WHY DO SELLERS AT AUCTIONS BID FOR THEIR OWN ITEMS? THEORY AND EVIDENCE
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Schmalenbach Business Review ◆ Vol. 56 ◆ October 2004 ◆ pp. 312 – 337 Michael Beckmann* WHY DO SELLERS AT AUCTIONS BID FOR THEIR OWN ITEMS? THEORY AND EVIDENCE** ABSTRACT This paper illustrates, both theoretically and empirically, the determinants of seller bidding at auctions. Based on search theoretical considerations, seller bids are explained as the seller’s rejection of submitted price offers that fall short of his reservation price. The search model allows to derive testable implications on the seller’s bidding behavior. Using a unique data set from German auction houses, the estimation results provide evidence that supports the search theoretical implications. For example, seller bidding is comple- mentary to the presence of bidding rings at auction. Moreover, art and antique auctions turn out to be particularly susceptible to seller bidding practices. JEL-Classification: C25; D44; D83. Keywords: Auctions; Reservation Price; Search Model; Seller Bids. 1 INTRODUCTION At many auctions an interesting phenomenon can be observed. During the ongo- ing bidder competition, the seller of the item to be auctioned announces price offers for his own property. This behavior seems counterintuitive, as the owner of an item should be interested in selling the item at auction, not buying it. However, plausible explanations may be derived by taking into account the possible dissatis- faction of the seller with the way the bidding is going. Hence, a rationale for seller bidding is that to avoid an award below his reservation price, the seller rejects the price offers submitted from real bidders. Thus, the seller’s bid can be considered as the seller’s response to an unsatisfactory bidder competition. The result of seller bidding is either an award to the owner of the commodity who is then both seller * PD Dr. Michael Beckmann, University of Freiburg, Department of Economics, BWL III, Platz der Alten Synagoge, D-79085 Freiburg im Breisgau, Germany, Tel.: +49-761-203-2392, Fax: +49-761- 203-2394, e-mail: Michael.Beckmann@vwl.uni-freiburg.de. ** I have benefited greatly from the discussions with Dietmar Bresch, Julia Deimel, Klaus Kammerer, and Bernd Schauenberg, whose suggestions have been of great value. Special thanks go to them all, but in particular I am very grateful to Dietmar Bresch for his competent advice and patience, while discussing the search model. Furthermore, I would like to thank the participants and discus- sants of the Fourth Symposium on the Economic Analysis of the Firm at the University of Frankfurt initiated by the German Economic Association of Business Administration, GEABA. Especially, I would like to thank Bernd Frick, who has agreed to prepare the co-presentation of my paper, for his very helpful suggestions. Finally, I am indebted to two anonymous referees for their construc- tive and continuative comments. Any remaining errors are, of course, my own. 312 sbr 56 (4/2004)
Seller Bids and buyer (buy-back bidding), or an award to a regular bidder who has been bid- den up artificially by the seller’s intervention (shill bidding)1. The analysis in this paper explicitly addresses seller bidding in the sense of buy- back bidding for several reasons. First, buy-back bidding is the more general vari- ant of seller bidding, because the seller’s participation in competitive bidding inherently involves the possibility of a self-award, regardless of whether he aims at buying the item back or bidding up other prospective buyers artificially. Second, in contrast to shill bidding, buy-back bidding per se is not illegal, although some auctioneers contract for special clauses that completely exclude seller bidding. Finally, buy-back bidding involves uncertain costs that depend on the selling price to be borne by the owner of an item. I.e., the natural consequence of buy-back bidding is that the owner must compensate the auctioneer twice, as both the seller and the buyer of the item, without having sold the item. When seller bidding is the costly expression of a seller’s rejection of submitted price offers, a further issue concerns the determination of seller bidding practices. So far, there are neither theoretical nor empirical studies that explain the determi- nants of seller bids. Only the use of seller bids as a means to fight bidder cartels has been suggested, for example, in Graham/Marshall (1987), Smith (1989), and Wolfstetter (1996). In these studies, seller bidding is considered as ‘pulling bids off the chandelier’ or ‘inventing bids off the wall’ 2. Hence, seller bids are presumed to be fictitious bids to protect against successful price fixing agreements intended to reduce the bidder competition at auctions. However, apart from this understand- able interest, seller bidding may also be encouraged by other causes that have previously been ignored theoretically and empirically. The fact that despite its apparent practical relevance, the phenomenon of seller bidding at auctions and its determination has not yet been discussed in the litera- ture motivates the paper. Based on a simple search model the rationale of seller bidding in the well-known English auction format will be discussed first. Typically, models of search behavior have been applied in a labor market context, where unemployed workers are searching for jobs and must decide whether or not to accept certain job offers. The idea of assigning search models to the determination of reservation prices at auctions was first noted by Ashenfelter (1989) 3 and applied by Ashenfelter/Graddy (1998). This paper extends the former approach by develop- ing a search model that allows the owner of an item to search for an acceptable price offer, and explicitly includes the opportunity of seller bidding. Based on some comparative static results and additional intuitive considerations, testable implica- 1 The term ‘buy-back’ in the context of auctions has been introduced by Smith (1989), p. 100, while ‘shill bidding’ has been originated by Engelbrecht-Wiggans (1987), p. 764, and Kumar/Feldman (1998). Because shill bidding is clearly illegal, when the seller aims at price boosting, he will pre- sumably not attend the auction himself but instead instruct a confederate who is unknown to the auctioneer and the bidders to bid up prospective buyers. The feature of successful shill bidding practices is an artificially driven bidder competition that results in a higher selling price than the seller would otherwise receive without such intervention. However, by using shill bidding the seller obviously faces the risk of realizing an unintended buy-back. 2 See Graham/Marshall (1987), p. 1221; Smith (1989), p. 150; Wolfstetter (1996), p. 391. 3 See Ashenfelter (1989), p. 26. sbr 56 (4/2004) 313
M. Beckmann
tions on seller bidding are then derived. An empirical examination of these implica-
tions is enabled by the availability of a unique data set containing not only infor-
mation on market structures and the organization of the auction market in Ger-
many, but also on such sensitive issues such as ring bidding and seller bidding.
The paper is organized as follows: Section 2 describes the idea of search behavior
and seller bidding and distinguishes between limit prices and reservation prices.
Section 3 presents an elementary search model for seller bidding and includes
comparative static results as a theoretical basis. Section 4 contains the econometric
analysis that examines the determinants of seller bidding empirically. Section 5
summarizes the main results of the paper and briefly addresses techniques the
auctioneer can pursue to protect against seller bidding practices.
2 SEARCH BEHAVIOR, LIMIT PRICES, AND RESERVATION PRICES
The idea behind modeling seller bidding is straightforward and similar to that of
models on job search examined, for example, by McCall (1970), Mortensen (1970),
and Franz (1999) 4. In analogy to a situation in which an unemployed worker is
looking for an attractive job offer, the seller is interested in achieving a sufficient
price for his commodity for sale. An unemployed worker will only accept a job
offer if the compensation exceeds a particular reservation wage. In the same way,
the owner of an object to be auctioned must decide at what price he would be
indifferent between selling now and waiting for the next auction 5. Hence, the
search process is characterized by the seller’s sequential procedure and the reser-
vation price is the result of his search.
Seller bidding is taken as a rejection of the submitted price offers. Instead of sell-
ing his commodity at a price below his reservation price, the seller prefers to
repurchase the item and thus to have the opportunity to offer it at another auc-
tion. However, buy-back bidding involves sizeable search costs, as the seller has
to bear the seller’s commission, the buyer’s premium, and of course opportunity
costs 6. The amount of search costs compared to the expected benefits of a buy-
back determines the seller’s decision to bid for his own item.
In the literature on auctions, the reservation price is typically defined as the fixed
minimum price that must be reached by competitive bidding in order to award the
item successfully. Any price offer below that price level will be rejected by the
owner, so the auction sale fails. Hence, the effective meaning of the reservation
price corresponds to the definition of a limit price. However, limit prices and
reservation prices may also have different meanings, so their magnitudes might
deviate substantially. This reconsideration is important for the understanding of
seller bidding.
4 See Franz (1999), pp. 205 – 211.
5 See Ashenfelter/Graddy/Stevens (2002), pp. 9 – 10.
6 Usually the auctioneer is paid by the seller and the buyer of the commodity. The compensation is
based on the performance of the auctioneer, i.e., the auctioneer only receives premiums from both
parties when the item has been knocked down. Irrespective of the auction type, the premiums are
frequently fixed at 15 percent of the auction price. See Beckmann (1999), pp. 185, 314 – 315.
314 sbr 56 (4/2004)Seller Bids If the seller’s reservation price and the fixed limit price are identical, items that do not reach that limit will usually go unsold, i.e., they will be returned to the owner who then must decide whether or not to re-supply the item at auction 7. In this context, Ashenfelter/Graddy (1998) and Ashenfelter/Graddy/Stevens (2002) have introduced models of the optimal reservation price. Although owners are covered by fixed limit prices and seller bidding is costly, the owner may decide to inter- vene in the competitive bidding when he wishes to establish a market price as a bidders’ price information for future auction sales, or when he fears the possible stigma effects of contagiously depressing future sales if the item goes unsold 8. Alternatively, the owner may also decide to enter his own bids to reach the level of the limit, and taking the risk of buying the item back when the limit is achieved. In another case, when the seller’s private reservation price exceeds the fixed limit price and competitive bidding reaches the limit but not the reservation price, seller bidding is likely to occur, because the seller’s acceptable price level is much higher than the official limit price that the bidders consider as the effective price floor. At auction, the limit price may be determined below the seller’s true reserva- tion price for at least three reasons. First, the auctioneer and seller may have dif- ferent perceptions on the level of the price floor, so in the end the negotiated limit price constitutes a compromise solution that does not really convince the seller. Second, the limit may be fixed below the reservation price for strategic reasons. For example, a relative low limit price might contribute to stimulating the competi- tive bidding more than would a relative high price floor that satisfies the seller’s own valuation of the item 9. If competitive bidding now does not meet the reserva- 7 Sometimes the auctioneer keeps the existence and the level of the fixed limit price secret (see McAfee/McMillan (1987), p. 729; Ashenfelter/Graddy (2003), pp. 780 – 782). Although this policy clearly contradicts theoretical implications that recommend revealing the seller’s valuation of the item (see Milgrom/Weber (1982)), it may be practical for several reasons. First, a secret limit price may serve to thwart bidding rings as the bidders are deprived from a useful focal point (see Ashenfelter (1989), p. 26; McAfee/McMillan (1992), p. 591; Carey (1993), p. 428). Second, the announcement of a relative high limit price could discourage some bidders from participating in competitive bidding, and may therefore lead to lower auction prices on average (see Vincent (1995)). Finally, the auctioneer sometimes takes up competitive bidding by announcing a potential auction price below the secret limit price, thus increasing the number of prospective buyers and the bidder competition (see Rasmusen (1997), p. 305). Recent empirical evidence on the auction price effects of public or secret limit prices has been provided by Bajari/Hortacsu (2000) and Katkar/Lucking-Reiley (2000) in the context of internet auctions. While Bajari/Hortacsu (2000) have found that secret limits tend to outperform posted limits especially for items with higher book values, Katkar/Lucking-Reiley (2000) have found just the reverse. According to their results from a field experiment, secret limit prices usually make sellers worse off, for example, by reducing the probability of the auction resulting in a sale or by lowering the expected auction price. 8 According to Ashenfelter (1989), p. 27, and Smith (1989), p. 103, the seller might fear that the future value of his item could be depressed contagiously if it goes unsold at a particular auction. If an item fails to sell, this failure can be thought of as revealing information on its value. Thus, the seller has an incentive to bid for his own commodity to create a documented market value. Other customers may perceive this market value as an informative signal for a realistic market price, so the seller can expect to avoid another failure, when the item is re-auctioned. Ashenfelter/Graddy (2003), pp. 773 – 774, have found some evidence to suggest that the future value of paintings that go unsold at auction is negatively influenced. 9 See Engelbrecht-Wiggans (1987), p. 764; Rasmusen (1997), p. 305. sbr 56 (4/2004) 315
M. Beckmann tion price even though the bids have reached the limit, the seller might refuse to accept the current price offer. However, as the item can, in principle, be awarded to the highest bidder, the seller can only inhibit an award below his reservation price if he purchases the item himself. Finally, despite the existence of a fixed limit price, the seller may not commit to a particular reservation price but hold his aspiration level flexible until he has watched the bidding progress 10. If, for exam- ple, the demand for a seller’s item at auction is higher than expected, the seller might respond by spontaneously raising the reservation price beyond the level of the previously fixed limit. In making this adjustment, the seller tries to avoid sell- ing the item for much less than it is obviously worth. However, when the rise in bidding does not reach the enhanced reservation price, the seller is likely to buy his own item back and try to auction it again later on the basis of the new aspira- tion level. However, at many auctions it is unusual to fix limit prices at all 11. In this case, therefore, any positive price offer may directly involve an award. Alternatively, the seller or an agent who acts on behalf of the seller might announce a price offer that corresponds to the introduction of a virtual limit price 12. Hence, buy-back bids serve as a check on prices guaranteeing that no bidder can virtually steal an item 13. Therefore, even in the absence of a fixed limit price, sellers are unlikely to refrain from estimating their own private reservation prices. Furthermore, if the highest bid does not meet the owner’s private reservation price, the only way for him to prevent an award at an inadequate price is to buy back the item. 3 A SEARCH MODEL OF SELLER BIDDING To illustrate the motivation for seller bidding, a simple search model that follows the proceedings of Mortenson (1970), Ashenfelter/Graddy (1998), and Franz (1999) is introduced. The analysis is not strictly embedded in a particular auction model. The auction itself is not explicitly modeled. Implicitly, the analysis assumes the general conditions of an affiliated values auction model derived in Milgrom/Weber (1982) rather than the much more specific premises of the independent private values model or the common value model. The reasons for this method are twofold. First, the underlying data set is not restricted to a particular type of auc- tion goods, for example, art and antiques. In fact, the data reflect a wide variety of items to be auctioned (see subsection 4.1), so the assumptions of any restrictive auction model would not be appropriate. Second, Beckmann (1999) and Ashen- felter/Graddy (2003) have found indications that contradict the frequently claimed notion that art objects exemplify and satisfy the premises of the independent pri- vate values model, in which all bidders have uncorrelated private valuations of the item for sale. Again, the assumption of a specific auction model does not appear to be very helpful in the present context. 10 See Smith (1989), p. 100; Graham/Marshall/Richard (1990); Levin/Smith (1996), p. 1281. 11 See Engelbrecht-Wiggans (1987), p. 764; McAfee/McMillan (1987), p. 729; Smith (1989), p. 101. 12 See Engelbrecht-Wiggans (1987), p. 764. 13 See Smith (1989), p. 139. 316 sbr 56 (4/2004)
Seller Bids
The model has an open time horizon, where seller bidding may occur in any of
the periods of time. First of all, a risk-neutral seller of an item to be auctioned is
supposed to act on the assumption of a time-invariant density function of identi-
cally distributed bids fX (x) 14. However, the seller has no information on the effec-
tive price offers of the bidders. Price offers either occur periodically at auctions
and are then accepted or rejected by the seller, or they do not occur. In this envi-
ronment the seller must balance the expected costs associated with an additional
search and the expected revenue of the next auction 15. Finally, it is assumed for
simplicity that the limit price, if one has been fixed at all, does not equate the
seller’s reservation price xr but that the reservation price exceeds the limit price.
The decision problem of the seller can then be described as follows: When at least
one bidder enters a price offer x , the seller can choose either to accept or reject
the submitted price offer. With probability αit (xr ) = α(xr ), the seller accepts the bid
for his item i at auction t 16, where α depends on the reservation price of the seller
xr . Every time the seller receives a price offer he works out the revenue from
accepting it and the expected revenue from rejecting it and continuing the search.
The acceptance or rejection of a price offer is determined by the reservation price
xr which the seller chooses at the beginning of period t = 0 in such a way as to
maximize his expected revenue from search. Therefore, the seller will only accept
a best bid that at least equals his reservation price xr , i.e., x ≥ xr . The correspond-
ing acceptance and selling probability α (xr ) is
x
α (x r ) = P (x | x ≥ x r ) = ∫ f X (x ) dx , (1)
xr
where x– is the upper bound of possible price offers. The integral captures all
price offers that at least equal xr , so these offers will not be rejected by the seller.
The expected value of a bid x that will be accepted by the seller in the next
search step can then be calculated as
x x f X (x ) ∫ xxr x f X (x ) dx
h (x r ) = E (x | x ≥ x r ) = ∫ dx = . (2)
xr 1 − FX (x r ) α (x r )
At a particular auction, the probability of being auctioned α (xr ) is inversely
related to the reservation price xr , because
14 Ashenfelter/Graddy/Stevens (2002) relax the assumption of a stationary price distribution in their
model by accounting for price shocks that lead to changing price distributions over time. Since the
authors confront their model with time-series data on auction sale rates at art auctions, this relax-
ation is essential for their proceeding. However, in this study the assumption of a time-invariant
bid distribution does not appear to be very restrictive, as the paper aims at obtaining general infor-
mation on the determination of seller bidding. In addition, the investigation utilizes cross-sectional
data and no time-series data.
15 The fact that the exact amount of search costs is unknown to the searcher, so search costs have to
be treated endogenously, represents an important extension of conventional search models.
16 This formulation acts on the assumption of stationary strategies.
sbr 56 (4/2004) 317M. Beckmann
∂α (x r )
= − f X (x r ) < 0 . (3)
∂x r
Moreover, an increase in the reservation price enhances the expected auction
price once an item is sold:
∂α (x r )
∂h (x r )
−
∂x r
[ ]
h (x r ) − x r
= >0 (4)
∂x r α (x r )
as h (xr ) > xr . However, with probability 1 − α (xr ), the seller rejects a price offer x.
The seller will reject x if his reservation price xr exceeds his revenue from auction-
ing the item, i.e., xr > x (≥ xl) with xl as the official limit price. In this case the
seller will bid for his own item 17 and must then pay (s + b) w to the auctioneer,
where s, 0 ≤ s < 1, is the seller’s commission, b, 0 ≤ b < 1, is the buyer’s premium,
and w = (1 + p)x is the seller bid. Since the seller rejects the highest price offer
from a real bidder x , he is forced to outbid the current price offer that is reflected
by the fixed surcharge p, 0 < p < 1 18. As a result, this auctioning attempt has failed,
because the item could not have been sold regularly. In addition, the seller has
suffered a financial loss. Moreover, since successful auctioneering requires at least
one more auction, the seller must bear fixed search costs per period c, for exam-
ple, due to opportunity costs in association with finding another bargain.
Since the transformation w = g (x) = (1 + p)x is a continuous monotonic increasing
function of x , the pdf of w is written as 19:
∂ g −1 (w )
(
fW (w ) = f X g −1 (w ) ) ∂w
=
1
(
f g −1 (w ) ,
(1 + p ) X ) (5)
where g − 1(w) = x = w/(1 + p) is the inverse function of w. Using w = (1 + p)x , the
expected value of w conditional on x < xr can be computed as
xr
xr w f X (x ) (1 + p ) ∫ x f X (x ) dx
k (x r ) = E (w | x < x r ) = ∫ dx = 0
. (6)
0 FX (x r ) 1 − α (x r )
Analogous to (4), an increase in the reservation price also enhances the expected
buy-back price, provided that the item cannot be auctioned successfully:
17 As shown in section 2 seller bidding may also occur, when xr = xl .
18 The use of surcharges fixed as a percentage of the preceding bid is very common, for example, at
art auctions.
19 See, for example, Lindgren (1976), pp. 46 – 57, and Freund (1992), pp. 266 – 268.
318 sbr 56 (4/2004)Seller Bids
∂α (x r )
∂k (x r )
−
∂x r
[ (1 + p ) x r − k (x r ) ]
= >0 (7)
∂x r 1 − α (x r )
as k (xr ) < xr . However, if an item fails to be auctioned, this failure does not exclu-
sively involve search costs. Inherent is also the enjoyment the owner receives
from possessing the item. This inherent enjoyment per period is denoted by z.
Just as the search costs c, the amount of this enjoyment is determined by the time
interval ∆ an owner is likely to have to wait to re-auction the item 20. Hence, the
consequences for the owner of not selling the object can be summarized as
(z − c)∆ − (s + b)k (xr ). Since k is a function of xr , this expression demonstrates the
partly endogenous nature of the search costs. On the other hand, if the owner
sells the item, it is assumed that he can lend this revenue freely at an interest rate
r defined per period t. Therefore, his income per period after the auction sale is
(1 − s)h (xr )r∆.
Prior to deciding to sell his item at a certain auction, the owner will balance the
present values of the revenues associated with an acceptance of the price offer
and a rejection plus additional search, respectively, to calculate the optimal reser-
vation price xr . Applying the formula for an infinite geometric series Σ∞t = 0 y t =
1/(1 − y) if | y | < 1, the present value of accepting a price offer is
∞ (1 − s ) x r r∆
VA = ∑ = (1 + r∆) (1 − s ) x r (8)
t = 0 (1 + r∆)
t
with 1/(1 + r∆) as the discount rate per period of length ∆. However, if the seller
rejects the price offer and decides to continue the search, the present value of the
directly following search step is given by
∞ α (x r ) (1 − s ) h(x r ) r∆
(z − c ) ∆ − (s + b ) k (x r ) + ∑ .
t =1 (1 + r∆) t
The last term describes the present value of the seller’s income streams in all
future periods provided that he accepts the price offer in period t = 1. However, if
the seller again rejects the price offer in t = 1 but accepts in t = 2 his expected rev-
enue is
(z − c ) ∆ − (s + b ) k (x r ) ( r ) (1 − s ) h(x r ) r∆ .
∞ α x
(1 − α (x r )) 1 + r∆
+ ∑
(1 + r∆) t
t =2
20 See Ashenfelter/Graddy (1998), p. 16. Hence, ∆ allows the time until the next auction to vary in
length.
sbr 56 (4/2004) 319M. Beckmann
Adding up the expected revenues of the future periods of time leads to
1 − α (x r ) 1 − α (x r ) ∞ α (x r ) (1 − s ) h(x r ) r∆
∞ t ∞ t
∑
t = 0 1 + r∆
[(z − c ) ∆ − (s + b ) k (x r )] + ∑
t = 0 1 + r∆ t =1
∑
(1 + r∆) t
.
Applying the formula for an infinite geometric series mentioned above, the pre-
sent value of rejecting a price offer is given by
(1 + r∆) [(z − c ) ∆ − (s + b ) k (x r ) ] + (1 + r∆) α (x r ) (1 − s ) h(x r )
VR = . (9)
r∆ + α (x r )
Equating (8) and (9) provides the optimal reservation price 21
(z − c ) ∆ − (s + b ) k (x r ) + α (x r ) (1 − s ) h(x r )
xr = . (10)
(1 − s ) (r∆ + α (x r ))
The computation of xr enables the derivation of comparative static results that
should facilitate finding the explanations for seller bidding. Since α, h, and k are
functions of xr , a comparative static analysis requires the use of total differentiation
instead of simple partial differentiation. First, the total differential with respect to b
is obtained as follows (the function G and ∂G /∂xr are determined in Appendix A):
dx r ∂G ∂b k (x r )
=− =− < 0. (11)
db ∂G ∂x r ∂k (x r )
(1 − s ) (r∆ + α (x r )) + (s + b )
∂x r
Intuitively, xr declines ceteris paribus when the buyer’s premium b increases. Fur-
thermore, the reservation price increases when the enjoyment from possessing an
object increases. Thus, in this case the owner should be less likely to sell the item:
dx r ∂G ∂z ∆
=− = >0.
dz ∂G ∂x r ∂k (x r )
(1 − s ) (r∆ + α (x r )) + (s + b ) (12)
∂x r
21 Note that in this search model the seller’s expectation of the bidders’ reservation prices, i.e. their
maximum willingness to pay, is captured by h (xr ). Although the present model clearly has the
character of a search model, it can also be related to models of optimal reservation prices provided
by auction theory, for example, in Riley/Samuelson (1981), Engelbrecht-Wiggans (1987), and
Levin/Smith (1996). In their simplest form with risk neutral, symmetric bidders and the indepen-
dent private values case, these models state that a seller benefits by imposing a reservation price
which exceeds his true valuation by an amount independent of the number of bidders (see, for
example, McAfee/McMillan (1987), pp. 706, 713 – 714). Also note that, as the empirical analysis uti-
lizes cross section data instead of time series data, the search model does not have to account for a
more dynamic perspective, for example a time conditional decline in the seller’s reservation price,
as required in the context of repeated auctions.
320 sbr 56 (4/2004)Seller Bids
Finally, the length of time between the auctions ∆ should have a negative effect
on the reservation price, because the remaining selling opportunities decrease:
dx r ∂G ∂∆ −z + c + x r (1 − s ) r
=− =− < 0. (13)
d∆ ∂G ∂x r ∂k (x r )
(1 − s ) (r∆ + α (x r )) + (s + b )
∂x r
This result is intuitively clear, because the seller will only put up an item for auc-
tion if (1 − s) xrr > z 22.
The outcomes of the comparative static analysis can be summarized in the follow-
ing propositions.
Proposition 1 A rising buyer’s premium induces the seller of an item to be auc-
tioned to reduce the aspiration level of his reservation price, which contributes to
increase the probability of a successful auction sale.
Proposition 2 The seller raises his reservation price for an object to be auctioned
when his enjoyment from possessing this object increases. As a consequence, the
owner is less likely to sell the item successfully.
Proposition 3 The length of time between auctions affects the level of the reserva-
tion price negatively. Therefore, relatively long intervals between subsequent auc-
tions tend to increase the probability of a successful auction sale for an individual
item.
Since the level of the seller’s reservation price explicitly influences the probability
of auction sale, it also implicitly influences the seller’s propensity to bid for his
own item and buy back the item. Seller bidding in terms of buy-back bidding is
encouraged when the current best bid does not satisfy the seller’s valuation. The
determinants of the probability of seller bidding are discussed in detail in subsec-
tion 4.2.
4 ECONOMETRIC ANALYSIS
The preceding section discusses the seller’s motivation to bid for his own item to
be auctioned. The crucial point is the seller’s rejection of the submitted price
offers. Now, the empirical investigation must identify the determinants of seller
bidding that follow from the theoretical implications. Since information on seller
22 Total differentiation with respect to c, s, and r is not displayed as these variables are not consid-
ered in the empirical investigation. As expected, dxr /dc and dxr /dr are negative as searching and
holding onto an item without auctioning becomes more costly, while the sign of dxr /ds is subject
to restrictions regarding r and ∆. However, this is not surprising as s must be paid by the seller,
irrespective of a successful auction sale or a buy-back incident. Therefore, the seller’s buy-back
decision is probably not affected by the level of s. Consequently, the influence of s on xr is also
less clear.
sbr 56 (4/2004) 321M. Beckmann bidding is only available at a qualitative level, the appropriate econometric strat- egy is the estimation of a binary choice model for the dichotomous outcomes, using the standard probit maximum likelihood approach. However, before esti- mating the binary choice model, the utilized data set will be described, the explanatory variables will be introduced, and some descriptive statistics revealing first insights of the matter will be reported. 4.1 DATA AND CATEGORIZATION OF THE AUCTION TYPES The outcomes in this paper are based on a survey conducted among German auc- tioneers and auction houses in the second term of 1993. Down to the present day this survey constitutes the only non-official data set on auctions in Germany that is based on cross-sectional or panel data level, therefore the survey is unique. More- over, the data set contains a sufficient number of observations for auction houses of all sizes and relevant sectors. Altogether, 587 questionnaires on the German auction market, its market structure, and organization were distributed. The effective population comprised 520 auction firms. The difference is the result of a not fully topical data set. In the period between collecting the auctioneers’ addresses and submitting the questionnaires, 67 auctioneers retired from their business or died. A total of 159 questionnaires is suitable for econometric analysis, which corresponds to a response rate of 30.6% and is therefore a satisfactory pro- portion relative to other surveys. In particular, this conclusion applies, given that the questionnaire also includes a few sensitive issues, so some auctioneers might not have wished to participate in the survey at all. Nevertheless, a sample size of 159 auction houses constitutes a solid basis for drawing meaningful and reliable conclusions from the econometric investigation. Comparing the population size used in this paper with the one published by the German Federal Statistical Office (Statistisches Bundesamt), the fact that the former is larger attracts attention. The Federal Statistical Office determines a population size of only 462 auction firms 23. The difference is explained by the fact that the survey was carried out at a later time. The investigation of the German Federal Statistical Office took place in 1987, i.e., three years before the German unification in 1990. Therefore, this data set could not, of course, contain any information on auction houses located in East Germany. In contrast, the data set used in this study includes several East German auction houses. Nevertheless, the larger popu- lation size indicates that the study covers the entire effective population, so the data are unlikely to suffer from any selection bias, but instead constitute a repre- sentative sample. In economic reality there is a wide range of commodities to be auctioned, and hence a wide range of different auction types has emerged. In general, used goods are sold at auctions. These goods include very different items, such as 23 See Statistisches Bundesamt (1991), pp. 52 – 53. 322 sbr 56 (4/2004)
Seller Bids paintings, stamps, or real estate 24. Since different market structures and conditions can be expected for different auction types, it is useful to divide the sample into separate categories representing the different types of goods to be auctioned 25. The following list provides an appropriate classification of the various auction types: • art and antique auctions, i.e., auctions of art, antiques, carpets, jewelry, and old toys, • auctions of stamps and coins, • auctions of basic commodities, e.g., auctions of lost property, personal assets, pledge goods, real estate, industrial goods, and horses, • auctions of consumption goods, e.g., fish, wine, fruits, and flowers. Due to their small number of responses, auctions of consumption goods could not have been considered in the econometric analysis. Thus, the evaluation has been restricted to auctions of art and antiques, stamps and coins, and basic commodi- ties. A more detailed classification for auctions of basic commodities is not useful because of the small subsample sizes within this broad category. To identify the sector affiliation of the auction houses the questionnaires have been analyzed by addressee. Usually, all the necessary information became available by proceeding in that way. If sector affiliation could not have been identified unambiguously, auctioneers have been categorized by evaluating the following question of the questionnaire: “Please enumerate at least three different items for sale in your auc- tion house during the last year”. 4.2 MODEL IMPLICATIONS, ADDITIONAL EXPLANATIONS, AND VARIABLES The discussion in section 3 closely relates the occurrence of seller bids to the seller’s dissatisfaction regarding the bidding ascend. Seller bidding is explained as the seller’s rejection of the price offers submitted for the item to be auctioned. The seller prefers to buy his own item back instead of leaving it to another bidder at an award below his reservation price. According to the comparative static results the inverse relationship between the reservation price xr and the buyer’s premium b is a straightforward outcome which directly follows from equation (11) and has been manifested in Proposition 1. Hence, xr decreases with the percentage of b. As a consequence, the probability that the seller rejects a submitted price offer 24 There are exceptions to this statement, as consumption goods like fish, wine, fruits, and flowers are also sold at auctions. These goods are, of course, unused. Another exception has just recently become popular. Nowadays (practically) new goods are also sold at internet auctions. 25 Since the auction sector in Germany is a relatively small segment with only a small number of establishments, neither the Federal Statistical Office nor the Federal Employment Services (Bundes- agentur für Arbeit) provide any further classification regarding auction types and the size of auc- tion houses. sbr 56 (4/2004) 323
M. Beckmann 1 − α (xr ) declines, which is equivalent to a declining seller bidding propensity 26. The effect of buyer premiums on seller bidding is measured by the variable BUY- ERPREM, which is a percentage of the realized auction price 27. According to (12) the reservation price increases with the enjoyment from possess- ing an object z, so the owner should be less likely to sell the item to a regular bid- der (see also Proposition 2). Although it is less clear how to measure differences in enjoyment between commodities, differences in z are likely to be idiosyncratic differences between items. More specifically, due to scarcity and other individual attributes of art and antiques a relative high z can most likely be assumed for the owners of these items. Consequently, the seller of a painting, for example, might prefer to repurchase his own commodity instead of accepting a price below his relative high reservation price. The effect of the enjoyment of possessing an item on seller bidding is measured by the two sector variables AA (art and antique auc- tions) and BC (auctions of basic commodities). The reference group is SC (auc- tions of stamps and coins). Finally, equation (13) demonstrates that the length of time between auctions ∆ is negatively related to the reservation price, because the remaining selling opportu- nities decrease with an increasing time interval ∆ (see also Proposition 3). Con- versely, short time intervals between the auctions indicate the presence of ample selling opportunities, and, thus, imply higher reservation prices and seller bidding propensities. The impact of remaining selling opportunities on the seller bid prob- ability is measured by the average number of auctions per year (AUCTIONS). This number varies substantially by item. Beckmann (1999) has found that owners of art and antiques must accept longer time intervals than owners of basic commodi- ties before they have a new opportunity to sell the item at the same auction house 28. The remaining hypotheses on the probability of seller bidding follow from addi- tional explanations that can be derived from intuitive considerations rather than the explicit predictions of the presented search model. For example, in the context of bidder competitions the revenue of the seller can be expected to rise when the number of customers attending an auction increases, because outbidding will usu- ally be intensified. Consequently, seller bidding should be less likely to be observed unless the seller adjusts his reservation price xr ad hoc. However, if the seller spontaneously marks up his reservation price xr at auction in response to observing a larger number of auction attendants than ex ante expected, the accep- tance probability will not be affected or the consequences will remain open, 26 Remember that in a buy-back incident the seller has to pay both the seller’s commission sw and the buyer’s premium bw, but only the latter is expected to affect his bidding behavior. The seller’s commission should not be a decisive factor for a buy-back decision, because this auction fee has to be paid by the seller irrespective of whether a real bidder or the seller himself gets the item knocked down. 27 A complete list of variables can be found in Appendix B. 28 See Beckmann (1999), pp. 94 – 101. 324 sbr 56 (4/2004)
Seller Bids respectively 29. Therefore, the explanatory variable CUSTOMER is introduced to measure the effect of the number of participants attending an auction on the prob- ability of seller bidding. On the contrary, a rising probability of seller bidding can be presumed in any case of less intensive bidder competitions. For example, the expected revenue of the seller will probably be impaired when bidding rings engage in competitive bid- ding. Bidding rings are actively interested in reducing competition and depressing prices to acquire the desired items cheaply 30. Hence, these coalitions appear to harm the seller’s interests. Moreover, a ring not only contributes to reducing the number of effective bidders, it also changes the effective distribution of the bids 31. Consequently, the seller is more likely to reject the highest bid, as he can reason- ably be assumed to continue holding on to his previously fixed reservation price xr . The impact of bid rigging on seller bidding is measured by a dichoto- mous variable CARTEL, which indicates whether or not auctioneers observe bid rigging practices at their auctions. Furthermore, the presence of retailers at auctions may contribute to less intense bidder competitions. Retailers in their capacity as resellers have a natural interest in low-priced acquisitions for their own businesses. Moreover, retailers may also have a strong incentive to collude 32. Therefore, in both cases retailers aim at keep- ing auction prices down. Consequently, the seller is more likely to reject a best bid x. The impact of retailers at auctions on the probability of seller bidding is measured by a dummy variable RETAILER that indicates whether or not retailers belong to the auctioneer’s customers. Milgrom/Weber (1982) have emphasized that to enhance the expected selling price, auctioneers should provide truthful information about the items being sold. For example, if auctioneers reveal information about the auction objects and their valuation prices, they reduce customers’ uncertainty on the quality of the item, and thus encourage the customers to bid less cautiously. As a result, one is less likely to observe the incident x < xr , and thus the seller is less likely to bid for his own item. The effect of well-informed bidders on seller bidding is captured by a dichotomous control variable INFO indicating whether or not the auction atten- dants are usually informed by the auctioneer about the items’ estimated values. 29 In the independent private values model, the optimal reservation price is independent of the num- ber of bidders. Thus, the probability that an item will be sold depends intrinsically on the number of bidders in an auction and increases with the number of bidders (see McAfee/McMillan (1987), p. 714; Wolfstetter (1996), pp. 392 – 393). In contrast to the independent private values case, the reservation price in a common value auction typically increases with the number of bidders (see McAfee/McMillan (1987), pp. 722 – 723). Hence, in the context of an independent private values model the probability of seller bidding should decrease with the number of bidders, but in the common value case the consequences on seller bidding remain open. 30 Current evidence on the postulated inverse relation between selling prices and the existence of cartels in a related context is provided by Scott Morton/Zettelmeyer/Silva-Risso (2001). The authors show that agents who have the job of improving market transparency at Internet car retailing sites are able to offer their clients new cars at significant lower prices than the clients can find on their own. 31 See McAfee/McMillan (1987), p. 725. 32 See Beckmann (2004), pp. 127, 132 – 133. sbr 56 (4/2004) 325
M. Beckmann
Despite the theoretical recommendation in terms of revealing trustworthy informa-
tion, auctioneers sometimes engage in systematic manipulation of the estimated
prices for strategic purposes 33. Chanel/Gerard-Varet/Vincent (1996) and Bauwens/
Ginsburgh (2000) found strong indications for strategic undervaluation, while
Beggs/Graddy (1997) found both systematic under- and overestimation, when
there are in-house valuations. In contrast, if an external expert fixes the item’s val-
uation price on behalf of the auctioneer, this expertise should provide objective
and trustworthy information on the item’s market value. An external expert should
have no incentive to fix a valuation price for strategic reasons. As a consequence,
bidders have no reason to doubt the authenticity of the expertise. Analogous to
the preceding case, this information accumulation may involve more aggressive
bidder competitions, so the seller is dissuaded from buy-back bidding 34. The effect
of an external expertise on the probability of seller bidding is measured by a
dummy variable EXPERT, which indicates whether or not an external expert is
usually employed to estimate the valuation for the auction goods.
The argument proceeds in a similar way when auctions are usually attended by a
homogeneous bidder clientele. These mostly established bidders can be consid-
ered very interested and informed about the items put up for auction. Moreover,
due to specific passions, many collectors might have a marked willingness to pay,
which tends to increase the expected revenue of the seller. Since the seller acts on
his fixed reservation price xr regardless of the presence of established bidders at a
particular auction, he is more likely to accept the highest bid x, when established
bidders are present at auction. The influence of a homogeneous bidder clientele
on seller bidding can be measured by a dummy variable HOMOGEN that indicates
whether or not auctions are usually attended by the same customers.
Finally, one control variable for firm size is added to the econometric model,
because seller bidding, for example, may occur more often at larger auction
houses. The effect of firm size on seller bidding is measured by the auctioneer’s
average sales per year. Since original information about the auctioneers’ sales is
only available at an ordinal scale, the ordinal observations are standardized to
generate the continuous explanatory variable SALES. This method follows the
strategy of Bresnahan/Brynjolfsson/Hitt (2002), who generally standardize
explanatory variables measured at an ordinal scale to derive a more precise inter-
pretation. Therefore, in this paper standardized values are computed from the
– )/s , where η
original values, i.e., SALES = (ηi − η – is the mean and s is the stan-
η η
dard deviation of the ordinal observations ηi 35.
33 See Ashenfelter/Graddy (2003), pp. 777 – 779.
34 This analysis implies that the seller is less well informed about the strategic estimation prices of the
auctioneer or the price enhancing effect of external expertises than the auctioneer and the bidders.
However, this assumption is quite realistic, because the auctioneer is unlikely to reveal the infor-
mation that the bidders rather trust the estimations of external experts than the auctioneer’s own
valuations.
35 The average sales volumes per year have been categorized into nine groups. The intervals are
defined as follows: 1: DM 25,000 – 50,000; 2: DM 50,000 – 100,000; 3: DM 100,000 – 250,000; 4:
DM 250,000 – 500,000; 5: DM 500,000 – 1,000,000; 6: DM 1,000,000 – 2,000,000; 7: DM 2,000,000 –
5,000,000; 8: DM 5,000,000 – 50,000,000; 9: > DM 50,000,000. DM = German Marks.
326 sbr 56 (4/2004)Seller Bids 4.3 DESCRIPTIVE STATISTICS The following tables show that seller bidding is standard operating procedure at German auction houses. Table 1 refers to the auctioneers’ experiences with seller bids at their own auctions. Table 1: Seller bidding in the auctioneer’s own auction house (in %) Auction type ALL BC AA SC Seller bids can be observed 38.9 34.4 48.9 34.2 Seller bids cannot be observed 61.1 65.6 51.1 65.8 N 149 64 47 38 Note: ALL represents total sample size, i.e., all auction houses in the data set irre- spective of any categorization. N is the number of observations. The results indicate that especially auctioneers of art and antiques are confronted with seller bidding. Approximately 50 percent of the art and antiques auctioneers encounter seller bidding at their own auctions, but these practices are encoun- tered in only about 34 percent in the category basic commodity auctions. The per- centages for the category auctions of stamps and coins are close to those obtained for basic commodity auctions. These bivariate results provide the first indications in terms of the inherent enjoyment the owner receives from possessing an item. In Table 2 the sample is divided into auctions with and without seller bidding. Applying simple mean tests, the table provides first insights in terms of a bivariate correlation of seller bidding and the considered determinants. The tests show significant differences for the explanatory variables CARTEL, RETAILER, AUCTIONS, HOMOGEN, and EXPERT. This finding means that seller bidding is more likely to observe when auctions are attended by bidding rings and professional retailers, and that it is less likely to occur when auctions are con- ducted frequently (which contradicts the expectations), when auctions are usually attended by an established bidder clientele, and when the items’ valuations are undertaken by external experts. However, although most of these bivariate out- comes are in line with the search theoretical considerations, one cannot conclude that these variables are the effective determinants of seller bidding and that BUY- ERPREM, CUSTOMER, INFO, and SALES do not affect seller bidding either at all or to only a minor extent. Therefore, these bivariate analyses are typically not suffi- cient to explain seller bidding, because other potential determinants not taken into account could have a significant impact. Bivariate correlations can even be gener- ated by omitted variables. Therefore, to obtain unbiased results, a multivariate analysis is necessary. sbr 56 (4/2004) 327
M. Beckmann
Table 2: Two-sample mean tests
Test Variable N Auction houses with Auction houses p-value
seller bidding without seller bidding
t BUYERPREM 147 12.6 12.9 0.364
t AUCTIONS 136 8.1 14.7 0.023
t CUSTOMER 140 429.6 535.3 0.216
Pr CARTEL 134 68.5 33.7 0.000
Pr RETAILER 149 82.7 68.1 0.023
Pr INFO 149 75.8 70.3 0.230
Pr EXPERT 149 15.5 26.3 0.059
Pr HOMOGEN 149 29.3 42.8 0.048
t SALES 120 0.007 -0.014 0.453
Note: The means of the variable SALES have been calculated from standardized
– )/s , where η
values, i.e., SALES (ηi − η – is the mean and s is the standard devia-
η η
tion of the ordinal observations ηi . The means of the variables AUCTIONS and
CUSTOMER have been calculated from original values. Outliers have been elimi-
nated. The mean values of the remaining variables are displayed in percent. The
Pr-test performs a two-sample test on the equality of proportions using large sam-
ples statistics and has been applied for the qualitative variables instead of the stan-
dard t-test. All p-values are based on one-tailed tests. N is the number of observa-
tions.
4.4 PROBIT ML ESTIMATION OF THE DETERMINANTS OF SELLER BIDDING
In the general probit model, the probability that a binary outcome variable
yi ,i = 1,…n, takes on the value 1 is modeled as a non-linear function of a linear
combination of K independent variables xi = (xi 1,xi 2,…,xiK ), i.e.,
Pr ( yi = 1| xi ) = Φ(xi β) . (14)
Here, Φ (·) is the cdf of a standard normal random variable and β is the vector of
coefficients. Referring to the analysis in subsection 4.2, the econometric model of
seller bidding has the form (see Model 2 in Table 3)
y i* = β 0 + β1 BUYERPREM i + β 2 AAi + β 3 BC i + β 4 AUCTIONSi
+β5 CUSTOMERi + β 6 CARTELi + β 7 RETAILERi + β 8 INFOi (15)
+β 9 EXPERTi + β10 HOMOGEN i + β11 SALESi + vi ,
328 sbr 56 (4/2004)Seller Bids
where yi* is the seller bidding propensity in auction house i, vi is a stochastic error
term, and
if y i* > 0, i.e., auctioneer i observes seller bidding,
SELLERBIDi = 1 (16)
0 otherwise .
Since the seller’s decision criteria to bid for his own property are not observable,
equation (15) represents a latent model. Only the results of the decision process
are observable. They can be illustrated by the dichotomous variable specification
in equation (16).
Apart from the usual representation of the models in coefficient form, the table
contains the marginal effects which enable a more meaningful interpretation 36. For
any continuous explanatory variable xk the marginal effect is defined as
∂ Pr (SELLERBID = 1| x )
= φ (xβ) βk , (17)
∂ xk
where φ (·) is the pdf corresponding to Φ(·). The marginal effect reports the
change in the seller bid probability for an infinitesimal change in each of the vari-
ables. For dummy variables the marginal effects reflect the discrete change of xk
from zero to one in the seller bid probability
∆ Pr (SELLERBID = 1| x )
= Pr (SELLERBID = 1| x , x k = 1)
∆ xk (18)
− Pr (SELLERBID = 1| x , x k = 0) .
The t-statistics are computed with robust standard errors according to White
(1980) 37. Table 3 contains two specifications, where the explanatory variable AUC-
TIONS is excluded in Model 1 and added to the variable set of Model 2 38. The pur-
pose of this method is to investigate the predicted opposite effects of z (the enjoy-
ment from owning and not selling an item measured by AA) and ∆ (the length of
time between the auctions measured by AUCTIONS) on seller bidding. As shown
in Table 1, art and antique auctions seem to be especially susceptible to seller bid-
ding. On the other hand, art and antiques auctioneers conduct only a small num-
36 See Long (1997), pp. 71 – 75.
37 The application of robust instead of conventional standard errors has no substantial effect on the
significance level of the coefficients.
38 Other specifications have also been estimated. For example, instead of introducing the standard-
ized variable SALES to the model a set of dummy variables representing the individual sales classes
have been added. Moreover, an interaction term of the variables CARTEL and AA has been gener-
ated to account for a probably complementary effect on the seller bid probability. Finally, the nat-
ural logarithm of the variable CUSTOMER has been taken to introduce an alternative to the original
variable. However, in neither of the cases the alternative specification contributes to improve the
model estimations significantly. By the way, as pointed out by Ai/Norton (2003), the interpretation
of the marginal effects of interaction terms in non-linear probit models in terms of sign, magnitude
and statistical significance is not trivial and can lead to misleading inference.
sbr 56 (4/2004) 329M. Beckmann
Table 3: Probit ML estimates for the determinants of seller bidding
Model 1 Model 2
Explanatory variables Ek ~ Ek ~
Ek Ek
BUYERPREM -0.078** -0.030 -0.086** -0.033
(-1.99) (-2.07)
AA 0.659* 0.255 0.672* 0.261
(1.86) (1.84)
BC 0.653 0.251 0.694 0.268
(1.30) (1.26)
AUCTIONS 0.001 0.001
(0.08)
CUSTOMER 3.110-5 1.210-5 5.210-5 2.010-5
(0.12) (0.21)
CARTEL 1.021*** 0.377 0.912*** 0.342
(3.30) (2.90)
RETAILER 0.875* 0.302 0.986** 0.341
(1.91) (2.03)
INFO 0.041 0.016 0.131 0.050
(0.13) (0.40)
EXPERT -0.906** -0.298 -0.933** -0.310
(-2.09) (-2.07)
HOMOGEN -0.615** -0.231 -0.629** -0.239
(-2.16) (-2.12)
SALES -0.044 -0.017 -0.033 -0.013
(-0.26) (-0.18)
CONSTANT -0.512 -0.484
(-0.71) (-0.63)
Wald test 26.59*** 24.39**
McFadden’s Pseudo-R2 0.219 0.213
N 106 100
Note: The dependent variable is SELLERBID. */**/*** denotes significance at the 10
percent- / 5 percent- / 1 percent-level. The β̃k describe marginal effects according
to (17) and (18), respectively. The values in parentheses display robust t-statistics
according to White (1980). The Wald test and McFadden’s Pseudo-R2 indicate the
quality of the model estimation and show acceptable values. N is the number of
observations.
330 sbr 56 (4/2004)Seller Bids ber of auctions per year relative to other auctioneers 39. This outcome suggests that one should be less likely to see seller bidding at art and antique auctions. Hence, adding the variable AUCTIONS to Model 2 also aims at investigating which of the two is the dominant effect. The estimation results confirm the search theoretical considerations. The most striking result is that bid rigging and seller bidding are complements, where bid rigging practices determine seller bidding significantly 40. Hence, there is some evi- dence that bidding rings contribute substantially to depressing auction prices, which induces the owner of a particular item to announce a buy-back bid to avoid an award below his reservation price. The corresponding marginal effect is β˜k = 0.377 in Model 1 and β˜k = 0.342 in Model 2, i.e., a discrete change of the explanatory variable CARTEL from zero to one increases the probability of seller bidding at about 35 percent. Furthermore, significant coefficients are obtained from the variables BUYERPREM, RETAILER, EXPERT, HOMOGEN, and AA. Therefore, the first conclusion is that the seller bidding probability is a declining function of the buyer’s premium. Accord- ing to the estimates, a one-unit decline in the percentage of the buyer’s premium increases the probability of seller bidding at about 3 percent. Hence, low buyer premiums explicitly reduce the costs of repurchasing, and therefore contribute to reducing the seller’s search costs. As a result, low buyer premiums enhance the attractiveness of buy-backs at auctions when the seller is dissatisfied with the progress of the bidding. Second, the probability of seller bidding increases with the presence of retailers at auctions by about one third. Obviously, retailers con- tribute to depressing auction prices, which in turn more frequently involves x < xr . Third, the results indicate that external expert opinions and seller bidding are, in fact, inversely related, so the seller is more likely to refrain from active bidding. According to the results, the existence of an external expertise decreases the prob- ability of seller bidding at about 30 percent. Fourth, the presence of homogeneous customers at auction also contributes to reduce the probability of seller bidding. The corresponding marginal effect is − 23 percent. Finally, the estimates support the descriptive findings of Table 1 that art and antiques auctions are particularly susceptible to seller bidding practices. More pre- cisely, art and antiques auctions are about 25 percent more vulnerable to seller bidding practices than are the reference group auctions of stamps and coins. Adding the variable AUCTIONS changes neither the magnitude nor the significance of AA. Moreover, the variable AUCTIONS itself is insignificant. Therefore, the deci- sive factor for the owner of an item to enter seller bids is his inherent enjoyment 39 See Beckmann (1999), pp. 94 – 101. 40 One may also assume a reverse relation, i.e., ring bidding may be a response to seller bidding. However, for the econometric modeling, this potential (mutual) dependency is of minor impor- tance because the determinants of ring bidding only affect the decision processes of the cartel members and not the seller’s calculus. Consequently, simultaneity problems are less likely. In the context of this paper, the variable CARTEL can be considered strictly exogenous. Moreover, the bidding progress in a real English auction does not allow bidders to form cartels spontaneously after having observed or suspected seller bidding practices. sbr 56 (4/2004) 331
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