ONLINE APPENDIX
Auctions versus Posted Prices in Online Markets
by Einav, Farronato, Levin and Sundaresan
This online appendix contains four sections. Appendix A provides a more general version
of the model from Section 2. Appendix B includes additional charts and tables that are
referenced in the main paper. Appendix C reports alternative speci…cations for our main
results, using di¤erent matching criteria, as discussed in Section 3. Appendix D provides
cross-country evidence on the decline of eBay auctions. A separate document, Appendix E,
contains the survey we sent to eBay sellers, and complete responses.
Appendix A. Extended Model
The model in Section 2 assumes that all buyers have the same value v. We mention in the
text that allowing heterogeneity in buyer valuations would not change the main results. Here
we describe this extension.
There are n 1 potential buyers, indexed by i = 1; :::; n. Buyer i has a value vi = v + wi ,
where v is a common value for all buyers drawn from a distribution f , and each wi is an
idiosyncratic value drawn independently from a distribution g. The distributions f and g
are both log-concave. Let w(1) ; :::; w(n) denote the order statistics of the idiosyncratic value
draws, and v (k) = v + w(k) be the kth order statistic of the buyer valuations. All buyers have
a common reservation value u, and auction disutility .
If the seller o¤ers a posted price p, the probability of sale is
QF (p) = Pr v (1)
p .
u
If the seller o¤ers an auction with reserve price r, the probability of sale is
QA (r) = Pr v (1)
u
r .
Therefore (as in Figure 3) the posted price demand curve is a vertical translation of the
auction sales curve: QF (r + ) = QA (r). That is, setting a posted price of r + gives an
equivalent probability of sale as running an auction with reserve price r.
Next, the expected auction price given reserve price r is
pA (r) = r + E max v (2)
u
1
r; 0 j v (1)
u
r
0 :
We claim that the second term is decreasing in r. This is because
E max v (2)
=E v
r; 0 j v (1)
u
(2)
u
Pr v (2)
rjv
u
(2)
u
u
0 j v (1)
r
r
r
0
0
u
r
0 :
Log-concavity of the distributions f (v) and g(wi ) is preserved for the distribution of v + wi ,
and for the corresponding order statistics (Barlow and Proschan, 1966).1 Moreover, the mean
residual lifetime E [vi j vi r0 ] r0 of a random variable whose distribution is log-concave is
decreasing in r0 . So E v (2)
u r j v (2)
u r 0 is decreasing in r.
(2)
It remains to be proven that Pr v
u r 0 j v (1)
u r 0 is also decreasing in r. Let H be the cumulative distribution function of vi = v + wi and n the number
of bidders. Then
Pr v (2)
u
r
0 j v (1)
u
r
0
Pr v (2)
u r 0
Pr [v (1)
u r 0]
n 1
nH (r + + u) [1 H(r +
= 1
[1 H n (r + + u)]
nH n 1 (r + + u)
:
= 1
Pn 1 k
H (r + + u)
1 + k=1
=
+ u)]
The last term is an increasing function of r, so Pr v (2)
u r 0 j v (1)
u r 0
is decreasing in the reserve price.
With this established, it follows that the posted price demand curve is steeper than the
auction demand curve. To see this, for any q de…ne r such that q = QA (r). Then the
vertical distance between the auction demand curve and the posted price demand curve at
q is pA (r) (r + ), which is decreasing in r, and hence increasing in q. Furthermore, at
q = 0, we have pA (r) = r < r + . So the auction demand curve starts below the posted
price demand curve. At q = 1, we have p (r) = E v + w(1)
u, whereas the relevant
(1)
posted price is v + w u, so provided < E v + w
(v + w), the auction demand curve
ends higher.
Therefore the posted price demand curve crosses the auction demand curve once from
above as in Figure 3. Under this condition, the comparative statics in the main text with
respect to c, u, and are straightforward. In particular, an increase in any of these parameters makes it more likely that the best posted price will dominate an auction with an
optimal reserve price.
1
Barlow, Richard E., and Frank Proschan (1966). “Inequalities for Linear Combinations of Order Statistics from Restricted Families.” Annals of Mathematical Statistics 37(6), 1574-1592.
2
Appendix B. Additional Tables and Figures
This Appendix includes additional Tables and Figures that were referenced but not included
in the main text.
Appendix B Figures
Figure B1: Auction Discount for Di¤erent Auction Subsamples
Figure B2: Distribution of Number of Unique Bidders per Auction
Figure B3: Distribution of Auction Reserve Prices
Figure B4: Distribution of (Normalized) Auction Sale Prices
Figure B5: Components of the Auction Demand Curves
Figure B6: Listing-Level Demand Estimates for 2005, 2007
Appendix B Tables
Table B1: Comparing the Matched Listings Sample to all eBay Listings
Table B2: Auction Success and Discount over Time
Table B3: Auction Success and Discount for Di¤erent Subsamples
Table B4: Estimation Results for Listing-Level Demand Curves
Table B5: Classifying Categories using Principal Component Analysis
Table B6: Listing-Level Demand Estimates for Di¤erent Categories
Table B7: Model Estimates for 2005, 2007
Appendix C. Alternative Matching Criteria
In the paper, we de…ne a set of matched listings to be the same item sold by the same
seller within the same calendar year. A potential concern with this de…nition is that a full
calendar year is a long period: demand conditions may change, the seller’s information about
the item value may change, or the seller’s listing strategy may evolve. Such time-varying
changes within a matched set of listings could a¤ect the causal interpretation of our main
results.
To address these types of concerns, in this appendix we replicate our main results (Figure
8, Figure 10, Table 2, and the key numbers from Figure 7) using seven alternative criteria
for matching listings. Matching De…nition I shortens the time period for matching listings
to a calendar-quarter, so that we identify matched listings as being listings of the same item
by the same seller o¤ered within a calendar quarter (that is, within January-March, within
April-June, and so on). This provides less comparable listings for any given listing in the
sample, but arguably demand conditions and seller information are more likely to be stable
within a quarter than within a year.
3
We next explore the possibility that there might be life-cycle e¤ects for any given item,
and these life-cycle e¤ects or time trends in the demand for the item could confound our
results. Such a confounding problem might arise if, for example, demand for the item fell
over time and the seller also shifted sale format from posted price toward auctions. We use
two alternative methods to identify and address possible time trend or product life-cycle
issue. For both methods we start with our baseline sample (same item, same seller, same
year) or matched listings.
The …rst of the two approaches relies on the regression model
pij = aj +
j tij
+ "ij :
Here j indicates a matched set, i indicates a posted-price listing within the set, pij is the
normalized posted price associated with the listing, and tij is a calendar time indicator
(measured in weeks). We run this regression separately for each matched set. The coe¢ cient
j , which is estimated separately for each matched set, captures a time trend in the listed
price for the item. The idea in this regression is that if demand for the item is changing
systematically over time due to product life-cycle or because the supply of potential buyers
begins to be exhausted, and the seller is responsive in terms of selling approach (which might
confound our results), we should be able to pick this up as well from seeing changes in the
listing price.
The table below reports the resultant distribution of the estimated j ’s across matched
sets, separately for 2003 and 2009. For the median item in our sample, there is no trend in
the posted price over time (the median j in both 2003 and 2009 is zero). However, some
items do exhibit systematic price trends, including some items with sizeable price decreases
over time. The average j is negative although relatively small (corresponding to a 0.7% per
week price decrease in 2003 and 0.3% decrease per week in 2009, with the average matched
set covering about 8-9 weeks).
`
Sample
N
Mean
Std. Dev.
2003
2009
23,057
83,685
-0.007
-0.003
0.059
0.036
10th pctile 25th pctile 50th pctile 75th pctile 90th pctile
-0.031
-0.019
-0.010
-0.006
0.000
0.000
0.002
0.002
0.015
0.010
These results motivate a set of robustness checks where we restrict the sample to items
that exhibited stable posted prices over time. For Matching De…nition IIa we trim the items
in the bottom 10% and top 10% of the j distribution, and focus on the 80% of the matched
sets that have j estimates between the 10th and 90th percentiles. For 2009, none of these
items have a posted price trend greater than 0:1% per week or less than 0:3% per week.
4
For Matching De…nition IIb, we restrict attention to matched sets with an absolute value of
j that is less than 0.01. For Matching De…nition IIc, we restrict attention to matched sets
with an absolute value of j that is less than 0.005. These last two de…nitions mean that for
any item that makes the sample, its price trend over ten weeks (a relatively long time for a
matched listing in our sample) was no more than plus or minus one percent.
Our last approach relies on a similar regression model
Aij =
j
+
j tij
+ uij :
Again j index matched sets and i listings, except that now we include both auction and
posted price listings and the dependent variable Aij is an indicator for whether the listing
is an auction listing. The idea here is that if sellers are responding to systematic trends
in demand and changing their mix of auctions and posted price listings accordingly, it will
show up in the time trend of their sale composition. Similarly, if sellers start listing an item
using auctions to gain information, then switch to posted prices as they learn more about
the item value, we will pick this up as a systematic trend in sale format. In principle, either
of these mechanisms might confound our interpretation of the results in the paper. As in
the above regression, we estimate a separate j for each matched set of listings.
The table below reports the distribution of the estimated j ’s across matched sets, separately for 2003 and 2009. For the median item, there a slight trend away from auctions in
2003 (0.6% per week), and essentially no trend at all in 2009 (0.1% per week fall in auctions).
However, as with the posted price trend estimates, we do see some items where the seller
moved more signi…cantly in one direction or the other.
`
Sample
N
Mean
Std. Dev.
2003
2009
23,057
83,685
-0.012
-0.005
0.083
0.070
10th pctile 25th pctile 50th pctile 75th pctile 90th pctile
-0.082
-0.055
-0.036
-0.023
-0.006
-0.001
0.017
0.015
0.049
0.041
The presence of some matched sets that exhibit a systematic trend toward or away from
auctions motivates our next robustness check, in which we focus only on matched listings with
a relatively stable mix of auction and posted price listings over time. For Matching De…nition
IIIa, we trim items with estimated j s in the bottom 10% and top 10% of the distribution,
and focus on the 80% of the matched sets that have j estimates between the 10th and 90th
percentiles. This restricts us to items where the composition of listings is shifting toward
auctions by less than 5% over a ten week period, and shifting away from auctions by no more
than 5-8 percent over the same ten week period. For Matching De…nitions IIIb and IIIc, we
adopt even more stringent criteria and restrict attention to matched sets whose estimated
5
have an absolute value less than 0.03, and less than 0.015 respectively. For the items that
survive into these samples, the mix of auctions to posted prices is highly stable over the
observed time period.
The results from all seven alternative matching de…nitions, as well the baseline results
from the main text, are presented in the following Appendix Tables C1 and C2, and in
Appendix Figures C1-C3. The striking feature of these tables and …gures is that although
there are some small variations in the exact estimates as we try di¤erent matching de…nitions,
the results reported in the paper are highly robust to restricting to matched listings that
appeared in short time windows, exhibited stable posted pricing, or a stable format mix. This
suggests that while we certainly cannot rule out the types of life-cycle or shifting demand
or learning e¤ects that plausibly might be present in the data, they do not seem to play a
major role in driving our main empirical results.
j
Appendix D. Cross-Country Evidence
Appendix Figures D1(a), D1(b), and D1(c) replicate Figure 1 in the paper for di¤erent
countries. Figure 1 showed the share of active auction listings relative to the combined
auction and posted price (Buy-It-Now) active listings, and similarly the share of auction
transaction volume in dollars relative to the combined auction and posted price transaction
volume, for eBay.com, which is eBay’s US-based platform. Here we construct the same
Figure for ten additional countries where eBay operates a separate marketplace.
The countries are:
Germany
United Kingdom
Italy
France
Spain
Austria
Canada
India
Philippines
Australia
6
For all the European countries, Canada and Australia, we have data back to January 2004.
These country patterns look very similar to the United States. The one possible exception
is auction revenue in Austria, which has remained relatively high although auctions have
diminished greatly in their listing share. In India, the data starts in January 2005. Here the
auction share of revenue starts below 40%, and declines sharply but not until 2011. In the
Philippines, the data starts at the end of 2007, and shows a steady decline in the auction
share.
7
Appendix Figure B1: Auction Discount for Different Matched Listing Subsamples
0.2
0.18
18.6%
An identical posted price listing is
available on the auction end date
No identical posted price listing is
available on the auction end date
18.2%
17.3%
0.16
14.4%
0.14
0.12
11.3%
10.9%
11.3%
0.1
0.08
0.06
0.04
2.2%
0.02
0
2003
2005
2007
2009
Figure presents the implied auction discounts for two different matched listings subsamples, auctions with concurrent posted price listings and auctions without,
based on estimating equation (2) in the main text for the years 2003, 2005, 2007, and 2009.
Appendix Figure B2: Distribution of Number of Unique Bidders per Auction 0.5
0.45
2003
2009
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Number of Unique Bidders
Figure presents the distribution of the number of unique bidders of the successful auction listings from the 2003 and 2009 matched listings data.
15
>15
Appendix Figure B3: Distribution of Auction Reserve Prices
0.30
2009 sold auctions
2009 unsold auctions
0.25
2003 sold auctions
2003 unsold auctions
Fraction
0.20
0.15
0.10
0.05
0.00
[0‐0.1]
(0.1‐0.2]
(0.2‐0.3]
(0.3‐0.4]
(0.4‐0.5]
(0.5‐0.6]
(0.6‐0.7]
(0.7‐0.8]
(0.8‐0.9]
(0.9‐1]
(1‐1.1]
(1.1‐1.2]
>1.2
Start price / reference value
Figure presents the distribution of the normalized reserve prices of the auction listings from the 2003 and 2009 matched listings data. Each column is divided in
two separate groups, corresponding to the auction listings that did not sell (bottom), and those that resulted in a sale (top).
Appendix Figure B4: Distribution of (Normalized) Auction Sale Prices
0.3
2003
2009
0.25
Fraction
0.2
0.15
0.1
0.05
0
Sale price / reference value
Figure presents the distribution of the normalized sale prices of the successful auction listings from the 2003 and 2009 matched listings data.
Appendix Figure B5: Components of the Auction Demand Curves
Sale Curves
Price Curves
0.8
1.4
2003
0.7
2009
Price (normalized) conditional on sale
0.6
Probability of sale
2003
1.2
2009
0.5
0.4
0.3
0.2
1
0.8
0.6
0.4
0.2
0.1
0
0
0
0.2
0.4
0.6
0.8
1
1.2
0
Reserve price (normalized)
Figure presents a graphical version of the estimation results reported in Appendix Table B4.
0.2
0.4
0.6
0.8
Reserve price (normalized)
1
1.2
Appendix Figure B6: The Relative Auction Demand Curve in 2005 and 2007
2005
1.2
1.1
1.1
Price (normalized) conditional on sale
Price (normalized) conditional on sale
2003
1.2
1
0.9
0.8
Auction
Posted price
0.7
1
0.9
Auction
Posted price
0.8
0.7
0.6
0.6
0.5
0.5
0.1
0.2
0.3
0.4
0.5
Probability of sale
0.6
0.7
0.1
0.8
0.2
0.3
0.4
0.7
0.8
0.9
0.7
0.8
0.9
2009
2007
1.2
1.2
1.1
1.1
Price (normalized) conditional on sale
Price (normalized) conditional on sale
0.5
0.6
Probability of sale
1
0.9
Auction
Posted price
0.8
0.7
1
0.9
Auction
0.8
Posted price
0.7
0.6
0.6
0.5
0.5
0.1
0.2
0.3
0.4
0.5
0.6
Probability of sale
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
Probability of sale
Figure replicates Figure 8(a) and 8(b) from the main text, and in addition adds corresponding panels for the intermediate years (2005 and 2007).
Appendix Table B1: Comparing the Matched Listings Sample to all eBay Listings
Number of Listings (000s)
Share of Auctions
Auction Success Rate
Posted Price Success Rate
Auction Start Pricea
Posted Pricea
Auction Sale Pricea
Transacted Posted Pricea
Most frequent category
2nd most frequent category
3rd most frequent category
4th most frequent category
5th most frequent category
All eBay
Matched Listings
Sets w/ >=10 Listings
Mixed sets w/ >=10 Listings
723,329
0.62
0.42
0.25
525,738
0.57
0.30
0.21
255,722
0.58
0.29
0.18
49,380
0.75
0.30
0.27
28.4
111.0
39.7
66.9
(171.8)
(478.6)
(163.1)
(236.4)
Clothing,Shoes&Acc. (15.5%)
Jewelry&Watches (10.8%)
Collectibles (9.3%)
Books (8.2%)
Sports Mem. (5%)
28.2
111.2
33.3
60.6
(173.0)
(483.5)
(131.4)
(212.4)
Clothing,Shoes&Acc. (15.1%)
Jewelry&Watches (12.4%)
Books (8.3%)
Collectibles (7.6%)
Home&Garden (5.2%)
21.8
119.5
27.0
50.5
(133.1)
(511.8)
(76.3)
(160.4)
Jewelry&Watches (17.3%)
Clothing,Shoes&Acc. (11.9%)
Home&Garden (6.5%)
Collectibles (5.3%)
Books (5.1%)
25.4
81.7
32.1
48.1
(138.0)
(353.0)
(86.2)
(145.0)
Jewelry&Watches (19.3%)
Clothing,Shoes&Acc. (14.4%)
Home&Garden (6.5%)
Sporting Goods (5.5%)
Health&Beauty (5.1%)
Mixed sets w/ >=10 Listings and Mixed sets w/ >=10 Listings, sales sales of both
of both, and >=3 Listings of each
33,743
0.78
0.36
0.38
19.9
56.5
32.5
46.3
(64.5)
(191.3)
(79.2)
(123.7)
Jewelry&Watches (18.9%)
Clothing,Shoes&Acc. (11.8%)
Home&Garden (6.6%)
Sporting Goods (6.2%)
Health&Beauty (6.1%)
20,874
0.72
0.35
0.34
22.5
52.9
35.6
45.2
(73.6)
(162.3)
(86.0)
(114.8)
Jewelry&Watches (15.3%)
Clothing,Shoes&Acc. (11.5%)
Sporting Goods (7.2%)
Health&Beauty (6.7%)
Consumer Electronics (6.6%)
Final Sample
5,924
0.71
0.36
0.34
22.9
52.7
35.6
45.7
(49.9)
(106.3)
(69.6)
(96.2)
Jewelry&Watches (13.5%)
Clothing,Shoes&Acc. (10.7%)
Sporting Goods (7.5%)
Home&Garden (7.2%)
Consumer Electronics (6.3%)
Table presents summary statistics for our 2009 matched listings sample relative to the entire eBay marketplace in 2009 (first column) and intermediate sample
restrictions. Patterns for the 2003 sample are qualitatively similar.
a All price variables are in current dollars, and include shipping fees.
Appendix Table B2: Auction Success and Discount over Time
2003
Dependent variable: 1 if item purchased
2005
2007
2009
Auction Indicator
0.0813
(0.0010)
0.0437
(0.0006)
0.0583
(0.0005)
0.115
(0.0005)
Constant
0.403
(0.0008)
0.373
(0.0004)
0.397
(0.0003)
0.25
(0.0004)
Matched Set
1,168,033
Matched Set
4,064,319
Matched Set
5,456,389
Matched Set
5,924,448
Fixed Effects
No. of obs. (listings)
2003
Dependent variable: log(sale price)
2005
2007
2009
Auction Indicator
‐0.0467
(0.0013)
‐0.138
(0.0008)
‐0.144
(0.0006)
‐0.165
(0.0005)
Constant
3.099
(0.0010)
3.078
(0.0006)
3.343
(0.0004)
2.998
(0.0004)
Matched Set
528,230
Matched Set
1,635,185
Matched Set
2,340,739
Matched Set
1,963,350
Fixed Effects
No. of obs. (listings)
Table presents the results from estimating equations (1) and (2) in the main text for the years 2003, 2005, 2007, and 2009. The graphical representation of the
above results is presented in Figure 7 of the paper. The top panel reports the results from a linear probability regression of sale on a dummy for whether the listing
is an auction listing, and they include seller‐item fixed effects. The bottom panel include only successful listings, i.e. listings that resulted in a sale. The specification
is similar to the top panel, with the dependent variable being the (log) sale price.
Appendix Table B3: Auction Success and Discount for Different Subsamples
A. Auctions with a concurrent posted price listing of the same item:
Dependent variable: 1 if item purchased
2003
2005
2007
2009
Dependent variable: log(sale price)
2003
2005
2007
2009
Auction Indicator
0.0959
(0.0015)
0.0319
(0.0007)
0.0649
(0.0006)
0.11
(0.0006)
‐0.113
(0.0020)
‐0.173
(0.0011)
‐0.186
(0.0009)
‐0.182
(0.0005)
Constant
0.433
(0.0007)
0.374
(0.0004)
0.401
(0.0003)
0.248
(0.0004)
3.183
(0.0011)
3.077
(0.0006)
3.411
(0.0004)
3.017
(0.0004)
Fixed Effects
No. of obs. (listings)
Matched Set Matched Set Matched Set Matched Set
623,472
2,670,128
3,664,597
4,579,688
Matched Set Matched Set Matched Set Matched Set
285,553
1,040,252
1,548,565
1,447,246
B. Auctions without a concurrent posted price listing of the same item:
Dependent variable: 1 if item purchased
2003
2005
2007
2009
2003
Dependent variable: log(sale price)
2005
2007
2009
Auction Indicator
0.0707
(0.0012)
0.0494
(0.0007)
0.0553
(0.0006)
0.111
(0.0007)
‐0.0215
(0.0014)
‐0.109
(0.0010)
‐0.113
(0.0007)
‐0.144
(0.0008)
Constant
0.385
(0.0008)
0.373
(0.0004)
0.376
(0.0003)
0.266
(0.0004)
2.993
(0.0010)
3.035
(0.0006)
3.201
(0.0003)
3.038
(0.0005)
Fixed Effects
No. of obs. (listings)
Matched Set Matched Set Matched Set Matched Set
964,049
2,726,061
4,256,290
3,083,239
Matched Set Matched Set Matched Set Matched Set
405,648
1,085,119
1,698,714
969,727
Table is similar to Appendix Table B2, but estimates the regressions separately for two subsamples of the auction listings. The top panel includes auction listings for
which there is a posted price listing belonging to the same matched set that is active on the auction end date. The bottom panel includes auction listings that do
not have such a concurrent posted price listing.
Appendix Table B4(a): Estimation Results for Auction Demand Curves
Dependent Var.
2003 Auction Sample
Normalized sale price, 1 if purchased
conditional on sale
2009 Auction Sample
Normalized sale price, 1 if purchased
conditional on sale
Constant
0.724
(0.005)
0.676
(0.006)
0.832
(0.002)
0.623
(0.002)
Normalized start price is <0.3
Omitted
Omitted
Omitted
Omitted
‐0.053
(0.007)
‐0.104
(0.007)
‐0.135
(0.008)
‐0.173
(0.011)
‐0.226
(0.007)
‐0.266
(0.007)
‐0.348
(0.007)
‐0.373
(0.008)
‐0.391
(0.009)
‐0.399
(0.008)
0.0508
(0.007)
0.0902
(0.016)
0.0974
(0.008)
0.144
(0.008)
0.209
(0.008)
0.281
(0.008)
0.368
(0.008)
0.451
(0.008)
0.56
(0.009)
0.945
(0.012)
‐0.174
(0.003)
‐0.251
(0.004)
‐0.32
(0.003)
‐0.401
(0.003)
‐0.468
(0.002)
‐0.534
(0.002)
‐0.599
(0.002)
‐0.621
(0.003)
‐0.638
(0.006)
‐0.673
(0.007)
‐0.026
(0.002)
‐0.00356
(0.003)
0.0505
(0.002)
0.12
(0.002)
0.198
(0.002)
0.272
(0.002)
0.358
(0.002)
0.434
(0.002)
0.539
(0.003)
0.741
(0.006)
Matched Set
748,545
Matched Set
365,266
Matched Set
4,185,969
Matched Set
1,509,727
Normalized start price in (0.3‐0.4]
Normalized start price in (0.4‐0.5]
Normalized start price in (0.5‐0.6]
Normalized start price in (0.6‐0.7]
Normalized start price in (0.7‐0.8]
Normalized start price in (0.8‐0.9]
Normalized start price in (0.9‐1]
Normalized start price in (1‐1.1]
Normalized start price in (1.1‐1.2]
Normalized start price is >1.2
Fixed Effects
No. of observations (listings)
Table presents estimation results that give rise to the auction demand curves reported in the paper. The analysis is based on estimating equations (4) and (5) in the
paper, using only auction listings. The right‐hand‐side variable is the normalized auction start price, categorized in 11 bins, as well as fixed effects for each item in
the matched listing sample. The sample for the second and fourth columns is restricted to successful listings only. Appendix Figure B5 provides a graphical
presentation of these results. In all specifications, we weight each item by its total number of (auction and posted price) listings to make results comparable (in
terms of compositional differences) between auctions and posted price demand curves.
Appendix Table B4(b): Estimation Results for Posted Price Demand Curves
2003 Posted Price Sample
2009 Posted Price Sample
1 if purchased
1 if purchased
Constant
0.452
(0.005)
0.521
(0.010)
Normalized posted price is <0.7
Omitted
Omitted
0.0299
(0.010)
0.0566
(0.011)
0.0305
(0.008)
0.0021
(0.007)
‐0.0392
(0.005)
‐0.0762
(0.007)
‐0.119
(0.007)
‐0.0475
(0.011)
‐0.083
(0.011)
‐0.108
(0.011)
‐0.143
(0.010)
‐0.219
(0.010)
‐0.24
(0.010)
‐0.232
(0.010)
Matched Set
419,488
Matched Set
1,738,479
Dependent Var.
Normalized posted price in (0.7‐0.8]
Normalized posted price in (0.8‐0.85]
Normalized posted price in (0.85‐0.9]
Normalized posted price in (0.9‐0.95]
Normalized posted price in (0.95‐1.05]
Normalized posted price in (1.05‐1.1]
Normalized start price is >1.1
Fixed Effects
No. of observations (listings)
Table presents estimation results that give rise to the posted price demand curves shown in Figure 8 of the paper. The analysis is based on estimating equation (6)
in the paper, using only posted price listings. The right‐hand‐side variable is the normalized posted price, categorized in 8 bins, as well fixed effects for each item. In
all specifications, we weight each item by its total number of (auction and posted price) listings to make results comparable (in terms of compositional differences)
between auctions and posted price demand curves.
Appendix Table B5: Classifying Categories using Principal Component Analysis
Category
Collectibles
Fan Shop
Toys
Clothing
Jewelry
Crafts
Books
Sport
Music
Home
Electronics
Health
PCs
Phones
DVDs
Share of listings classified in eBay catalog
Share of sales from multi‐unit listings
Share of "new" listings
Share of duplicate listings
Score (Principal Component Analysis)
0.0001
0.0001
0.0008
0.0000
0.0001
0.0004
0.6591
0.0143
0.4649
0.0028
0.0535
0.0007
0.0222
0.0508
0.7848
0.17
0.14
0.27
0.17
0.21
0.42
0.22
0.34
0.16
0.51
0.57
0.54
0.61
0.61
0.35
0.08
0.10
0.13
0.22
0.10
0.13
0.16
0.28
0.38
0.20
0.23
0.27
0.25
0.22
0.50
0.60
0.61
0.65
0.70
0.84
0.78
0.74
0.74
0.73
0.82
0.81
0.82
0.79
0.87
0.79
‐1.73
‐1.62
‐0.83
‐0.36
‐0.04
0.39
0.47
0.72
1.20
1.23
1.64
1.68
1.69
2.05
3.04
Using 2009 listings, the 33 main eBay categories are ranked from most idiosyncratic to least idiosyncratic according to their scores from a principal component
analysis that includes the following variables: share of items that are classified in the eBay catalog, share of sales from multi‐unit listings, share of listings with the
word “new” in the title, share of duplicate listings. The table reports the 15 largest categories, with their corresponding scores. As described in the main text, we
use this ranking to select five “idiosyncratic” categories (Collectibles, Fan Shop, Toys, Jewelry, and Clothing) and five “commodity” categories (Personal Computers,
Phones, DVDs, Health, and Electronics).
Appendix Table B6(a): Auction Demand Curve Estimates for “Commodity” Categories
Dependent Var.
2003 Auction Sample
("Commodity" categories only) Normalized sale price, 1 if purchased
conditional on sale
2009 Auction Sample
("Commodity" categories only) Normalized sale price, 1 if purchased
conditional on sale
Constant
0.799
(0.007)
0.834
(0.005)
0.841
(0.004)
0.666
(0.002)
Normalized start price is <0.3
Omitted
Omitted
Omitted
Omitted
0.0801
(0.012)
0.014
(0.012)
‐0.146
(0.011)
‐0.243
(0.012)
‐0.296
(0.012)
‐0.408
(0.010)
‐0.43
(0.013)
‐0.454
(0.017)
‐0.433
(0.018)
‐0.000402
(0.008)
‐0.0161
(0.009)
‐0.0405
(0.007)
0.0442
(0.007)
0.104
(0.008)
0.185
(0.007)
0.259
(0.008)
0.361
(0.009)
0.671
(0.019)
‐0.176
(0.005)
‐0.2
(0.006)
‐0.336
(0.005)
‐0.444
(0.005)
‐0.517
(0.005)
‐0.588
(0.006)
‐0.623
(0.006)
‐0.655
(0.006)
‐0.703
(0.007)
‐0.0178
(0.004)
‐0.00222
(0.004)
0.0773
(0.003)
0.168
(0.003)
0.228
(0.003)
0.308
(0.003)
0.376
(0.004)
0.488
(0.004)
0.674
(0.007)
Matched Set
152,905
Matched Set
88,659
Matched Set
1,062,388
Matched Set
432,147
Normalized start price in (0.3‐0.4]
Normalized start price in (0.4‐0.5]
Normalized start price in (0.5‐0.7]
Normalized start price in (0.7‐0.8]
Normalized start price in (0.8‐0.9]
Normalized start price in (0.9‐1]
Normalized start price in (1‐1.1]
Normalized start price in (1.1‐1.2]
Normalized start price is >1.2
Fixed Effects
No. of observations (listings)
Table is similar to Appendix Table B4, except that the sample only includes products that are in the top five “Commodity” categories (see Appendix Table B5).
Appendix Table B6(b): Auction Demand Curve Estimates for “Idiosyncratic” Categories
Dependent Var.
2003 Auction Sample
("Idiosyncratic" categories only) Normalized sale price, 1 if purchased
conditional on sale
2009 Auction Sample
("Idiosyncratic" categories only) Normalized sale price, 1 if purchased
conditional on sale
Constant
0.634
(0.010)
0.726
(0.011)
0.793
(0.003)
0.563
(0.003)
Normalized start price is <0.3
Omitted
Omitted
Omitted
Omitted
‐0.0318
(0.015)
‐0.0378
(0.016)
‐0.126
(0.012)
‐0.197
(0.012)
‐0.227
(0.012)
‐0.294
(0.012)
‐0.319
(0.013)
‐0.329
(0.014)
‐0.377
(0.013)
0.0167
(0.016)
‐0.00918
(0.016)
0.0555
(0.012)
0.15
(0.012)
0.234
(0.012)
0.304
(0.012)
0.398
(0.013)
0.511
(0.014)
0.93
(0.018)
‐0.119
(0.006)
‐0.27
(0.005)
‐0.381
(0.004)
‐0.481
(0.004)
‐0.537
(0.004)
‐0.585
(0.004)
‐0.609
(0.004)
‐0.634
(0.005)
‐0.634
(0.005)
‐0.0175
(0.004)
0.0262
(0.004)
0.127
(0.004)
0.238
(0.003)
0.32
(0.003)
0.414
(0.003)
0.494
(0.004)
0.587
(0.004)
0.776
(0.007)
Matched Set
258,606
Matched Set
94,872
Matched Set
1,539,602
Matched Set
462,941
Normalized start price in (0.3‐0.4]
Normalized start price in (0.4‐0.5]
Normalized start price in (0.5‐0.7]
Normalized start price in (0.7‐0.8]
Normalized start price in (0.8‐0.9]
Normalized start price in (0.9‐1]
Normalized start price in (1‐1.1]
Normalized start price in (1.1‐1.2]
Normalized start price is >1.2
Fixed Effects
No. of observations (listings)
Table is similar to Appendix Table B4, except that the sample only includes products that are in the top five “Idiosyncratic” categories (see Appendix Table B5).
Appendix Table B6(c): Posted Price Demand for “Commodity” and “Idiosyncratic” Categories
"Commodity" categories
2003 Posted Price Sample
2009 Posted Price Sample
Dependent Var.
"Idiosyncratic" categories
2003 Posted Price Sample
2009 Posted Price Sample
1 if purchased
1 if purchased
1 if purchased
1 if purchased
Constant
0.531
(0.011)
0.661
(0.020)
0.382
(0.008)
0.465
(0.013)
Normalized posted price is <0.7
Omitted
Omitted
Omitted
Omitted
0.0286
(0.022)
0.0584
(0.016)
0.0488
(0.014)
‐0.0213
(0.012)
‐0.0522
(0.015)
‐0.103
(0.014)
‐0.0455
(0.025)
‐0.145
(0.022)
‐0.221
(0.021)
‐0.324
(0.021)
‐0.342
(0.022)
‐0.326
(0.021)
0.0478
(0.017)
0.0646
(0.012)
0.0237
(0.013)
‐0.0362
(0.009)
‐0.0573
(0.012)
‐0.0789
(0.010)
‐0.0465
(0.016)
‐0.0724
(0.014)
‐0.107
(0.014)
‐0.168
(0.014)
‐0.175
(0.014)
‐0.178
(0.014)
Matched Set
96,440
Matched Set
423,517
Matched Set
143,335
Matched Set
531,102
Normalized posted price in (0.7‐0.8]
Normalized posted price in (0.8‐0.85]
Normalized posted price in (0.85‐0.9]
Normalized posted price in (0.9‐0.95]
Normalized posted price in (0.95‐1.05]
Normalized posted price is >1.05
Fixed Effects
No. of observations (listings)
Table is similar to Appendix Table B4, except that the sample includes products that are in either the top five “Commodity” categories (left) or “Idiosyncratic”
categories (right). See Appendix Table B5 for more details about category classification.
Appendix Table B7: Calibrated Values of λ and u in 2005 and 2007
2003
2005
2007
2009
λ
0.08
0.18
0.15
0.16
u
0.00
0.03
‐0.01
0.11
Table presents calibrated values of λ and u using the sets of matched listings in years 2003, 2005, 2007, and 2009. The estimates for 2003 and 2009 replicate those
that are reported in Table 2 of the main text. Note that the zero value for u for 2003 is a normalization used throughout.
Appendix Table C1: Auction Discount Estimates, Alternative Matching Criteria
Auction discount in 2003
(std. error)
Number of Listings in 2003
Auction discount in 2009
(std. error)
Number of Listings in 2009
Baseline
Def. I
Def. IIa
Def. IIb
Def. IIc
Def. IIIa
Def. IIIb
Def. IIIc
‐0.047
‐0.075
‐0.064
‐0.067
‐0.071
‐0.041
‐0.051
‐0.073
(0.001)
528,230
(0.002)
274,433
(0.001)
430,270
(0.001)
322,632
(0.002)
251,642
(0.001)
460,788
(0.002)
369,701
(0.002)
263,315
‐0.165
‐0.161
‐0.165
‐0.166
‐0.166
‐0.167
‐0.169
‐0.171
(0.000)
1,963,350
(0.001)
1,169,556
(0.001)
1,597,551
(0.001)
1,438,610
(0.001)
1,133,211
(0.001)
1,720,033
(0.001)
1,540,254
(0.001)
1,157,556
Table reports the estimates of the auction discount estimated from a regression of the logarithm of the sale price (conditional on sale) on an auction indicator and
seller‐item fixed effects as shown in equation (2) of the paper. The first column (“Baseline”) replicates the results from the paper (see Figure 7 and Appendix Table
B2). The rest of the columns report parallel estimates that use the different alternative definitions for matched sets, as detailed in Appendix C.
Appendix Table C2: Calibration Results for Alternative Definitions of Matched Sets
Panel A. Calibrated values
2003
Baseline
Def. I
Def. IIa
Def. IIb
Def. IIc
Def. IIIa
Def. IIIb
Def. IIIc
0.08
0.12
0.08
0.09
0.10
0.08
0.10
0.12
u2003
‐‐‐‐‐ Normalized to zero ‐‐‐‐‐
2009
0.16
0.17
0.14
0.13
0.15
0.17
0.18
0.21
u2009
0.14
0.14
0.16
0.17
0.13
0.14
0.13
0.15
Panel B. Success rates (q*)
Posted price success (2003)
0.40
0.47
0.39
0.37
0.36
0.39
0.39
0.41
Auction Success (2003)
0.48
0.58
0.47
0.44
0.42
0.47
0.47
0.48
Posted price success (2009)
0.25
0.27
0.24
0.24
0.24
0.24
0.24
0.24
Auction Success (2009)
0.37
0.40
0.35
0.34
0.34
0.35
0.35
0.34
0.09
0.06
0.06
0.04
0.05
0.09
0.08
0.09
Change in u
0.14
0.14
0.16
0.17
0.13
0.14
0.13
0.15
Relative importance of λ vs. u (2003 quantities)
3.58
1.94
2.53
1.64
2.50
3.87
4.14
4.12
Relative importance of λ vs. u (2009 quantities)
1.91
1.20
1.28
0.84
1.31
1.96
2.08
2.07
Panel C. Relative effects of  and u
Change in λ
Table reports the calibration results using alternative definitions for matched sets, as detailed in Appendix C. The first column replicates the baseline results from
Table 2 in the main text.
1.2
1.2
1.1
1.1
Price (normalized) conditional on sale
Price (normalized) conditional on sale
Appendix Figure C1: Figure 8(a) for Alternative Definitions of Matched Sets
1
0.9
0.8
Auction
Posted price
0.7
1
0.9
0.8
0.7
Auction
0.6
0.6
Posted price
0.5
0.5
0.2
0.3
0.4
0.5
Probability of sale
0.6
0.7
0.1
0.8
0.3
0.4
0.5
0.6
0.7
1.2
1.2
1.1
1.1
1.1
1
0.9
0.8
0.7
Auction
Price (normalized) conditional on sale
1.2
0.6
1
0.9
0.8
0.7
Auction
0.6
Posted price
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1
0.9
0.8
0.7
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Posted price
0.9
0.1
1.2
1.2
1.1
1
0.9
0.8
0.7
Auction
0.6
Price (normalized) conditional on sale
1.2
Price (normalized) conditional on sale
1.3
1.1
1
0.9
0.8
0.7
Auction
0.6
0.5
0.6
Probability of sale
0.7
0.8
0.9
0.5
0.6
0.7
0.8
0.9
1.1
1
0.9
0.8
0.7
Auction
0.6
Posted price
0.5
0.5
0.5
0.4
Posted price
Posted price
0.4
0.3
Probability of sale
1.3
0.3
0.2
Probability of sale
1.3
0.2
Auction
0.5
Probability of sale
0.1
0.9
0.6
0.5
0.1
0.8
Posted price
0.5
Price (normalized) conditional on sale
0.2
Probability of sale
Price (normalized) conditional on sale
Price (normalized) conditional on sale
0.1
0.1
0.2
0.3
0.4
0.5
0.6
Probability of sale
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Probability of sale
Figure replicates Figure 8(a) from the paper using the different alternative definitions for matched sets, as detailed in Appendix C. The top left panel replicates the
baseline results reported in the main text (Figure 8(a)), the top right panel is based on Definition I, the middle row of panels uses Definitions IIa, IIb, and IIc, and the
bottom row of panels uses Definitions IIIa, IIIb, and IIIc.
1.2
1.2
1.1
1.1
Price (normalized) conditional on sale
Price (normalized) conditional on sale
Appendix Figure C2: Figure 8(b) for Alternative Definitions of Matched Sets
1
0.9
0.8
Auction
Posted price
0.7
1
0.9
Auction
0.8
Posted price
0.7
0.6
0.6
0.5
0.5
0.1
0.3
0.4
0.5
0.6
Probability of sale
0.7
1.2
1.2
1.1
1.1
1
0.9
Auction
0.8
Posted price
0.7
0.3
0.4
0.5
0.6
0.7
0.8
Auction
Posted price
Auction
0.8
Posted price
0.7
0.3
0.4
0.5
0.6
0.7
0.8
0.1
0.9
1.1
0.9
Auction
0.8
Posted price
0.7
0.6
1
0.9
Auction
0.8
Posted price
0.7
0.6
0.7
0.8
0.9
0.5
0.6
0.7
0.8
0.9
1
0.9
Auction
0.8
Posted price
0.7
0.5
0.5
0.5
Probability of sale
0.4
0.6
0.6
0.5
Price (normalized) conditional on sale
1.1
Price (normalized) conditional on sale
1.1
0.4
0.3
Probability of sale
1.2
0.3
0.2
Probability of sale
1
0.9
0.9
1.2
0.2
0.8
1
1.2
0.1
0.7
0.5
0.2
Probability of sale
Price (normalized) conditional on sale
0.6
0.6
0.1
0.9
0.5
1.1
0.7
0.5
0.4
1.2
0.8
0.6
0.3
Probability of sale
0.9
0.5
0.2
0.2
0.9
1
0.6
0.1
0.8
Price (normalized) conditional on sale
0.2
Price (normalized) conditional on sale
Price (normalized) conditional on sale
0.1
0.1
0.2
0.3
0.4
0.5
0.6
Probability of sale
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Probability of sale
Figure replicates Figure 8(b) from the paper using the different alternative definitions for matched sets, as detailed in Appendix C. The top left panel replicates the
baseline results reported in the main text (Figure 8(b)), the top right panel is based on Definition I, the middle row of panels uses Definitions IIa, IIb, and IIc, and the
bottom row of panels uses Definitions IIIa, IIIb, and IIIc.
Appendix Figure C3: Figure 10 for Alternative Definitions of Matched Sets
1.2
1.1
Start price or Posted price
1
0.9
0.8
0.7
Auction 2003
Posted price 2003
0.6
Auction 2009
Posted price 2009
0.5
0.4
0.1
0.2
0.3
0.4
0.5
0.6
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1
0.9
0.8
0.7
Auction 2003
Posted price 2003
0.6
1
0.9
0.8
0.7
Auction 2003
Auction 2009
0.5
0.2
0.3
0.4
0.5
0.2
0.4
0.5
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1
0.9
0.8
Auction 2003
Posted price 2003
1
0.9
0.8
0.7
Auction 2003
Posted price 2003
0.6
Auction 2009
Posted price 2009
0.3
0.4
Probability of sale
0.5
0.6
0.3
0.4
0.5
0.6
0.5
0.6
1
0.8
0.7
Auction 2003
Posted price 2003
Auction 2009
0.5
Posted price 2009
0.4
0.2
0.2
0.9
0.6
Auction 2009
0.5
0.4
Start price or Posted price
1.4
1.3
0.1
Posted price 2009
Probability of sale
1.4
0.5
Auction 2009
0.1
0.6
1.3
Start price or Posted price
Start price or Posted price
0.3
1.4
0.6
Posted price 2003
Probability of sale
Probability of sale
0.7
Auction 2003
0.4
0.1
0.6
0.7
0.5
0.4
0.1
0.8
Posted price 2009
Posted price 2009
0.4
1
0.9
0.6
Posted price 2003
0.6
Auction 2009
0.5
Start price or Posted price
1.4
Start price or Posted price
Start price or Posted price
Probability of sale
Posted price 2009
0.4
0.1
0.2
0.3
0.4
Probability of sale
0.5
0.6
0.1
0.2
0.3
0.4
Probability of sale
Figure replicates Figure 10 from the paper using the different alternative definitions for matched sets, as detailed in Appendix C. The top left panel replicates the
baseline results reported in the main text (Figure 10), the top right panel is based on Definition I, the middle row of panels uses Definitions IIa, IIb, and IIc, and the
bottom row of panels uses Definitions IIIa, IIIb, and IIIc.
Appendix Figure D1(a): Auction Share on eBay in Other Countries
Germany
UK
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
Share of active listings
0.1
0
Jan‐04
Share of active listings
0.1
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
Jan‐13
0
Jan‐04
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Italy
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
Jan‐11
Jan‐12
Jan‐13
Jan‐10
Jan‐11
Jan‐12
Jan‐13
0.2
Share of active listings
0
Jan‐04
Jan‐10
France
1
0.1
Jan‐09
Share of active listings
0.1
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
Jan‐13
0
Jan‐04
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Figure replicates Figure 1 (which used the US platform, eBay.com) using data from the eBay platform in other countries for which data was available. Note that due
to data availability the observation period varies slightly across platforms.
Appendix Figure D1(b): Auction Share on eBay in Other Countries
Austria
Spain
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
Share of active listings
Share of active listings
0.1
0
Jan‐04
0.1
Share of revenues
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
0
Jan‐04
Jan‐13
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
Jan‐13
Canada
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Share of active listings
0.1
0
Jan‐04
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
Jan‐13
Figure replicates Figure 1 (which used the US platform, eBay.com) using data from the eBay platform in other countries for which data was available. Note that due
to data availability the observation period varies slightly across platforms.
Appendix Figure D1(c): Auction Share on eBay in Other Countries
India
Philippines
1
1
0.9
0.9
0.8
0.8
0.7
0.7
Share of active listings
0.6
0.6
Share of revenues
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
Share of active listings
0
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
0
Jan‐07
Jan‐13
Share of revenues
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
Jan‐13
Australia
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Share of active listings
0.1
0
Jan‐04
Share of revenues
Jan‐05
Jan‐06
Jan‐07
Jan‐08
Jan‐09
Jan‐10
Jan‐11
Jan‐12
Jan‐13
Figure replicates Figure 1 (which used the US platform, eBay.com) using data from the eBay platform in other countries for which data was available. Note that due
to data availability the observation period varies slightly across platforms.