Reputation and Adverse Selection:
Theory and Evidence from eBay∗
Maryam Saeedi
The Ohio State University
September 17, 2014
Abstract
How can actors in a marketplace introduce mechanisms to overcome possible inefficiencies
caused by adverse selection? Using a unique dataset that follows sellers on eBay over time, I show
that reputation is a major determinant of variations in price. I develop a model of firm dynamics
where firms have heterogeneous qualities unobservable by consumers. Reputation is used as a
signal of private information. I structurally estimate the model to uncover buyers’ utility and
sellers’ costs and qualities. Removing the reputation mechanism increases low-quality sellers’
marketshare, lowers prices, and consequently reduces the market size by 61% and consumer
surplus by 48%.
∗
I am indebted to Patrick Bajari and Thomas Holmes for their valuable advice. I would also like to thank
V.V. Chari, Alessandro Dovis, Konstantin Golyaev, Larry Jones, Patrick Kehoe, Kiyoo-il Kim, Tina Marsh, Ellen
Mcgrattan, Minjung Park, Amil Petrin, Erick Sager, Jack Shen, Ali Shourideh, Neel Sundaresan, Steve Tadelis,
Robert Town, Joel Waldfogel, Thomas Youle, and Ariel Zetlin-Jones, as well as the participants of the Applied Micro
Workshop and Applied Micro Seminar of the University of Minnesota, IIOC, the Ohio State University, Carnegie
Melon University, Arizona State University, State University of New York at Stony Brook, UCLA, Charles River
Associates, Revolution Analytics Inc., and eBay Research Labs’ Reading Group. Any remaining errors are my own.
Correspondence: [email protected]
1
1
Introduction
In recent years, there has been a surge in the use of online marketplaces, such as eBay and Amazon,
where trading occurs in a very decentralized fashion. While these marketplaces have proved to be
popular, they have given rise to asymmetric information problems: sellers can misrepresent the
objects they sell, or they can mishandle the shipping of the items sold. Various reputational
mechanisms have been introduced to remedy these problems. While the role of reputation in
overcoming adverse selection problems is known (e.g.,Holmstrom [1999], Mailath and Samuelson
[2001], Board and Meyer-ter Vehn [2010], and Board and Meyer-ter Vehn [2011], among others), the
empirical validation of this claim, in a dynamic setting, remains unexplored. This paper sheds light
on the value of reputation in overcoming adverse selection by studying reputation among sellers in
the eBay marketplace.
The eBay marketplace, as many authors have pointed out (Resnick et al. [2006], Brown and
Morgan [2006], Lucking-Reiley et al. [2007], Kollock [1999], and Yamagishi and Matsuda [2002],
among others), is plagued by information asymmetries and the problem is somewhat alleviated
using the eBay reputation system.1 Moreover, as Bar-Isaac and Tadelis [2008] mention, eBay
provides a very good environment for economists to study the effects of reputation on sellers’
actions and profits. First, economists can observe all of the sellers’ characteristics observable by
buyers. Second, sellers and buyers have little-to-no interactions with each other outside the eBay
website; thus, buyers do not have additional information about the sellers, which is unobservable
to a researcher. Third, economists can track sellers over time, which gives them extra information
about sellers that is unobservable to buyers. This information can then be potentially used to
estimate underlying model parameters.
I examine sellers on eBay and use a unique dataset that follows them over time. To show the
value of reputation, I first analyze the determinants of price variation in a set of homogeneous
1
For a summary of papers on the effect of eBay feedback system refer to Bajari and Hortaçsu [2004].
2
goods (iPods). Second, I develop and estimate a model of sellers’ behavior over time, in which
sellers have heterogeneous unobserved qualities and build up their reputation over time by selling
objects and acquiring eBay registered-store and/or powerseller status. Finally, using the estimated
model, I perform two main counterfactuals to analyze the effect of reputation on profits and market
outcomes.
In order to empirically analyze the role of reputation, I examine the data on sellers of iPods
between 2008 and 2009, which contains around 168,000 items sold. The dataset follows sellers on
eBay and collects the number of items sold, the information provided by sellers on their website,
the final price of items sold, and sellers’ characteristics. Consistent with other studies on eBay, my
study shows considerable variation in the prices of iPods sold. In this context, there are two main
variables of interest related to reputation: powerseller status and eBay registered-store status. A
seller becomes a powerseller if s/he sells 100 items per month over three consecutive months or more
than $1,000 worth of goods per month for three consecutive months. Moreover, the percentage of
his/her positive feedback must be higher than 98%. A seller can also acquire an eBay registeredstore status by paying a monthly fee of $16-$300 dollars.
Using these two variables as proxies for reputation, I show that reputation has a significant
role in explaining price variations. In particular, prices of new iPods are positively correlated with
reputation. Among sellers of new iPods, being a powerseller, ceteris paribus, increases prices by
approximately $5 dollars, while being an eBay registered-store, ceteris paribus, increases prices by
approximately $6. Although search costs and other factors can also contribute to price dispersion
among identical objects, I posit that the variation in prices cannot only be accounted for by search
costs.
The above empirical analysis, although suggestive, cannot inform us about the value of reputation. Reputation, or an uninformed outsider’s belief about a seller, is a dynamic variable that
sellers builds over time. Hence, we need a dynamic model of sellers’ reputation in order to estimate
3
its value. Using a dynamic model, one can think about the value of reputation in current eBay’s
reputation mechanisms. To do so, I equip standard models of firm dynamics with adverse selection and reputation. To the best of my knowledge, this is the first study to estimate the value of
reputation using a structural model of firm dynamics.
In theoretical work on reputation, asymmetric information is modeled differently. In some
papers, asymmetric information is modeled as an adverse selection on sellers side, i.e., Chari et al.
[2014], others model it as moral hazard, i.e., Friedman and Resnick [2001], and some model it as
a combination of the two, i.e., Holmstrom [1999] and Mailath and Samuelson [2001]. Asymmetric
information on eBay can be modeled as either sellers with exogenous type, adverse selection, or
by assuming sellers’ type is endogenous, moral hazard or the combination of the two, citecaho04.
However, I do not have access to sellers’ effort level and/or cost parameters, or the outcome of
the individual sales; therefore, I cannot identify sellers’ effort and item quality separately. To
overcome this problem, I model the reputation as a pure adverse selection model. This simplifying
assumption can cause an underestimation on the effect of reputation, since in absence of reputation
mechanism, sellers will potentially decrease their effort which can lead to even sharper decline in
items’ qualities in the market.
The structural model in this paper consists of two sets of agents: buyers and sellers. Buyers
are short-lived and derive utility from purchased goods, while sellers are long-lived and can sell
different quantities of items over time. Sellers are heterogeneous in the quality of the goods they
are selling. The higher the quality of a good, the higher the buyers’ utility from purchasing one unit
of that good.2 At the beginning of the game, sellers draw their persistent level of quality, and future
qualities fluctuate around this level by an i.i.d. shock. To capture adverse selection, I assume that
qualities are privately known to sellers; buyers do not observe the quality of an object. Moreover,
buyers are short-lived and they do not observe the quality of the object bought by previous buyers
2
Although quality can be thought to affect cost, this way of modeling quality helps me identify sellers’ quality
levels.
4
from the same seller, i.e., it is not possible to learn through previous observations of quality. This
is a simplifying assumption; however, using click-through data from eBay Inc. Nosko and Tadelis
[2014] report that less than 0.1% of buyers on eBay consider the extended data available for sellers
on eBay website and most of buyers only depend on the aggregated data available on the listing
page; i.e., aggregated feedback ratings and number, and powerseller and store status.3
In the environment described above, I introduce eBay’s reputation system: eBay registeredstore and powerseller status. High-quality sellers can choose to pay a monthly fee to become eBay
registered stores and must fulfill two requirements to become powersellers: sell more than the
quantity threshold set by eBay; and have a quality higher than the quality threshold. Buyers value
high-quality sellers to low-quality sellers and therefore are willing to pay a higher price for an item
sold by high-quality sellers. They use the above two signals to distinguish high-quality sellers from
low-quality sellers. Consequently, sellers value the signals as well and are willing to pay the cost,
either in terms of a monthly fee or in terms of selling more than the static optimum.
In order to model the interaction between sellers, I use the equilibrium concept introduced by
Weintraub et al. [2008]: Oblivious equilibrium. This concept assumes that when making their
choice, sellers do not take into account the choices by other sellers and only consider a long-run
stationary aggregate choice by others. This equilibrium concept makes the model tractable and
approximates Markov Perfect equilibrium when the number of sellers grows.
I estimate the model using two main procedures. First, I identify the stochastic process for
qualities by using the model implication that the optimal quantity choice of sellers is increasing in
their persistent level of quality. This relationship allows me to non-parametrically estimate qualities
using the quantity choices of sellers. Then, using the approach of Bajari et al. [2007], I identify
3
Buyers also have access to feedback left by previous buyers; however, this is not a complete history of items
sold by a seller nor is considered by most of buyers evidenced by lack of impact of these two variables on price, it
is discussed in more detail in Section 2. To get the result discussed in the paper, I need to have a population of
buyers who will use the implied information of having powerseller or store status and do not exploit the information
about the size of the sellers directly. As click data shows, many buyers do not take this additional data into account,
probably because of intangible cost of deducting procedure.
5
sellers’ cost parameters. This process assumes the observed data is the outcome of the sellers’
maximization problem and sellers’ behaviors are their optimal behaviors. This assumption implies
that perturbing sellers’ behaviors in various directions can only decrease their profits. Thus, using
these perturbations, one can estimate deep parameters of the model by minimizing a loss function.
The loss function is defined as the sum of the occasions in which a seller’s perturbed value function
becomes higher than the original value function.
Using the above model, I perform three counterfactuals to estimate the value of reputation. In
the first counterfactual, I remove eBay’s reputation mechanisms. This implies that the problem
solved by sellers becomes a static problem and that there is no dynamic incentive for sellers to
change their behavior. Under this change in policy, low-quality sellers’ profits increase, while
high-quality sellers’ profits decrease. Moreover, as a result of removing the reputation mechanism,
the market share of low-quality sellers increases, while that of high-quality sellers decreases. In
particular, the change in the policy decreases buyers’ surplus by 48%, total sellers’ profit by 85%,
and total eBay’s profit by 60%. This finding suggests that reputation, by increasing the market
share of high-quality sellers, decreases adverse selection in the marketplace.
The second counterfactual I conducted is an attempt to decompose the effects of reputation on
the composition of items. In this counterfactual, I assume that sellers are forced to sell the same
number of items as they used to sell in the world with reputation. The only change is that buyers
do not observe any signals. In this case, the equilibrium price is a weighted average of prices for
different types of sellers in the original setting. This change has no effect on total sellers’ profit,
consumer surplus, or eBay’s profit.
In the third counterfactual, I estimate the effect of adding warranty as a substitute for the
reputation mechanism. Sellers can provide a warranty, promising that the quality of the item
provided is higher than a given threshold. As a result of increase in high-quality sellers’ profit,
total sellers’ profit goes up. Depending on the level of quality threshold, buyers’ welfare and eBay’s
6
profit can increase or decrease compared to the no-signaling case. However, at certain quality
thresholds, surplus values will get very close to those with a reputation mechanism, and sometimes
even higher.
Related Literature. This paper contributes to two lines of literature: theoretical papers
on reputation and empirical work on reputation systems. Bar-Isaac and Tadelis [2008] have an
excellent summary on both lines. Although many papers have explored these topics, to the best
of my knowledge, this paper is the first to empirically estimate the role of reputation based on a
dynamic model of firm behavior.
In this paper, reputation can help mitigate adverse selection problems similar to an extensive
literature on modeling reputation as beliefs about behavioral types (i.e., Milgrom and Roberts
[1982], Kreps and Wilson [1982], Holmstrom [1999], and Mailath and Samuelson [2001] to name a
few).4 The closest paper is perhaps Holmstrom [1999], where managers have private productivity
types and an outsider can learn about the type over time. My paper departs from this line of
research, in that I abstract form learning. Reputation in the model developed here is the mechanism
introduced by the marketplace (in this case eBay) that can help signal sellers’ private types.
There exists empirical literature examining the reputation mechanism, as well as papers on
eBay itself. Bajari and Hortaçsu [2004] and Dellarocas [2005] have excellent summaries of this line
of literature. Examples of major empirical work in this area are Resnick and Zeckhauser [2002],
Melnik and Alm [2002], Houser et al. [2006], Resnick et al. [2006], Masclet and Pénard [2008] , and
Reiley et al. [2007]. These papers study the role of the feedback system on eBay. They find positive
correlation between the price of an item and the feedback that a seller has received. Cabral and
Hortacsu [2009] empirically study the feedback system in a dynamic setup, and they find that the
first negative feedback has a negative effect on sellers’ exit rate, but consecutive negative feedback
ratings do not have large effects on sellers’ performance and exit rates. I build on these papers by
4
Many papers have applied the techniques introduced in this literature to more applied problems. See Chari et al.
[2014], Board and Meyer-ter Vehn [2010], and Board and Meyer-ter Vehn [2011]
7
providing evidence of the effect of powerseller status and/or eBay registered-store status on sellers’
revenues and profits and by structurally estimating the value of reputation using a dynamic model
of reputation.
In my analysis, empirical and theoretical, reputation and adverse selection play key roles. A
few studies have pointed out the significance of the adverse selection problem on eBay. Using a
novel approach, Yin [2003] shows that the final price of the object is negatively correlated with
the dispersion in the perceived value of the object. This observation implies that the higher the
dispersion in perceived value, the higher the discount at which the buyers are willing to purchase
the good. This points to the existence of information asymmetries and their negative effects on the
final price of an item. Lewis [2011], however, shows that by selectively revealing information, sellers
decrease the dispersion of the perceived value and thereby increase their final price. He considers
the number of photos and the amount of text a seller provides for an object to be the main source
of revealing information and finds that the final price increases with the number of photos and the
amount of text uploaded on the auction page.
The paper is organized as follows: in Section 2, I describe the dataset analyzed in this paper
and I give an overview of the market structure on eBay. In Section 3, I develop the dynamic
model of sellers’ behavior and their interactions with buyers through eBay. In Section 4, I describe
the identification procedure for the deep parameters of the model. In Section 5 , I describe the
estimation of the model. In Section 6, I perform three counterfactual exercises to estimate the
value of reputation. Finally, Section 7 concludes the paper.
2
Data
The dataset consists of all transactions of iPod sales on the eBay website over eight months between
2008 and 2009. Summary statistics of the data are shown in Table 1. This market is a narrow
market, which enables me to understand factors that affect customers’ preferences. I collected
8
data from the eBay website using a spider program.5 The program searched for all completed
iPod listings and saved the information contained on the eBay website into a file. The program
ran frequently to collect new data points. I further analyzed the data and collected variables of
interest, e.g., items’ characteristics, sellers’ characteristics, and listing format.
iPods come in different models and each model has several generations. Each generation of a
model can have varying levels for internal memory. In the new generations of a model usually the
available options for the internal memory increase. The newest model introduced is “iPod Touch”
and the first model introduced is “iPod Classic.” Some iPod models, such as “iPod Mini”, are
out of production. Figure 1 shows the time-table of different models of iPods produced by Apple
and their initial date of release and their price at the launching time. One important advantage
of studying the iPod market is the homogeneity of these products. Additionally, there are few or
no promotions outside the eBay website for these products, and their price usually stays the same
before the introduction of a new generation of iPods.
2.1
eBay
Data was collected from eBay, an online auction and shopping website, where individuals can sell or
buy a wide variety of items. It is the largest online auction website on the Internet. In early 2008,
eBay counted hundreds of millions of registered users, more than 15,000 employees, and revenues
of almost $7.7 billion.6
Sellers can sell their items either through an auction or by setting a fixed price for their item, an
option called “Buy it Now.” The auction mechanism is similar to a second price or Vickrey auction.
A seller sets the starting bid of an auction and bidders can bid for the item. Each bidder observes
all previous bids, except for the current highest bid. A bidder should bid an amount higher than
the current second highest bid, plus some minimum increment.7 If this value is higher than the
5
The program is written in python, a scripting language.
source: http://en.wikipedia.org/wiki/eBay
7
The increment is a function of the second highest bid, fixed for all auctions, and is set by eBay.
6
9
current highest bid, the bidder becomes the new highest bidder. Otherwise, he becomes the second
highest bidder. The winner has to pay the second highest bid, plus the increment or his/her own
bid, whichever is smaller. Auctions last for three to ten days and they have a pre-determined and
fixed ending time that cannot be changed once the auction is active.
After each transaction on the eBay website, sellers and buyers can leave each other feedback.
Feedback can be negative, neutral, or positive. A summary of feedback history for sellers is available on the auction page. After 2007, buyers can also rate sellers in four different criteria: Item
as Described, Communication, Shipping Time, and Shipping and Handling Charges. This extra
information is not shown on the auction page, but is accessible through the seller’s webpage.
Figures 2 and 3 show a snapshot of a finished auction page and also bid history for the same
item. At the top of the page, there is information about the object and its bid history. On the top
right side of the page, information about the seller can be found. The rest of the page contains more
detailed information about the object sold in the auction. Bidders have access to the bid history
page, which shows previous bidders’ short form IDs, their bids, and the time they submitted their
bid.8
Sellers can register as an “eBay store.” An eBay store pays lower listing fees but must pay a
fixed monthly fee to eBay. In addition, it should follow eBay policies and have a high seller standard
rating.9 Sellers can become “powersellers” if they have a high enough feedback score, have sold
more than a fixed value in the past three months, and have a high seller standard rating.10 This
information is observed by the buyers on the listing page, as well.
8
eBay stopped showing the complete ID of bidders in 2007, mentioning the following reasons: to keep the eBay
community safe, enhance bidder privacy, and protect eBay’s members from fraudulent emails.
9
Seller standard rating includes many different variables, such as low open disputes, few number of low Detailed
Seller Ratings, and no outstanding balance. Buyers can rate sellers based on different aspects, communication, item
as described, shipping fee and speed, in Detailed Seller Ratings.
10
The requirements for becoming a powerseller are as follows:
Three-Month Requirement: a minimum of $1,000 in sales or 100 items per month, for three consecutive months.
Annual Requirement: a minimum of $12,000 or 1,200 items for the prior twelve months.
Achieve an overall Feedback rating of 100, of which 98% or more is positive.
Account in good financial standing.
Following eBay rules.
10
2.2
Data Summary
Table 1 shows the data summary of variables used in this paper. eBay registered-store and powerseller status are indicator variables. As shown in Table 1, 36% of listings in my dataset are sold by
eBay registered stores and 48% are sold by powersellers. I further focus on sellers with at least 10
sales in my data since small sellers with very few sales may not act optimally. This will reduce the
total number of sellers from 46,552 to 769, which makes the problem more tractable; in addition,
it reduces total number of transactions to 84,301, about half of the original data.
Two other variables associated with the reputation of sellers that have been studied in depth in
literature, Bajari and Hortaçsu [2004], are the “Seller Feedback Number” and the “Seller Feedback
Percentage.” The Seller Feedback Number is the total number of positive feedback minus the total
negative feedback received by the seller. Feedback percentage is the percentage of positive feedback
that sellers have received. In my dataset. The standard deviation of feedback percentage is very
low and most sellers have a feedback percentage higher than 99%. In my dataset, the effect of these
two variables on price is very small and studied in more detail in the next section. In addition,
Table 10 shows very small effect for feedback percentage or even with negative sign for number of
feedbacks. This finding is due to the fact that one of the requirements for becoming a powerseller is
to have a feedback percentage higher than 98%, and another requirement is to have a high volume
of sales on the eBay website. Therefore, the main effects of feedback percentage and number are
embedded in powerseller status.
Most of the items sold on the eBay website in my dataset were sold using an auction method,
and only 8% of them were sold using a fixed price method. Therefore, in the model section, I
assume that sellers are setting the quantity and the price is determined in the market. In an eBay
auction setting, sellers can set a secret reserve value, where if the final bid is lower than this value,
11
the trade will not occur. Only 4% of listings have used this option; thus I do not model it further.
I also collect a set of characteristics for items listed, such as the condition of the item, new,
refurbished, or used, the level of internal memory of an iPod, and the make of iPod. Most iPods
sold on eBay are used items with 25% of listings being new and 19% being refurbished. One would
expect to see a higher effect for reputation when I focus on used items, since there are more sources
of adverse selections for those items: the battery may not be working, the screen may be scratched,
or the touch pad screens may not work properly, etc. In Appendix B, I show that the effect of
powerseller and registered-store status increase, when I focus on used items.
2.3
Reputation and Price
The eBay registered-store and powerseller status signal sellers’ quality. They show that sellers are
following eBay rules closely and have a good track record. Table 2 shows the final prices of items
sold on eBay are higher when sellers are powersellers, or when they are eBay registered stores. The
first column of Table 2 shows the average price of all iPods in my data. Having registered-store
status or powerseller status increases the average final price for sellers. This increase in price may
be a result of a selection problem: if sellers with powerseller status or registered-store status tend
to sell items with higher value, they will get a higher price not due to higher reputation. This
selection problem can be accounted for by controlling for the item characteristics. Specifically, I
use the regression formulation that I later use to estimate the buyers’ demand to show the fitted
values for for an iPod with the average characteristics observed in data. The average fitted prices
are shown in the third and fourth columns, the average price goes up for sellers with powerseller
and store status by 15% and 5% respectively. The last two rows of this table studies the effect
of moving from the average of lowest 25% of feedback percentage observed in data to the average
of highest 25% of feedback ratings for sellers in my dataset on price, when controlling for item
characteristics the effect on the price is negative and sellers with higher positive feedback receives
12
a lower price. This finding is consistent with findings in Cabral and Hortacsu [2009].11
Another reason for observing price differences can be unobservable heterogeneity among sellers
or items. The number of sellers with status change was not large enough to exploit the price change
for sellers as they change their status.12 In Table 9, I control for more observable characteristics
such as amount of text or number of pictures provided to control for observable differences among
sellers. Adding these controls does not reduce the effect of reputation signals. Further, I study
new and used items separately. Used items are potentially heterogenous as their condition can vary
from “Like New” to “Not working, for Parts”, which is not observable in my data. On the other
hand, new items are less prone to these unobservable characteristics especially for iPods. As shown
the effect of powerseller is higher for used items as expected but the effect is still positive for new
items. In Table 2, I included the average prices for “New iPod Nano”. As shown in the table, the
effect of acquiring status do not disappear even for very homogenous group of items sold by sellers.
Additional to the effect of reputation on prices, it can have an effect on sellers’ decision about
the number of items they list over time. Therefore, it has a dynamic effect on sellers, especially
for powerseller status, by requiring sellers to sell more than the threshold set by eBay for three
consecutive months to be eligible for the powerseller program. To estimate the dynamic effects of
reputation on sellers’ actions and profit, I develop a dynamic model of reputation. The model also
enables me to simulate the actions of sellers in absence of these reputational variables for a complete
comparison between the two regimes and to estimate the effect of reputation on the market.
11
Cabral and Hortacsu [2009] further study the dynamic effect of negative feedback on sellers actions. They find
that the most important effect of negative feedbacks are preventing the very low quality sellers from participating,
as the first negative feedback increases the probability of exit for sellers substantially. However, they do not find big
impact on the prices.
12
In a more recent paper, Hui et al. [2014], my coauthors and I study the effect of Top Rated seller status by
studying sellers who change their status. Top Rates Status is a new reputation signal on eBay with very similar
characteristics as powerseller status, with one of its requirements being having powerseller status. In this paper, we
use various differences in differences studies to show that the increase in price as a result of getting the reputation
badge comes mainly from the signaling aspects rather than learning or other omitted variables. Particularly, we look
at sellers whose status has changed multiple times and the price effect they receive for their successive status change.
In another robustness check, we consider sellers who are close to the requirements, just few items sold less or above
the change. The study in the paper shows that the effect we observe from the price regression is mainly as a result
of signaling rather than unobserved heterogeneity.
13
3
Model
To capture the dynamic effect of reputation, I developed a dynamic model of reputation similar to
Holmstrom [1999] and Mailath and Samuelson [2001]. There are two major players in this market:
buyers and sellers. eBay is the informed market designer. Sellers have heterogeneous qualities,
which are unobservable to the buyers. eBay can observe the quality of sellers and has set up the
signaling mechanism for sellers to signal their quality to buyers.13 This reputation system helps
buyers distinguish high-quality sellers from low-quality sellers and to give the sellers with higher
quality a higher profit.
3.1
eBay
eBay is the market designer in this setup and sets different mechanisms for sellers to signal their
quality. I assume it observes the quality of sellers. eBay can observe these values based on the
history of sellers in the market. It also has access to more detailed information about sellers, which
is not disclosed to the buyers, such as the number of disputes a seller received from buyers.
Mechanisms that I model in this paper are similar to those of powerseller status and registeredstore status. Sellers who sell more than Qp , a threshold set by eBay, for three consecutive periods
and have quality, rjt , higher than µp , are signaled as powersellers. A seller should not pay any fixed
or monthly fee to be included in this program.
Sellers who have quality, rjt , higher than a threshold set by eBay, µs , can register their account
as an eBay registered store. They have to pay a monthly fee to eBay to participate in this program,
cs .
13
In this paper, eBay is not optimizing the reputation mechanism. I am taking the strategy of eBay as given and I
model this very closely to the eBay rules. In this paper, I do not model the process in which eBay is using to identify
sellers’ quality levels. The procedure can be think of as one similar to the current practice of eBay, having thresholds
for different signals of quality, i.e., feedback ratings, detailed seller ratings, and dispute rates, as well as complying
with eBay rules and regulations. I do not observe the outcome of the transactions in terms of buyer satisfactions, as
I do not have access to the post transaction data which makes the model unidentifiable.
14
3.2
Buyers
There is a measure M of buyers and N of sellers. Buyers are short-lived and cannot track sellers
over time. Each period, every buyer decides to either buy one of the items offered by one of the
sellers or to buy the outside good.14 Buyers do not observe the quality of sellers. Instead, they only
observe two signals that are correlated with sellers’ quality: powerseller status and registered-store
status.
The buyer i gets random utility uijt from purchasing an iPod from the seller j at the time
period t:
uijt = −αpjt + βr rjt + ξt + ξjt + ijt
where pjt is the price of the item sold by the seller j at the time period t. rjt is the quality of
the seller j at the time period t, which is unobservable to buyers.15 To determine this variable,
buyers receive two signals in the form of powerseller status and registered-store status. ijt is the
unobservable utility random variable with the logit distribution. Note that I do not model buyers’
choice of type of iPod explicitly, I assume that buyers and sellers are trading an iPod with average
characteristics of iPods in my dataset.16
I will show that buyers infer information about the seller’s quality based on powerseller and
registered-store status, as well as the seller’s equilibrium strategy. This inference leads to a structural demand function based on equilibrium parameters and the two reputational signals. I will
further discuss the demand structure in Section 3.5.
14
The outside good is buying another model of an MP3 player on eBay.
Seller’s quality represents information about them that is important for buyers, such as sellers’ honesty about
the item characteristics or customer service.
16
Modeling endogenous choice of type of iPods to buy and sell will add complications to the model which even
though interesting is not in the scope of this paper.
15
15
3.3
Sellers
Sellers are born with a persistent level of quality, ηj . In each period, assumed to be one month,
sellers decide on quantity of items to list on the eBay’s website, qj , and their store status, φjt .
Sellers can potentially obtain two signals: powerseller status, φp , and registered-store status, φs .
As mentioned before, sellers will sell an iPod with average characteristics of iPods in my dataset.
Timing of sellers’ decision is described in Figure 4. At the beginning of each period, sellers
learn about the shock to their quality, γjt , which is i.i.d. distributed with distribution G.17 Their
quality at period t is:
rjt = ηj + γjt
Having determined their level of quality at this period, sellers’ powerseller status, φpt , is determined
by the following formulation:
φpjt = 1 ⇔



 qjt−1 + qjt−2 + qjt−3 > 3Qp
(1)


 rjt > µp
After knowing their powerseller status and quality level, sellers make a decision about their store
status if rjt > µs . Next, they choose the number of items they want to sell. Sellers’ profit function
at time t is:
π(qjt , φpjt , φsjt , Qt ) = p(qjt , φpjt , φsjt , Qt )qjt − cqjt − cs φst
where Qt is the total quantity of iPods provided in the market. c is the marginal cost of acquiring
an iPod for sellers. This is as modeled the cost of an average iPod or averaged marginal cost of
different iPod types. I can easily change the model and estimation procedure to estimate different
17
In this paper, I have assumed that sellers’ quality is determined exogenously and sellers cannot select their quality
directly by making an effort or investing in quality, as formulated in prior theory papers (e.g., Holmstrom [1999],
Mailath and Samuelson [2001], Board and Meyer-ter Vehn [2010], and Board and Meyer-ter Vehn [2011]). The main
reason for this simplifying assumption in the model is the lack of data. I do not observe sellers’ quality and their
level of investment or any other variable about the way they run their online store; therefore, I cannot estimate the
two variables separately.
16
cost values for different types of iPods; however, I am not modeling sellers choice of type of iPod
to sell and in simulations they will select an iPod with average characteristics of iPods sold in my
dataset. On the other hand, the findings of this paper cannot be extended easily to the case of
sellers with different marginal cost levels of obtaining iPods, of the same condition and type, which
can lead sellers to different pricing scheme and consequently different equilibrium outcome.18 cs is
the monthly fee of being a registered store. This fee is set and charged by eBay. The price of the
iPods in the market is p(qjt , φpjt , φsjt , Qt ). The price is the outcome of the buyers’ problem and in
Section 3.5, I will discuss the demand function formulation in detail.
Sellers interact with each other in an oblivious equilibrium, the concept introduced by Weintraub
et al. [2008]. In this equilibrium concept, sellers do not take into account the state variables of every
other seller in the market, but consider a long-run stationary aggregate choice by other sellers. This
helps me later in the estimation process.
Given q− = {qjt−1 , qjt−2 , qjt−3 }, I can formulate sellers’ decision problem as follows:
Z
p s
0
0
V (ηj , γ, q− ) = maxs π(qj , φj , φj , Q) + β V (ηj , γ , q− )g(γ)dγ
qj ,φj
(2)
subject to:
q0− = (qj , qj,−1 , qj,−2 )
φsj = 0
if
φpj = 1
if
ηj + γ < µ s



 qj,−1 + qj,−2 + qj,−3 > 3Qp
(3)


 ηj + γ > µ p
18
Recall that I am focusing at the sellers with at least 10 iPod sales and they are all professional sellers on eBay
and they potentially face the same upstream market. Moreover, iPods are very standard items and there are not that
many promotions for them outside eBay. I have tried to contact some of the big sellers in my sample and get some
sense of their sources of obtaining the iPods, to verify this assumption; however, none of the sellers respond to my
correspondence as they do not want to share their sources to lower competition.
17
Let q ∗ (η, γ, q0− ) be a non-negative integer and φs∗ (η, γ, q0− ) be a binary function that solve the
above problem. β is sellers’ discount factor.
There is no entry into this economy after period 0. There is no permanent exit from the market,
either. Sellers can decide to sell no items one period, which can be interpreted as exiting the market;
however, they can return to the market without paying a fee in the next period.
3.4
Equilibrium
I use the oblivious equilibrium concept as introduced by Weintraub et al. [2008]. Equilibrium is a
set of quantities, characteristics of sellers, buyers’ beliefs, average total quantity, and prices, such
that:
• given quantities, characteristics of sellers, and buyers’ beliefs, prices are the outcome of buyers’
demand function;
• sellers are maximizing their value function given buyers’ demand function, buyers’ beliefs,
and total quantity in the market;
• requirements for powerseller and registered-store status are determined based on eBay requirements;
• buyers’ beliefs are consistent with sellers’ behavior;
• total quantity in the market is consistent with sellers’ individual quantity choices; and
• the market clears.
Note that when sellers maximize their value function, they do not take into account other sellers’
individual actions and their state space in the market; instead, they take into account the total of
these values. This is the major feature of an oblivious equilibrium as discussed in Weintraub et al.
[2008], and it approximates the Markov Perfect equilibrium as in Ericson and Pakes [1995] when
18
the number of sellers is large. This method is based on the idea that when the number of sellers is
large, the individual sellers’ shocks average out because of the law of large numbers and the average
state remains roughly the same. In this paper, the number of sellers used in the estimation section
is more than 700. Weintraub et al. [2006] show that when the number of sellers is in the order
of magnitude of 100, the error caused by using the oblivious equilibrium instead of the Markov
Perfect equilibrium is very low.
If instead of oblivious equilibrium I use Markov equilibrium concept, then each sellers action
should be optimal given the choice of every other seller. However, given that the other sellers
choice only enters the seller decision through the price, further the effect of the other sellers in
the market on the price is only through the changes in market share of a given seller, the only
important statistics for sellers are the total size of the market. However, in Markov equilibrium
sellers can potentially predict that smaller or larger portion of the sellers will become Powerseller
in the future but tracking their individual actions before.
3.5
Demand Formula
Buyers do not observe sellers’ quality ; but sellers’ quality affects their utility. Suppose first that
buyers do not observe any signal from sellers. Then their expected utility from buying an item is:
E(uijt ) = −αpjt + βr E(rjt ) + ξt + ξjt + ijt
Assume that a seller only sells one type of good each period. Then the market share of seller j at
time t, given that the distribution of error terms is coming from the logit distribution, is:
sjt =
exp(−αpjt + βr E(rjt ) + ξt + ξjt )
P
1 + exp(−αpj 0 t + βr E(rj 0 t ) + ξt + ξj 0 t )
19
Following Berry [1994], I assume the utility of outside good is normalized to zero. Then I can
decompose the formulation for the market share, using the formulation of outside good share, s0t :
log(sjt ) − log(s0t ) = −αpjt + βr E(rjt ) + ξt + ξjt
Therefore:
pjt = (−log(sjt ) + log(s0t ) + βr E(rjt ) + ξt + ξjt )/α
The demand function can be generalized in the case that buyers observe signals of quality, such as
powerseller, φpjt , and registered-store status, φsjt . In this case, buyers’ expected utility function is:
E(uijt |φpjt , φsjt ) = −αpjt + βr E(rjt |φpjt , φsjt ) + ξt + ξjt + ijt
The same set of analysis as above leads to the following pricing function:
pjt = (−log(sjt ) + log(s0t ) + βr E(rjt |φpjt , φsjt ) + ξt + ξjt )/α
where E(rjt |φpjt , φsjt ) is the expectation of a seller’s quality based on its two reputational signals.
This expectation is endogenously determined by equilibrium decisions of sellers in the market and
is subject to change based on the market setup.
Note that φpjt and φsjt are binary variables and can only be zero or one. Let r̄mn = E(rjt |φpjt =
m, φsjt = n). Then, E(rjt |φpjt , φsjt ) can be written as:
E(rjt |φpjt , φsjt ) = r̄00 + (r̄10 − r̄00 )φpjt + (r̄01 − r̄00 )φsjt + (r̄00 − r̄10 − r̄01 + r̄11 )φpjt φsjt
Substituting the above expression into the demand function formula leads to the following formu-
20
lation:
pjt = [−log(sjt ) + log(s0t ) + ξt + ξjt ]/α
+βr /α[r̄00 + (r̄10 − r̄00 )φpjt + (r̄01 − r̄00 )φsjt + (r̄00 − r̄10 − r̄01 + r̄11 )φpjt φsjt ]
= [−log(sjt ) + log(s0t )]/α + r̄00 βr /α + βp φpjt + βs φsjt + βps φpjt φsjt + [ξt + ξjt ]/α
(4)
This formulation can be used to estimate the parameters of the demand function, which gives us
a mean to estimate deep parameters of buyers’ utility function. The estimation method for the
above formula will be discussed in Section 5.
4
Equilibrium Characterization and Identification Procedure
In this section, I characterize sellers’ equilibrium quantity choice in more detail. Using this result,
I describe the method to identify the main parameters of the model based on the data. These
parameters include sellers’ unobservable quality, their cost parameters, and buyers’ utility function.
These are the deep parameters of the model that affect buyers and sellers’ decisions, and are used
in my counterfactual analysis. In particular, I assume they are invariant if we remove powerseller
and registered-store status, and sellers cannot signal their quality anymore. Focusing on the key
implication of the model (policy functions are increasing as a function of quality), I show how it
helps to identify unobserved qualities.
4.1
Analysis of Quantity Choice
One of the decisions sellers make each period is the number of items to sell. Given eBay’s market
structure, i.e., sellers sell their items in auctions, I have assumed that sellers do not set the prices,
but rather the number of items to sell. In this setting, this is a dynamic decision that sellers are
making, since the number of items they sell will affect their powerseller status in the future. In
21
other words, there is a dynamic complementarity between sellers’ quality and quantity choices. The
following proposition states sellers’ quantity choice is increasing in their persistent level of quality,
η. This is one of the main implications of the model that helps to identify sellers’ quality.
Proposition 1 Suppose that the solution to the functional equation (2) is unique. Then, the policy
function q ∗ (η, γ, q− ) is increasing in the persistent level of quality, η.
Proof. Here, I sketch the proof. Appendix A contains a complete and more detailed version of the
proof. Recall the functional Equation 2 in Section 3.3. To prove the proposition, I use a method
similar to Hopenhayn and Prescott [1992] adopted from Topkis [1998], and I show the objective
function has increasing differences. First note that the optimal choice of φs does not affect future
values. Hence, I can define the following period profit function:
π̂(η, γ, q, q−1 , q−2 , q−3 ) = max π (q, φs , φp )
{z
}
|
φs ∈{0,1}
(5)
q−
subject to:
φs = 0
if
φp = 1
if
η + γ < µs ,



 q−1 + q−2 + q−3 > 3Qp


 η + γ > µp
I prove the proposition in three steps:
Step 1. π̂ (η, γ, q, q−1 , q−2 , q−3 ) is supermodular in (η, q) and in (η, q−i ) for i = 1, 2, 3.
Step 2. I show that the solution to the functional Equation 2 is supermodular in (η, q−i ) for
i = 1, 2, 3.
Step 3. The policy function is increasing in quality η.
The intuition for this result is the dynamic complementarity between sellers’ quality and quantity choices. That is, a seller with a higher persistent level of quality will have a higher probability
22
to meet the quality eligibility of powerseller status in the future. Moreover, given the results of
demand estimation, being a powerseller increases the final sale price for sellers. Thus a seller, with
a high persistent level of quality, has more incentive to sell more items to meet the quantity eligibility of powerseller status. Proposition 1 also makes it clear that the only determinant of firm size
dynamics is reputation; sellers are willing to increase their size in anticipation of future powerseller
and registered-store status. Absent these mechanisms, firms have no incentive to change their size.
Another implication of the model on the quantity choice of sellers is that optimal quantity
choice can be represented as a function of sellers’ persistent level of quality, their powerseller and
registered-store status, and their quantity in the last two periods. Controlling for powerseller and
registered-store status allows us to drop sellers’ transitory shock to quality, γjt , as well as their
quantity three periods ago, q−3 .
Lemma 1 The policy function q ∗ (η, γ, q− ) can also be represented as q ∗ (η, φs , φp , q−1 , q−2 ).
Proof. Sellers choose the quantity of items to sell after the powerseller status has been determined
and they have selected registered-store status. The profit function of sellers, π(qj , φpj , φsj ), and their
expectation of continuation value function,
R
V (ηj , γ 0 , q0− )g(γ)dγ, are not directly a function of γ
or q−3 . Therefore, sellers’ choice of quantity should not depend on γ or q−3 after we control for φpj
and φsj .
The above lemma will help in in modeling sellers’ choice of quantity in Section 5. Note that
Proposition 1 can also be extended to the policy function with this new representation, and this
policy function is also weakly increasing in the persistent level of quality.
4.2
Identification Procedure
Three main sets of parameters need to be identified: buyers’ utility function, sellers’ unobservable
quality, and sellers’ cost parameters. The first two sets of parameters is estimated using a three-step
procedure. The third set is identified using a two-step method similar to Hotz and Miller [1993]
23
and Bajari et al. [2007].
19
The three-step procedure is used to estimate the unobservable sellers’ quality and buyers’ utility
function. An overview of the procedure is as follows:
1 Estimating the structural demand function. This gives us an estimate of α, βp , βs , and βps .
2 Estimating the realized policy functions. Given Proposition 1 and Lemma 1, the quantity choice
of sellers can be used to identify the quality of sellers. By controlling for powerseller and
registered-store status and sellers’ quantity choice in the last two periods, the fixed effects for
sellers are an index for sellers’ persistent level of quality.
3 Using the Simulated Method of Moments to estimate the deep parameters of the model. Having
an index of sellers’ permanent level of quality from the second step, sellers’ quality using two
moments from the demand function, (Equation 4), can be parametrically estimated.
(r̄10 − r̄00 )/βp − (r̄01 − r̄00 )/βs = 0
(r̄10 − r̄00 )/βp − (r̄00 − r̄10 − r̄01 + r̄11 )/βps = 0
(6)
I also use the average number of powersellers and the average number of registered stores in
addition to the above moment conditions to simultaneously estimate sellers’ quality, quality
thresholds for powerseller and registered-store status, and βr , the coefficient of quality in the
utility function of buyers. The estimation procedure will be discussed in detail in Section
5.2.3.
The next step is estimating the cost parameters of sellers using a two-step estimator method
similar to the method in Hotz and Miller [1993] and Bajari et al. [2007]. The method uses the
basics of revealed profit to estimate the deep parameters of the model and, in this case, to estimate
19
Some of the steps in identifying unobservable quality and cost parameters do overlap.
24
the cost parameters: the average monthly cost sellers should pay to become a registered-store on
eBay, cs , and the average cost of obtaining an iPod for sellers, c.
In the first step of this method, I estimate the structural demand function of buyers and policy
functions of sellers. Then assuming the estimated policy functions are the optimal choices of
sellers, any perturbation of these functions should yield a value function lower than the original
value function when I use the original policy function. The cost parameters are those that satisfy
the above condition. The two-step estimation procedure is as follows:
1A estimating the structural demand function;
1B estimating the realized policy functions;
2A perturbing the policy functions;
2B simulating the model using the original policy functions and the perturbed policy functions;
and,
2C defining the loss function as a function of the model parameters,
X
(Vperturbed (θc ) − Voriginal (θc ))2 1[(Vperturbed (θc ) − Voriginal (θc )) > 0]
sellers,perturbations
where C is the vector of cost parameters; Vperturbed (θc ) is the value function using perturbed policy functions; and Voriginal (θc ) is the value function using the original policy functions.20 1[Vperturbed (θc ) − Voriginal (θc ) > 0] is an indicator function that is equal to one if
Vperturbed (θc ) − Voriginal (θc ) > 0, and it is otherwise equal to zero. If this expression is positive, it means that the seller’s value function is higher for perturbed policy functions, which
cannot be the case if C is the true cost parameter. The summation is taken over all sellers
and different perturbations.
20
The results are robust to other definitions of loss function, i.e., sum of the absolute values of deviations.
25
2D Estimating the cost parameters after minimizing the loss function as defined above. Under the
true cost parameters of the model, the estimated policy functions is optimal. Therefore, the
cost parameters that minimize the above loss function are consistent.
5
Estimation
In this section, I estimate the deep parameters of the model using the identification procedure
explained in Section 4.2.
5.1
Estimating Structural Demand
To estimate the structural demand function, I use the demand Equation 4 derived in Section 3.5.
This formula translates into a simple OLS regression of price over the logarithm of the sellers’ share
minus the outside good’s share, powerseller status, registered-store status, and characteristics of
the item and listings. Various variables for characteristics of listings and items are considered,
Section B reviews some of different setups for demand. Unlike the demand function in the model,
we have included item characteristics in this regression; however, in simulations, I use the average
characteristics of iPods in my dataset when picking the iPod.21 Also note that this formula does
not have any structural error term; there is no firms’ unobservable quality, which is observable to
buyers but not to econometricians.
Table 3 shows the results of the regression and it is worth discussing. The effect of changes
in log(s0 ) − log(sj ) is captured by 1/α and it is positive. This means that when sellers sell more
items, they sell at a lower price per unit. Therefore, the demand function is elastic. Moreover, the
coefficient of powerseller status is positive, which shows that the expectation of quality is higher for
sellers with powerseller status. Finally, the coefficient of registered-store status is positive, which
shows that the expectation of quality is higher for sellers who are a registered-store than for sellers
21
This method gives similar results as having an intercept which will represent average price of items sold by sellers
who do not have powerseller or store status; however, it makes the counterfactual studies easier.
26
who are not a registered-store. Both of these observations are consistent with Section 3: sellers
with high level of quality become powersellers and registered stores.
Moreover, the above regression also determines how characteristics of the iPods sold affect their
price. Compared to used iPods, new iPods have a premium of $37.48 on average and refurbished
iPods have a premium of $13.11 on average. Each extra gigabyte of internal memory on an iPod
results in an extra $1.42 in price. I have also included a fixed effect for the type of iPods: Nano,
Touch, Classic, Mini, Video, and Shuffle; their coefficients were as expected, with the highest for
Touch and lowest for Shuffle. Time period fixed effects are also included to treat the seasonal fixed
effects, each month considered to be a period. I carry out additional robustness checks on this
demand formulation by adding more characteristics of sellers and focusing on a subset of data.
These checks can be seen in Appendix B.
5.2
Estimating Policy Functions and Sellers’ Quality
In this section, I estimate sellers’ policy functions and their persistent level of quality using their
original actions. Sellers have two policy functions in this model: number of items to sell and
registered-store status. Based on Section 4, persistent level of quality, ηj , can be identified using
sellers’ dynamic quantity choice.
Powerseller status is a function of sellers’ performance in the last three months and their unobservable quality; these two numbers should be higher than two cut-off values, set by eBay, Qp and
µp . I estimate µp later by matching the average percentage of powersellers in the market to that
of the simulated model.
In the following section, I go into detail estimating each policy function as well as quality. I
assume that sellers decide on their registered-store status each period, and this variable can affect
their decisions on the number of items to sell.
27
5.2.1
Quantity Choice
One of the decisions that sellers make each period is the number of items they list on the eBay
website. Note that most transacted items on eBay in my dataset are sold using the auction method;
therefore, I assume that sellers do not set prices and they decide on the number of items to sell.
The price is then determined in the market using the demand function estimated is Section 5.1.
Sellers’ optimal quantity choice depends on their persistent level of quality, powerseller status,
registered-store status, and their choice of quantity in the last two periods as discussed in Section
4.1. I can control for all of the parameters except for unobservable persistent level of quality, ηj . I
have also shown in Proposition 1 in Section 4.1 that sellers’ quantity choice is an increasing function
of their persistent level of quality. Therefore, after controlling for all other variables, sellers’ fixed
effect can be interpreted as an index of quality. In Section 5.2.3, I parametrically estimate the value
of quality based on sellers’ fixed effect estimated in this section.
Sellers’ decision can be modeled using a discrete choice model, in which sellers can choose
any non-negative number. I have considered Poisson and Negative Binomial distribution models.
The latter matches the data the best, as shown in Figure 5. The intuition behind the binomial
distribution is that sellers decide on the mean of the number of items they want to purchase, but
they are faced with an inventory shock, which can lead to higher or lower number of items sold.
However, having dynamic data enables me to disentangle the effect of an inventory shock and the
seller’s fixed effect.22 In this figure, the original data represents the ratio of time that sellers in
the market have sold n number of items. The dashed line shows the probability prediction of
estimated Poisson distribution over different number of sales, taking the average over all sellers in
the market; the doted-dashed line shows the probability prediction using the estimated Negative
Binomial distribution.
When estimating the Negative Binomial distribution with sellers’ fixed effects and time fixed
22
Without considering the inventory shock the model is rejected as there can be a seller who has the same observable
characteristics in two period and different quantity choices.
28
effect, I use the following formula:
qtj ∼ nb(φst , φpt , qt−1 , qt−2 , νj , δt , κ)
The estimated coefficients of qjt−1 , φst , φpt and κ–the dispersion parameter of Negative Binomial
distribution–are shown in Table 4. To estimate the probability of each event for each seller, I use
the following formula:
ρjt = exp([φst , φpt , qjt−1 , qjt−2 , ] ∗ β + νj + δt )
r = 1/κ
p(0) = (r/(r + ρjt ))r
p(k) = p(k − 1) ∗ (r + k − 2)/(k − 1) ∗ ρjt /(ρjt + r);
where p(k) is the probability that the seller j at time period t sells k items. Note that ρjt , the
average number of items a seller lists in the market, is affected by registered-store status, powerseller
status, and sellers’ fixed effects. The dispersion parameter, κ, is the same for all sellers.
While eBay decides on the thresholds for powerseller and registered-store status based on ηj ,
eBay decisions can be interpreted as a cut-off for νj , since since νj is a non-decreasing function of ηj .
They are used later on to estimate the threshold levels set by eBay, µp and µs . I also parametrically
estimate the level of ηj as a function of νj in Section 5.2.3.
5.2.2
Registered-Store Status
Sellers who meet the quality requirement for achieving registered-store status can register as eBay
registered stores, for which they pay a monthly fee and will be shown as an eBay registered store
on the listing page. I assume that sellers decide on their registered-store status each period after
knowing the shock to their quality and, therefore, their powerseller status.
29
Sellers who meet the quality requirement can choose to become a registered store and, according
to the model, this decision is a function of their state variables, the shock to their quality, and
powerseller status. However, when making the decision about registered-store status, the value of
current shock will not affect their profit this period and the following periods; therefore, it will not
enter their decision-making process. Thus, sellers’ choice of registered-store status, after qualifying
for the status, is a function of their powerseller status, persistent level of quality, and their quantity
in the past two periods: φs∗ (η, φp , q−1 , q−2 ). I use the index for quality estimated in the previous
section to control for sellers’ persistent level of quality. This decision is a binary choice for sellers
and I model it using the logit distribution. Table 4 shows the results of the regression.
5.2.3
Estimating Unobservable Quality
In this section, I estimate sellers’ unobservable persistent level of quality. As mentioned in Proposition 1, the number of items sellers sell is increasing in their unobservable persistent level of quality,
ηj . Based on this proposition, I estimate νj , sellers’ fixed effect from the quantity choice function.
νj is an index of ηj and–through Proposition 1–is a non-decreasing function of this value. As explained in Section 4, I use the simulated method of moments by matching five different moments
from data and model: percentage of powersellers, percentage of registered stores, percentage of
powersellers and registered stores, and the two moments from demand shown in Equation 6.
I also assume the following parametric formulation for the ηj , which is increasing in ν:23
ηj = νj + λνj3
Then, by minimizing the joint differences between the simulated moment conditions using the
model and the calculated moments using the data, I estimate the value of λ, µp , µs , and variance
of random shocks to quality, γjt . Then using the estimate of λ, I can estimate the value for βr /α,
23
I have used different parametric functions and the result does not change much when additional polynomial terms
are added. Quadratic term is not consistent with the fact that η is increasing in ν.
30
the coefficient of rjt in the demand function. Table 5 shows the estimated values for λ and βr /α.
Note that βr /α is positive; therefore, buyers enjoy buying an item from a seller with a higher level
of quality.
5.3
Simulation
Using the first-stage estimation results and given an initial value for µs and µp , I can simulate the
model over time. To estimate the correct value of these two parameters, µs and µp , I match the
original and simulated results. I have data for nine months and each period in my model spans
over one month. Given the initial conditions, I simulate the model. Table 6 shows results after
simulating the model for nine periods. The results show that my simulations follow the original
data very closely. This means that the model estimates the actions of sellers accurately and I can
use this base model to estimate the cost parameters.
5.4
Perturbations
In the second step, I perturb the policy functions, simulate actions of sellers over time, and estimate the value functions of sellers for each perturbation. This helps in determining some out-ofequilibrium revenue values for sellers. To get the perturbations, one should only perturb one seller
at a time; otherwise, one may find another equilibrium of the model, which can potentially yield
higher expected profits for some sellers.
Moreover, perturbations should give us movement in both directions and both small and big
changes in the variables; i.e., to have changes in actions of sellers in both directions and have enough
inequalities to determine the value of cost parameters. To get estimates for the cost parameters, I
perturb the policy function associated with the number of sales and registered-store status.
31
5.5
Estimation
Having the perturbed actions of sellers and also their original simulated actions over time, I can
estimate the expected value function for sellers, given a set of initial conditions for cost parameters.
True cost parameters result in higher expected value functions driven by original policy functions
compared to those driven by perturbed policy functions. To estimate the cost parameters, I construct a loss function as explained in Section 4.2. Cost parameters are the parameters that minimize
this function.
Table 7 shows the estimated cost parameters for two different specifications. In the first specification, I force the monthly cost of becoming a registered store to be zero and I estimate the
marginal cost of acquiring an iPod for sellers that rationalize sellers’ choices. Note that this is the
cost associated to the average iPod in the data as I do not explicitly model the choice of iPod.
In the second specification, I jointly estimate the marginal cost of acquiring an iPod for sellers,
as well as the monthly fee for becoming a registered store. The monthly fee charges by eBay for
registered-store status is between $15-$300 for different types of stores, which I abstract from modeling, and my estimate for the monthly fee is $13.62 per month. Standard deviations are estimated
using bootstrapping method. First to get a sample of cost estimation, I run the above method
repeatedly. Next, I use the sample to resample data with substitution and estimate the mean and
standard errors of the cost parameters.
6
Counterfactual: Value of Reputation
Given the estimated values for sellers’ cost and quality, and buyers’ utility function, I can run
various counterfactuals to estimate the overall effect of reputation on the market. In the first
counterfactual, I assume sellers have no means of signaling their quality and I recalculate the
equilibrium demand and surplus. In the second counterfactual, I assume sellers are forced to sell
the same number of items as the original problem; however, they cannot signal their quality. This
32
counterfactual helps us understand the mechanism that affects the change in consumers’ surplus
and sellers’ profit. In the final counterfactual, I assume sellers whose quality level is higher than a
set threshold can provide warranty to buyers. Warranty promises that seller’s quality is higher than
this threshold; otherwise, the seller must refund the buyer in full. Warranty increases high-quality
sellers’ profit and decreases low-quality sellers’ profit, by giving buyers the ability to distinguish
between the two groups. Warranty, in this case, can be used as a substitute for reputation.
6.1
No Reputation Mechanism – Optimal Quantity
As mentioned before, the powerseller status and registered-store status are tools used by eBay to
signal sellers’ quality. This will help a high-quality seller to sell more products on eBay. Furthermore, it helps buyers recognize high-quality sellers and have an overall better experience in the
marketplace. To find the overall effect of reputation, I run a counterfactual in which no powerseller
or registered-store status exists. Without these quality signals, sellers are all pooled together.
Therefore, high-quality sellers cannot receive price or quantity premiums.
In absence of reputational signals, buyers’ demand function will change, as well as the problems
that sellers face. Buyers will no longer observe reputational signals for quality. Consequently,
buyers cannot infer sellers’ quality based on these signals. On the other hand, as sellers cannot
signal their quality levels to buyers, those with different quality levels will face the same problem.
6.1.1
Sellers’ Problem
In the absence of reputation in the market, sellers are pooled together and cannot signal their
quality. I assume they are competing in a Cournot equilibrium, given the new demand function in
the market. I further assume we have a symmetric equilibrium in the market. I also assume sellers
face the same inventory shock as the original problem.24 Sellers maximize their expected profit,
24
In Section 5.2.1, I assumed that sellers faced an inventory shock; and even though the average number of items
they sell is equal to their optimal number, they may end up with a larger or smaller number of items. The dispersion
was assumed to be the same for all sellers in the market. When performing counterfactuals, I assume that this
33
given their marginal cost and the number of items sold by other sellers in the market. Their period
t profit function is:
π(qjt ) = p(qjt )qjt − cqjt
The expectation is taken over the inventory shock that sellers face. The dispersion is assumed to
be unaffected by the policy change and to remain the same for all sellers. Sellers’ choice is not
dynamic in this set-up, as it is assumed that buyers do not observe sellers’ past actions. The goal
is to find the Nash equilibrium–that is, sellers’ choice of average number of items to sell should be
optimum, given other sellers’ choice. Sellers face the same final price and the same sellers’ problem;
therefore, I assume they face a symmetric equilibrium, qjt = qt .
6.1.2
Demand Function
In the new setup, buyers do not observe sellers’ quality; nor do they observe any signals related
to that quality. Hence, only the expected value of sellers’ quality affects buyers’ expected utility
function. The expectation is taken over all the listings and sellers in the market. Note that
since sellers cannot make any signals about their quality, there is no observable heterogeneity
among sellers. Given sellers’ quality comes from distribution function L estimated from the original
problem, buyers’ expected utility function is:
Z
Z
uijt qt l(rjt )drjt / qt l(rjt )drjt
Z
Z
= −αpjt + βr rjt l(rjt )drjt / l(rjt )drjt + ξt + ξjt + ijt
E(uijt ) =
dispersion parameter remains the same. The number of items sold will follow a Negative Binomial distribution with
a fixed dispersion rate for all sellers.
34
Given the above utility function and assuming that ijt follows an extreme value distribution, the
demand function as explained in Section 3.5 will be as follows:
Z
pjt = (−log(sjt ) + log(s0t ))/α + βr /α
rjt l(rjt )drjt + ξt /α + ξjt /α
(7)
where α has the same parametric values as estimated parameters in Table 3 in the previous section,
implying they are invariant to the changing policies of eBay. I use the results in Section 5.2.3 to
estimate βr /α
R
rjt l(rjt )drjt , which gives me an estimate of βr /α and also an estimate of rjt =
ηj + γjt . Note that γ is distributed i.i.d. with a mean of zero.
6.1.3
Estimation and Result
To estimate the optimal level for qt , I start with an initial guess, q. I then estimate the best response
of a seller when the other sellers choose q using simulation, and call this optimal level B(q). Next,
I change the initial guess to a number between q and B(q). I repeat these two steps until q and
B(q) are close enough, thereby achieving the optimal level of qt .
After solving for sellers’ new policy functions, I simulate the model to get sellers’ expected value
function, eBay’s Profit, and buyers’ surplus. The results are shown in Table 8. As a result of the
policy change, consumer surplus has decreased by 48%, eBay Profit by 60%, and the total sellers’
profit by 85%.
One of the reasons I get large effects as a result of removing the reputation mechanism is that,
in my original setting, among sellers who are not powersellers, those with higher quality levels sell
more. Recall that, to become a powerseller, a seller must reach a quantity threshold set by eBay.
Therefore, high-quality non-powersellers have incentive to sell more items than their static optimal
values because they have higher probabilities of becoming powersellers in the future. This will give
us a high value for the average quality of items sold even by non-powersellers. Figure 7 shows the
number of items sold by both powersellers and non-powersellers. Sellers with higher quality values
35
sell more, and powersellers have extra incentive to sell more to retain their powerseller status.
Thus in case of no signaling, the average price of items drops even below the price of items sold by
non-powersellers. This will result in a substantially lower number of items sold in the marketplace,
and subsequently, lower eBay profit and even lower consumer surplus despite lower prices.
6.2
No Reputation Mechanism – Fixed Quantity
In this case, when we take sellers’ quantity choice to be the same as their original quantity choice,
the price they will induce will change. Using the formulation in the previous section, the new
demand function will be:25
Z
pjt = (−log(sjt ) + log(s0t ))/α + βr /α
Z
qj rjt l(rjt )drjt /
qj l(rjt )drjt + ξt /α + ξjt /α
The difference between the above equation and Equation 7, the demand function for the first
counterfactual, is in different quantities for different sellers, qj . Two firms with the same size and
the same characteristics of items obtain the same price and price is not a function of their quality
levels. Estimated value for βr /α
R
R
qj rjt l(rjt )drjt / qj l(rjt )drjt is around $2.00 per iPod; this is the
average value of quality of items sold by all sellers.
This case does not have any real aggregated effect for buyers or sellers, given the formulation
for profit and the utility function. Buyers obtain the same average utility as the original set-up,
with the difference being that some lucky buyers receive a high-quality iPod without the quality
premium and unlucky buyers receive a high-priced, low-quality iPod. Given the linear set-up for
the quality and price in the utility function, the different effects cancel each other.
Low-quality sellers are better off, while high-quality sellers are worse off. Note that in this case,
we kept the quantity of items sold the same as that of the original problem’s; however, given the
25
I assume that buyers do not infer sellers’ quality based on their quantity choice. Otherwise, they can potentially
know sellers’ persistent level of quality because they cannot observe sellers’ quantity, or it would be costly for them
to obtain that information.
36
new lower price, high-quality sellers have incentive to sell fewer items. If we allow sellers to adjust
their quantity, high-quality sellers would lower their quantity, which would lead to lower average
quality, and would lower the price for everyone. This cycle would continue until the equilibrium
converges with that of the first counterfactual.
6.3
Warranty
Warranty can be a substitute for reputation mechanism. In this section, I consider a simplified
set-up for warranty. Sellers can voluntarily provide warranty for the items they sell on the market.
They would guarantee that their quality is above a threshold and if proven wrong, the buyer can
return the item for full refund. For simplicity, I assume that the threshold is fixed for all sellers and
announced by eBay. In this case, sellers will be divided into two groups; sellers with high-quality
and warranty and sellers with low-quality and no warranty.26 Buyers’ expected utility function is:
E(uijt |w) = −αpjt + βr E(rjt |w) + ξt + ξjt + ijt
where w is equal to 1 if the seller provides warranty and 0, otherwise. Demand function from the
above formula is similar to the ones in the previous section. I assume that in the equilibrium, all
sellers with high- and low-quality choose to sell the same number of items, qH and qL , respectively.
However, sellers still face inventory shocks. To find qL and qH , I start from an initial value and
first find the fixed point of best response function for low-quality sellers, given qH . Given qL∗ from
last step, I find the fixed point of best response for high-quality sellers. I continue these steps until
convergence. The surplus numbers are shown in Table 8. Different levels of surplus are shown for
quality thresholds corresponding to top 5%, 10%, and 50% of sellers providing warranty. Note that
when the threshold goes to − inf or + inf the surplus values converge to the case of no signaling.
As shown in Table 8, warranty can be a good substitute for reputation. When providing
26
Note that by assumption sellers with low quality have no incentive to pretend to be of high quality, and sellers
with high-quality benefit from grouping into high-quality sellers; therefore, they choose to provide a warranty.
37
warranty, total sellers’ profit goes up. This higher total profit is a results of high-quality sellers
getting separated from low-quality sellers and obtaining substantially higher profits. However, lowquality sellers suffer as a result of receiving even a lower price compared to the no-reputation case.
Consumer surplus and eBay’s surplus can be lower or higher than the no-reputation case: when
only a few sellers are signaled, the price for these sellers goes up considerably, and the quantity of
other sellers goes down even more, which in turn leads to lower consumer surplus and eBay’s profit.
When the threshold is at 50%, all surplus values are higher than those in the case of reputation.
Note that this increase does not necessarily imply that warranty is a better choice than reputation,
for several reasons. First, the reputation mechanism set by eBay is not the optimal mechanism,
and it can potentially improve. Second, the warranty considered in this case is simplified, and it is
difficult to implement the thresholds.
In this counterfactual exercise, I replace reputation with warranty. This study is related to few
other studies in which authors investigate the relationship between reputation and warranty. The
difference is that they consider an environment with a reputation mechanism and they estimate the
effect of adding a warranty mechanism, instead of replacing the reputation mechanism altogether.
Roberts [2011] finds that added warranty do not substitute for reputation. He does not find big
effects except for sellers with very low reputation signal. Cai et al. [2013] find that warranty can
potentially have negative effect on the level of trust. This effect come with a higher entry of low
quality sellers as buyers are willing to buy from sellers with low reputation level. On the contrary,
Hui et al. [2014] find that warranty affects the value of reputation and, in addition, increases the
total welfare.
7
Conclusion
This paper uncovers the value of the eBay marketplace’s reputation mechanism. To do so, a model
of firm dynamics where sellers have heterogeneous qualities unobservable by consumers is developed.
38
Reputation is used as a signal to buyers in order to improve allocations. By structurally estimating
this model, this study uncovers deep parameters of buyers’ utility and sellers’ costs, as well as
their unobservable qualities. The estimated model suggests that reputation has a positive effect on
the expected profits of high-quality sellers, as well as their market share. To establish the value of
reputation, a counterfactual is performed. The findings show that removing reputation mechanisms
put in place by eBay significantly decreases the profits of high-quality sellers; moreover, it increases
the market share of low-quality sellers, while decreasing that of high-quality sellers. Lastly, buyers’
welfare and eBay’s profit drop as a result of removing the reputation mechanism. In addition, the
effect of adding warranty as a substitution for the reputation mechanism is studied. The findings
indicate adding warranty overcomes part of inefficiencies of adverse selection.
Some extensions of the model are worth discussing. One is to consider additional sellers’ characteristics (e.g., age in the market, amount of text entered, number of photos entered). I have
intensively studied these extensions for the limited number of sellers in the study. The cost estimates for these variables were mainly small and did not affect the overall outcome.
An important extension to the model is endogenizing the level of quality as a choice parameter
for sellers. There are both empirical and theoretical challenges in implementing this extension.
First, it would be necessary to have feedback from buyers to sellers, such as the eBay disputes
system, which is considered much more informative than the regular feedback system. This would
allow for estimating the percentage of time that sellers would provide low-quality service as a
function of their reputation. Using this estimate, it would be possible to determine whether sellers
abuse their reputation, or whether the long-run value of reputation is high enough to sustain highquality service for a long period of time.
Another extension worth mentioning is endogenizing the entry/exit of sellers into/out of the
market. In this case, sellers would receive a signal of their reputation upon entry into the market and
they could decide whether to remain in the market or exit. This would provide better understanding
39
of the effect of reputation on the market and on the distribution of active sellers in the market. In
the case of entry/exit, high-quality sellers would exit the market after removal of the reputation
system, which would in turn increase the adverse effects.
40
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Appendix A
Proof of Proposition 1
Proposition 2 Suppose that the solution to the functional equation, Equation 2, is unique. Then,
the policy function q ∗ (η, γ, q− ) is increasing in quality η.
Proof. Recall Equation 2 in Section 3.3. To prove the proposition, I use a method similar to
Hopenhayn and Prescott [1992], adopted from Topkis [1998], and I show that the objective function
has increasing differences. To do so, first note that the optimal choice of φs does not affect future
values. Hence, I can define the following period profit function:
π̂(η, γ, q, q−1 , q−2 , q−3 ) = max π (q, φs , φp )
{z
}
|
φs ∈{0,1}
(8)
q−
subject to:
φs = 0
if
φp = 1
if
η + γ < µs ,



 q−1 + q−2 + q−3 > 3Qp


 η + γ > µp
I prove the proposition in three steps:
Step 1. π̂ (η, γ, q, q−1 , q−2 , q−3 ) is supermodular in (η, q) and in (η, q−i ) for i = 1, 2, 3.
Step 2. The solution to Equation 2 is supermodular in (η, q−i ) for i = 1, 2, 3.
Step 3. The policy function is increasing in quality η.
Step 1. Must show π̂ (·) is supermodular in (η, q) and in (η, q−i ) for i = 1, 2, 3. For (η, q), note
that when q 0 > q and η 0 > η then:
π̂ η 0 , γ, q, q− − π̂ (η, γ, q, q− ) ≤ π̂ η 0 , γ, q 0 , q− − π̂ η, γ, q 0 , q−
To formulate the above differences, note that given the analysis in Section 3.5 and Equation 4, the
45
price for any seller is given by:
p (q, φp , φs , x) = f (q) + βp φp + βs φs + βps φs φp + βx x
for some function of q, f (q). This implies that:
π̂ η 0 , γ, q, q− − π̂ (η, γ, q, q− ) = βp φp η 0 , γ, q− + βs φs η 0 , q, γ, q− + βps φs η 0 , q, γ, q− φp η 0 , γ, q−
−βp φp (η, γ, q− ) − βs φs (η, q, γ, q− ) − βps φs (η, q, γ, q− ) φp (η, γ, q− )] q
− φs η 0 , q, γ, q− − φs (η, q, γ, q− ) cs
Moreover, in the solution to the auxiliary problem (8),
φs (η, γ, q, q− ) = 1 iff (βs + βsp φp (η, γ, q− )) q ≥ cs and η + γ ≥ µs
where φp (·) is given by (3). Note that both of the functions φp and φs are increasing in their
arguments. I prove the supermodularity claim by showing the following inequalities:
βp φp η 0 , γ, q− − φp (η, γ, q− ) q ≤ βp φp η 0 , γ, q− − φp (η, γ, q− ) q 0
φs η 0 , q, γ, q−
βs + βps φp η 0 , γ, q− q − cs − φs (η, q, γ, q− ) ([βs + βps φp (η, γ, q− )] q − cs )
≤ φs η 0 , q 0 , γ, q−
βs + βps φp η 0 , γ, q− q 0 − cs − φs η, q 0 , γ, q− [βs + βps φp (η, γ, q− )] q 0 − cs
The top inequality is simply coming from the fact that φp (η, γ, q− ) is increasing in η. Moreover,
to show that the bottom inequality is satisfied, I can only focus on a case where φs (η, q, γ, q− ) <
φs (η 0 , q, γ, q− ) and φs (η, q 0 , γ, q− ) = φs (η 0 , q 0 , γ, q− ) = 1. Note that the LHS of the bottom
46
inequality is given by
βs + βps φp η 0 , γ, q− q − cs
Moreover, since φs (η, q, γ, q− ) = 0, I must have that [βs + βps φp (η, γ, q− )] q − cs < 0. Therefore,
the following expression is higher than the LHS of the bottom inequality
βs + βps φp η 0 , γ, q− q − cs − ([βs + βps φp (η, γ, q− )] q − cs )
= βps φp η 0 , γ, q− − φp (η, γ, q− ) q
Moreover, since φs (η, q 0 , γ, q− ) = φs (η 0 , q 0 , γ, q− ) = 1, the RHS of the inequality is given by
βps φp η 0 , γ, q− − φp (η, γ, q− ) q 0
and hence the inequality is satisfied by the fact that φp (η, γ, q− ) is an increasing function of η.
Hence, I have shown that π̂ (η, γ, q, q− ) is supermodular in (η, q).
To show supermodularity in (η, q−i ), note that π̂ (·) is only a function of q−1 + q−2 + q−3 and
therefore, I only need to show supermodularity with respect to q−1 . That is, I need to show that
0 >q
if η 0 > η and q−1
−1
0
π̂ η, γ, q, q−1
, q−2 , q−3 − π̂ (η, γ, q, q−1 , q−2 , q−3 )
0
≤ π̂ η 0 , γ, q, q−1
, q−2 , q−3 − π̂ η 0 , γ, q, q−1 , q−2 , q−3
The argument is similar to the previous case. Any changes in profits, as a result of a change in
q−1 , come from changes in φp . That is, for the above differences not to be zero, I need to have
0 +q
q−1 +q−2 +q−3 < 3Q ≤ q−1
−2 +q−3 . Moreover, since all of the rules specified above for becoming
0 ,q ,q
powerseller and registered store are cutoff rules for η + γ, whenever φp η, γ, q, q−1
−2 −3 >
p
0
0 ,q ,q
φp (η, γ, q, q−1 , q−2 , q−3 ), I must have φp η 0 , γ, q, q−1
−2 −3 > φ (η , γ, q, q−1 , q−2 , q−3 ). Hence,
47
the above inequality must hold. This concludes our proof of supermodularity of π̂.
Step 2. Here I show that the solution to the functional equation above is supermodular. To
do so, since the set of continuous supermodular functions is closed, it is sufficient to show that the
transformation associated with the Bellman equation preserves supermodularity. That is for any
function v (η, γ, q− ) that is supermodular in (η, q−i ), the following function is also supermodular
in (η, q−i ):
Z
v̂ (η, γ, q− ) = max π̂ (η, γ, q, q− ) + β
q
v η, γ 0 , (q, q−1 , q−2 ) g (γ) dγ
To show this, note that the function
Z
ṽ (η, γ, q, q− ) = π̂ (η, γ, q, q− ) + β
v η, γ 0 , (q, q−1 , q−2 ) g (γ) dγ
is supermodular. Therefore, by Lemma 1 in Hopenhayn and Prescott [1992], the function v̂ (η, γ, q− )
is also supermodular. This concludes Step 2.
Step 3. Given the above steps, the objective function in the Bellman equation is supermodular
in (η, q) and (η, q−i ). Now suppose to the contrary to the proposition, that there exists η 0 > η such
that the optimal solution under (η 0 , γ, q− ), q 0 , is lower than the optimal solution under (η, γ, q− ),
q. Given γ, q− , define the following function:
Z
f (η, q) = π̂ (η, γ, q, q− ) + β
v η, γ 0 , (q, q−1 , q−2 ) g (γ) dγ
which is supermodular in (η, q). Hence,
f (η, q) − f η, q 0 ≤ f η 0 , q − f η 0 , q 0
By optimality of q under η and uniqueness of the policy function, the LHS of the above inequality
is positive; hence, the RHS is also positive. This contradicts the fact that q 0 is optimal under η 0 .
48
Hence, the policy function q ∗ (η, γ, q− ) must be increasing in η. Similarly, I can show that it is
increasing in q−i .
Appendix B
Demand Function Estimation Robustness
As mentioned in the data section, I estimate a structural demand function based on the buyers’
utility function. In this section, I run a simple OLS regression of price over additional characteristics
of sellers, and characteristics of items sold by them, to show the robustness of the results when it
comes to the effect of powerseller and registered-store status. The results in this section show that
when we control for sellers with a high level of sales, we still see the positive effect of powerseller
and registered-store status. Moreover, when we control for the condition of the items sold, if they
are new or used, we see that the powerseller and registered-store status still have a positive effect,
with a higher effect when we are only looking at used items.
Table 9 reports the OLS results. The first column includes only the seller characteristics.
In addition to powerseller and registered-store status, I also include other sellers’ characteristics:
number of days a seller has been active in the market, which I will call “age”, the amount of
information entered by sellers on the listing page, whether sellers have provided their phone number
in their listing page, the existence of “About-me” page,27 and whether the listing was in a fixed
price format (i.e., “Buy in Now”).
Table 9 also shows that being a powerseller or a registered-store on eBay has a positive effect
on the price. The coefficient of the age variable shows that being on the eBay website for one
additional year gives a seller about a three-dollar boost in the final price. Additionally, having
more text has a positive effect on the price.28 The About-me coefficient has a negative effect on
the price. The reason behind this effect is that the option of having an About-me webpage was
27
Sellers can enter a webpage called About-me and explain their business on this page for buyers to see.
Note that the two variables, text and description size, represent different measures of information entered on the
webpage. They are highly correlated and having only one of them in the regression results in a positive coefficient.
28
49
more popular during the starting days of eBay. However, iPods are a newer sub category on eBay,
and most of the big sellers in this category are newer sellers. This result in the coefficient on the
About-me variable picks up the effect of older versus newer sellers.
Column II represents the coefficients when we only consider the characteristics of the items
sold on eBay. As expected, if the condition of the iPod is new or refurbished, it results in a price
premium. High internal memory of iPods also results in higher prices. I also added dummy variables
for different brands of iPods, which also have the expected coefficients.
Column III of Table 9 includes both seller and item characteristics. The effect of powerseller and
registered-store status is lower compared to the results in Column I. This shows that powersellers
and registered stores tend to sell better quality products; when we control for item characteristics, the effect of powerseller and registered-store status diminishes. However, the effect of these
reputation-related variables is still very high; the premium on powerseller status is $29, which is
about 15% of the average price of iPods sold. The premium on registered-store status is about
$8.6, which is about 5% of the average price of iPods sold.
Column IV represents only sellers with more than 25 sales in my sample. The effect of registeredstore and powerseller status declines when we only focus on this sample of data. This change in
the effect of the reputational signals arises because we are in a pool of sellers with a higher volume
of sale, and therefore higher experience. So the signal for these sellers is less important than for
smaller sellers with lower volume of sales.
Buyers take the reputation of sellers more into account when they are buying an item with a
less pre-determined value, i.e., used goods versus new goods. Table 10 shows the regression results
for used versus new items. Powerseller and registered-store status have remarkably higher effects
for a used item versus a new item. The market value of a new iPod is pre-determined. In this case,
buyers may be more confident to buy from a more trustworthy seller because they expect a better
shipping experience and better communications, or, in the extreme case, fear of receiving a used
50
iPod as a new iPod from a less reputable seller. On the other hand, when buying a used iPod, there
are many aspects of the item quality that can be misrepresented by a fraudulent seller, leading to
a very high value of reputation for sellers.
In the last column of Table 10, I include feedback scores and feedback percentages to the
regressors in the third column. After the end of a transaction, seller and buyer can leave feedback
for each other. This feedback can be positive, negative, or neutral. Feedback percentage is the
percentage of positive feedback among all feedbacks that a seller has received. Feedback score is
the number of positive feedbacks received, minus the number of negative feedbacks received by
a seller. Many of the papers written about the effects eBay’s reputation mechanism only focus
on sellers’ feedback scores and feedback percentages. This regression shows that, controlling for
powerseller and registered-store status, these two variables do not have a high effect on final price.
Feedback percentage is a number between 0 and 100, with an average of 99% for the active sellers
on the market. When comparing a seller with a perfect feedback percentage, 100%, and a seller in
the 25% percentile, having a 98% feedback percentage, the effect of feedback percentage on price is
$0.75. The coefficient on feedback score is negative when we control for sellers’ size, showing that
this coefficient does not carry additional information for buyers in terms of reputation.
51
List of Figures
1
2
3
4
5
6
7
Different models of iPods and their prices over time. . . . . . . . . .
Snapshot of an iPod Auction . . . . . . . . . . . . . . . . . . . . . .
Snapshot of Bid History page . . . . . . . . . . . . . . . . . . . . . .
Timing of Sellers’ Choices and Shocks . . . . . . . . . . . . . . . . .
Probability Distribution of the Number of Sales, Original vs. Poisson
Binomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Total Quantity Sold by non-Powersellers . . . . . . . . . . . . . . . .
Total Quantity Sold by both Powersellers and non-Powersellers . . .
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and Negative. . . . . . . .
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54
55
56
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Figure 1: Different models of iPods and their prices over time.
53
Figure 2: Snapshot of an iPod Auction
54
Figure 3: Snapshot of Bid History page
55
Figure 4: Timing of Sellers’ Choices and Shocks
56
0.5
Actual Data
Poisson
Negative Binomial
0.45
0.4
Probability
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
2
4
6
8
10
12
Number of Sales
14
16
18
20
Figure 5: Probability Distribution of the Number of Sales, Original vs. Poisson and NegativeBinomial
57
1200
Powerseller=0
Number of items sold
1000
800
600
400
200
0
−15
−10
−5
0
nuj
5
Figure 6: Total Quantity Sold by non-Powersellers
58
10
15
6000
Powerseller=1
Powerseller=0
Number of items sold
5000
4000
3000
2000
1000
0
−15
−10
−5
0
5
10
15
nuj
Figure 7: Total Quantity Sold by both Powersellers and non-Powersellers
59
20
List of Tables
1
2
3
4
5
6
7
8
9
10
Data Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reputation and Price . . . . . . . . . . . . . . . . . . . . . . . . .
First-Stage Estimation, Demand . . . . . . . . . . . . . . . . . .
First-Stage Estimation, Policy Functions . . . . . . . . . . . . . .
Parametric Estimation Unobserved Quality . . . . . . . . . . . .
Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cost Estimations . . . . . . . . . . . . . . . . . . . . . . . . . . .
Change in Per Period Consumer Surplus, sellers and eBay Profit
Regression Result for iPod . . . . . . . . . . . . . . . . . . . . . .
Regression Result for iPod, New vs. Used Items . . . . . . . . . .
60
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Table 1: Data Summary
Characteristics of Listings and iPods sold
Variable
Obs
Mean
Std. Dev Min
eBay registered store 174280
0.36
0.48
0
174280
0.48
0.50
0
Powerseller
Feedback Number
174154 14120.3 48971.8
-3
Feedback Percentage
22366
99.22
1.88
33.3
Sold with Buy it Now 174273
0.08
0.27
0
Buy it Now option
174280
0.29
0.45
0
Secret Reserve
174280
0.04
0.27
0
Number of Bidders
146597
7.29
4.82
0
Items Sold
167199
1.00
1.84
0
New Item
174280
0.25
0.43
0
Refurbished Item
174280
0.19
0.40
0
Internal Memory
159234
19.68
27.51
1
61
Max
1
1
1026575
100
1
1
2
30
180
1
1
240
Table 2: Reputation and Price
Average Prices
Fitted Values
All iPods New iPod Nano Average Item
New, Nano, 8GB
All Sellers
$131.81
$132.95
$136.51
$135.34
Non-Powersellers & Non-Store $130.70
$130.15
$122.18
$131.19
Registered Stores
$135.96
$134.09
$128.80
$139.96
Powersellers
$134.95
$137.44
$137.79
$140.90
Powersellers & Stores
$139.90
$135.29
$145.35
$142.09
Lowest 25% Feedback
$134.60
$135.34
Highest 25% Feedback
$136.68
$135.51
Note: The first two columns represent the average price of items sold by each group of sellers. The
third and fourth columns show the fitted values for the price of items sold by each group. The third
column shows the average characteristics of an iPod sold during the time period and the fourth
column shows the price of a new iPod Nano sold by each group.
62
Table 3: First-Stage Estimation, Demand
log(s0 ) − log(sj )
Powerseller
Registered Store
Powerseller* Store
New
Refurbished
Internal Memory
iPod Model & time
Fixed Effect
R2
63
Coef
4.05
15.60
6.62
0.93
37.48
13.11
1.42
0.94
Price
Std. Dev.
0.06
0.42
0.65
0.73
0.38
0.33
0.01
Table 4: First-Stage Estimation, Policy Functions
Coef
Std. Dev.
Quantity Choice Registered Store
0.65
0.34
Powerseller
0.33
0.15
q−1
0.003
0.0007
q−2
-0.001
0.0004
Dispersion
0.90
0.03
Registered Store Powerseller
1.54
0.10
q−1
0.013
0.002
q−2
0.008
0.001
Fixed Effect
-0.37
0.04
Constant
-2.33
0.10
Note: The first part of the table is the coefficients for negative binomial regression. This regression also includes fixed effects for sellers. The second part is the estimation of a binary logit model for
registered-store status choice for sellers.
64
Table 5: Parametric Estimation Unobserved Quality
Effect of Quality on Price
λ
βr /α
Parameter
0.24
3.34
65
Table 6: Goodness of Fit
Model Original Data
Powerseller
0.75
0.83
Registered Store
0.59
0.58
Sales
91.6
87.5
Revenue
14,033
12,636
Average simulated results after
simulating the model for nine periods.
66
Table 7: Cost Estimations
iPod’s Cost
Registered Store
Coef.
116.83
–
Specifications
I
II
Std. Dev. Coef. Std. Dev.
0.47
116.08
0.56
–
13.62
2.06
67
Table 8: Change in Per Period Consumer Surplus, sellers and eBay Profit
Original
Total Consumers’ Surplus 233,190
Total Sellers’ Profit
181,080
eBay’s Profit
113,590
Notes: The numbers in this table are
all sellers are assumed to be active.
No
Reputation
5%
121,600
108,290
26,380
123,100
45,777
45,595
for the surpluses in the
68
Warranty
10%
139,580
175,680
63,164
last period
50%
246,910
316,840
129,890
where
Table 9: Regression Result for iPod
Price
Powerseller
Registered Store
Age
Phone
Text
Description
About Me
Buy it Now
New
Refurbished
Internal Memory
Nano
Mini
Classic
Shuffle
Touch
Video
I
80.04
(0.75)
40.67
(0.65)
0.01
(0.00)
21.19
(0.72)
-0.003
(8.0E-05)
0.001
(2.4E-05)
-14.89
(0.91)
26.20
(3.26)
II
31.02
(0.52)
11.04
(0.39)
1.43
(0.02)
87.72
(0.34)
52.02
(0.60)
44.33
(1.80)
27.82
(0.31)
195.66
(0.52)
58.99
(1.16)
0.93
III
29.26
(0.81)
8.62
(0.42)
0.008
(0.0002)
0.68
(0.50)
-0.001
(4.3E-05)
0.0004
(1.4E-05)
-15.07
(0.53)
36.62
(2.09)
29.43
(0.55)
3.32
(0.45)
1.40
(0.02)
46.16
(1.05)
3.62
(1.25)
2.50
(1.98)
-14.37
(1.05)
152.11
(1.17)
19.69
(1.50)
0.94
IV
9.29
(0.31)
4.31
(0.36)
0.005
(0.0001)
-5.39
(0.40)
-0.0004
(4E-05)
0.0002
(1.2E-05)
-5.69
(0.37)
5.38
(0.54)
48.27
(0.34)
12.42
(0.32)
1.41
(0.008)
64.89
(0.30)
34.02
(0.46)
24.94
(0.70)
7.07
(0.34)
179.61
(0.41)
43.63
(0.58)
0.92
R2
0.72
I: Only Sellers’ Characteristics
II: Only Item Characteristics,
III: Both Sellers’ and item Characteristics,
IV: Both Sellers’ and item Characteristics, Sellers > 25 Sales
Standard errors in parentheses
* p<0.05 ** p<0.01 *** p<0.001
69
Table 10: Regression Result for iPod, New vs. Used Items
Powerseller
Registered Store
Age
Phone
Description Size
Text
About me
Buy it Now
New
Refurbished
Internal Memory
Nano
Mini
Classic
Shuffle
Touch
Video
Original
29.27***
(0.82)
8.62***
(0.42)
0.008***
(0.0002)
0.68
(0.49)
0.0004***
(0.00001)
-0.001***
(0.00004)
-15.07***
(0.53)
36.62***
(2.09)
29.43***
(0.55)
3.31***
(0.44)
1.40***
(0.017)
46.16***
(1.051)
3.62**
(1.25)
2.50
(1.98)
-14.37***
(1.06)
152.1***
(1.17)
19.69***
(1.49)
Price
New Items Used Items
6.37***
35.95***
(1.51)
(0.91)
0.36
11.53***
(1.09)
(0.45)
0.01***
0.006***
(0.0007)
(0.0002)
-7.84***
5.58***
(1.28)
(0.58)
-0.0001*
0.0006***
(0.00004)
(0.00002)
0.001***
-0.002***
(0.0001)
(0.00004)
-1.16
-13.75***
(1.59)
(0.55)
-31.29***
66.24***
(3.24)
(2.33)
45.35***
(8.16)
19.41***
(2.37)
209.0***
(3.28)
106.8***
(4.56)
0.51
(0.47)
1.36***
(0.08)
41.17***
(1.14)
-4.41**
(1.35)
-0.23
(2.05)
-14.00***
(1.15)
147.6***
(1.26)
16.17***
(1.54)
0.96
0.94
1.55***
(0.07)
101.40***
(2.67)
Feedback Percentage
Feedback Score
R2
0.94
Standard errors in parentheses
* p<0.05 ** p<0.01 *** p<0.001
70
Feedback
17.41***
(0.80)
15.49***
(0.42)
0.008***
(0.0002)
-3.95***
(0.46)
0.0005***
(0.00001)
-0.001***
(0.00004)
-15.77***
(0.48)
24.95***
(2.07)
36.96***
(0.54)
15.13***
(0.41)
1.48***
(0.02)
38.79***
(0.99)
-1.76
(1.28)
-12.87***
(1.98)
-15.40***
(0.98)
147.1***
(1.09)
15.63***
(1.43)
0.37***
(0.006)
-0.00006***
(0.000002)
0.95