Focusing on Demand: Using eBay data to

analyze the demand for telescopes.

Christopher P. Adams

Laura L. Bivins∗

Bureau of Economics, Federal Trade Commission

Email: cadams@ftc.gov or lbivins@ftc.gov

Draft

January 17, 2003

Abstract

This paper analyzes the value of using data from on-line auctions to determine product market definitions and competitive effects of mergers. Traditionally this type of demand analysis has been based on retail transaction

data, particularly “scanner” data. However, such data is not always readily

available and may be difficult to interpret. Auction data, particularly data

from on-line auctions like eBay may be easy to access and may be much

easier to interpret. The authors analyze data from a series of auctions for

3 different types of telescopes, held over a 8 week period. The results suggest that the demand for telescopes is very elastic and that the two types

of telescope designs (the Schmidt-Cassegrain and the Maksutov-Cassegrain

designs) are in different product markets, supporting a position taken by the

Commission in a recent case.

∗The authors would like to thank George Deltas, Dan Hosken, Mike Moiseyev, David

Schmidt, Mike Vita, Bill Vogt, two anonymous referees and other FTC colleagues for useful

discussions on these issues. However, all errors are our own. Note also that this paper does

not necessarily represent the views of the Commission or any individual Commissioners.

1
1 Introduction

Antitrust economists working at the FTC and the DOJ are routinely asked to

determine the answer to two questions when evaluating a potential merger:

• What is the product market?

• What will be the competitive effects of the merger?

Traditionally, evidence from interviews and documents have been complemented by econometric evidence based on retail price and transaction

data. Recently, the use of scanner data has become widespread. This data

allows for the estimation of cross-price elasticities which are used to determine product market definitions, and own-price elasticities which are used

to determine the price effects of a merger.1 Unfortunately, transaction data

is not always available, and even when such data is available the results may

not be easy to interpret.2 On the other hand, on-line auction data may be

readily available from sites such as eBay.com. It is possible that auction data

is able to provide enough information to identify each bidder’s “willingness

to pay” for the item and thus the demand curve for the item. Further, it

may be possible to determine an individual’s willingness to pay for multiple

items and thus identify a demand system over multiple products.

This paper presents an analysis of eBay auction data for three types of

telescopes, Meade’s ETX90EC, ETX125EC and LX200, that retail for between $500 and $1,500. This data was collected over an eight week period

in April, May and June of 2002, and includes information from over 58 separate auctions with over 200 separate bidders. The data was used to estimate

the demand for the three telescopes and calculate own-price and cross-price

elasticities. The results suggest that demand for these telescopes is very elastic. This result corresponds with our understanding that these telescopes are

1See Hosken et al. (2002) for a discussion of some of the issues involved with using such

data.

2Such data often suffers from the classic “simultaneity” problem, in that changes in

price may be the result of changes in demand rather than changes in supply. See Nevo

(2000) for an excellent introduction to one possible solution, the BLP model.

1
expensive luxury items, generally bought by hobbyists and high end consumers. The results also suggest that the Schmidt-Cassegrain telescopes and

the Maksutov-Cassegrain telescopes are in different product markets. This

result supports the claim that was made by the Commission in a previous

merger case regarding this industry,3 as well as in the more recent merger

case.4

EBay and other online auction houses may be a rich source of data for

economists analyzing the market structure of certain industries. There exists

a number of papers that have used data from online auctions to analyze different aspects of the auction mechanism and the value of information available

to buyers and sellers. For example, Lucking-Reiley et al. (2000), Livingston

(2002) and Hasker et al. (2001) discuss the importance of seller’s ratings,

reserve prices and the length of the auction, and Roth and Ockenfels (2000)

analyze the effect of the fixed endpoint of eBay auctions as compared to the

“going, going, gone” feature of Amazon.com auctions. While it is not the

focus of the paper, Hasker et al. (2001) analyze the effect on bids of characteristics of computer monitors sold on eBay (flat screen, dpi, size), the good

being sold (like new, refurbished), as well as the auction (secret reserve price).

There are also a number of papers that look at the question of whether bids

in auctions can be used to infer demand functions. In particular, Haile and

Tamer (2002) propose two different methods of bounding demand curves (actually the distribution of private values) from English auction data similar

to the data found in eBay auctions. The authors use these methods to make

predictions on reserve price policies from timber auction data. The analysis

presented below will explicitly look at inferring demand from eBay auction

data and discuss some of the concerns relating to this type of inference.

The rest of the paper proceeds as follows. Section 2 discusses the data

and how it was obtained. It also describes the telescopes and provides some

background information on the product market. Section 3 analyzes the demand for these telescopes, based on high bids from the eBay auctions. This

section will present own-price and cross-price demand elasticities and discuss

3FTC v. Harbour Group Investments, 1990 WL 198819 (D.D.C. 1990).

4http://www.ftc.gov/opa/2002/05/meadecelestron.htm.

2
some of the issues and concerns with the estimations. Section 4 concludes.

2 EBay Data on Bids for Cassegrain Telescopes

2.1 Product Market

Telescopes come in three major optical configurations, refractors, reflectors

and catadioptric (mirror-lens). The first type of telescope to be invented was

a refractor. These telescopes were developed by Galileo and use lenses to

magnify the light. The major advantage of refractors is that they can give a

sharp image of the object. Refractors are generally used for observing planets, the moon and the sun. The next to be developed was the reflector. This

type of telescope was developed by Sir Isaac Newton. This telescope uses

a mirror at its base to focus and magnify the light. The major advantage

of reflectors is that they can be made at very large apertures very cheaply.

This means that they can let in a lot of light, enabling the observer to view

very faint objects, such as small galaxies. Newest are the catadioptric optical systems, including the Schmidt-Cassegrain and the Maksutov-Cassegrain

designs. These telescopes are also reflectors but they use multiple mirrors to

increase the focal distance (the magnification) in a smaller physical space.

These are good all-purpose telescopes that tend to have large apertures and

large focal lengths for their physical size. The two ETX models are MaksutovCassegrain designs, while the LX200 is a Schmidt-Cassegrain design.

The most important characteristic of the telescope is aperture size. Magnification and light gathering ability are both functions of the aperture size.

Light gathering ability is a function of the area of the mirror or lens, and thus

a function of the square of the telescope’s diameter. The greater the light

gathering ability the fainter the objects that can be seen. The ETX90EC

is the smallest at 90mm (3.5 inches), then the ETX125EC at 125mm (4.9

inches), and largest is the LX200 at 200mm (7.9 inches). Our understanding

of the product market suggests, that the actual design difference between the

3
two Maksutov-Cassegrains (ETX90EC and ETX125EC) and the SchmidtCassegrain (LX200) is not as important as the difference in aperture (a 3

inch difference between the ETX125EC and the LX200).

In the 1990 case, the Commission argued that the appropriate antitrust

market was for 8 inch Schmidt-Cassegrain telescopes (of which the LX200

is one).5 Only two firms manufactured and sold 8 inch Schmidt-Cassegrain

telescopes in the United States, Meade and Celestron, and these two firms

were planning to undertake a joint venture. This joint venture was seen by

the Commission as being equivalent to a merger. Because of their high quality

optics, relatively low prices and relatively compact size, these telescopes were

the most popular telescope for the serious amateur astronomer. Due to

the Commission’s actions, the merger was never consummated. Since 1990,

both companies have introduced a line of smaller and cheaper MaksutovCassegrain telescopes. Two of Meade’s Maksutov-Cassegrain telescopes are

the ETX90EC and the ETX125EC. The ETX series is the most popular

type of telescope sold by Meade, with sales of around $70 million dollars

annually,6 although the Schmidt-Cassegrain remains highly prized by the

serious hobbyists.7 Recently the Commission stated, “that the two companies

together would monopolize the market for Schmidt-Cassegrain telescopes and

would eliminate substantial actual competition between Meade and Celestron

in the market for performance telescopes.”8

2.2 Auctions Methods on EBay

EBay runs a second price English auction for a variety of consumer goods,

including telescopes. The auction is “second price” because the winner pays

5At the time, the Maksutov-Cassegrain designs were made by very small scale manufacturers and were substantially more expensive than the comparable Schmidt-Cassegrain

designs.

6This estimate is based on Meade’s 2001 10K filing with the SEC and statements by

Meade CEO, John Diebel, at the April 2002 Press Conference.

7See “astro note” 19 from the Astronomy League (http://www.astroleague.org) for a

discussion of the different types of telescopes.

8http://www.ftc.gov/opa/2002/05/meadecelestron.htm

4
the next highest bid, and they are “English auctions” because bids are ascending. A typical eBay auction lasts for 7 days, although the seller can

decide to have an auction last for 3, 5, or 10 days. When a potential bidder

views a current auction on eBay, they see a description of the item for sale.

This description is up to the seller’s discretion, but is usually fairly detailed

and may include a picture of the item. The bidder can also review the recent

history of the seller and ratings by previous customers. Most importantly,

the bidder observes the current high bid for the item. They also observe

information on other bidders for that auction including when they bid, but

not what their bid was.9 Lastly, all bidders know the exact time remaining

before the close of the auction.10

After observing this information, the bidder may decide to bid on the

item. The amount entered by the bidder is actually a “proxy” bid. That

is, eBay will take that bid and automatically bid slightly above the next

highest bidder up to the amount entered. For example, lets assume the

bidding increment is $1 and say that the current high bidder is “bidmaniac”

and the current high bid is $47. Then “scopeme” enters the auction with

a bid of $300. What happens next depends on the actual bid entered by

bidmaniac. If it is $50, then scopeme becomes the high bidder and $51

becomes the current high bid. If, however, bidmaniac entered a bid of $302,

then bidmaniac remains the highest bidder and the current high bid is $301.

This system allows the bidder to leave the auction, without having to worry

about being outbid, as the proxy system will keep on bidding automatically.

If however, a bidder is outbid, then eBay can notify them by email. The

winner of the auction, is the highest bidder (at the earliest time if there is a

tie), at the end of the auction. The winner pays an amount slightly above

the next highest bid.

9The bidder’s ID is clickable and provides a recent history of that bidder’s transactions,

as well as ratings from sellers or buyers involved in those transactions.

10An important difference between eBay auctions and Amazon.com auctions is that

eBay auctions have a precise end point. Roth and Ockenfels (2000) discuss the effect of

this difference in detail.

5
2.3 EBay Auction Data

At the close of each auction, eBay provides the following information: a

description of the product, including photos and other information at the

seller’s discretion, the date and time of each bid, the identification name for

each bid (their eBay account name), and the amount of each bid, except for

the highest bid.11 We collected data from 31 auctions for the ETX90EC, 20

auctions for the ETX125EC and 7 auctions for the LX200 during April, May

and June of 2002. Table 1 presents some summary statistics for the auctions

that we observed. These figures clearly show that the ETX90 is the most

popular of the three telescopes, with greater numbers of both buyers and

sellers. Note that the retail prices are for the basic units which don’t come

with tripods or the “go to” system in the case of the ETX products (both are

included in the price of the LX200). Winning bids are greater than the retail

prices because many of the telescope auctioned come with accessories. Note

also that the retail price for the LX200 is actually the retail price for the

equivalent Celestron telescope, as the current version of the LX200 includes

GPS tracking hardware and is significantly more expensive.

Table 2 presents summary statistics of important characteristics of the

actual telescopes sold. Note that we did not include auctions with very small

number of bidders. The telescopes themselves are second hand, while the

sellers may be individual owners or stores. The product itself may be fairly

new or even “in the box.” For example, one seller stated that their ETX90EC

was

“...a great piece of glass for viewing your cosmic neighbors from

your backyard. The package includes the ETX-90 telescope, a

hard carrying case made to fit, a tripod, t-adaptor to connect

to your SLR camera, a hand controller, an upgraded lens, and a

right-angle viewfinder. I’ve used it only twice over the past year

11The exact information on the high bid depends on how much greater it is than the

second highest bid. If the difference between the two high bids is less than the increment,

then the high bid is observed. Otherwise, the amount listed for the high bid is equal to

the second highest bid plus the increment.

6
ETX90 ETX125 LX200

Number of Auctions 31 20 7

Number of Bidders 157 98 44

Average Bidders 6.7 6.9 7.9

Average Bid $394.68 $785.19 $1166.39

Average High Bid $506.47 $966.68 $1555.07

Highest High Bid $830 $1349.01 $1750

Lowest High Bid $270 $680 $1331.50

Retail Price (Basic) $495 $895 $1,499

Table 1: Summary Statistics of Telescope Auctions

to catch a glimpse of Saturn’s rings and Jupiter’s moons. It is in

excellent condition.”

Sellers often describe their telescope as being “like new” or “as if new”.

Hasker et al. (2001) shows that this type of statement is an important determinant of computer monitor prices. Another important characteristic of the

Meade telescopes is the inclusion of the “go to” or Autostar computer controller. All of Meade’s telescopes come with a computer located in the mount

of the telescope. Once the telescope is aligned, this computer can point the

telescope at any of the thousands of celestial objects that are programmed

into the computer’s database.12 The Autostar controller allows the user to

access the computer. The other vital accessory is the tripod, especially for

the larger telescopes. The camera adapter (T-adapter) allows a 35mm SLR

camera to be attached to the telescope for celestial photography.

Table 3 presents information on the 85 bidders who bid in more than

one auction for one of the three products during the time in which the data

was being collected. The first row states that for bidders who bid multiple

times and bid on the ETX90, 56 % bid only on the ETX90, 39 % also bid

on the ETX125, and 11 % also bid on the LX200. Of the 85 bidders who

12This system is also fairly simple to align. The process involves setting the telescope

level and pointing north, entering time and location (unnecessary with GPS), and correcting the alignment against two prominent stars.

7
ETX90 ETX125 LX200

“Like New” 20 % 56 % 42 %

“Go to” 53 % 86 % 58 %

Tripod 64 % 71 % 100 %

Camera Adapter 18 % 12 % 27 %

Table 2: Summary Statistics of Telescope Characteristics

ETX90 ETX125 LX200 N

ETX90 .56 .39 .11 54

ETX125 .53 .45 .10 40

LX200 .32 .21 .63 19

Table 3: Tracking Bidders Across Products (85 Bidders)

bid multiple times, 54 bid on the ETX90. Note that the choices are not

exclusive and so the percentages add to more than 100%. The numbers suggest an important characteristic of the telescope market. That is, bidders

on the Schmidt-Cassegrain (LX200) are more likely to only bid on that telescope and not on the Maksutov-Cassegrain (ETX90 and ETX125) telescopes,

while bidders for the Maksutov-Cassegrain telescopes are unlikely to bid on

the Schmidt-Cassegrain. These statistics support the Commission’s position

that the two telescope designs are not in the same antitrust product market.

This table also highlights an important characteristic of eBay data, which is

that it is possible to follow people across a series of auctions for related products providing the Commission with information on how customer’s perceive

differentiated products.

8
3 Inferring Demand for Telescopes from EBay

Data

3.1 Estimation Techniques

We use bids from these auctions to estimate the demand for the ETX90, the

ETX125 and the LX200. If in the population, we know each person’s value

or “willingness to pay” for each particular telescope, then we can calculate

the demand for each telescope. At each price, all those people with values

greater than the price will buy a telescope and choose the telescope with the

highest consumer surplus, giving the quantity demanded at that price. By

changing the prices and recalculating demand for the three telescopes at the

new prices, we can calculated own and cross-price elasticities. If however, we

have valuations for a random sample of the population then we can estimate

the demand. The eBay data gives a sample of the population, although

not a random sample of the population. The sample is a self-selected group

willing to bid on telescopes on eBay. This sample is also not a sample of each

person’s valuation, but rather a sample of each person’s bid for a particular

telescope. The following is a list of assumptions necessary to use this data

to estimate demand.

Assumption 1 The sample represents buyers for new telescopes.

Assumption 1 captures three issues. First, it assumes that eBay bidders

for telescopes are representative of the general population of telescope buyers. Unfortunately, we are not aware of any demographic information on

either eBay bidders or telescope buyers. However, in 2002 there were over 50

million registered eBay users, and there is no reason to expect an substantial

difference between the two groups. Second, it assumes that eBay bidders

are randomly selected out of the population of telescope buyers. Due to the

low cost of searching and bidding on-line, such buyers may have a greater

elasticity of demand than off-line buyers. Therefore, our estimates may be

biased to the high side. Third, it is based on people buying second-hand

9
telescopes. It is not clear how this affect the interpretation of our elasticity

estimates.

Assumption 2 Each bidder’s highest bid in each auction is equal to that

bidders value for the product being auctioned.

We assume that the highest bid that a person makes in a particular auction is equal to that person’s valuation for the product sold in that auction.

There are two characteristics of eBay auctions that justify this assumption.

First, as discussed above, eBay uses a “proxy” bidding system. That is, it

asks the bidder to enter their “maximum” bid for the item, and then it automatically bids the lowest amount such that the bidder with the highest

maximum is the highest bidder. In a sealed bid second-price auction, the

weakly dominant strategy is for the bidder to bid their valuation for the

product. In fact, eBay states that this is what each person should do (Roth

and Ockenfels (2000)). Second, eBay is an English (ascending price auction),

and in the “button model” of such an auction, each bidder holds down a

button up until their valuation is reached. The last person holding down

her button wins the auction. Therefore, even if people don’t understand the

proxy bidding system, they should remain in the auction and keep bidding

until their valuation is reached.13 However, there are good reasons to think

that people do not bid their valuations, and these are discussed at the end

of this section.

Assumption 3 Bidder i’s high bid in auction j is

log(Bij ) = log(vij ) = Xjβ + log(2ij ) (1)

Where Bij is bidder i’s highest bid in auction j, vij is bidder i’s value

for the item sold in auction j, Xjis the observable characteristics of the

item, and 2ij is the error term. This assumption allows the estimation of

a “hedonic” bid model using OLS. It states that bids vary linearly with

respect to characteristics of the product that is being auctioned. We can

13EBay offers the option of emailing the bidder once they have been outbid.

10
interpret Xjβ as representing the “common value” for the telescope and 2ij

as representing the “private value” for the telescope. In the results section,

β and 2ij are estimated using OLS.

Assumption 4 Each Bij represents a distinct buyer, k.

Assumption 5 Each buyer, k, has a value vkl for each of the three telescopes, denoted l ∈ {ET X90, ET X125, LX200}.

Assumptions 4 and 5 form the basis for the demand estimation. Even

though one bidder may bid in multiple auctions, their bids in the different

auctions are assumed to represent distinct bidders. These is mainly done

for simplicity. The fact that bids are not independent can be accounted for

by bootstrapping the standard errors. The distribution of errors (private

values) across the three telescopes is accounted for by Assumption 6. This

method allows the own and cross-elasticities to be calculated without making

unreasonable assumptions on the distribution of errors. The distribution of

errors is drawn from the actual residuals, with correlation across telescopes

based on the actual probability that different bidders bid across different

types of telescopes.

Assumption 6

vkl =







exp(Xlβ + log(2k)) if j = l

exp(Xlβ + log(2k)) w/prob p if j 6= l

0 w/prob 1 − p if j 6= l

(2)

Where p is calculated from Table 3. For example, for a buyer k whose bid

comes from an ETX90, their value for the ETX90 is exp(XET X90β +log(2k)).

While, buyer k’s value for the ETX125 is either 0 or exp(XET X125β+log(2k)).

Which, depends on the probability that a bidder on the ETX90 will also bid

on the ETX125. In this case, p = .39. Setting the buyer’s value to 0 is

somewhat arbitrary. The important point is that the buyer’s value is “low

enough” so as not be included in the cross-elasticity calculation.

11
Demand is estimated in three steps. Step 1 estimates βˆ using OLS and

Equation (1), where the Xj variables include dummies for the ETX90, the

ETX125, a dummy for “like new”, a dummy for the “go to” system, a dummy

for a tripod, and a dummy for a camera adapter.

Step 2 calculates the “new” value of each of the three types of telescopes

for every observation (that is for every bidder’s high bid in every auction).

This is done using βˆ, the estimated residual (2ij ), and the probabilities of

bidding across products calculated from Table 3, where each telescope is

assumed to be “like new” and have no camera adapter. Additionally, in the

case of the LX200, the telescope is assumed to have a tripod and “go to”.

In the case of the ETX90 and the ETX125, the telescope is assumed to have

neither. Therefore, for bidder i who bid in auction j, where auction j is for

an ETX90 telescope, their value for the ETX90, vij (ET X90), that is “like

new” and doesn’t have any accessories is given by,

vij (ET X90) = exp(XET X90βˆ

ET X90+Xlikenewβˆlikenew+βˆconstant+log(2ij )) (3)

Next we need to determine what the “like new” value is for products that

were not bid upon by an individual bidder. Here we use the probabilities of

bidding across products to give us our estimates. For example, if the bidder

is from an auction for the ETX125, the probability a priori that bidder has a

positive value for the ETX90 is 53 % which, from our data, is the proportion

of ETX125 bidders who bid multiple times and bid on the ETX90. Thus, for

bidder i who bid in auction j, where auction j is for an ETX125, their value

for the ETX90 that is “like new” and doesn’t have any accessories is given

by

vij (ET X90) =







exp(Xβˆ

ET X90 + log(2ij )) with probability .53

0 with prob (1 − .53).

(4)

To summarize, for each observation (ij) we calculate vij (ET X90), vij (ET X125)

and vij (LX200). If ij is from an ETX90 auction, then vij (ET X90) is defined by Equation (3). While vij (ET X125) and vij (LX200) could be either

positive (using the OLS estimates and the residual (2ij )) or 0. The propor12
tion that are 0, is determined by the probabilities from Table 3, and the

observations are assigned 0 at random.14

Step 3 uses these valuations and the prices to determine whether each

bidder i for auction j will purchase an ETX90, an ETX125, a LX200 or

nothing. An ETX90 is purchased if

1. vij (ET X90) > PET X90, and

2. vij (ET X90) − PET X90 > vij (ET X125) − PET X125, and

3. vij (ET X90) − PET X90 > vij (LX200) − PLX200,

where Pjis the retail price of product sold in auction j.

3.2 Results

Table 4 presents the results for the OLS estimates.15 The assumption that

bidders bid their values for each telescope is of major concern. One argument

is that higher bidders or “later” bidders are going to bid much closer to their

value than lower bidders or earlier bidders. The results are estimated on

four different samples. The first column shows the estimates for a sample

restricted to the top 8 bidders in each auction, the second column estimates

the regression on a sample restricted to the top 4 bidders in each auction, the

third column is for the bidders who bid on the last day of the auction, and

the fourth column is for bidders who bid in the last 4 hours of the auction. A

concern with these estimates is sample selection bias. A possible alternative is

to use quantile regression (Koenker and Hallock (2001)). These results don’t

seem to depend crucially on the sample that is used, however it is necessary

to look at the elasticity estimates for each sample. Step 2 calculates the log

residuals using the estimated coefficients for Equation (1). Table 5 presents

the mean value for the telescopes, assuming that every buyer has a positive

14An alternative is to just use the people who bid across products, but the sample is

very small, given the variation in the characteristics in the telescopes.

15The standard errors are from the OLS estimates, however the bootstrap standard

errors were similar.

13
Top 8 Bidders Top 4 Bidders Last Day Last 4 Hours

ETX90 -.97 -1.03 -.93 -.98

(.06) (.04) (.04) (.05)

ETX125 -.34 -.45 -.41 - .43

(.07) (.04) (.04) (.05)

“Like New” .12 .07 .08 .06

(.04) (.03) (.03) (.03)

“Go to” .15 .22 .21 .24

(.05) (.03) (.03) (.04)

Tripod .21 .22 .21 .24

(.05) (.03) (.03) (.03)

Adapter .22 .12 .06 .06

(.05) (.03) (.03) (.04)

Constant 6.59 6.84 6.82 6.87

(.07) (.05) (.05) (.06)

N 400 226 178 113

R2.60 .86 .86 .89

Table 4: OLS estimates (Standard Errors)

14
Top 8 Top 4 Last 24 hours Last 4 hours

ETX90 328.00 336.26 400.00 387.69

(99.40) (65.77) (66.77) (59.47)

ETX125 618.45 654.04 671.46 669.99

(187.42) (117.45) (112.08) (102.78)

LX200 1241.20 1585.17 1541.94 1651.40

(376.14) (284.67) (257.38) (253.33)

Table 5: Mean Value by Telescope Type (Standard Deviation)

value for every telescope. Step 3 uses the values for each type of telescope

for each bidder in each auction to calculate the demand system for the three

telescopes. The assumption is that each bidder in each auction is a distinct

individual demander of telescopes.

Table 6 presents the own-price and cross-price elasticities for the three

types of telescopes, calculated at retail prices for the basic telescope (presented in Table 1) using the sample of the top 8 bidders for each auction.

The numbers presented are the absolute value of the ratio of a percentage

change in the demand for the telescope named at the top of each column over

a 10 % increase in the price of the telescope named in the left hand column.

This table shows that the own-price elasticity of demand for the three types

of telescopes is very high, confirming our intuition that these are expensive

luxury items. It also shows that while there is a lot of movement between

the ETX models (the Maksutov-Cassegrain design), especially down from the

ETX125 to the cheaper ETX90, there is no movement between either ETX

model and the LX200 (the 8 inch Schmidt-Cassegrain). Table 7 presents the

own-price and cross-price elasticity measures calculated at retail prices for

the sample of bidders who bid in the last day. The results show that the

demand elasticities are higher for this population. However, there is still no

movement between the two telescope designs.

15
ETX90 ETX125 LX200

ETX90 3.33 0 0

ETX125 13.33 5 0

LX200 0 0 5

Table 6: Demand Elasticities at Retail Prices (Basic) - Top 8

ETX90 ETX125 LX200

ETX90 5.56 10 0

ETX125 0 10 0

LX200 0 0 4.83

Table 7: Demand Elasticities at Retail Prices (Basic) - Last Day

3.3 Issues and Concerns

There are three major concerns with using data from eBay auctions to infer

demand for new telescopes. First, in many cases the telescopes sold on eBay

are second-hand. Second, we do not have a random sample of potential

telescope buyers. Third, bidders may not actually bid their valuation (or

willingness-to-pay) for the telescope.

In regards to the first concern, there does not seem to be a major lemons

problem with the market and the telescopes seem to hold their value well.

We see from Table 1 that the retail price for the ETX90, ETX125 and the

LX200 is $495, $895, and $1,499 respectively. The average sale price on

eBay is higher because these auctions include accessories. For example, the

retail price for the ETX90 does not include the “go to” system or a tripod,

while a high proportion of ETX90s sold on eBay come with these accessories. The overall success of eBay suggests that it has been able to resolve

the lemons problem in a great number of markets (Cohen (2002); Livingston

(2002)). While the estimated coefficients are calculated using all of the telescope auctions, the demand elasticities are calculated at the value for “like

new” telescopes.

The second concern is a concern with any data used to infer demand for

16
the whole population. It is likely that data from different supply channels

(speciality telescope retailers, camera shops, department stores) will each

give different estimates of elasticity. The value of the data collected from

a particular channel, depends on how important that channel is. The telescopes analyzed in this paper are sold on Amazon.com, Ritz Camera (Wolfe

Camera), Scope City (a major speciality telescope retailer), the Discovery

Store and Astronomics (another major speciality telescope retailer). It seems

reasonable to suspect that data collected from eBay is going to give higher

elasticities of demand than data collected from a speciality telescope retailer

like Scope City.16 Another issue is that eBay bidders on telescopes may not

be representative of buyers of telescopes. However, it is not obvious why there

would be a substantial difference between the two groups. EBay users are

likely to have higher incomes than the general population, however telescope

buyers are also likely to have higher incomes than the general population.

The third concern with these estimates is the assumption that each person

bids their valuation. A more reasonable assumption would be that each

person bids below their valuation for the telescope.17 Unfortunately, knowing

that bidders are bidding under their valuation and that the demand curve

may be biased in this way, does not tell us whether the estimate for the

elasticity is too high or too low. Haile and Tamer (2002) discuss this issue in

detail and present two methods for “bounding” the demand curve, by making

two assumptions. First, that each bidder bids below their valuation. Second,

that the final auction price is above each losing participants valuation for the

item. The authors show that with a large number of auctions (around 200),

it is possible to get very tight bounds with just these two assumptions by

using general characteristics of order statistics. Hasker et al. (2001) makes

the assumption that last minute bids (literally) are equal to the bidder’s

valuation for the item. Their argument is that in the last minute of an

16Speciality stores are more likely to have customers with a high interest in buying a

telescope. It would be good to test this hypothesis, however the data for such a comparison

is not currently available.

17See Arora et al. (2002) for an estimate of how eBay bidders discount their bids to

account for the “option” value of future auctions for the same good.

17
auction on eBay, it is “as if” the auction is a sealed bid second price auction

and therefore Vickery’s result applies.18

Two other issues are that the data may be censored and that arbitrage

may affect the demand estimates. Censoring may occur because when a

potential bidder arrives at an eBay auction, the current price may already be

above their willingness to pay.19 Censoring is a major problem for estimating

the whole demand curve using this kind of data. However in this case it is

not a major concern because we do not estimate the whole demand curve,

just the elasticities at retail prices. Arbitrage is likely to be a problem in

many markets, particularly those with low transaction costs. Arbitragers

may introduce supply shocks into the data reducing the accuracy of the

demand estimates. However, telescopes have substantial transaction costs

because they are difficult and expensive to ship. The telescopes analyzed in

this paper are quite large, fairly heavy and quite fragile.

4 Conclusion

EBay data may provide a solution to a number of problems faced by economists

analyzing demand in particular industries. The data has a number of important characteristics, including the fact that it is based on bids in second

price auctions, and thus may allow the economist to directly estimate demand

characteristics. This paper analyzes the demand for three types of telescopes

ranging in price from $500 to $1,500. The results suggest that the demand for

telescopes is highly elastic, and that the smaller Maksutov-Cassegrain designs

are not a close substitutes for the larger more expensive Schmidt-Cassegrain

designs. There are, however, a number of concerns about the assumptions

necessary to generate these results. The authors believe that much more

research needs to be done before an accurate conclusion can be drawn about

18Note, such bidders may still discount in order to account for future auctions (Arora

et al. (2002)).

19See Zhang et al. (2002) for a discussion of how to account for this problem. Note

however that a disproportionate number of bidders bid at the end of the auction. In our

data, 38% of bidders bid in the last day, and over 25% of those bid in the last 20 minutes.

18
the overall value of using data from on-line auctions for antitrust purposes.

References

Arora, Ashish, Hao Xu, Rema Padman, and William Vogt, “Optimal

Bidding in Sequential Online Auctions,” 2002. Heinz School of Public

Policy, Carnegie Mellon University.

Cohen, Adam, The Perfect Store: Inside eBay, first ed., Little, Brown and

Company, 2002.

Haile, Philip A. and Elie T. Tamer, “Inference with Incomplete Model

of English Auctions,” Journal of Political Economy, 2002. Forthcoming.

Hasker, Kevin, Raul Gonzalez, and Robin Sickles, “An Analysis of

Strategic Behavior and Consumer Surplus in eBay Auctions,” October

2001. Rice University.

Hosken, Daniel, Daniel O’Brien, David Scheffman, and Michael

Vita, “Demand System Estimation and its Application to Horizontal

Merger Analysis,” FTC Working Paper April 2002.

Koenker, Roger and Kevin F. Hallock, “Quantile Regression,” Journal

of Economic Perspectives, 2001, 15 (4), 143–156.

Livingston, Jeffrey, “How Valuable is a Good Reputation? A Sample

Selection Model of Internet Auctions,” September 2002. University of

Maryland.

Lucking-Reiley, David, Doug Bryan, Naghi Prasad, and Daniel

Reeves, “Pennies from EBay: the Determinants of Price in Online Auctions,” January 2000. Vanderbilt University.

Nevo, Aviv, “A Practicioner’s Guide to Estimation of Random-Coefficients

Logit Models of Demand,” Journal of Economics and Management Strategy, 2000, 9 (4), 513–548.

19
Roth, Al and Axel Ockenfels, “Last Minute Bidding and the Rules of

Ending Second-Price Auctions: Theory and Evidence from a Natural Experiment on the Internet,” 2000. Department of Economics, Harvard.

Zhang, Alex, Dirk Beyer, Julie Ward, Tongwei Liu, Alan Karp,

Kemal Guler, Shailendra Jain, and Hsiu-Khuern Tang, “Modeling the Price-Demand Relationship Using Auction Bid Data,” July 2002.

Hewlett-Packard.

20