Auctions with resale opportunities: an experimental study.
Jog, Chintamani ; Kosmopoulou, Georgia
I. INTRODUCTION
Standard results in auction theory presume mostly the absence of
resale options. However, the sale prices of government-owned assets or
public resources are often determined by resale opportunities. Examples
include spectrum license auctions and the ensuing sale of
telecommunication companies in the last decade, real estate sales, and
more recently the sales of rights to emit pollutants, especially
greenhouse gases in established emission trading schemes (ETSs or cap
and trade schemes). The applicability of a market framework with resale
as a foreseeable option extends to (re)allocation of common pool or
common property resources which include fisheries, wildlife preserves,
and surface water resources (White 2006).
When bidders are offered an option to resell in a secondary market
they adjust their bids in the primary auction market. Adding a resale
opportunity introduces a common value element to an otherwise private
value auction (Haile 1999). If the winner of an auction has all the
bargaining power in the resale market (in what we call a
seller-advantaged resale regime), there will be a speculative interest
in acquiring the item at the auction stage knowing there is a chance to
resell it (Hafalir and Krishna 2008). On the other hand, if the loser of
the auction has all the bargaining power in the resale market (in a
buyer-advantaged resale regime), such an interest is limited and the
common value at the auction stage is restricted. Thus we would expect
more aggressive bidding and higher resale prices in a seller-advantaged
resale regime. In both cases, the common value created by the resale
opportunity would lead to a symmetrization of bids; in equilibrium,
bidders should behave as if they compete in a symmetric auction for a
common value whose size is determined by the structure of the resale
market.
In this work, we explore the impact of the resale market structure
on bids, linking them to efficiency and auction revenue. We use
controlled experiments that mimic the theory to study first price
auctions with asymmetric bidders that have resale opportunities. We find
higher bids on average in a seller-advantaged resale regime than in a
buyer-advantaged resale regime. Interim efficiency, measured in terms of
the proportion of efficient outcomes realized at the conclusion of the
auction stage, is the same across regimes but higher in magnitude than
predicted. Final efficiency is high irrespective of the structure of the
secondary market. In the seller-advantaged resale regime, we find
statistically significant differences in the bid distributions,
consistent with other experimental work (see Georganas 2011). In the
buyer-advantaged resale regime, we provide some evidence in support of
bid symmetrization; in highly asymmetric environments, however,
conforming to the equilibrium strategy may generate undesirable risks
for those with values in the upper quartiles of the support.
Our motivation stems from our interest in studying and predicting
the effectiveness of ETSs. ETSs are seen as a successful marketbased
approach to handle the issue of pollutants and their ill-effects
including climate change. The structure of the secondary market for
permits can have a significant effect on bidding behavior, initial and
final allocative efficiency in ETSs. A sizable portion of the emission
allowance futures and option contract trades are carried out via the
over the counter (OTC) exchange through bilateral negotiations. (1)
Under these circumstances, one can expect firms on either side to
exploit bargaining power. The secondary market for Regional Greenhouse
Gas Initiative (RGGI) allowances, for example, was a buyer's market
(indicated by low prices and volume of trading) until very recently,
when prices started to rise and brought about a reversal in the trend.
In the near future, more stringent caps may generate higher demand in
the secondary market, thereby shifting the bargaining power more from
buyers to sellers. The California Cap-and-Trade program was launched in
November 2012 as the second largest emission trading market in the world
right behind the European Union Emissions Trading Scheme (EUETS). It
attempts to regulate emissions via reducing the cap by 2%-3% a year
leading to a projected reduction from 522 MT/person/year in 2010 to 85
MT/person/year in 2050. (2,3) The stringent caps are likely to shift
market power from buyers to sellers. The questions we ask are: How will
prices and efficiency be impacted from such a shift? Since we do not
have the ability to link directly bids in the primary and secondary
markets for emission permits, neither do we have direct knowledge of
firm expectations at the time of bidding, what can we learn from our
experimental subjects? Is bidding behavior conforming to the theory? Is
final efficiency as high as predicted by the model?
The paper is structured as follows. The next subsection reviews
related literature. Section II presents the theoretical framework
followed by equilibrium bid and (ex-ante) efficiency predictions.
Section III describes the experimental design. Section IV presents the
main results and related discussion. The final section offers concluding
remarks.
A. Related Literature
Cox, Roberson, and Smith (1982) introduced the notion of a resale
opportunity as an expository device to explain value generation to
experimental subjects. They postulate that values are generated out of
idiosyncratic resale opportunities where the winning bidder could resell
the object to the auctioneer for a predetermined monetary value. The
recent literature discussed below links resale opportunities to the
existence of a secondary market among auction participants introducing a
common value component to auction competition.
Haile's (1999) theoretical paper is among the earliest to
analyze auctions with resale as a two-stage game. Using the first price,
second price, and English auction settings, he shows that valuations are
determined endogenously when forward-looking bidders take into account
the possibility of resale in a secondary market. Hence, the revenue at
the auction stage depends on the resale market structure and the
information linkage between primary and secondary markets. He tests
empirically this result in Haile (2001) using data on U.S. Forest
Service timber sales. Haile (2003) extends the theoretical research by
constructing a two-stage game, using three auction formats (first price,
second price, and English auctions) in the first stage and two auction
formats (optimal and English) in the second stage. He focuses on the
effect of the resale market on equilibrium bidding strategies.
More recently, Hafalir and Krishna (2008, 2009) and Cheng and Tan
(2009) have studied revenue generation and market efficiency in
independent private value (IPV) auctions with resale. These papers
consider two types of bidders with asymmetric value distributions.
Hafalir and Krishna focused on the revenue ranking between first and
second price auctions with resale. One of the major insights from this
work is the symmetrization property. Given the resale market structure,
for every first price asymmetric auction with resale (FPAR), there is an
equivalent first price symmetric auction without resale. Asymmetric
bidders behave as if they are competing in a symmetric auction for a
common surplus determined by the nature of resale competition. In
equilibrium, their bidding distributions are the same for those two
auctions. We show theoretically that bid-equivalence between types
should hold in the buyer-advantaged resale case due to symmetrization
and provide a quantile regression analysis that permits testing across
the distribution of values.
On the experimental front, there have been very few related
studies. Mueller and Mestelman (2002) report experimental evidence on
revenue and efficiency effects under the monopoly/monopsony
(seller/buyer-advantaged) structures using a double auction setting.
In their experiments, the subjects are assigned the tradable
coupons before the double auctions begin. Hence, their setting
effectively has only one stage.
Lange, List, and Price (2004) build upon Haile (1999) and provide
experimental support for the result that bids are higher in auctions
with resale than those without, emphasizing the common value element.
Their setup is a two-stage game with the second-stage market structured
in some experiments as an English Auction and in others as an Optimal
Auction. Players decide on the bids only during the first stage. The
second stage allocation is automated and hence players do not make any
decisions at this stage.
Georganas and Kagel's (2011) study is the closest to ours.
Their study also builds upon Hafalir and Krishna (2008) but their focus
is on a comparison of bidding behavior across resale and no resale
scenarios. The resale scenario is the seller-advantaged resale regime.
Our paper compares the trade-off between revenue and efficiency across
auctions with seller- and buyer-advantaged resale. This is the first
experimental test of such a revenue-efficiency trade-off and could shed
light on the continuing debate about the optimal way to allocate
emission permits.
More recently, Georganas (2011) and Jabs-Saral (2012) have studied
English auctions with resale using experiments. While Georganas (2011)
employs quantal response function (QRE) analysis to explain the
signaling in English auctions with resale, Jabs-Saral's (2012)
focus is on the demand reduction and speculation following the shift of
bargaining power from buyer to seller in the resale stage. Unlike
Jabs-Saral's work, our paper uses an asymmetric value structure and
explores the impact of the form and characteristics of the secondary
market on efficiency.
We study a two-stage model, consisting of an initial first price
auction followed by a resale stage structured either as a seller- or a
buyer-advantaged market. The theoretical framework is built upon the
model by Hafalir and Krishna (2008)). First, we solve explicitly for
equilibrium bidding strategies in the buyer-advantaged resale regime and
provide a comparison to corresponding strategies under seller-advantaged
resale. Then, we perform experiments and compare observed patterns of
behavior to theoretical predictions.
II. THEORETICAL FRAMEWORK
Two risk-neutral bidders are participating in a first-price IPV
sealed bid auction. After the conclusion of the auction the winner has
the opportunity to participate in a seller-advantaged (buyer-advantaged)
resale market. The winner (loser) of the first stage auction can make a
take-it-or-leave-it offer to sell (buy) the object to (from) the same
opponent. Both bidders' values are drawn from independent uniform
distributions with different supports. The weak bidder's value is
an independent and identically distributed (iid) draw from U[0,
[a.sub.w]] wherein [a.sub.w] is set at 10 in all experimental sessions
that follow. The strong bidder's value is an iid draw from U[0,
[a.sub.s]] wherein [a.sub.s] takes on the values 20 and 40 in two
treatments of the experiment. We refer to the former treatment as S20
and the latter as S40.
Bidding distributions and the type of resale regime are common
knowledge among the players. Players only know their own values and
their own bids during the course of the game. They do not learn the
private values or bids of their opponents.
Consider first the auction followed by a seller-advantaged resale
market. This implies that the winner of the first auction has all the
bargaining power in the secondary market. Initially, we state the
problem in general terms using F(*) as the cumulative density function.
The problem for a bidder j winning the primary auction with a bid b
is to determine an optimal price p that maximizes the revenue function
[R.sub.j]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [phi] is the inverse bidding function. The first term is the
expected payoff from selling in the second stage. The term in the
bracket is the probability that the price is less than or equal to the
opponent's value. The second term in this expression is the
expected payoff of bidder i when the price exceeds the opponent's
value and there is no trade.
Consequently, the problem for bidder j choosing the optimal bid in
the primary auction market can be stated as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where the first term is the expected revenue from the resale stage
and the second term is the cost to bidder j.
Similarly, consider the auction followed by a resale market with
buyer-advantage. The loser of the first auction has all the bargaining
power in the secondary market. The problem for bidder j losing the
primary auction with a bid b is to determine an optimal price r that
maximizes the following resale profit [S.sub.j]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The term in brackets is the probability of trade, which is
determined by the resale price being greater than or equal to the
opponent's value. Hence, [S.sub.j](r, b) represents the maximum
expected revenue received from the resale stage by bidder j.
The problem for bidder j choosing the optimal bid in the primary
auction market is then
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [F.sub.i]([[phi].sub.i](b)) is the probability of winning in
the first stage.
The equilibrium bidding functions for each regime under the
assumption of uniform distribution of values are described in Table 1
where again, [a.sub.s] and [a.sub.w] are the upper bounds of the strong
and weak bidder's support, respectively and [v.sub.i] is the value
for individual bidder i. The bid functions for the seller-advantaged
resale regime follow directly from Hafalir and Krishna (2008) using the
symmetrization property. The results under the buyer-advantaged resale
are derived along the same lines but require some elucidation. (4) The
weak bidder's value distribution sets an upper bound for the
pricing distribution in the secondary market. The highest price offered
by the strong bidder in the resale market should not exceed the upper
bound of the weak bidder's value distribution. The equilibrium bid
function for the buyer-advantaged resale is defined over two intervals.
For the first part, it is exactly the same as that in the
seller-advantaged resale regime. However, note that the bid and the
resale price can never exceed the weak bidder's highest value.
Hence for bids greater than [a.sub.w]/2, the optimal price is merely
[a.sub.w]. Once the resale price bound is known, we can derive
equilibrium bidding strategies for each player. The bidding functions
are monotonic, continuous, and increasing.
The optimal price in each regime depends on the inverse bidding
functions and [[phi].sub.i](b) and [[phi].sub.j](b). The price function
is p = 2b in the seller-advantaged resale regime. Under the
buyer-advantaged resale regime, the price function is r=2b for bids less
than or equal to [a.sub.w]/2 and r = [a.sub.w] for bids exceeding
[a.sub.w]/2. In our setup, resale happens invariably from weak to strong
bidders. Note that the weak bidder's value distribution
stochastically dominates the resale price distribution under the
buyer-advantaged resale regime. On the other hand, the resale price
distribution under the seller-advantaged resale regime lies halfway
between the strong and weak bidder's value distributions.
Under the seller-advantaged resale regime, the speculative motive
leads to higher resale prices causing the weak types to bid higher at
the auction stage. Weak bidders who can successfully resell the good
capture a larger surplus. However, the cost of quoting higher final
prices is the increased likelihood of overestimating the (strong)
opponent's value and hence, higher final inefficiency. On the other
hand, there is lack of any significant speculative motive under the
buyer-advantaged resale. This, along with the resale structure that
gives all bargaining power to the strong bidder translates the upper
limit of the weak bidder's support ([a.sub.w]) to an inevitable
upper bound for the resale price. Because the weak type never bids
higher than [a.sub.w] under the buyer-advantaged resale, an offer of
[a.sub.w] from the strong type will always be accepted, leading to
higher final efficiency.
This model leads to the following market behavior arising from the
equilibrium conditions:
PROPOSITION 1. For any asymmetry between the bidders ' value
supports, the equilibrium average bids and resale prices under the
seller-advantaged resale regime are higher than those under the
buyer-advantaged resale regime.
Proof. See the Appendix.
Note that, the equilibrium bids for weak- and strong-type bidders
are in proportion to the ratio of their value distribution, i.e., for a
given value, the weak bidder bids twice as much as the strong bidder in
the S20 treatment and four times as much in the S40 treatment under both
regimes. This pattern arises as a consequence of the equivalence of
bidding strategies between two distinct games leading to the following
property.
SYMMETRIZATION PROPERTY. The bid distributions for weak and strong
bidders are identical within each regime.
Finally, the following proposition provides an efficiency
comparison across regimes.
PROPOSITION 2. Interim efficiency is identical under both the
seller- and buyer-advantaged resale regimes. Higher predicted resale
prices under the seller-advantaged resale regime lead to lower final
efficiency.
Proof. See the Appendix.
Despite the price-efficiency tradeoff established here, the level
of final efficiency remains high across regimes.
III. EXPERIMENTAL DESIGN
Our experimental design incorporates the details of this theory. We
have two types of bidders and two resale regimes. Since our focus is on
understanding bidding behavior across resale regimes, we kept the player
types constant throughout the course of a session. Instructions were
distributed to subjects at the beginning of each session. There were 40
rounds in each session divided equally between the seller-advantaged and
the buyer-advantaged resale regimes. The software was developed using
z-Tree (Fishbacher 2007).
Players received 65 ruchmas (our experimental currency) as the
show-up fee that was used as initial capital in the S20 treatment. For
the S40 treatment, players received 100 ruchmas to account for a larger
disparity in the value distributions of bidders. The conversion rate was
1$ = 13 ruchmas. At the beginning of every session, instructions were
read to the players accompanied by a Power Point presentation. (5)
There were two practice rounds followed by 20 rounds played for
cash under each regime. Valuations were drawn randomly for each round.
The players were reminded of their types at the beginning of each round.
Each player was matched with an opponent of the other type, and the
matching was changed randomly from one round to another. The information
revealed was in line with the theoretical model. Each player knew his
own type and own private value. At the end of the auction, each player
was informed whether he won or not. In the second stage that followed
immediately, the winning (losing) player had an opportunity to make a
take-it-or-leave-it offer to sell (buy) to (from) the same opponent
under the seller (buyer)-advantaged resale treatment. If the player did
not want to sell (buy), he was advised to quote a price of 9999 (0)
ruchmas. Each round concluded with the final payoff displayed to each
player depending on the outcome. The resale rules and players'
value distributions were common knowledge. We did not provide the
players with a history of their bidding or earlier prices, because we
wanted them to treat each round independently as much as possible. The
instructions emphasized that each draw of value was separate. After two
practice rounds (periods) and 20 paid rounds of seller-advantaged resale
treatment, players were informed about the change in resale treatment.
This was followed by another two practice rounds and 20 paid rounds of
the buyer-advantaged resale treatment. A brief questionnaire followed
that asked the players about some demographic information related to
their major, previous experience participating in auctions, risk
preferences, and gender. (6) The player's ending balance was shown
on the screen at the end of the questionnaire. This concluded a typical
session. Players received their earnings in Sooner Sense credit on their
university identity cards, which could be used for purchases around
campus. The players were recruited from the undergraduate and graduate
student population at the University of Oklahoma, Norman campus. For the
S20 treatment, the number of subjects per session varied from 4 to 12
with a total of 68 participants. For the S40 treatment, the number of
subjects per session ranged between 6 and 12 with a total of 54
participants.
IV. RESULTS AND DISCUSSION
A. Descriptive Statistics
In Table 2, we show some of the descriptive statistics from the S20
and S40 treatments. As seen from the table, the average bids and
standard deviations are higher under the seller-advantaged resale regime
than under the buyer-advantaged resale regime.
While bidding in rounds 11-20 is isolated to examine more
experienced bidders, the qualitative results remain the same across.
(7,8)
We also provide a non-parametric test to compare bid distributions
across regimes to test findings in Proposition 1. We employ the
Mann-Whitney test under the null of equality of bid distributions for
the two regimes to test for difference in the location across the two
samples. For both treatments, we reject the null at p<.05 (S20: p
value = .0065 and S40: p value = .0374). Given the results of this test,
the prediction that average bids are higher under the seller-advantaged
resale regime than the buyer-advantaged resale regime is borne out.
[FIGURE 1 OMITTED]
Figures 1 and 2 describe bids as a function of values using box and
whiskers plots for the S20 and S40 treatments, respectively. Graphs are
separated by bidder type and resale regime. The boxes represent the
interquartile range and the whiskers extend up to the outermost data
point within 1.5 times the interquartile range. The solid lines
represent equilibrium bids and the dashed lines indicate bids equal to
values. Overall, the box plots are consistent with the descriptive
statistics showing relatively higher bids and greater dispersion for the
seller-advantaged resale regime and more so as the asymmetries
intensify. Strong bidders bid on average above their equilibrium bids
and shade their bids more at higher values. Because bidding higher than
the weak bidder's highest equilibrium bid is a dominated strategy
for the strong bidder, the observed pattern of bids tapering off for the
strong bidder is consistent with the previous studies (Gueth,
Ivanova-Stenzel, and Wolfstetter 2005) of onestage asymmetric auctions.
Overbidding compared to equilibrium level is a commonly observed
phenomenon in the experimental literature (Kagel 1995). It is also seen
in these graphs, and it is more pronounced among strong bidders. Weak
bidders (9) tend to bid closer to their equilibrium bids except at the
lower end of the value distribution under the seller-advantaged resale
regime.
[FIGURE 2 OMITTED]
B. Bid Deviation from Value under the Prospect of Resale
The equilibrium bidding strategies under a first price auction
imply some degree of bid deviation from value, (10) calculated as
([v.sub.i] - [b.sub.i])/[v.sub.i] for each bidder i. While the
equilibrium bidding strategies under seller-advantaged resale require a
constant proportion of bid deviation for both types of bidders, those
under buyer-advantaged resale require a higher proportion of bid
deviation at higher values.
In Table 3, we present the average degree of actual and predicted
bid deviations from value under both resale regimes for the two
treatments. Weak bidders with lower values, on average, bid above their
values under both resale regimes. Strong bidders do not bid above their
values. Under the buyer-advantaged resale, with only one exception, the
empirical observations are both qualitatively and quantitatively closer
to the equilibrium predictions than in the seller-advantaged resale
case.
C. Symmetrization of Bid Distributions
An important property of the equilibrium is the symmetrization of
bid distributions under both regimes. The underlying idea is that both
weak and strong bidders treat the auction with resale as equivalent to
an auction without resale that has a common value component determined
by the resale stage structure. Hence, we expect the bid distributions
for weak and strong bidders within a given resale structure to be the
same.
The kernel density estimates of bid distributions for weak and
strong bidders under the seller-advantaged and buyer-advantaged regimes
in the S20 and S40 treatments are depicted in Figure 3. The bidding
distributions under seller-advantaged resale for the S20 treatment
(top-left panel) exhibit close similarities to those in Georganas and
Kagel (2011). (11) The bid distributions for weak and strong bidders are
much closer under the buyer-advantaged regime than under the
seller-advantaged regime (see the top-right panel). A possible reason
for this could be the lack of significant speculative motive on the
bidder's part in the first stage. The two bottom panels show kernel
density estimates of the bid distributions for the two bidder types
under each regime for the S40 treatment. The bid distributions for weak
and strong bidders appear quite distinct. A Kolmogorov-Smirnov (K-S)
test provides formal evidence of differences in size, dispersion, or
central tendency. The test rejects the null of no difference between
weak-and strong-type bidder distributions for both regimes and both
treatments at a probability value less than 1%. (12)
The analysis so far has explored qualitative distributional
differences without providing controls for bidder and auction
heterogeneity. Next, we present a quantitative analysis that controls
for unobserved heterogeneity among bidders and differences in auction
and bidder measurable characteristics. We first perform mean level
analysis and then apply quantile regression techniques to investigate
how bidding aggressiveness varies for different values and types of
bidders across the distribution. The basic econometric model of the
relation between values and bids for both bidder types that is derived
directly from the equilibrium strategies is
(1) [b.sub.iat] = [[beta].sub.1] [v.sub.iat] + [[beta].sub.2[
([v.sub.iat] x [A.sub.i]) + [z'.sub.iat] [delta] + [u.sub.iat]
where the unit of observation is a bid submitted by bidder i, in
auction a, in round t of a session. Our dependent variable is the bid
[b.sub.iat]. The value of the bidder i in auction a, and round t is
[v.sub.iat] Ai is an indicator variable that takes value 0 or 1 for a
strong- and weak-type bidder, respectively. Hence, the coefficient
[[beta].sub.2] measures the differential effect of values on bids
between a weak and a strong bidder. The vector z contains a set of
variables used to control for observed heterogeneity across bidders and
auctions. They capture a bidder's attitude toward risk, his/her
gender, academic level, and previous participation in real-life
auctions. It includes indicators of the order of an auction in the
experimental sequence, and the number of available bidders of each type
in a session. We use a random effects model with [u.sub.iat] -
[c.sub.iat] + [[alpha].sub.i]. Considering the possibility that the
standard errors may be underestimated (Moulton 1990), we report
"cluster-robust" standard errors where the clustering is done
by players. (13) The coefficients of our interest are [[beta].sub.1],
and [[beta].sub.2]. As mentioned in Section II, weak bidders bid twice
as much as strong bidders in the S20 treatment and four times as much in
the S40 treatment. Hence, we expect ([[beta].sub.1] - [[beta].sub.2] in
the S20 treatment under each regime and ([[beta].sub.2] =
3([[beta].sub.1] in the S40 treatment.
[FIGURE 3 OMITTED]
A simple quantile regression model allows us to investigate more
systematically how the effect of key controls varies across the
conditional distribution of bids reducing the impact of outlier values.
Because there is a differential effect by bidder type upon bids across
the value distribution, the model can shed light on symmetrization
property. Following Koenker and Bassett (1978) and Koenker (2005) we
propose the following simple quantile regression model:
(2) Q[b.sub.iat] ([tau]|[x.sub.iat]) = [x.sub.iat] [gamma]([tau])
where Q(. l.) is the [tau]-th conditional quantile function,
[gamma]([tau]) = ([[beta].sub.1] ([tau]), ([[beta].sub.1] ([tau]),
[delta]([tau])' is the vector of parameters, and [x.sub.i] =
[[v.sub.iat], [v.sub.iat] x [A.sub.i], [z'.sub.iat]] is the vector
of covariates.
The quantile model is estimated via optimization by finding
(3)[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[rho].sub.[[tau]](u) = u([[tau] - I(u < 0)) is the
quantile regression "check function." We restrict attention to
three quantiles ([tau] = 0.25,0.50,0.75).
In Table 4. we report mean level and quantile regression results
for bids in the seller-advantaged and buyer-advantaged regimes under the
S20 and S40 treatments. We use F-tests of the difference in bidding
intensity between strong and weak bidders under the two regimes to test
for symmetrization. (14) Our results suggest that there is no support
for this theory for the seller-advantaged resale regime, and that is
consistent with other findings featuring similar levels of asymmetries
(Georganas and Kagel 2011). We find, however, evidence of symmetrization
under the buyer-advantaged resale regime in the S20 treatment. In the
S40 treatment, the conditional quantile regression results based on
0.25, 0.5 quantile estimates suggest that bidding distributions are
identical for low-value bidders but a look at the mean and upper
quantile regression estimates makes apparent that this pattern is
breaking down for bidders with high values.
D. Resale Price Comparisons
According to Proposition 1, we expect higher resale prices under
the seller-advantaged resale regime compared to the buyer-advantaged
resale regime. The disparity in resale prices can be perceived as an
indication of speculative behavior on the part of the weak bidder under
the seller-advantaged resale regime that is significantly reduced in the
buyer-advantaged resale regime. The top four panels of Figure 4 show the
kernel density estimates of auction and resale prices by treatment and
resale regimes.
The average realized (predicted) prices in the seller-advantaged
resale regime are 8.17 (7.5) in the S20 treatment and 12.37 (12.5) in
the S40 treatment. The corresponding prices in the buyer-advantaged
resale regime are 6.75 (6.67) and 8.08 (15) (8.00), respectively. Final
prices are expected to increase on average by l2.44%-56.25% depending on
the treatment. The final price differences across regimes are not
matched by final efficiency reductions when one moves from the buyer to
the seller-advantaged resale regime as we will show in the next section.
The probability distribution functions in the bottom two panels of
Figure 4 present a better--more direct--picture of differences among
realized prices across regimes. It becomes obvious that there is a
greater likelihood of high prices in the seller-advantaged resale
regime. The experimental data shows higher resale prices on average
under selle-radvantaged resale as expected and provides support for
Proposition 1. For the S20 treatment, on average, the resale price is
33% higher under the seller-advantaged resale than under
buyer-advantaged resale conditional upon trade in the resale stage (p
value = .0000). For the S40 treatment, the average resale price
conditional on trade at the resale stage is about 28% higher under the
seller-advantaged resale than under the buyer-advantaged resale (p value
= .0012). We further employ Mann-Whitney tests to compare the equality
of resale price distributions under the seller-advantaged and the
buyer-advantaged resale conditional upon trading at the resale stage.
The null of equality of resale prices is rejected for both the S20 (p
value = 0.0032) and the S40 (p value = 0.0104) treatments.
[FIGURE 4 OMITTED]
E. Efficiency Comparisons
We consider two definitions of efficiency. In the first definition
(E-l), we use the ratio of number of outcomes wherein a high-value
bidder wins to the total number of outcomes. In Table 5, we describe the
interim (auction stage) and final (resale stage) efficiency comparisons
for both treatments using data from all periods. (16) Interim efficiency
is predicted to be the same while expected final efficiency is reduced
by 4.54%-12.16% in the seller-advantaged regime depending on the
treatment. Interim efficiency is higher than predicted but almost equal
across regimes for the S20 treatment. The final efficiency levels are
also similar with the seller-advantaged resale registering higher actual
efficiency than predicted. For the S40 treatment, interim efficiency for
both regimes is much higher than predicted. Final efficiency for the
buyer-advantaged resale is relatively higher providing support for
Proposition 2 only in this case.
We also report efficiency calculations based on another widely used
measure. This definition (E-2) employs the average value of the ratio
[v.sub.i]/max {[v.sub.i], [v.sub.-i],}, where the numerator, [v.sub.i],
is the owner's value at a given stage and the denominator is the
maximum of the values of everyone else who is part of the market at that
stage. Unlike E-1, which relies on the count of efficient versus
inefficient outcomes, E-2 focuses on the average magnitude of realized
surplus. In Table 6, we report the predicted and actual efficiencies
based on this approach. Actual interim efficiencies for the S20
treatment are about the same across regimes and similar to the
predictions. Actual final efficiencies are also similar in magnitude for
the two regimes but lower than predicted. For the S40 treatment, the
observed interim efficiencies are higher than predicted and even more so
for the buyer-advantaged resale. The observed final efficiencies are
much closer to the predictions, implying a higher lost surplus under the
seller-advantaged resale compared to the buyer-advantaged resale.
Higher than predicted interim efficiency is the result of strong
(weak) type bidders bidding higher (lower) than the equilibrium level
precluding the need for resale. Getting a closer look at the
price-efficiency trade-off, in selecting a bidding strategy one takes
into account the likelihood of missing a beneficial trade opportunity
which has a high cost (in terms of lost value) across regimes. On the
other hand, distributional asymmetries across bidder types generate an
upper bound for prices only in the buyer-advantaged resale case
increasing price differentials across regimes. The result is a highly
variable price but not much of a difference in final efficiency.
V. CONCLUSIONS
We derive equilibrium bidding distributions in an auction with the
buyer-advantaged resale and compare them to those derived in Hafalir and
Krishna (2008) for auctions with seller-advantaged resale. The shift of
bargaining power from seller to buyer tends to reduce speculative
tendencies on the bidder's part, leading to differential revenue
and efficiency outcomes. Our experimental results show that bids are
indeed higher under the seller-advantaged resale regime than the
buyer-advantaged resale regime across both treatments and the bid
differential ranges between 12.31% and 33.64%. The average winning bids
under seller (buyer) advantage for the S20 and the S40 treatments are
7.61 (6.73) and 12.22 (9.15), respectively. The average auction and
resale prices are higher under seller-advantaged resale while this
increase in prices is not matched by efficiency reductions.
Our model predicts that when the buyer has complete advantage in
the resale market, the average auction and resale prices are the lowest.
Despite the fact that the model and experimental evidence is on limiting
cases of bargaining power distribution, the comparative static
predictions are reflected in the course of RGGI prices over the last 5
years. (17)
In Figure 5, we see a relatively higher ratio of the number of bids
to the number of allowances at the beginning of the RGGI program
reflecting a seller's market. The opposite trend is observed from
December 2009 through December 2012 with a reversal since then. Resale
market prices track auction prices very closely, even more so when the
seller's power is diminishing. Our theory and experimental evidence
shed some light into bids, prices, and expectations for market
efficiency. While prices are expected to fluctuate significantly as
market power shifts hands, inefficiencies are not expected to either be
significant or vary widely.
In our experiments, the actual number of efficient outcomes, both
interim and final, are higher than predicted by the theory generating
small differences in allocative efficiency across regimes (between 0.38%
and 4.82%). Across all cases considered, the minimum amount of surplus
realized is still no less than 93.64%. Our quantitative analysis,
providing controls for bidder and auction level characteristics, offers
some support to symmetrization only in the buyer-advantaged case. In
highly asymmetric cases though, high-value weak and strong bidders
differentiate their bidding strategies.
[FIGURE 5 OMITTED]
ABBREVIATIONS
ETS: Emission Trading Scheme
EUETS: European Union Emissions Trading Scheme
FPAR: First Price Asymmetric Auction with Resale
IPV: Independent Private Value
OTC: Over the Counter
QRE: Quanta! Response Function
RGGI: Regional Greenhouse Gas Initiative
doi: 10.1111/ecin.12120
APPENDIX
EQUILIBRIUM BID DISTRIBUTIONS UNDER THE BUYER-ADVANTAGED RESALE
Proof. Our setup is the same as in Hafalir and Krishna (2008).
There are two risk neutral bidders, bidding in an auction with the
possibility of resale having no liquidity constraints. Bidder i's
private value is drawn from a regular distribution, [F.sub.i], with
virtual valuation equal to [x.sub.i] - (1 - [F.sub.i](x))/[f.sub.i](x),
that is increasing in x, where [F.sub.i], i = s,w is the value
distribution for bidder i. Given this setup, resale happens invariably
from the weak to the strong bidder. The idea that converts this
two-stage game into a single-stage equivalent auction is the
symmetrization property. Assuming that [F.sub.s] (x) < [F.sub.w](x)
for all x, the FPAR is characterized by the following system of
differential equations
(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
It is the same as a first-price symmetric auction without resale
(FPWR) characterized by
(A2) d/db In F [[phi] (b)] = 1 /([phi] (b) - b)
where F(*) is the common distribution derived from [F.sub.s] and
[F.sub.w] defined over [0, [bar.p]]. With [bar.p] as the upper bound of
the price in the resale stage, we derive [bar.b], the highest bid and
then we can solve for bidding functions from the system of differential
equations in (A4).
The problem under the buyer-advantaged regime can be tackled in a
similar way. For the purpose of exposition, we refer to weak bidder as
"he" and strong bidder as "she" in the following
discussion. Note that the weak bidder does not have any control over the
resale price. He can only accept or reject the offer made by his
opponent. The strong bidder knows her own bid, her private value, and
the upper bound of the weak bidder's value distribution. The weak
bidder's value distribution is [0,[a.sub.w]] and [a.sub.w] <
[a.sub.s], by assumption. Hence, it will be suboptimal to offer anything
above [a.sub.w], because all offers above this threshold is strictly
dominated. Therefore, the resale price will be drawn from an interval
[O. [a.sub.w]], which is the same as the weak bidder's value
distribution. Using the idea of equivalence, and given [F.sub.s] and
[F.sub.w] with [F.sub.s] (x) < [F.sub.w](x) for all x, the FPAR is
characterized by the following system of differential equations
(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
which is equivalent to a first price symmetric auction without
resale FPWR characterized by
(A4) d/db ln [F.sub.w](*)= 1/([phi](b) - b)
with [F.sub.w] (*) the common distribution over [0, [a.sub.w],].
For r [greater than or equal to] [a.sub.w], the solution satisfies
the system of differential equations
(A5) d/db ln [F.sub.k] [[phi].sub.k] (b)] = 1/(r(b)-b) [for all]k =
s,w
subject to the following boundary conditions:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For r = [a.sub.w], the solution satisfies the system of
differential equations
(A6) d/db ln [F.sub.k] [[phi].sub.k] (b)] = 1/([a.sub.w] - b) [for
all]k = s,w
subject to the following boundary conditions:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
PROPOSITION 1
Proof. Using the mean value theorem, the average value of bid
function for the seller-advantaged resale is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
For the buyer-advantaged resale, average value of the bid function
is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
It would suffice to show that the difference between these two
expressions is increasing for all [a.sub.s] > [a.sub.w]. The
derivative of this difference with respect to [a.sub.s] is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Because the bid functions for weak and strong bidders are
proportional, a similar exercise would yield identical answers for the
weak bidder's case under both resale structures.
The proof of higher average resale prices follows a similar
reasoning. For seller-advantaged resale, the average resale price is:
(A7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For buyer-advantaged resale, it is:
(A8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Subtracting Equation (A8) from (A7) gives
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
PROPOSITION 2
Proof. Using the equilibrium bidding strategies, the likelihood of
a strong type bidder winning the auction stage under seller-advantaged
resale is:
(A9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Under a buyer-advantaged resale, the likelihood of a strong-type
bidder winning the auction stage is:
(A10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The likelihood of a strong type having a value higher than the weak
type is:
(A11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Thus, interim inefficiency (18) is calculated as the difference
between Equations (A11) and (A9) in the seller-advantaged resale regime
and Equations (All) and (A10) in the buyer-advantaged resale regime.
Showing that interim inefficiency under any of the regimes is exactly
the same requires us to show that expressions (A9) and (A10) are
identical. Subtracting Equation (A 10) from (A9) yields this result.
The likelihood of strong bidder not accepting the offer and having
a value higher than weak bidder constitutes final inefficiency under the
seller-advantaged resale. It is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Holding [a.sub.w] constant, as [a.sub.s] [right arrow] [infinity],
the final inefficiency converges to 1/4 in the limit.
The final inefficiency under the buyer-advantaged resale is given
by the likelihood of a weak bidder not accepting the offer and having a
value lower than the strong bidder. It is calculated as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Holding [a.sub.w] constant, as [a.sub.s] [right arrow] [infinity],
the final inefficiency goes to 0 in the limit.
Hence, the seller-advantaged resale structure leads to the lowest
number of (predicted) trades, whereas the buyer-advantaged resale
structure leads to the highest number of (predicted) trades in the
resale stage. This leads to the respective levels of predicted final
efficiencies and completes the proof.
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SUPPORTING INFORMATION
Additional Supporting Information may be found in the online
version of this article:
APPENDIX S1: Instructions
(1.) Market Monitor Report, Regional Greenhouse Gas Initiative,
2010.
(2.) The urgency to step up efforts to meet carbon reduction goals
was underlined in the 2010 World Bank report that has been revisited by
the news media after hurricane Sandy hit the east coast (see the
Washington Post article by Howard Schneider, November 19, 2012.)
(3.) At the international level, in the climate change conference
of 2011, held in Durban, South Africa, the countries of the EU and a
number of other developed countries have signed up to a second
commitment period of the Kyoto Protocol that ends in 2013. This will
ensure that there is still some form of legally binding treaty in place
to cut carbon emission before the new agreement made by 190
participating countries including the United States, China, and India
takes effect at the end of 2020 (Gray 2011). There have been
speculations about possible market concentrations in the event of
international cap and trade systems developing down the line. It is
suggested that the United States will be a dominant buyer and the
countries from the former Soviet Bloc would be dominant suppliers of
pollution permits under Annex I of Kyoto protocol (Nordhaus and Boyer
1998). This might give enormous leverage to the supplier countries to
exercise their market power and drive up allowance prices.
(4.) Refer to the Appendix for a complete derivation.
(5.) The instructions and presentation are available upon request
(Appendix SI).
(6.) For instance, a question on previous experience read as:
"Have you previously participated in real-life auctions? Please
click yes or no."
(7.) The numbers in the second column represent value intervals for
the weak and strong bidders. For the buyer-advantaged regime, the
bidding strategies become non-linear for values greater than 6.67 in the
S20 treatment and greater than 4 in the S40 treatment. For the strong
bidder, the relevant values are 13.34 and 16 for the two treatments,
respectively. The value intervals are constructed to account for these
cutoffs while splitting the remaining value intervals equally to achieve
a reasonable spread.
(8.) We compare average and median bids by player types to find,
once again, evidence of higher bidding under the seller-advantaged
resale than under the buyer-advantaged resale. All results are robust to
the exclusion of sessions with low number of participants (n = 4.6).
(9.) Georganas and Kagel attribute underbidding by weak types to
negative profits for greater disparity among value distributions.
(10.) It is usually referred to as bid shading. However, in this
case the equilibrium bids could be above or below the value. Hence we
use the term bid deviation here instead. We thank a referee for this
suggestion.
(11.) Georganas and Kagel reject the symmetrization property for
sufficiently large asymmetries similar to the level existing here in
S20.
(12.) We tested the normalized (relative) bid distributions to
control for differences in the theoretical distribution of bids. They
yield similar results.
(13.) We estimated the model using both fixed effects and random
effects. A Hausman specification test indicated that the preferred model
was the random effects model.
(14.) As mentioned earlier, the hypotheses tested are that
[[beta].sub.2] = ([[beta].sub.1] and ([[beta].sub.2] = 3([[beta].sub.1]
for the S20 and the S40 treatment, respectively.
(15.) Seemingly higher auction prices (winning bids) in S40
buyer-advantaged resale are driven by a few high bids in auctions that
did not result in resale.
(16.) The calculations for both tables using periods 11-20 are
consistent with these numbers.
(17.) The proof of the continuity in the price/bidding-efficiency
tradeoff as we vary the distribution of bargaining power between these
extreme cases can be provided by the authors upon request.
(18.) Interim efficiency is obtained by subtracting interim
inefficiency from unity.
CHINTAMANI JOG and GEORGIA KOSMOPOULOU *
* The authors would like to thank the Office of the Vice President
for Research at the University of Oklahoma for financial support. Any
opinion, findings, and conclusions or recommendations expressed in this
material are those of the authors and do not necessarily reflect the
views of the National Science Foundation.
Jog: University of Central Oklahoma, 100 N. University Drive,
Edmond, OK 73013. Phone (405) 974-5225, Fax (405) 974-3853, E-mail
cjog@uco.edu
Kosmopoulou: National Science Foundation, 4201 Wilson Blvd,
Arlington, VA 22230; Department of Economics, University of Oklahoma,
308 Cate Center Drive, Norman, OK 73019. Phone (405) 325-3083, Fax (405)
325-5842, E-mail georgiak@ou.edu
TABLE 1
Equilibrium Bidding and Resale Price Functions
Seller-Advantaged Resale
Strong Bidder (([a.sub.s] + [a.sub.w])/4[a.sub.s])[v.sub.s]
Weak Bidder (([a.sub.s] + [a.sub.w])/4[a.sub.w])[v.sub.w]
Resale Price (([a.sub.s] + [a.sub.w])/2[a.sub.w])[v.sub.s]
Buyer-Advantaged Resale
Strong Bidder (([a.sub.s] + [a.sub.w])/4[a.sub.s])[v.sub.s]
[a.sub.w] - [a.sub.s][a.sup.2.sub.w]/([v.sub.s]
([a.sub.s] + [a.sub.w]))
Weak Bidder (([a.sub.s] + [a.sub.w])/4[a.sub.w])[v.sub.w]
[a.sub.w] - [a.sub.s][a.sup.3.sub.w]/([v.sub.w]
([a.sub.s] + [a.sub.w]))
Resale Price (([a.sub.s] + [a.sub.w])/2[a.sub.s])[v.sub.s]
[a.sub.w]
Buyer-Advantaged Resale
Strong Bidder [for all] 0 [less than or equal to] [v.sub.s]
[less than or equal to] 2[a.sub.w][a.sub.s]/
([a.sub.w] + [a.sub.s])
[for all] 2[a.sub.w][.sub.s]/([a.sub.w] + [a.sub.s])
[less than or equal to] [v.sub.s]
[less than or equal to] [a.sub.s]
Weak Bidder [for all] 0 [less than or equal to] [v.sub.w]
[less than or equal to] 2[a.sup.2.sub.w]/
([a.sub.w] + [a.sub.s]
[for all]2[a.sup.2.sub.w]/([a.sub.w] + [a.sub.s])
[less than or equal to] [v.sub.w]
[less than or equal to] [a.sub.w]
Resale Price [for all] 0 [less than or equal to] [v.sub.s]
[less than or equal to] 2[a.sub.w][a.sub.s]/
([a.sub.w] + [a.sub.s])
[for all] 2[a.sub.w][a.sub.s]/([a.sub.w] + [a.sub.s])
[less than or equal to] [v.sub.s]
[less than or equal to] [a.sub.s]
TABLE 2
Average Auction Bids by Type, Treatment, and
Value Blocks
Player Value
Type Block Seller Advantage Buyer Advantage
S20 Treatment
Rounds All 11-20 All 11-20
Weak 0-3.34 2.60 2.48 2.31 2.32
(2.79) (2.20) (2.12) (2.10)
3.34-6.67 5.18 5.18 4.68 4.66
(1.94) (1.93) (1.61) (1.32)
6.67-10 7.48 7.45 7.04 7.06
(2.00) (2.00) (1.56) (1.37)
Strong 0-6.67 2.70 2.66 2.55 2.43
(1.78) (1.74) (1.62) (1.58)
6.67-13.34 6.76 6.62 6.14 5.91
(2.19) (2.24) (1.83) (1.92)
13.34-20 9.53 9.37 7.78 7.47
(3.20) (3.06) (2.61) (2.48)
S40 Treatment
Rounds All 11-20 All 11-20
Weak 0-4 4.14 2.52 2.04 1.98
(4.70) (2.41) (1.90) (1.78)
4-7 6.85 6.12 4.78 4.72
(4.71) (3.52) (1.60) (1.23)
7-10 9.53 8.99 7.48 7.30
(5.94) (5.63) (2.97) (1.85)
Strong 0-16 5.20 5.26 4.45 4.28
(3.94) (3.41) (3.11) (3.04)
16-28 11.26 10.78 8.95 8.62
(5.72) (5.33) (4.19) (4.16)
28-40 16.81 14.37 12.03 11.78
(9.99) (9.07) (7.11) (6.70)
Note: Standard deviations are in parentheses.
TABLE 3
Average Degree of Bid Deviation from Value
Player Value
Type Block Seller Advantage
S20 Treatment
Bid deviation Actual Predicted
([v.sub.i] - [b.sub.i])/[v.sub.i]
Weak 0-3.34 -3.15 0.25
3.34-6.67 -0.05 0.25
6.67-10 0.10 0.25
Strong 0-6.67 0.17 0.62
6.67-13.34 0.32 0.62
13.34-20 0.42 0.62
S40 Treatment
Bid deviation Actual Predicted
([v.sub.i] - [b.sub.i])/[v.sub.i]
Weak 0-4 -5.52 -0.25
4-7 -0.24 -0.25
7-10 -0.13 -0.25
Strong 0-16 0.10 0.69
16-28 0.48 0.69
28-40 0.50 0.69
Player
Type Buyer Advantage
S20 Treatment
Bid deviation Actual Predicted
([v.sub.i] - [b.sub.i])/[v.sub.i]
Weak -2.95 0.25
0.08 0.25
0.15 0.28
Strong 0.30 0.62
0.37 0.62
0.52 0.64
S40 Treatment
Bid deviation Actual Predicted
([v.sub.i] - [b.sub.i])/[v.sub.i]
Weak -0.59 -0.25
0.12 -0.15
0.11 0.10
Strong 0.37 0.69
0.59 0.71
0.64 0.77
TABLE 4
Mean Level and Quantile Regression Results for
Actual Bids
Quantiles
Variables 0.25 0.5 0.75
Treatment S20 seller-advantaged resale
Value([[beta].sub.1]) .489 * .534 * .589 *
(.014) (.019) (.025)
Value x weak bidder .331 * .323 * .272 *
indicator ([[beta].sub.2]) (.023) (.025) (.032)
p Value ([H.sub.0] : [[beta].sub.2] =
[[beta].sub.1]) .000 .000 .000
Treatment S20 buyer-advantaged resale
Value ([[beta].sub.1]) .394 * .404 * .443 *
(.019) (.021) (.032)
Value x weak bidder .401 * .424 * .389 *
indicator ([[beta].sub.2]) (.025) (.028) (.037)
p Value ([H.sub.0]; [[beta].sub.2] =
[[beta].sub.1]) .858 .658 .417
Treatment S40 seller-advantaged resale
Value ([[beta].sub.1]) .303 * .346 * .435 *
(.029) (.032) (.056)
Value x weak bidder .569 * .546 * .411 *
indicator ([[beta].sub.2) (.041) (.047) (.074)
P Value ([H.sub.0] : [[beta].sub.2] =
3[[beta].sub.1]) .005 .000 .000
Treatment S40 buyer-advantaged resale
Value ([[beta].sub.1]) .200 * .242 * .267 *
(.022) (.023) (.022)
Value x weak bidder .578 * .626 * .596 *
indicator ([[beta].sub.2]) (.040) (.034) (.037)
p Value ([H.sub.0] : [[beta].sub.2] =
3[[beta].sub.1]) .810 .315 .030
Mean
Variables Level
Treatment S20 seller-advantaged resale
Value([[beta].sub.1]) .499 *
(.031)
Value x weak bidder .228 *
indicator ([[beta].sub.2]) (.038)
p Value ([H.sub.0] : [[beta].sub.2] =
[[beta].sub.1]) .000
Treatment S20 buyer-advantaged resale
Value ([[beta].sub.1]) .402 *
(.031)
Value x weak bidder .306 *
indicator ([[beta].sub.2]) (.048)
p Value ([H.sub.0]; [[beta].sub.2] =
[[beta].sub.1]) .167
Treatment S40 seller-advantaged resale
Value ([[beta].sub.1]) .427 *
(.056)
Value x weak bidder .395 *
indicator ([[beta].sub.2) (.089)
P Value ([H.sub.0] : [[beta].sub.2] =
3[[beta].sub.1]) .000
Treatment S40 buyer-advantaged resale
Value ([[beta].sub.1]) .302 *
(.044)
Value x weak bidder .472 *
indicator ([[beta].sub.2]) (.070)
p Value ([H.sub.0] : [[beta].sub.2] =
3[[beta].sub.1]) .017
Notes: Standard errors are in parentheses. N= 1,348 for
S20 SA resale, N = 1,358 for BA resale. N= 1,080 for S40
SA resale and S40 BA resale.
* Denotes statistical significance at the 1% level.
TABLE 5
Allocative Efficiency (E-l) in Percent
Interim Final
Predicted Actual Predicted Actual
S20 seller advantage 75.00 80.71 87.50 90.80
S20 buyer advantage 75.00 80.11 91.67 90.42
S40 seller advantage 62.50 77.03 81.25 87.96
S40 buyer advantage 62.50 79.25 92.50 92.78
TABLE 6
Efficiency Measured by Realized Surplus (E-2)
in Percent
Interim Final
Predicted Actual Predicted Actual
S20 seller advantage 91.67 91.37 97.56 96.40
S20 buyer advantage 92.07 91.73 99.00 96.91
S40 seller advantage 79.70 85.66 93.25 93.64
S40 buyer advantage 81.06 89.34 98.38 97.34
