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Lin et al.
Reputation Distribution and Consumer-to-Consumer Online Auction Market
Structure: An Exploratory Study
Zhangxi Lin1
The Rawls College of Business Administration
Texas Tech University
Lubbock, TX 79409-2101
Dahui Li
Labovitz School of Business and Economics
University of Minnesota Duluth
Duluth, MN 55812-2496
Balaji Janamanchi
The Rawls College of Business Administration
Texas Tech University
Lubbock, TX 79409-2101
Wayne Huang
Department of MIS, College of Business
Ohio University
Athens, OH 47501
Abstract
The rapid growth of the consumer-to-consumer online auction market demands research
into its market structure and future trends. We propose that online reputation is becoming
an important indicator of online traders' business capacity in the auction market. Based on
the data sampled from eBay.com, we find that seller reputation, rather than buyer
reputation, is lognormally distributed. Following Gibrat's law and the theory of firm's
entry and exit, we further explore the reputation data to study the dynamics of the online
market. Implications of the findings are discussed
Keywords: Online auction market; reputation; market structure; lognormal distribution;
Gibrat’s Law; entry and exit.
1
Corresponding author. Email address: zlin@ba.ttu.edu
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1. Introduction
The consumer-to-consumer (C2C) online auction market has experienced phenomenal growth in
recent years and has become the most active segment of e-markets today. eBay, the fastest-growing C2C
online auction marketplace, is highlighted as one of the most profitable e-commerce companies because
of its continuous innovation. In 2002, a total of $14.87 billion was transacted on eBay.com, with more
than 12 million items listed across 18,000 categories on any given day [8]. Forrester [13] forecasts that
online retail sales in the US will reach nearly $230 billion by 2008. These figures appear to be
remarkable, considering the fact that fraud has been plaguing the C2C online auction market since its
emergence [2, 23]. Studies show that online fraud incidents failed to undermine the fast growth of C2C
online auction markets because of the increasing availability and effectiveness of online reputation
scoring systems (in short, reputation systems) in electronic marketplaces [3, 25]. Online reputation
systems record and report an online trader’s reputation according to other traders’ feedback. The
information available from a reputation system helps to improve prospective traders’ trust and conviction
in conducting online transactions. It also reduces the chances of fraud because typically traders are
expected to maintain good reputation records in order to maximize their profits. In this way a reputation
system may not only serve as a guide to otherwise clueless entrants but also help enhance the
predictability of existing traders’ behavior and honesty.
The online reputation system has attracted researchers from the behavioral sciences and
economics to investigate the new issues of reputation in the e-market, such as the effects of online
reputation on trader’s trust (e.g. [3]) and auction price (e.g. [29]). The observability of the reputationestablishing process and the numerical availability of reputation data have contributed to the proliferation
of these studies. In classical economics studies, reputation is recognized as an intangible asset that can
indicate a firm's potential for doing business [31]. Yet, reputation becomes partially visible in the context
of C2C online auction markets because summarized reputation scores are reported by reputation systems.
This visibility is why the quantitative research of reputation for the electronic market becomes realistic
and feasible. However, to our knowledge, these valuable data have not been used in examining the role of
reputation in the electronic markets at the macro level.
Research into structure and dynamics of electronic markets is definitely important. In the last
decade, the world has witnessed the fast growth of a world economy empowered by electronic commerce
[4]. Online businesses have been mushrooming in the electronic marketplace and leading the trend of the
new economy. In particular, the C2C online auction market has attracted wide attention because it has
made virtually every Internet user a potential firm in the sense of electronic commerce. The growth of the
firm has been considered “central to any explanation of the growth of an economy” [17]. Therefore,
understanding the issues in e-market structure (including the capacity distribution of online traders,
market evolution patterns, and the influence of reputation system mechanism on market dynamics) will
help researchers, practitioners, and policy makers identify the growth trend of the e-market, estimate the
long-term impact of e-commerce on the economy, and implement effective strategies and policies in ebusiness operations.
Initiated by Robert Gibrat in 1931 [14], market structure research investigates issues such as
firm’s growth pattern, firm’s entry and exit, and market concentrations [30]. The research uses firm size,
revenue, value added, payroll, and new capital expenditure to measure firm capacity and has reached
consistent though not identical conclusions [32]. Different from previous studies, our method uses
reputation as the measure of firm capacity to study electronic market structure. In the business context,
there are many different economic and non-economic signals about a conventional firm's capacity, such
as marketing information, accounting reports, social responsibility, media visibility, and so on [11]. The
rationale of our method is that reputation can be basically regarded as the impression and assessment of a
social entity's esteem or desirability [11]. A social entity, either an individual or a firm, builds his or its
reputation based on all past behaviors [5]. At the macro level, sociologists and business scholars have
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long recognized reputation as an indicator of social stratification [26] and industrial stratification [12],
which helps to categorize a person or a firm into different strata. Similarly, the online reputation also
signals the firm’s capacity in the online context.
Following the insights provided by market structure theories, this paper is intended to investigate
how the distributions of online traders’ reputation scores reflect the structure of the C2C online auction
market and how the distribution changes reflect the transition of the market status. In general, our
research findings will shed light for understanding how the traditionally intangible reputation becomes
tangible in reputation systems and plays an important role in e-marketplaces.
So far, our research has produced exciting outcomes that validate our method. In particular,
investigating the applicability of classical market structure theories to electronic markets opens the door
for us to apply other theories from the industrial organization field to the e-market. The rest of this paper
is organized as follows. First, we present a review of background literature about market structure.
Second, we explain our main concepts, research methodology, and data collection approach. Third, we
provide a comprehensive analysis of the data and report relevant results. Finally, we discuss research
implications and identify several further research issues.
2. Market Structure Research
Our research on the structure of the online C2C auction market follows the economics literature
concerning market structure in light of Gibrat’s Law or the Law of Proportional Effect [14]. Gibrat
suggests that the expected value of the increment of a firm’s size in a period of time is proportional to the
current size of the firm; in other words, firm growth rate is irrelevant to size. Applying the Central Limit
Theorem [15], this proposition leads to the result that size of firm is lognormally distributed, which is
 − [ln( x ) − µ ]2 
1
 with mean E[X] = exp(µ + σ2/ 2) and variance
exp
2
2
σ
σx 2π


2
2
Var[X] = exp(2µ + 2σ )- exp(2µ + σ ) [1].
described as g(x, µ, σ2) =
Gibrat’s Law initiated an important line of economic research that has flourished for more than
70 years. In his comprehensive literature review, Sutton [30] identifies several “legacy” research strands
developed since Gibrat’s work. The early literature is called “Growth-of-Firm”; it investigates the growth
pattern with regard to firm size and revenue distributions and distribution changes over time, in support of
Gibrat’s Law. Representative research efforts in this literature include the verification of the proportionate
of firm size growth by Kalecki [20], stochastic modeling and public policy discussion by Simon and
Bonini [27], and multi-sectional verification of firm growth rate by Singh and Whittington [28].
Although Gibrat’s Law has provided a basis of statistical regularity for mathematical modeling in
investigating the trend of market growth, studies show that Gibrat’s Law is not satisfactory in explaining
evidence from empirical data. Starting in the 1980s, attention was focused on econometric issues and the
dissatisfactions mentioned in the early literature. Representative studies include those by Mansfield [22];
Hall [16]; Evans [9, 10]; and Dunne, Robert and Samuelson [7]. These studies mainly address firm
capacity measurement with more statistical regularities, such as firm’s life cycle; formation of firm
capacity distributions was extended to include consideration of effects of firm entry and exit. Mansfield
[22] finds that Gibrat’s Law does not work consistently in different situations and may be interpreted in
several ways, depending on how data were analyzed empirically. For example, the annual growth rates of
some industries may be largely uncorrelated with prior characteristics of the firm [16]. The empirical
studies by Evans [9, 10] suggest that in many cases the relationship between growth and firm size is not
constant but rather decreasing. Hart and Oulton [17, 18] find that there is no significant relationship
between firm size and growth when testing larger firms, and that Gibrat’s Law works only when firm size
is small. According to Hart and Oulton, firm growth could be affected by some stochastic shocks “that
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may outweigh the systematic forces that the resulting skew size distribution of firms by output will appear
to be generated by a multiplicative stochastic process” ([17, pp.1244-1245]). Because the disturbance
term in Gibrat’s model is assumed normally distributed, the final outcome is that firm size is lognormally
distributed. In this sense, the work by Hart and Oulton supports Gibrat’s Law with the new enhancement.
Thus far, the research in market structure has enriched the understanding and application of
Gibrat’s Law with constant efforts from different studies. The research on market structure since the
1980s, such as the exit and entry of firms [21], the cross-industry study of market structure [9],
technology factors [30], financial constraints [6], etc., is important in today’s e-market research because
of its in-depth explanation of empirical data beyond the capability of Gibrat’s Law. Due to the limited
size of this paper, we apply only a small portion of the market structure theories to examine the structure
of electronic market.
3. Research Methodology
3.1 Reputation: the Indicator of Online Business Capacity
Practically speaking, reputation scores are the only publicly accessible measures of online trader
capacity in the market. For example, eBay reports a trader’s reputation in terms of several different
components that reflect the trader’s behavioral performance in previous online transactions. We assume
that each individual trader, a seller in particular, can be treated as a business unit or a virtual firm. A
reputation score that a seller has received in a period from online C2C transactions can be treated the
same as the capacity of a firm. A historically accumulated reputation score can reflect the status of an
online trader in the market. Therefore, a trader's reputation records suggest his/her relative position
compared with other traders and competitors. Further, the changes in the C2C online auction market
structure are accompanied and thereby influenced by the growth of different traders’ reputation scores,
the entry of new traders, and the exit of existing traders. Thus, an investigation of the transition pattern of
trader reputation scores in the C2C online auction market may well represent the evolution of the general
market structure.
It is important to distinguish traders with regard to their roles as seller, buyer, or bidder in
different trades because their online reputation data may have different implications to the electronic
market structure. In particular, the distinction between a bidder and a buyer is subtle. Only one of the
bidders in an auction will become the buyer. Any bidder in one auction could be either a seller or a buyer
in another. In a specific auction, a bidder is just a potential buyer who may finally win the auction. So, the
reputation distribution of bidders can reflect the reputation distribution of prospective buyers, although a
bidder cannot be a buyer until the end of the auction. For this discussion, we define a trader as a seller
when he or she is selling an item in a trade, regardless of what role that person plays or will play in other
trades, and define a trader as a buyer when he or she is bidding an item in a specific auction, regardless
whether or not that person will finally win the bid.
3.2 eBay’s Reputation System
eBay’s Feedback Forum is the most popular and successful online reputation system, and it has
been the data source for most of the previous studies of online reputation. A trader’s reputation is
measured by an overall rating, which is counted and saved as a number. After an auction, both the buyer
and the seller can rate each other using the services provided by Feedback Forum. A positive comment
from a unique trading partner adds one point to the net reputation score, and a negative comment deducts
one point from the net reputation score; a neutral comment has no effect on the net reputation score.
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As Figure 1 shows, Feedback Forum provides detailed summary classified into positive, neutral
and negative feedbacks received during the past 12-, 6-, and 1-month periods. The net reputation feedback
score is highlighted and also shown in parenthesis after the trader ID. Other reputation-related
information is also presented, such as the starting date of the account. In this paper we call all these
counts of reputation feedback reputation scores.
Figure 1: A Trader’s Reputation Profile
A net reputation score signals a trader’s reputation in the C2C online auction market; the trader’s
total reputation score in a given time period has the same implications as a business entity’s size,
implying its capacity in the context of traditional market structure. Thus, we can treat a trader’s net
reputation score as his or her accumulated credits in the market and his or her total number of reputation
feedbacks (transaction volumes in a given period of time) as his capacity for doing business.
Using the reputation data from eBay’s Feedback Forum may lead to concerns about the validity
and completeness of the data because not every transaction between a pair of traders is followed by a
feedback. According to Resnick and Zeckhauser [24] the feedback rate is 52.1 percent from buyers to
sellers and 60.6 percent from sellers to buyers. Nevertheless, because the observable reputation scores
may significantly affect decisions, the data collected from eBay.com may be suitable for this study, if we
assume that the probability a trader receives a feedback comment is identically distributed.
Another factor that has been checked is whether shill bidding could distort the auction price of
some items and affect the accuracy of the reputation data.2 However, because price is not considered in
this research, the distorting effect of shilling is negligible. If a seller overdid shilling and had to take the
resulting high price, some “dry” transactions will have occurred. eBay.com calculates net reputation
scores based on the number of feedbacks from unique trader IDs; therefore, the effect of “dry”
transactions can be effectively eliminated because of the costs associated with generating new trader
accounts.
3.3 Data Collection
Our data collection method consisted of three basic procedures. The first procedure is a manual
collection of trader IDs, called ID Sampling. eBay’s auctions are divided into several categories, each
including a variable number of subcategories at different hierarchical levels. We first randomly selected a
certain number of first-level subcategories. Then we recorded the seller IDs associated to the items that
were close to the top of the list in each subcategory. While handling each seller ID, we also recorded the
IDs of traders who were bidding for these items. There was no restriction on how many buyers were
chosen with regard to one item in the process of auction as long as the number of buyers in a subcategory
2
According to Vendio (http://www.vendio.com/help/gettingstarted/glossary-ac.html), shilling is “Fraudulent
bidding by the seller (using an alternate registration) or an associate of the seller in order to inflate the price of an
item.”
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reached the required level. We removed all replicated IDs.
The second procedure, Data Retrieving, involved collecting reputation data using the trader IDs
obtained from the first procedure. Once a set of trader IDs have been sampled, they can be repeatedly
used in the Data Retrieving procedure at different time points. This enabled us to analyze the changes and
trends of trader reputation data using time series. The selected data fields for studying trader reputation
are positive, neutral, and negative feedbacks in six-months and net reputation score.
The third procedure is Transaction Analyzing. Based on the trader IDs obtained from the
sampling procedure, we searched the trader’s transaction history data. The history data recorded the role
of a trader as either a seller or a buyer in a trade, which was the basis for calculating the total number of
selling and buying transactions a trader completed.
Obviously, ID sampling is the most important procedure in predetermining the quality of the data.
To make our data analysis robust, we did ID sampling twice. In the first ID sampling, done in January
2003, we obtained 408 seller IDs and 408 buyer IDs from 50 subcategories. The second round of ID
sampling was done two months later with larger ID sets: 2000 seller IDs and 1526 buyer IDs were
selected from about 200 subcategories. The different sizes of ID sets allow us to verify the consistency of
data analysis outcomes based on different sample sizes. We performed the Data Retrieving procedure
right after ID sampling for both seller and buyer. Then, we repeated the data retrieval process using the
same ID sets six months after the first data retrieval. The results of data collection are presented in Table
1.
Table 1: Descriptions of Reputation Datasets
Dataset
ID #
Data
type
Initial
Collection Date
Sample
size
Traders whose net
reputation scores > 0
Traders whose
six-month total > 0
S-030116
Seller
01/16/2003
408
402 (98.5%)
396 (97.1%)
B-030120
Buyer
01/20/2003
408
337 (82.6%)
315 (77.2%)
S-030320
Seller
03/20/2003
2000
1967 (98.9%)
1953 (97.7%)
B-030322
Buyer
03/22/2003
1526
1288 (84.4%)
1240 (81.3%)
We define those traders with a nonzero net reputation score as active traders. According to the
analysis of transaction history data as shown in Table 2, about 90 percent of active sellers sold more than
they bought, and about 90 percent of active buyers bought more than they sold. The average reputation
score for those sellers who bought more than sold is lower than the average reputation score for other
sellers. The average reputation score for those buyers who sold more than bought is higher than the
average reputation score for other buyers. Therefore, the seller datasets can well represent the active
sellers’ reputation distributions and the buyer datasets can serve the same purpose for the active buyers.
Table 2 Compositions of Active Traders
Dataset
Classification
%
11.0%
Average Net
Reputation
184
Average sixmonth Total
47
S-030116
Sellers who bought more than sold
S-030320
Regular sellers
89.0%
1692
667
Sellers who bought more than sold
14.8%
156
52
Regular sellers
85.2%
1358
529
B-030120
Buyers who sold more than bought
9.5%
336
136
Regular buyers
90.5%
78
39
B-030322
Buyers who sold more than bought
10.6%
664
172
Regular buyers
89.4%
90
34
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4. Data Analysis and Findings
4.1 Lognormality of Reputation Distribution
11
9
10
8
7
Ln(x)
Ln(x)
(a2): Seller’s six-month total reputation scores (S-030116)
(a1): Seller’s net reputation scores (S-030116)
50
50
45
45
Counts (Out of 315 Samples)
Counts (Out of 315 samples)
6
5
4
3
2
1
50
45
40
35
30
25
20
15
10
5
0
0
11
9
10
8
7
6
5
4
3
1
2
Counts (Out of 396 samples)
50
45
40
35
30
25
20
15
10
5
0
0
Counts (Out of 402 samples)
To analyze reputation score distribution, we first plotted the histograms of logarithm-transformed
reputation data, i.e., Y = Ln(X), where X is the original reputation data and Y is the transformed reputation
data. Figure 2 shows the histograms of net reputation scores and six-month total reputation feedbacks
collected in January 2003. For seller datasets, the graphic distributions are close to bell-shaped normal
distributions. On the other hand, the shapes of the buyer dataset distributions are not symmetric. A large
number of buyers had original reputation scores of 1, and log-transformed reputation scores of 0.
Therefore, shapes of buyers’ reputation distributions are more right-skewed than those of sellers.
40
35
30
25
20
15
10
5
40
35
30
25
20
15
10
5
0
0 0.5 1
9
8
7
6
5
4
3
2
1
0
0
1.5 2 2.5 3
3.5 4
4.5 5 5.5 6 6.5 7
Ln(x)
Ln(x)
(b2): Buyer’s six-month total reputation scores (B030120)
(b1): Buyer’s net reputation scores (B-030120)
Figure 2: Histograms of Reputation Scores
Note: There is a zero-count for x = 0.5 of the x-axial. This is because reputation scores come in integers and there is
no integer x whose natural logarithm falls into (0, 0.5]. We can verify that ln(1) = 0 is counted for group x ≤ 0 and
ln(2) > 0.5 falls into the range (0.5, 1].
Table 3: Descriptions of Reputation Scores
Dataset
S-030116
Type of Score
Net Scores
6-month Total
B-030120
Net Scores
6-month Total
S-030320
Net Scores
6-month Total
B-030322
Net Scores
6-month Total
* p<0.05 ** p<0.001
Sample Size
402
396
337
315
1967
1953
1288
1240
Mean
5.900
4.983
3.271
2.669
5.577
4.716
3.610
2.917
6
Variance
3.342
3.310
3.208
2.570
3.246
3.067
3.705
2.706
Skewness
-0.158
-0.164
-0.064
-0.172
-0.025
-0.069
-0.101
-0.018
Kurtosis
-0.127
-0.174
-0.753
-0.462
-0.173
-0.054
-0.690
-0.644
Wald-Stat
2.139
2.231
8.194*
4.364
2.651
1.780
27.72**
21.49**
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We conducted the Wald test on the datasets collected at two different time points (January 2003
and March 2003), following the formula: Wald-stat = degree_of_freedom * (skewness2 / 6 + kurtosis2 / 24)
[15], where Wald stat ~ χ2(d=2). As shown in Table 3, all Wald-statistics of seller reputation scores passed
the test given the critical value χ2(d=2, α = 0.05) = 5.99, while only the Wald-statistics of buyer six-month total
feedbacks passed the same test.
According to Table 3, we have the following findings from the lognormality tests: 1) Seller
reputation data, including net reputation scores and six-month total reputation feedbacks, are
approximately lognormally distributed. 2) The lognormality of buyer reputation is mixed: Net reputation
scores fail to pass the lognormality test, although the distribution of their six-month total reputation
feedbacks is approximately lognormal. It is impressive that Wald-tests of seller data collected at different
time points showed consistent outcomes.
4.2. The Growth of C2C Online Auction Market
According to Gibrat’s Law, the formation of lognormal distributions is the result of firm’s
proportionate growth rate. We examined the change of traders’ total reputation feedbacks (transaction
volumes) after a six-month interval with each time point denoted as t0 and t1 respectively. After removing
outliers and traders whose records became invalid in the second round of data collection, we obtained the
records of surviving sellers and surviving buyers (Table 4). We compared the means of log-transformed
total reputation feedbacks in the six-month window. The results of repeated measure t-test as illustrated in
Table 4 show that the average of buyer six-month total feedbacks significantly increased during t0 to t1 (p
< 0.001). However, the changes of average seller six-month total feedbacks from different datasets were
not consistent. The average of six-month total feedbacks based on dataset S-030116 showed a significant
increase after six months, while that of S-030320 did not.
Table 4. T-test of Reputation Growth
Dataset
S-030116
S-030320
B-030120
B-030322
* p<0.001
Sample Size
352
1745
293
1061
Mean at t0
5.030
4.755
2.696
3.015
Mean at t1
5.229
4.726
3.179
3.170
t-value
4.19*
1.19
6.85*
4.02*
Further, we analyzed the growing pattern of total reputation feedbacks, in the form of ln(Y(t1)) =
β0 + βln(Y(t0)), where Y(t0) is the reputation score at time t0, and Y(t1) is the reputation score at time t1. In
the light of Gibrat’s Law, we hypothesized β to be equal to ‘one’ to indicate proportionate growth. The
results of OLS regression are shown in Table 5. Based on the values of the coefficient estimates in a
confidence interval of 95 percent significance, the regression results failed to support β = 1 for both net
reputation scores and total reputation feedbacks across all samples. The OLS regression estimate of β for
each sample is significantly below 1, which suggests that the surviving traders who previously transacted
less grew faster than those traders who transacted more.
Table 5. Proportionate Test of Reputation Growth (OLS regression)
Dataset
S-030116
S-030320
B-030120
B-030322
β
Sample Size
352
1745
293
1061
Estimate
0.86544
0.88728
0.65013
0.65773
Std. Error
0.02473
0.0133
0.04023
0.02154
7
Confidence Interval
Lower 95% Upper 95%
0.8168
0.9141
0.8612
0.9134
0.5709
0.7293
0.6155
0.7
R
2
0.7778
0.7186
0.4729
0.4682
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The above findings are consistent with recent research, which has revealed the limitation of
Gibrat’s Law. Since the 1960s, several different models have been conceived to explain why the
distribution of firm size is not consistently proportionate [9, 17, 18, 19]. Among them, the work by Hart
and Oulton [17] is a representative effort in revealing the pattern of firm growth with the concentration on
stochastic models. We followed their data analysis approach in the follow-up analysis.
First, we divided the seller sample (S-030522) into several smaller categories based on the total
feedbacks at t0, with total feedbacks falling into such ranges as (0, 10], (10, 20], (20, 40], etc. We then
calculated the geometric means of each range at t0 and t1 respectively. A growth trend figure was shown
as Figure 3, with a 45 degree line imposed. According to Gibrat’s Law, all the points should fall on the 45
degree line as an indication of proportionate growth. However, Figure 3 shows that almost all the points
except for that from the range of (0,10] are lying on the line. The smaller sellers grow more quickly than
other sellers. We speculate that Gibrat’s Law does not hold for the whole sample because we have
included these smaller sellers. There may be a non-linear relationship between the reputation scores at t0
and t1.
Reputation Growing Trend
Geometric Mean of Reputation at t1
(log)
10
8
6
4
2
0
0
2
4
6
8
10
Geometric Mean of Reputation at t0 (log)
Figure 3. Seller Reputation Growth
We then performed several sequential OLS regressions, as shown in Table 6. The top section of
Table 6 indicates that the regression coefficients (β), increasing from 0.392 to 0.887, are significantly
below 1 for all the data ranges, even when larger sellers were added to the sample. On the other hand, the
regression coefficients are near unity, decreasing from 1.27189 to 0.96811, when smaller sellers were
included. We could not reject the unity hypothesis when we included only those sellers with reputation
scores greater than 10 at t0. Gibrat’s Law still holds for these groups of sellers, although the test for sellers
with reputation scores greater than 2560 indicated that β was not unity (β=1.21853, p=0.05). Thus, the
conclusion based on the general regression with overall sample was misleading. Smaller sellers had a
greater influence on the overall estimate than larger sellers.
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Table 6. Reputation Growth by Ranges (OLS regression)
(a) Seller
β
6-Month
Total at
t0
<=10
<=20
<=40
<=80
<=160
<=320
<=640
<=1280
<=2560
<=5120
Total:
>10
>20
>40
>80
>160
>320
>640
>1280
>2560
>5120
Sample
Size
Estimate
135
268
482
737
997
1253
1449
1597
1659
1722
1745
1610
1477
1263
1008
748
492
296
158
86
23
0.392
0.416
0.489
0.620
0.688
0.750
0.810
0.843
0.863
0.877
0.887
0.968
0.989
0.998
1.028
1.027
0.995
1.033
1.057
1.219
1.272
6-Month
Total at
t0
<=2
<=4
<=8
<=16
<=32
<=64
<=128
<=256
<=512
Total:
>2
>4
>8
>16
>32
>64
>128
>256
>512
Sample
Size
Estimate
128
211
321
459
626
800
931
1002
1043
1061
933
850
740
602
435
261
130
59
18
0.360
0.487
0.413
0.353
0.408
0.511
0.573
0.604
0.640
0.658
0.744
0.808
0.884
0.910
0.926
0.986
1.068
0.919
1.664
Confidence Interval
Lower
Upper
95%
95%
0.105
0.680
0.238
0.594
0.371
0.607
0.538
0.703
0.626
0.749
0.702
0.797
0.772
0.849
0.811
0.877
0.834
0.894
0.850
0.905
0.861
0.913
0.938
0.998
0.957
1.021
0.961
1.034
0.985
1.071
0.975
1.080
0.936
1.055
0.945
1.121
0.920
1.194
1.002
1.435
0.678
1.866
Std
Error
0.145
0.091
0.060
0.042
0.031
0.024
0.020
0.017
0.015
0.014
0.013
0.015
0.016
0.019
0.022
0.027
0.030
0.045
0.069
0.109
0.286
Geometric
Mean
1.721
1.534
1.405
1.295
1.202
1.138
1.102
1.079
1.067
1.052
1.047
1.143
1.174
1.194
1.242
1.259
1.200
1.285
1.366
1.575
1.825
R
2
0.050
0.074
0.121
0.229
0.327
0.434
0.540
0.615
0.658
0.698
0.719
0.718
0.710
0.698
0.685
0.666
0.688
0.646
0.599
0.599
0.486
(b) Buyer
β
Confidence Interval
Lower
Upper
95%
95%
-0.247
0.967
0.172
0.802
0.216
0.610
0.226
0.479
0.318
0.498
0.444
0.578
0.518
0.628
0.556
0.652
0.596
0.685
0.616
0.700
0.691
0.798
0.749
0.867
0.816
0.952
0.828
0.993
0.819
1.033
0.836
1.136
0.842
1.295
0.542
1.295
0.567
2.761
Std.
Error
0.307
0.160
0.100
0.065
0.046
0.034
0.028
0.025
0.023
0.022
0.027
0.030
0.035
0.042
0.054
0.076
0.114
0.188
0.518
9
Geometric
Mean
3.460
2.358
1.838
1.425
1.213
1.090
1.029
0.986
0.972
0.961
1.112
1.193
1.294
1.374
1.463
1.571
1.679
1.691
2.656
R
2
0.011
0.043
0.051
0.061
0.113
0.220
0.310
0.375
0.434
0.468
0.449
0.458
0.467
0.439
0.400
0.394
0.405
0.295
0.393
Decision Support Systems
Lin et al.
The estimate could not tell exactly which group of sellers grew fastest. Therefore, following the
method by Hart and Oulten [17], we defined the reverse regression model ln(Y(t0)) = α0 + αln(Y(t1)).
Then, we obtained the geometric mean of the coefficient γ = (β/α)0.5, which is suggested to be a reliable
estimate for the growth rate [17]. Based on data in the column of “geometric mean” in Table 6, we found
that sellers with the highest reputation scores grow faster than any other group of sellers (mean=1.823), or
the growth of the sellers at the very upper tail of the whole distribution is the fastest. This is a rich-getricher phenomenon. The second fastest group is the smallest sellers (sellers with reputation scores ≤ 10)
(mean =1.72). However, the R2 for this group of sellers is very small (0.05), indicating that there is a large
percentage of variance not explained by the regression model. So, our conclusion about the smaller sellers
should be viewed with caution.
We did the same analysis on buyer reputation data (B-030322). Table 6 shows that the buyer’s
reputation score growth pattern is somewhat different from the seller’s. Due to limited paper size, we will
rely on readers to compare the two tables and identify the major differences.
4.3. Trader Entry and Exit
Dunne, Roberts and Samuelson [7] find that turnover among firms in US manufacturing industry
was substantial; generally, the entering and exiting firms were considerably smaller than existing firms,
and new firms had high rates of failure. The entry and exit of traders is also important to understanding
the dynamics of electronic market and the active traders’ market power. However, there are two issues.
First, normally there is no sunk cost for a new trader to start a trading account. Second, exiting the emarket does not generate any extra pecuniary costs. Since traders appear as a “pseudonym” in the market,
which is handled electronically, traders can freely enter and exit. The only difference is in the
accumulated net reputation score. A new entrant has a zero net reputation score and an exiting incumbent
trader will lose the potential benefit of his or her net reputation score.
Consider a simple reputation score transition model with non-decreasing reputation score (Figure
4). Three statuses of a trader’s online account can be identified: out of market, inactive account, and
active account. Here we assume the change of an active account is a simple increment by 1.3 The
reputation distribution of active traders is determined by the rates of three state transitions: the transition
from N = 0 to N > 0, the increment of N, and nullifying of N after the trader exits from the market.
Nt = Nt-1 +1
Nt: reputation scores at time t
Inactive
Traders
Nt = 0
Trade
Active
Traders
Nt > 0
Quit
Out of market
No account
Set up account
Figure 4: A State Transition Diagram
3
In a more general situation, the change of the reputation score could be +1, -1 and staying unchanged
because no feedback was received after a trade.
10
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Lin et al.
We further define two types of traders regarding their transition statuses: Entrant, whose net
reputation score just changed from zero to positive, and Exited trader, whose online trading account was
just closed. The following are five findings in accordance with these definitions:
1) The statistics from the reputation datasets indicate that about 10 percent of sellers registered with
eBay.com within the previous six months and about 30 percent of buyers registered in the same
period (Table 7).
2) At the beginning, there were more buyers with zero reputation score than sellers with zero reputation
score (Table 8).
3) The entry rate of sellers was lower than that of buyers in a six-month period and the exiting rate of
seller was higher than that of buyer in the same period. Consequently, after six months, the number of
active buyers increased while the number of active sellers declined (Table 8).
4) As expected, the average net reputation score and average total feedbacks of entrants (both sellers and
buyers) in the six-month study period were lower than those of the whole sample (Table 9). However,
the averages of entrant sellers were lower than the ones for entrant buyers, while the average net
reputation and total six-month feedbacks of sellers were much higher than those of buyers.
5) The average net reputation score and average total feedbacks of exited sellers in the last six months
were lower than those of the whole sample (Table 9). In contrast, the average net reputation score and
average total feedbacks of exited buyers in the six-month study period were higher than those of the
whole sample.
Table 7. Newly Registered Traders
Dataset
Initial Population
S-030116
S-030320
B-030120
B-030322
408
2000
408
1526
Newly Registered in the
Last Six Months
41
184
120
463
% of the Total
10.1%
9.2%
29.4%
30.3%
Table 8. Trader Population Change
Dataset
Initial Population
Total Rep. > 0
Rep. = 0
Exited
S-030116
408
402
6 (1.5%)
32 (7.8%)
S-030320 2000
1967
33 (1.7%) 167 (8.4%)
B-030120
408
337
71 (17.4%)
13 (3.2%)
B-030322 1526
1288
238 (15.6%) 116 (7.6%)
The percentage is referred to the initial population.
Six Months Later
Survived Rep. > 0
376
369
1833
1807
395
361
1410
1311
Rep. = 0
7 (1.7%)
26 (1.3%)
35 (8.6%)
99 (6.5%)
Table 9. Comparisons of Average Reputation
Dataset
S-030116
S-030320
B-030120
B-030322
Average Net Reputation
Score
All
Entrants
Exited
Sample
Traders
1504
2.83
1085
1160
5.24
860
85
6.77
182
149
8.47
178
11
Average 6-Month Total
Feedbacks
All
Entrants
Exited
Sample
Traders
590
5.33
236
451
9.18
272
40
10.1
101
51
10.3
59
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Lin et al.
5. Discussion
We have found that the average number of transactions by sellers is higher than that by buyers;
seller reputation data are consistently lognormally distributed but buyer data are not; and a higher
percentage of sellers exited from the market than buyers, while a higher rate of new buyers entered the
market than sellers. Although there is a continuous distribution of buying and selling proportion between
a pure buyer and a professional seller and it is common that a trader may change his role between a buyer
and a seller from auction to auction, the differences of dynamic patterns between sellers and buyers
revealed from the reputation data imply that the underlying mechanism regarding their different natures of
doing business in the C2C online auction market has clearly driven traders to become sellers and buyers.
This has also been confirmed previously by the reputation dataset summarized in Table 2. The following
are the discussions based on the findings from the reputation data.
5.1. The Limitation of Gibrat’s Law
Our findings are consistent with the research outcomes that have revealed the limitation of
Gibrat’s Law [9, 10, 14, 17, 18, 19]. In our study, seller reputation data, in terms of the net reputation
score and total reputation feedbacks, do not support the proposition of proportionate growth as suggested
by Gibrat’s Law, although the distributions of reputation scores are lognormal. The inconsistency
between the lognormal distribution and non-proportionate growth of the seller’s reputations may result
from the dynamic changing composition of the seller population, which is illustrated in Figure 5. The net
population of sellers at time point t1 consists of surviving sellers from t0 plus newly established sellers and
those transited from buyers. Therefore, we can rule out proportionate growth as the sole reason for the
formation of lognormal distributions of reputation scores, because the new composition of seller
population has undergone major changes due to the fast-moving pace in the electronic market.
Sellers who have
transited to buyers
Exited sellers
Sellers who will
transit to buyers
Surviving sellers
Sellers who will exit
Reputation
Distribution
at t0
Sellers who
were buyers
Sellers who will stay
Reputation
Distribution
at t1
Entrant sellers
t1
t0
t
Figure 5: The Evolution of Seller’s Population
In investigating the limitation of Gibrat’s Law, Ijiri and Simon [19] reveal that firm entry is an
alternative factor that contributes to firm size distribution. In addition, Evans [9, 10] and Dunne, Robert
and Samuelson [7] also identify the effect of firm exit on firm size distribution. Recently, Cabral and
Mata [6] report that firm size distribution of the Portuguese manufacturing industry is significantly rightskewed and evolves over time toward a lognormal distribution. Cabral and Mata suggest that using a
12
Decision Support Systems
Lin et al.
parametric Gamma distribution can better model market structure when firm size distribution evolves
without proportionate growth.
Consistently, the findings from our analyses can explain the formation of the lognormal
distribution when taking into account the effects of trader entry and exit. If trader entry and exit had not
had an effect on the distribution, the distribution of the reputation data should have been left-skewed
when the reputation score growth rate falls as the reputation score gets higher. In fact, as Table 9 shows,
entrants have lower average reputation score and add more weight to the lower end of the reputation
distribution. The more right-skewed histograms in Figure 2 and the negative values of skewness in Table
3 imply that the effect of entry has outweighed the effect of growth rate of traders with lower reputation
scores.
However, we notice that the average reputation scores of exited sellers are lower than the overall
averages. In addition, Table 8 shows that sellers have a higher exit rate than entry rate. These two factors
should have jointly skewed the distribution to the left. Since seller reputation scores are lognormally
distributed, there must be a net transition from buyers to sellers, another source of entry that finally offset
all the effects of left-skewing. Since the seller population is much smaller than the buyer population, this
net transition has much less impact on buyer reputation distribution.
The effect of buyer exit is quite different from that of seller exit. As the average reputation scores
of exited buyers are higher than the overall averages, the loss of the population at the higher end of the
reputation distribution will inevitably skew the distribution curve to the right. This extra right-skewing
effect could be the main reason why buyer net reputation distribution is not lognormal and the six-month
total feedback distribution is not consistently lognormal.
5.2. The Trends of C2C Online Auction Market
Two trends of eBay’s C2C online auction market can be identified based on the findings we have
obtained so far:
1)
The net population of traders is growing and the total transaction volume is increasing.
Since the feedback rates for sellers and buyers are at about the same level [24], the proportion
between the populations of buyers and sellers can be estimated as the ratio of average six-month total
feedbacks between buyers and sellers. So, according to Table 9, we can conclude that buyers outnumber
sellers in eBay’s C2C market and the buyer population change dominates the trend of online trader
population change. Then we can further derive that the trader population of the C2C market is growing.
Finally, the increasing population of traders and the non-decreasing average transaction volume as
supported by the t-test in Table 3 indicate the growing trend of eBay’s C2C online auction business.
2)
eBay’s C2C market is becoming a B2C market.
If exited sellers traded less than the average, the remaining sellers are more dedicated and their
average net reputation score will keep growing. In another aspect, the exited buyers had higher average
reputation scores than the averages for all buyers, implying the growth of average buyer reputation scores
has a limit. These differences between sellers and buyers will further distinguish the reputation
distribution patterns of sellers and buyers as well as distinguish them as firms and consumers respectively.
In this way there is a growing B2C submarket in eBay.com. However, since the transactions among
regular consumers are one of eBay’s basic business forms, C2C auctions will remain a main business
activity in eBay.com.
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Decision Support Systems
Lin et al.
6. Concluding Remarks
In this study we examine how reputation scores in the C2C online auction market reflect the
market structure. We suggest that online reputation scores become the important indicators for the
capacity of online firms in the electronic market because reputation systems have visualized their
reputation. We find that seller reputation scores, rather than those of buyers, are lognormally distributed.
Further, reputation scores of the whole population do not follow Gibrat’s Law of proportionate growth
because smaller traders grow faster than larger traders. However, the entry and exit of traders as another
factor affecting reputation score distributions can well explain why seller reputation distribution is still
lognormal. Our analyses suggest that eBay.com has been undergoing a sustained growth as a leading C2C
online auction marketplace.
Several limitations in the current research need to be mentioned. First, the effects of the type of
auctioned items on the market structure were not studied and, hence, we restricted our investigation of
market structure at the aggregate level. Second, the size of our study sample is not as large as those used
in previous market structure research. In order to examine both tails (lower and upper) of the reputation
distribution, a larger dataset is expected.
We suggest further market structure research on the C2C online market from three different
perspectives. First, a cross-sectional analysis of reputation score distribution should be applied to
examine the reputation score distributions of traders who are doing business in different auction
categories. Second, stochastic process modeling should be applied in studying trader entry and exit and
the transition between sellers and buyers. Third, reputation score distributions weighted by the transaction
amount should be used to examine the effect of monetary factors on the market structure to complement
counting-only data analysis.
Acknowledgements: The authors thank Pat Merrier, the Editor-in-Chief, and anonymous reviewers for
their helpful comments on the previous versions of this paper.
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Zhangxi Lin is an assistant professor of information system in the Rawls College of Business
Administration at Texas Tech University. He received an M.Eng. degree in computer science from
Tsinghua University in 1982, a M.S degree in economics in 1996 and a Ph.D. degree in information
systems in 1999 from the University of Texas at Austin. His research interests include electronic
commerce, network traffic management, information economics, and IT adoption in China. He has
worked in computer application development for about 20 years with experience in large-scale data
processing, management information systems, and e-commerce systems.
Dahui Li is an assistant professor in MIS at the University of Minnesota Duluth. He received his Ph.D. in
management information systems from Texas Tech University. His research focuses on business-toconsumer relationships, online community, and diffusion of technology innovation.
Balaji Janamanchi received his MS degree in MIS from Texas Tech University in 2001 and is since then a
fulltime instructor at Texas Tech. He is a fellow member of Institute of Chartered Accountants of India
since 1989 and has been in Auditing and Business Consulting as a Chartered Accountant in India from
1984 to 1999. He has extensive exposure to variety of businesses. His recent research interests include: ecommerce, operations management, and information systems.
Wayne W. Huang, Associate Professor at MIS Department, College of Business, Ohio University, USA.
He has worked as a faculty in universities in Australia, Singapore, and Hong Kong before. His main
research interests include Group Support Systems (GSS), electronic commerce, eLearning, knowledge
management systems, and software engineering. He has published more than 60 academic research papers,
including papers in leading IS journals such as Journal of Management Information Systems (JMIS);
IEEE Transactions on Systems, Man, and Cybernetics; Information & Management (I&M); IEEE
Transactions on Professional Communication; Decision Support Systems (DSS); International Journal of
Global Data Management (JGIM); and European Journal of Information Systems. He is on the editorial
board in I & M; JGIM; and Journal of Data Management (JDM).
16