily connect our model to standard models of two-sided latforms. The third related strand involves literature on cometing latforms (e.g. Ellison and udenberg (2003), Ellison, udenberg, and Mobius (2004)). The key difference between our model and cometing latform models is our assumtion that the number of bidders er seller is the same in online and offline latforms, and that a seller does not affect the seller-bidder ratio by choosing one latform over another. Although these simlifying assumtions do not contradict the emirical evidence in the aer, it can be relaxed if we allow bidders to choose between online and offline latforms. Our work is most directly related to Jin and Kato (2006, 2007), who exlore differences between online and offline latforms for baseball cards. Our modeling aroach differs in that we first derive an equilibrium seller strategy and then derive a quality ranking between latforms. The results of our one-dimensional model are similar to the results of Jin and Kato s model (2007). owever, when we introduce two-dimensional quality, our results are inconsistent with the conclusions of Jin and Kato (2007) and with the conclusions of our own one-dimensional model. Our emirical work differs in that we choose a multidimensional roduct with sale rices 100 times larger than the baseball cards in Jin and Kato (2007). Also, standardized quality certifying services are not widely available for our roduct, imlying a simler choice for our sellers than for baseball card sellers, who also must choose whether to certify quality. inally, our core emirical finding of no average quality difference between online and offline roducts contrasts with Jin and Kato s (2007) finding that lower quality uncertified items sort online. The remainder of the aer will introduce our model and its emirical imlications, discuss the data collection suorting our emirical analysis, introduce the core emirical results and conclude with a discussion of the imlications of the modeling and emirical efforts. 3

5 2. A Signaling Model of Quality Sorting We first introduce and derive results for a market featuring an item with a single quality attribute that is oaque to online bidders but transarent to offline bidders. We then use these core results to derive the equilibrium results for an item that features a second quality attribute that is transarent regardless of latform. 2.1 Sellers Consider a seller s S who wants to sell an item of quality q i, which can be high or low, i {, }. Define an item of high quality as tye q and an item of low quality as tye q. The robability that an item is of each tye is determined by nature and is erfectly observable by all layers. In articular, we denote the robability of a tye q item by and the robability of a tye q item by 1 and assume that is common knowledge. A seller has no valuation for the item itself. A seller s can offer an item of tye q q, q } for sale in one of two auctions: an online i { auction (e.g., in a latform like ebay) or an offline auction (e.g., in a traditional, in-erson latform). We use the terms latform and auction interchangeably here forward. The key difference between these two latforms is that the quality arameter is transarent to bidders in the offline latform and oaque in the online latform. By listing an item offline, a seller ays the offline latform owner a sale fee of δ where is the sale rice and (0,1) is a fixed share of the sale rice (commission), where is common knowledge. The seller s online listing cost is normalized to zero. The offline latform commission catures the lower efficiency of offline latforms in terms of search and transaction costs. or examle, in our data of used skid steers, offline auction house commissions range from 8% to 15% of the sale rice, while the ebay commission is caed at 1% of sale rice. The online and offline sale formats are the same: a second-rice oen outcry (English) auction. 1 1 We assume that online and offline auction formats are the same to simlify theoretical analysis. Since offline auctions of used machinery are usually conducted through second-rice oen outcry (English) auctions with soft ending times, theoretical redictions of an English auction accurately aroximate the behavior of bidders in actual offline auctions. In contrast, our data from online auctions of used machinery come from ebay latform, where most of the auction sales are conducted through second-rice oen outcry auctions with fixed end times. As Ockenfels and Roth (2006) have shown, the equilibrium bidding behavior in a second-rice oen outcry auction with fixed end time is different from the equilibrium bidding behavior in a canonical English auction. In articular, bidders on ebay may engage in late bidding or sniing. As a result, some bidders on ebay may not be able to lace their bids before auction end times. Consequently, holding bidders characteristics and auction rules constant, the exected rice in an offline auction with soft end time should be higher than the exected rice in an online auction with fixed end time. 4

6 2.2. Bidders A seller s faces s otential identical bidders in each latform. Each bidder demands only one item and derives her valuation of the item of each tye from a corresonding distribution function. A bidder s valuation of a tye q item is identically and indeendently distributed with a continuous cumulative distribution function (v) and a ositive suort [ V, ]. Similarly, a bidder s valuation of a tye q item, v, is identically and indeendently distributed with a continuous cumulative distribution function (v) and a ositive suort [ V, V ], where V V. 2 In addition, we assume that these distribution functions are stochastically indeendent. inally, we assume that bidders are indifferent between articiating in an online versus an offline auction, and bidders valuations are determined only by their ercetion of item tye. V 2.3. Strategies and Payoffs We assume that a seller of a single item has erfect knowledge of the tye of her item and decides between listing her item in an online versus offline latform. 3 ence, the seller emloys a behavioral strategy {(,1,(,1 )}, where [ 0,1] is the robability of listing offline a tye q item (high oaque quality), (1 is the robability of listing online a tye q item, [0,1] is the robability of listing offline a tye q item (low oaque quality), and (1 ) is the robability of listing online a tye q item. Since buyers have identically and indeendently distributed valuations, a reresentative bidder emloys an equilibrium bidding strategy in a second-rice auction, which deends on the distribution function of valuations given the item s tye. According to the clock model of Milgrom and Weber (1982), in a second-rice oen outcry auction a bidder with identically and indeendently distributed valuation v i ~ i bids her valuation v i unless she is the last bidder, in which case she bids the rice at which the revious remaining bidder droed out. Given this equilibrium bidding strategy, by listing an item in a latform with identical bidders who derive their valuations from the same distribution function i, a seller obtains the exected rice 2 The assumtion of non-overlaing suorts of distribution functions of valuations is imortant in derivation of our model redictions. Wherever aroriate we relax this assumtion and consider a more general case with overlaing suorts and additional restrictions on the shaes of distribution functions of valuations. 3 We rule out the ossibility that a seller may list her item in two latforms simultaneously, given that a sale in any latform is binding. ence, it is not ossible that a seller conducts two sales of a single item at the same time in different latforms and then chooses a sale with the highest realized rice. While some auctions on ebay or other online latforms intimate that the online auction can be truncated by sale of the item in a simultaneous offline osted rice sale, we leave analysis of such a situation as an extension for future work. 5

7 i V 0 s 1 s = vdg ( v), where G ( v) = ( v) ( 1) ( v) i is the distribution of the secondhighest order statistic. 4 i s i s i ote, however, that both the equilibrium bidding strategy and the exected rice deend on the distribution function of bidders valuations, which in turn deends on the bidders belief about the tye of item on sale. In articular, since bidders fully observe the oaque quality of items listed offline, for each item tye available in an offline auction bidders derive their valuations from the corresonding distribution function. owever, when bidders articiate in an online auction and cannot observe oaque quality, they derive their valuations from a mixture distribution function, which is a convex combination of a distribution function corresonding to an item of high oaque quality and a distribution function corresonding to an item of low oaque quality. Since bidders are identical, they form a common belief about the oaque quality of a listed item. et [ 0,1] denote the common belief that an item offered for sale online is of high oaque quality and (1 denote the common belief that an item offered for sale online is of low oaque quality. Then we can introduce exected rices for each latform given these beliefs. Since there are two distinct item tyes and bidders can erfectly distinguish between them offline, we define a menu of two rices in an offline latform. In an online latform bidders cannot distinguish between items of high and low oaque quality; hence, in an online latform we define only one rice. The menu of rices offline is {, }, where the subscrit denotes quality and the suerscrit denotes that the rice is formed offline. Each rice is defined as follows, i V i = vdg ( v), i {, }. The exected online rice, ( ), is a function of, the bidders belief that the item is of high quality. The suerscrit denotes that the rice is formed online. Given, we define: where V ( ) = vdg( v,, V G( v, = ( ( v) (1 ( v)) s 1 s ( s 1)( ( v) (1 ( v)) distribution of the second-highest order statistic for a mixture distribution ( v) (1 ( v) for all [ 0,1] and s is the same number of bidders online and offline. s V i is i the 4 or derivation of the exected rice, see Milgrom and Weber (1982) or Krishna (2009). 6

8 2.4. Equilibrium Before we roceed to equilibrium redictions, in emma 1 we derive the ranking of exected rices online and offline and the deendence of online exected rices on the belief arameter. emma 1 a) ) ( for [ 0,1]. E E b) If 1 < 2, then ( 1 ) < ( 2) for 1, 2 [ 0,1]. Proof: Aendix A. The results in emma 1 suggest the exected rice online is at least as high as the exected rice for an item of low oaque quality offline and at most as high as the exected rice for an item of high oaque quality offline. In art (b) we show that the online exected rice should increase if bidders attach a higher robability to a high oaque quality item aearing online. In the next roosition we show that a seller always lists an item of low oaque quality online. Proosition 1 It is an equilibrium strategy for a seller to list an item of low oaque quality (tye q ) online. Proof: Aendix A. In the next roosition we derive equilibrium conditions for the sorting of items of high oaque quality between online and offline latforms. We use the notion of a Perfect Bayesian Equilibrium (PBE) to derive results in Proosition 2. Proosition 2 et be the exected rice of tye q offline, be the exected rice of tye q offline, and ( be the exected rice online, where is the commonly known robability of a tye q item as determined by nature. Then the following holds: (a) If ( (1 ), then there are two PBE: (1) a seller lists both tye q and tye q online, and (2) a seller lists tye q offline and tye q online. (b) If ( (1 ) lists both tye q and tye q online., then there is a unique ooling PBE and a seller 7

9 (c) If (1 ) ( ) lists tye q offline and tye q online. Proof: Aendix A., then there is a unique searating PBE and a seller The results in Proosition 2 suggest that deending on the commonly known distribution of high and low oaque quality items, a seller of a high oaque quality item can list her item either online or offline. This is in contrast to the result in Proosition 1, where we show that a seller of a low oaque quality item always lists her item online. When the condition in art (c) of Proosition 2 holds, a seller of a high quality item always lists offline, and we have ure market segmentation with multile identical sellers of high quality items listing offline and multile identical sellers of low quality items listing online. When the condition in art (b) of Proosition 2 holds, the offline latform collases because multile identical sellers of both high and low quality items list online only. When the condition in art (a) of Proosition 1 holds, we have an imure market segmentation with ossibly some identical sellers of high quality items listing online and some offline and all sellers of low quality items listing online. An imortant imlication of Proosition 2 is that for single-dimensional items of oaque quality, whenever an offline latform exists, the oaque quality of items listed offline is no worse than the oaque quality of items listed online. We formally state this imlication in Corollary 1 and test it in the emirical section of the aer by aggregating quality across attributes. Corollary 1 or single dimensional goods, whenever an offline latform exists, the quality of items listed offline is no worse than the quality of items listed online Robustness to Assumtions Before moving to develoment of the two-dimensional model, which builds closely on the results of the one-dimensional model, we briefly summarize insights from Aendix B, which exlores the robustness of the key results to relaxation of several maintained assumtions. or exositional simlicity, we assume the same number of bidders for each seller both online and offline. Such an assumtion does not contradict our data, which draws from the same regional market for both online and offline items. urthermore, in our data, buyers are solely resonsible for transorting urchased items both from sellers in online auctions and from offline auction sites. These two assumtions suggest that the ool of bidders articiating in online and offline auctions is likely to be the same. owever, in Aendix B, we consider the case when 8

10 the number of bidders in online and offline auctions is different and the case when bidders are not identical. We find that as long as the difference in the number of bidders is such that results in emma 1 hold, the difference in the number of bidders online and offline does not change equilibrium strategies in Proositions 1 and 2 and the result in Corollary 1. If the number of bidders online exceeds the number of bidders offline so that the exected rice online exceeds the exected rice of a high oaque quality item offline, then the offline latform collases. If the number of bidders online is less than the number of bidders offline so that the exected rice online is less than the exected rice of a low oaque quality item offline, then the online latform collases. either of these redictions are suorted by our data; we observe a coexistence of online and offline latforms for high and low oaque quality items in our data. The introduction of risk heterogeneity in bidders references does no affect our results either as we assume both online and offline auction formats are both second-rice oen outcry auction, which result in equilibrium bidding strategies that are invariant to bidder risk attitudes. In Aendix B we also consider an extension of the one-dimensional quality model in which multile oaque quality tyes are introduced. We find that as the number of quality tyes aroaches infinity, the searating equilibrium in Proosition 2 collases, and a seller ools items of all quality tyes online. We find no evidence of this ure ooling result in our data Two-dimensional Quality In this section we generalize the model to include two quality dimensions by adding a second dimension that is transarent to bidders in both latforms. Consider quality to consist of two arameters: a transarent quality arameter, which is transarent to bidders on all latforms (e.g., general aearance), and an oaque quality arameter, which follows the observability of quality from the single-dimension version (e.g., engine or transmission quality). or simlicity we assume that the transarent quality arameter, t, can be either high or low, t {, }. The oaque quality arameter, i, can also be high or low, i {, }. Deending on whether the transarent and the oaque quality arameters are high or low, an item can be one of four ossible tyes: q,, q,, q,, q,, where the first subscrit indicates the transarent quality and the second subscrit indicates the oaque quality. The robability of each tye is determined by nature and is common knowledge. We denote the robability of a tye q, item by, t, i {, }, and assume that a = 1. t i t, i t, i{, } Bidders derive their valuations for each tye from a corresonding stochastically indeendent cumulative distribution function. Denote a cumulative distribution function of valuations for t, i 9

11 t, i tye q t, i by t, i ( v), v [ V t, i, V ], and t, i {, }. As before, we assume that for each transarent quality, the suorts of valuations for high and low oaque quality items do not t, overla, or that V, t {, }. 5 V t, We define a menu of rices for each tye online and offline. The menu for an item with high transarent quality is {,,, )}, where the suerscrit denotes whether the rice is, ( formed offline or online, the first subscrit letter in all three rices indicates that the rices belong to items of high transarent quality, and the second subscrits in the first two rices indicate whether the oaque quality is high or low. The argument in the third rice indicates the bidders belief that the item with high transarent quality has high oaque quality. The menu for an item of low transarent quality,, ( )} is defined in a similar fashion with the {,, only difference that indicates the bidders belief that the item of low transarent quality has high oaque quality. P E P, ( ),. By art (a) of emma 1, we have that P E P, ( ), and We next derive conditions for sorting items of different quality between online and offline latforms. Since bidders observe the transarent quality in both latforms, the market for items with two-dimensional quality essentially breaks into two searate segments: the market for items of high transarent quality and the market for items of low transarent quality. ence, the results and extensions of Proosition 1, Proosition 2, and Corollary 1 about the sorting of items with a single, oaque quality dimension are true for each segment. urther, the sorting of items across two latforms does not deend on the transarent quality er se, since by Proosition 1 all low oaque quality items are listed online, and by Proosition 2 the sorting of high oaque quality items only deends on robabilities,,,,,, and, and the offline latform sale commission. 6 In the next two corollaries we derive conclusions about the quality of items listed in the two latforms. In Corollary 2 we state that if the offline latform exists, then in the offline latform the oaque quality of items with a high transarent quality is no worse than the oaque quality of items with a low transarent quality. This is a direct consequence of Proosition 1: Since items with low oaque quality are always listed online, the oaque quality of items listed offline is 5 We do not imose any other restrictions on distribution functions of valuations for items of different tyes. In articular, we do make assumtions about the correlation between oaque and transarent quality. In the rest of the section, we derive redictions about correlation between oaque and transarent quality in each latform from the equilibrium behavior of sellers. 6 It is easy to see that, because the transarent quality arameter is universally observable, the introduction of additional transarent quality dimensions or additional transarent quality tyes should not affect sellers equilibrium strategies. All results should extend to models with multile transarent quality dimensions and/or tyes. 10

12 always high, regardless of their transarent quality. The emirical imlication of this corollary is that we should observe a non-negative correlation between oaque and transarent quality offline. Corollary 2 If the offline latform exists for items of high and low transarent quality, then the oaque quality of high transarent quality items listed offline is no worse than the oaque quality of low transarent quality items listed offline. In Corollary 3 we resent sufficient conditions when the oaque quality of items with high transarent quality listed online is no worse than the oaque quality of items with low transarent quality listed online, and when both the oaque and the transarent quality of items listed offline is no worse than the oaque and the transarent quality of items listed online. Corollary 3 [1] et t, i be the robability of tye q t, i and t (.) denote an inverse of a rice in an online latform, t, i {, }. a) The oaque quality of items with high transarent quality listed online is no worse than the oaque quality of items with low transarent quality items listed online if,, [ 1] < = ((1 ),,,,, b) The oaque and the transarent quality of items listed offline is no worse than the oaque and the transarent quality of items listed online if, < = ((1 ), [ 1],,,, ). ) and, (1 ),. Proof: Aendix A. Part (a) of Corollary 3 states that unless all items of high oaque and low transarent quality (e.g., skid steers with good engines and bad aint jobs) are listed offline, we cannot guarantee that, within the online latform, the oaque quality of high transarent quality items is higher than the oaque quality of low transarent quality items. This result means that there is necessarily a ositive correlation between transarent and oaque quality online only if all low transarent and high oaque quality items are listed offline, which can haen only if bidders have a sufficiently low belief that a low transarent quality item has high oaque quality. 11

13 Part (b) of Corollary 3 gives a sufficient condition for ure market segmentation, when all high oaque and high transarent quality items are listed offline and the rest of the items are listed online. In articular, art (b) of Corollary 3 states that the oaque and the transarent quality of items offline is no worse than the oaque and the transarent quality of items online, if items of high transarent and high oaque quality (e.g., both good engines and good aint jobs) are exclusively listed offline and if items of low transarent and high oaque quality (e.g., bad aint jobs and good engines) are exclusively listed online. The main conclusion in this section is that an introduction of an additional transarent quality dimension breaks down the unambiguous quality sorting imlication of the basic model with one-dimensional quality. Unless restrictive conditions of Corollary 3 are satisfied, without additional assumtions on the number of tractors of each tye and the weights of each quality tye, it is imossible to make any conclusions about the comarison of average quality across different latforms conditionally on some secific quality arameter or unconditionally on any quality arameters. To illustrate this oint, consider a lausible scenario when items of low transarent and high oaque quality (e.g., bad aint jobs and good engines) are listed offline, while items of high transarent and high oaque quality (e.g., good aint jobs and good engines) together with items of high transarent and low oaque quality (e.g., good aint jobs and bad engines) and items of low transarent and low oaque quality (e.g., bad aint jobs and bad engines) are listed online. 7 In this scenario, it is imossible to make any conclusion about the average quality of items in both latforms without any further information about the quantity of items of each tye and quality weights Emirical Predictions The model yields three redictions that we test in next sections using data on skid steer loaders sold online and offline near Columbus, Ohio. 1. Sellers sort items between auction latforms such that the quality of oaque attributes offline will be no worse than the quality of oaque attributes online, ceteris aribus (Corollary 1). 2. The items sellers sort to offline auctions will feature a non-negative correlation between the quality of transarent and oaque attributes (Corollary 2). 3. Prices for items with high oaque quality sold offline will be greater than or equal to rices for items sold online, which will be greater than or equal to rices for items with low oaque quality sold offline, ceteris aribus (emma 1). The model is silent about several facets of arallel online and offline markets, including: 7 ote that this scenario is consistent with art (a) of Corollary 3 and with our emirical findings. 12

14 4. The difference between the global quality (average of transarent and oaque attributes) of items offered online and offline (Corollary 3, art (b)). 5. The correlation between the quality of transarent and oaque attributes of items listed online is unknown (Corollary 3, art (a)). ote that a ositive correlation will emerge if bidders believe that it is not very likely that an item with low transarent quality will have high oaque quality. Analysis of our data can rovide insights into the qualitative nature of the model arameters governing these asects of the model for this articular market. 3. Data The data includes a samle of 70 used Bobcat skid steer loaders offered for sale within 200 miles of Columbus, Ohio between 2009 and Skid steer loaders are chosen because they are commonly used in a variety of ways by construction and farming enterrises, which lead to heterogeneity in wear and tear for a given age and hours, 8 and because they feature an active secondary market. A single brand is chosen to remove cross-brand heterogeneity and Bobcat is the chosen brand due to its large market share. Machines featuring more than one thousand hours of use are targeted to ensure sufficient quality heterogeneity. The online market chosen is ebay. We received daily s from ebay listing any items featuring the Bobcat name offered by a seller with a shiing address within 200 miles of Columbus, Ohio. All ebay listings featured hotos. Seller contact information for all machines meeting the targeting criteria of more than 1000 hours of use was rovided to a mechanic who contacted the seller to establish a time for the insection. 9 Mechanic requests for insection were never turned down and all sellers made available a machine matching the descrition in the ebay osting. Two sellers we soke with after the comletion of all insections noted that bidders and eventual buyers rarely insect the item rior to bidding. Offline markets consist of in-erson auctions conducted in the same region. We scanned a national website that comiles such auctions to identify Bobcat skid steer loaders advertised as art of local sale catalogs. Subject to availability, a mechanic traveled to the sales location during review hours and conducted an insection of all qualifying machines without revealing quality information to bidders. 8 ours refers to the hours of usage, which is maintained via a dashboard meter in much the same way as mileage is recorded by an odometer in cars. 9 ot all eligible machines were insected due to idiosyncratic conflicts with mechanics schedules. 13

15 The insection regime is consistent between online and offline auctions and consists of an hourlong standardized rocedure involving a checklist and tests develoed by a local Bobcat dealershi and taught to the mechanics through a day-long training session. The insection requires removing anels with aroriate tools to insect hidden arts and starting the machine to check for oerational integrity. More than 40 individual elements are rated on a four-oint scale (oor, fair, good, like new). At the end of the insection, six systems are rated on the same four-oint scale: general aearance, chassis, oerator station, hydraulics, drive train and engine. The ercent of tread remaining on the machine s wheels or tracks is also recorded. inally, mechanics verified and recorded each machine s hours, age and model/horseower. General aearance and tread wear are the systems with the greatest transarency, as general aearance consists of visual elements like aint and lack of dents that can be assessed via hoto, while detailed hotos can also reveal tire wear. The quality of the chassis and oerator s station are the next most transarent. Detailed ictures rovide insight to the general quality, though some issues remain oaque. or examle, hotos can reveal severely bent frames and loader arms that go into the chassis rating, but more subtle frame and undercarriage issues may be difficult to assess. ikewise, a icture can reveal whether a machine s oerator station still has all the handles and buttons that control key functions, but cannot reveal how smoothly the handles maniulate the machine. The hydraulics, drive train and engine feature the least transarency, as each system is best evaluated in erson and tyically requires oerating the machines for several minutes and exloring arts hidden behind safety anels secured by bolts. The natural log of the rating for the six systems and the natural log of the remaining tire tread are key exlanatory variables in our model of latform sorting. Three different mechanics articiated in the study, suggesting that each might emloy slightly different rating metrics desite common training and checklists. Such mechanic-secific differences could induce measurement error. To account for such differences and to minimize the otential for measurement error, we create an instrument by subtracting from each machine s rating the average log rating given by the mechanic for that system across all machines insected. In regression models, we check for robustness by using the raw ratings, the instrumented ratings and several other ossible instruments detailed in the tables of Aendix C. 4. Emirical Results In this section we exlore the redictions of the theoretical model and assess emirical regularities for which the model fails to yield redictions. Table 1 dislays summary statistics for the full samle of insected machines and searately for machines offered in each latform. rom the unconditional comarisons between online and offline machines, we find system-level quality ratings are statistically indistinct between the two latforms. Most other variables are also statistically similar, including a global quality measure that aggregates quality across the six 14

16 insected systems where weights used in aggregation are listed in the bottom of Table 1 and derived from discussions with officials at a regional Bobcat training facility. 10 ence, the ambient quality of items offered on ebay and at in-erson auctions is indistinguishable even among those attributes for which only a thorough detailed insection can reveal quality. The only statistically significant difference between machines offered on ebay and at in-erson auctions is that machines offered on ebay are older. To formally test our redictions concerning sorting of quality between latforms, however, we must consider ceteris aribus conditions Quality Sorting To investigate our model s core quality sorting redictions, we estimate a model of the robability that a machine is offered on ebay rather than at an in-erson auction as a function of machine attributes. The first column of Table 2 dislays a model in which only verifiable attributes are included in the robit model. In line with the summary statistics we find that older machines are more likely to be listed on ebay than at in-erson auctions. In columns 2 and 3 we introduce an additional variable reresenting overall quality across the six insected systems. either the weighted average quality nor an instrumented weighted average quality that accommodates ossible mechanic-secific differences in the use of the rating system yields a statistically significant coefficient. To be thorough, we use four different instruments for average quality in Table C1 (Aendix C). Two of the instrumented versions of average quality yield significant coefficients and in those cases the coefficients are ositive, suggesting that higher quality machines are directed toward ebay. In general, average quality coefficients are insignificant and rovide little evidence that sellers within this regional market are directing machines of lower average quality to ebay rather than to in-erson auctions. Result 1: Average overall quality is similar between machines offered online and offline. When quality ratings of individual systems are added to the model (columns 4 and 5), we find that the fit of the model increases substantially and that several system ratings are significant. When machines feature high quality in transarent systems such as tire tread, general aearance and chassis, they are more likely to be offered on ebay, while when machines have higher engine quality they are more likely to be offered at in-erson auctions. Again, these results are robust across both the uninstrumented quality ratings in column 4, the instrumented quality ratings in column 5 and a second aroach to instrumenting quality discussed in Table C2 (Aendix C). An argument could be made that ebay allows for an alternative signaling mechanism via reutation. To exlore this we re-estimate the models as a multinomial robit in which the 10 The weighting system suggested by the Bobcat dealer reflects the aggregation the dealer uses to formulate osted rices for used machines acquired via trade-in that they offer for sale at their facility. We also exlore formulations of the average quality variable that include tire tread as a searate comonent, but find that adding this comonent never changes any qualitative results in any of the emirical work conducted throughout the aer. 15

17 offering of a machine at an in-erson auction is the base category and offering a machine as a non-dealer on ebay and as a dealer on ebay are treated as alternative latforms. Within our samle of 32 ebay machines, 12 were offered by individuals who offered a single machine during the eriod of two years of our data collection, who we define as non-dealers, while 20 were offered by individuals who offered more than a single machine, who we deem dealers. Table C3 reorts the results of the latform sorting model with system-level quality ratings. The results for both ebay grous is generally consistent with the aggregated results from Table 2. Indeed, tests of differences between individual coefficients for dealer and non-dealers never reveal a statistically significant difference at standard levels (though joint tests reject ooling the two grous). While no statistical difference emerges between individual coefficients between the two ebay grous, a attern is noticeable where ebay dealers tend to have coefficients of larger absolute values than the non-dealer grou. or examle, the coefficient on engine quality for the ebay dealer grou is negative and significant when comared to the reference in-erson auction grou, while the ebay non-dealer coefficient is about 30% smaller and not statistically distinct from the reference grou (-value = 0.16). ence, while no statistical distinction can be made, the data leans towards reutation mining by ebay dealers for the key element of engine quality rather than reutation augmentation by ebay dealers. Result 2: Machines with high quality in a key oaque system (engine) sort to offline auctions while machines with high quality in transarent attributes including tire tread, general aearance and chassis sort to online auctions Correlations between Transarent and Oaque Attributes To investigate our model s redictions concerning the relationshi between the quality observed in transarent and oaque attributes, we calculate Searman rank correlation coefficients across quality levels of both individual systems and across quality as aggregated across transarent and oaque systems (Table 3). Correlations are reorted searately for machines offered on ebay and at in-erson auctions. When quality is aggregated across systems into a single transarent and a single oaque quality, both systems reveal significant ositive correlation between qualities. or offline auctions, where bidders can insect machines, our model redicts a nonnegative correlation between transarent and oaque systems, whereas our model cannot guarantee such a correlation for online auctions. ence, the similarity between the online and offline correlation coefficients is somewhat unexected. owever, this may stem from aggregation across systems, which may be imerfect. Alternatively, we could choose the more and less transarent individual systems and comare the correlation coefficients of individual systems between ebay and in-erson auctions. The least transarent system is the engine. or in-erson auctions, the correlation coefficient with the 16

18 three most transarent systems (tread, aearance and chassis) is ositive and significant, while for ebay auctions, only the correlation with chassis is statistically significant. Indeed, looking at correlations between the three least transarent systems (engine, drivetrain and hydraulics) and the three most transarent systems yields five ositive statistically significant relationshis among machines at in-erson auctions and only two significant correlations among machines offered on ebay. At this more granular level, a trend toward stronger ositive relationshis between oaque and transarent system quality does emerge among machines offered on latforms allowing for ersonal insection. Result 3: or machines offered offline, the quality of transarent and oaque systems is ositive and significantly correlated. Result 4: or machines offered online, the quality of transarent and oaque systems is ositive and significantly correlated, but the correlation tends to be weaker than that observed for machines offered offline Price Differences To investigate model redictions concerning rice generated in emma 1, we estimate models using the natural log of the maximum bid observed for each machine as the deendent variable. The use of secret reserve rices for agricultural and construction equiment is revalent on ebay (Olimov 2013), and for our samle this results in only 25% of listings on ebay resulting in a sale. owever, 19 ebay machines either sold or generated at least one bid, where we take the maximum bid regardless of sale as the market value for the machine. emma 1 imlies that, holding the transarent quality constant, rices will be highest for offline items with high quality oaque attributes and lowest for offline items with low quality oaque attributes. The emma imlies that rices for items offered online, where the quality of oaque attributes is unobserved by bidders, will fall in between with the exact rice level being driven by bidders common belief about the oaque quality of online items, which we do not measure in this market. or the uroses of this regression, we aggregate quality across transarent (general aearance, chassis, oerator station) and oaque (hydraulics, drivetrain and engine) systems using the same aggregation rules detailed in Table 3. urthermore, we dichotomize quality for the aggregated transarent and oaque attributes into high and low qualities by grouing machines that are above the median as high quality and the rest as low quality. We then regress verifiable attributes, a dummy for ebay and a dummy for high oaque quality on the natural log of the maximum bid. Results are reorted in Table 4 searately for machines of high and low transarent quality as we reject ooling high and low transarent quality machines into a single samle ((7,40) = 4.66, -value = ). 17