Silent auctions in the field and in the laboratory.

Isaac, R. Mark ; Schnier, Kurt

I. INTRODUCTION

The American Association of Fundraising Counsel estimates that there was $240.72 billion donated by private individuals, foundations, estates, and corporations to charities in 2003 and that total charitable giving amounts to approximately 2.2% of the gross domestic product (www.aafrc.org/press_releases/ trustreleases/americansgive.html). The total amount raised by charitable or nonprofit organizations includes not only direct contributions but also amounts raised through other activities, such as direct sales, raffles, and charitable auctions. Although the precise amount raised by charitable auctions is not known, the charitable auction is a ubiquitous form of fundraising. Even prior to the advent of Internet auctions as a decentralized form of sales, the multiple-good silent auction was a common form of fundraising for churches and other nonprofit organizations. Today they are still commonly used, and a Web search for "silent auction" will generate over 1.4 million hits, indicating that they are certainly not rare. Despite the frequent use of this auction institution, silent auctions are a relatively new area of research, but one that is certainly deserving of study.

The primary purpose of this article is to investigate and evaluate the performance of the silent auction using data from three naturally occurring fundraising auctions (two from a church, one from a private school) and from a series of six laboratory sessions. Although our ultimate goal will be to examine such standard benchmarks as revenue and efficiency, along the way this requires us to consider other attributes of silent auctions, such as the propensity of individuals to raise their own bid or to submit "jump" bids (bids in excess of the minimum required increment). The theoretical anomaly of jump bidding will be a major component of the investigation. Finally, we will compare our field and experimental results, asking whether our experimental design can serve as a useful test for further auction design research in the area of charity silent auctions.

It should be noted that the silent auction competes as a potential fundraising mechanism not only against other types of auctions but also against nonauction institutions, such as direct contributions or lotteries. We hope that the results we present will inform that discussion, but a comparison with nonauction processes is not a part of this article (and it should be noted that mechanism choice may depend on many things in addition to revenue). (1)

Section II of this article provides a report on the silent auctions and the data that are the basis for the empirical analysis in the paper. Section III presents several organizing models that might provide a useful reference for bidding strategies within the silent auction. Section IV presents analyses of the field data, including both descriptive statistics and formal estimation. Section V presents the design and results of a series of controlled laboratory experiments motivated by the silent auction. Section VI compares the field and experimental results. Section VII offers a summary and some thoughts on additional research on silent auctions.

II. THE SILENT AUCTION AND DATA OBTAINED FOR THIS STUDY

The silent auction, like any auction, is a collection of attributes of the bidders, the items for sale, and the rules for the auction. The following are attributes of a typical silent auction.

* There are multiple goods at auction.

* All items are displayed to all bidders, each of whom is free to bid on any number of the items.

* The auctions are held simultaneously for all goods and close according to a common clock (or, in another variant, to a random device, such as the burning down of a candle).

* The auctions are "silent" oral ascending auctions, that is, there is no auctioneer; each bidder writes his or her new (higher) bid on the item's bidding sheet. (2)

* This "tick" of the auction (above any prespecified minimum) is endogenous to the bidders' decisions in each auction; this allows for jump bidding.

* There is some charitable or public goods component to the seller's revenues.

The implications of some of these attributes merit further discussion.

Multiple Goods

The multiple-goods nature of a silent auction raises a couple of interesting possibilities. As in any multiple-good auction, there is the possibility that bidders have combinatorial values over the items. Yet the silent auction does not allow for combinatorial bidding. An argument can be made that it does allow bidders a chance to "adjust their portfolio" in real time to address combinatorial values. Altough combinatorial values are intriguing, they will not be a focus of this article. On the other hand, we will consider at length the feature of a typical silent auction that the goods are geographically dispersed. It takes time to move from one bidding station to another.

Endogenous Ascending Ticks (Possibility of Jump Bidding)

The possibility of jump bidding in silent auctions makes it similar to many other ascending auctions (e.g., those on eBay and Amazon.com). This is surprisingly unlike much of the prior theoretical and experimental work on ascending auctions. Traditionally, ascending oral auctions have been both modeled by theorists and operationalized by experimentalists as ascending clock auctions in which the experimenter/auctioneer raises the price according to a preset formula, and bidders drop out. (3) Jump bidding is not possible in a clock auction. Also, when a strategizing auctioneer tightly controls the tick, jump bidding is likely to be impossible or rare. When one begins to look at bidding patterns in silent auctions, it is critical that one does not reach conclusions based on a different (and perhaps inapplicable) version of the ascending auction.

Clock Closes the Auction

Most models of ascending auctions do not incorporate clock ending. The silent auction is like eBay and Amazon.com Internet auctions, which close with some form of a clock. For the silent auctions, one must also consider that auctions on multiple items close at the same time.

Seller Revenue as a Public Good

A significant charitable component of silent auctions is the donation (or reduced cost) to the charity of the items for sale at the auction. There is also the possibility of a second level of charity (or recognition of a public good) in a silent auction. Specifically, bidders may place a positive value on greater receipts to the seller, independent of their possession of any of the auctioned goods. An obvious research question is, "Do auctions behave differently when the seller's revenue takes on the attributes of a public good?"

This article reports on data from nine silent auction sessions, where each session actually consisted of an event of numerous simultaneous individual auctions. Three of the data sets are from naturally occurring field auction sessions. The first field auction is a church auction conducted in 1999. This auction was conducted by a large urban church with over 1000 members. The proceeds were used to benefit the church's

preschool. This auction offered 135 items for sale (we included only those that, from the records, appear to have gotten more than one bid). There were 88 active bidders. (4) The second auction was from the same church's 2000 preschool fundraiser. There were 194 items with 77 active bidders. (5) The third auction was conducted in 2001 by a private school. We received data on 181 items with 198 active bidders. (6) We will also report on data from six laboratory experimental sessions, but a discussion of the design is deferred until section V.

III. MODELS

Prior Models of Ascending Auctions

To our knowledge, there has been no comprehensive model of an auction with all of the attributes of the silent auction. The English auction has been extensively modeled, but usually as a single-unit auction and with exogenous ascension of prices. In the independent private values case comes the familiar result that it is a dominant strategy for each bidder to stay in the bidding until his or her value is called, with the exception of the winning bidder, who ceases bidding when he or she is the sole surviving bidder. Some of the attributes that distinguish the silent auction have been modeled separately, as will be discussed shortly.

Modeling for the Silent Auction

At this point, we will state more formally those distinguishing characteristics of the silent auction that might have implications for theoretical models. (7)

a. These are auctions where the revenue benefits a charity. This creates the possibility that the revenue to the seller becomes a public good.

Let [v.sub.i] be bidder i's value on a good, and let r be the revenue to the seller. Then, using a simple quasi-linear formulation, we can represent the utility to the winning bidders as [v.sub.1] - r + [u.sub.1](r), and to the losing bidders as [u.sub.j](r). Depending on the sum of the benefits for the public good, this could describe a classic free-riding situation, in which bidders, responding to private benefits, produce an inefficient level of the public good. Notice that unless there are side payments, a single person, the winning bidder, must bear the burden of providing the public good.

There are two possible scenarios by which such a public goods nature of the auction revenue could affect observed bidding behavior. One possibility is that in equilibrium, the bid functions of bidders are altered. (8) The second possibility is that, apart from the equilibrium bid incentives, bidders behave differently in the presence of a public good. This would be an extension of the well-documented fact that, in voluntary contributions public goods situations, provision of the public good is usually greater than the equilibrium (free riding) prediction. (9)

b. The multiple auctions are simultaneous.

To switch bidding attention from one item to another, the bidders have to move from one part of a room to another. The bidders cannot follow the bidding on distant multiple items at the same time. The passage of time between submitting a bid on one good and then submitting a bid on another good can be nontrivial, depending on the geographical layout of the auction room. This could lead to an inefficiently low-valued buyer winning an auction.

c. All auctions end with a clock.

Roth and Ockenfels (2002) have modeled two different versions of Internet ascending auctions with clocks. One version is a hard stopping clock (such as with eBay) the other is a flexible clock that remains open with late bidding activity (such as with Amazon.com). Their data confirm that the clock rule matters; specifically, there is more late bidding with the hard stopping rule.

In the church auctions the clock was preannounced and was the same for all items in the room. In the private school auction, ending times differed for different parts of the room. Because the ending time was not tied to bidding activity, there is the possibility that for any given item there are multiple bidders still active (that is, with values greater than the price on the bidding sheet) at the closing bell.

d. Jump bidding is possible.

Jump bidding is not only possible in an ascending auction, it may be an equilibrium, despite what one might expect from the clock formulation of the English (single-unit) ascending auction. Different theoretical questions must be asked. When a bidder is allowed to jump above the minimum tick, why would he or she do so (or not)? How much should he or she jump the bid? Most of the models that have addressed these questions have some overlap with the silent auction, but none covers all of the components. Rothkopf and Harstad (1994) consider a single-unit auction and a decision-theoretic bidder choosing an optimal bid increment. Depending on the distribution of bidder values, jump bidding is a possible outcome. Borgers and Dustmann (2004) have analyzed the data from a third-generation ascending wireless auction in the United Kingdom where jump bidding was possible. They point out that "straightforward bidding" (rational choice of items for bid plus no jump bidding) is an equilibrium but not a dominant strategy. Isaac et al. (2005) model a single-unit auction where jump bidding is not a typical signaling phenomenon but rather reflects either equilibrium strategic considerations, bidder impatience, or both. Even though their model has no clock, the possibility of bidder impatience may very well also capture the uncertainty imposed by the geographic dispersal of the bidding stations in a silent auction. Plott and Salmon (2004), studying both field data from U.K. wireless auctions and related experimental auctions, also conclude that the primary function of jump bids seemed to be speeding up the auctions. Speeding up the clock time of a silent auction is not possible, but jump bids could speed the generation of market information, which can be valuable as bidders must decide which auctions they want to monitor as the clock closes. Thus, the effect of speeding up the pace of the bidding (as opposed to speeding up the end of the auction itself) may be valued by a bidder. (10)

IV. THE FIELD SILENT AUCTIONS

Data Available for Analysis in the Field Silent Auctions

The data we collected from the three field auctions include a description of the goods, the bids in the order in which they were submitted, the minimum opening bids, the minimum bid increments, and a bidder ID number. Obviously, these data categories leave much to be desired from the point of view of evaluating models of individual behavior in such auctions. Most important, we largely have no information on bidder values (except for the retail value of a few items or gift certificates). (11) What we can construct from these data series are the jump bids. The jump bids will form the core of our analysis.

Jump Bids in the Silent Auction and the Received Models

Drawing upon the general design of silent auctions and the existing models, we can sketch four possible avenues by which jump bids could be a rational (even equilibrium) bidder choice: charitable, "see and be seen," impatience, and final-seconds crowding.

First, we consider two models in which the propensity to jump bid occurs at least partially in response to the public goods nature of the seller's revenue. In the simple charitable version the bidders value the seller's revenue regardless of who won the item. This means that in the model we introduced, u([r.sub.1]) = u([r.sub.j]). A variant of the charitable model also deserves some attention. These auctions are highly public. A large number of the bidders know each other. Bidders can watch which tables other bidders are visiting. And, although a bidder number is used in lieu of bidding by name, our impression is that these codes are only marginally private. This leads to the related concept that bidders raise prices in the auction not so much to encourage the production of the public good (the seller's revenue) per se but rather to see and be seen, specifically, to be seen as the person responsible for the seller's revenue. (12) In terms of the previous model this means, at the extreme, that u([r.sub.j]) = 0. As mentioned, several papers have modeled individual bidding behavior with charitable preferences in auctions. In second-price auctions, the analog of either the simple charitable model or the see-and-be-seen model leads to higher bid functions in second-price auctions. (13) In the strategically equivalent English auction, this can lead to bidding over the "value" (absent the charitable effects). By themselves these models do not address the issue of the influence of these factors on jump bidding. However, the results of Isaac et al. (2005) are suggestive that an increase in a bidder's limit value would increase jump bidding. (14)

Second are what we can call the two crowding models. One is similar to the models of jump bidding developed for single unit auctions: bidders are impatient to speed up the pace of the auction (which does not have to involve speeding up the close of an auction, an impossibility in silent auctions). Impatience could have the same origins as in single-unit auctions, or it could be specific to the silent auction (perhaps an impatience to obtain a geographic advantage). The results of Isaac et al. (2005) are that (with a single unit) impatience can play an important role in increasing the incidence of jump bidding. However, the geographical dispersion of the multiple units in a silent auction suggests a second crowding model: namely, that jump bidding represents a response to the fact that in the final seconds of the auction, a bidder may decide to "leave" a table, requiring him or her to enter what is, in essence, a final "sealed bid." (15) We call this hypothesis the "final seconds crowding" model.

Statistical Analysis of the Field Auctions: Descriptive Statistics

Table 1 offers the summary descriptive statistics on jump bidding. The following are some observations and implications for the data in Table 1.

Bidders Never Jump Their Own Bids. In a standard English auction framework, this would represent a minimal standard of rationality. However, jumping one's own bid might be part of a strategy for charitable bidding, see-and-be-seen bidding, or dealing with last second crowding.

Bidders seldom bid over publicly stated market values for items, although there is a difference in frequency between the church auctions and the school auction. Bidding over a clear market value could be a strong indication of either charitable or see-and-be-seen bidding, based on the arguments already presented. This kind of overbidding never happens in the church auctions, but it happens around 10% of the time in the school auction. Furthermore, in the school auction about half of the bids that exceeded stated value exceeded it by more than a minimum increment. The data in Table 1 report this measure only on items for which there were a clearly identifiable retail value (more common in the school auction). (16)

By themselves, the two observations are not suggestive of a strong presence of either charitable or see-and-be-seen bidding in the church auctions, with more ambiguity in the school auctions.

Bidders Frequently Submit Jump Bids. There is a major difference in the frequency between the church auctions (38.55% and 37.09% of all bids) versus the private school data (8.92%). As with any uncontrolled comparison with field data, there could be numerous suspects for this effect, ranging from the bidding population to the different auction lengths and differences in details of the auction environment. However, we note here one difference for particular attention: The size of the church auctions' minimum bid increment was substantially lower than that used in the school auction. Most items auctioned by the church used a minimum increment of $1, whereas at the school auction the minimum increments were usually either $5 or $10. We will examine this effect more formally during the parametric analysis.

Figure 1 displays the propensity of individual bidders to jump bid in the 1999 church auction, the 2000 church auction, and the 2001 school auction. This graph is a histogram in which an observation is a mean level of bid increments for a single bidder across all the bids that bidder placed in all the auctions that evening (we use a normalization that is relative to the minimum bidding increment). (17) The distribution is on percentage of all bidders in the auction. A Komolgorov-Smirnov test indicates that one cannot reject the hypothesis that the distributions in the church auctions in 1999 and 2000 are the same. One interesting property of these empirical distributions is that most of the bidders average $1 or less, with a general pattern of tailing down. However, in two of the cases there is a bump of bidders at relatively large levels apparently aggressively pursuing jump bidding.

[FIGURE 1 OMITTED]

Parametric Analysis of Jump Bidding in the Field Auctions

We now attempt a parametric analysis of jump bidding by item. The results were only partially successful because the estimations explain only a small part of the variation. Nevertheless, certain of the results appear to be robust and are informative to the question of bidder behavior. For each night of auctions (i.e., Church 1999, Church 2000, and School) we conducted two estimations: a probit analysis of the incidence of a jump bid of any magnitude, and a tobit regression on the magnitude of the bid increment. (18) The regressors included and a discussion of why they are of potential interest are as follows.

Number of Bidders. In the theoretical models of charitable behavior in the second price auction, the equilibrium limit bid levels typically do not vary with the number of bidders. However, the number of bidders effect has not been worked out for the question of jump bidding in an ascending auction given the bidder's value. If charitable bidders are hoping to increase the amount paid to the seller, they may set a target value for an item that they are willing to pay, even if the bidding of others in an ascending auction stops before that point. (Note that this implies a slightly different structure to charitable bidder preferences than the models discussed previously.) If this is the case, a bidder may be more inclined to use large jump bids if there are only a small number of other bidders. If there are a large number of other bidders, they may be more likely to free ride on the bids of others. If bidders want to see and be seen, do they care only about the final outcome of the auction (the assumption of the models), or do they also care about being seen as raising the bid as the ascending auction unfolds? If the latter, they would presumably engage in more flamboyant bidding in front of a larger number of other bidders. If bidders are impatient, one could make an argument about the effect of the number of bidders either way (again, Isaac et al. 2005 model only the case of two bidders). If individuals are worried about final-seconds crowding as the clock ends the multiple auctions, they will presumably be led to engage in more jump bidding the more crowded is that auction. (19)

Dummy First Bid; Dummy Second Bid (The Bid Is the First One in an Auction). Large initial jump bids right out of the gate would be more explicable for charitable bidders wanting to increase the seller's revenue, for bidders wanting to be seen as charitable, and for impatient bidders wanting to speed up the price ascension. We would not expect it to be a feature of final-seconds crowding. (20) It might be thought that this would be an easily measured variable. However, as we were analyzing the data, we discovered that the bid sheets (at least for the church auctions) were ambiguous as to whether jump bidding was possible on the first bid. Indeed, the incidence of jump bidding on the nominal first bid is very low. Thus, both variables are included, with the expectation that Dummy Second may be the operational first bid.

Dummy Last Bid (The Bid Is the Last One in an Auction). Large final jump bids would be consistent with the standard charitable model, with see-and-be-seen bidding, and with bidders worried about final-seconds crowding. It would not make as much sense for a phenomenon of bidder impatience.

Dummy "Craft." This is a somewhat arbitrary variable with the following background. One of the authors, when examining the description of the items at the church auction, noticed that some of them were actually made or created by members of the congregation, in some cases even by groups of children. This raises the possibility that bidders might have a specific, magnified charitable interest in increasing the sales prices on these items, or in being seen to make large bids on them. We also included "Dummy Craft x Dummy First," "Dummy Craft x Dummy Second," and "Dummy Craft x Dummy Last." (21)

Bid Sequence. This is a proxy for how far along in the auction the bidding is. Recall that these field data sets are not time stamped, so we don't know the clock time. However, we can measure, for example, in an eventual 14 bids, whether the bid was second or tenth out of 14. One would expect that attempts to speed up the bidding would occur, almost by definition, early on. Indeed the theoretical model of Isaac et al. (2005) shows jump bidding continues into the auction but decreasing as the auction progresses.

Jump bidding aimed at final seconds crowding would presumably increase as bid sequence increases. The effect on charitable activity is hard to pin down, and a see-and-be-seen model should show no effect.

Lag Bid. This picks up an effect on jump bidding as the revealed value of the goods increases either in time or across goods. A charitable bidder ought to be no more likely to submit a jump bid on an item that has already moved high up in the bidding. The pooling of the cross-sectional and time-series component makes the implications for speeding up the auction ambiguous. (22) Likewise, one could tell different stories about final-seconds crowding. Lag bid would seem to be of no import for the see-and-be-seen model.

Lag Jump Bid. A bidder worried about final-seconds crowding would presumably respond to the perceived jump bidding behavior of other bidders. One would expect that response to be positive. For a bidder hoping to increase the revenue of the seller, that effect should be negative (higher jump bidding by others means that I don't have to jump bid as much). For someone there to see and be seen, there should be no effect. Again, the effect on impatient bidders seems to be ambiguous. (23)

Value Variables. At the school auction, most items had a stated market value. So in only these auctions we included "bid/value" and "minimum increment/value" variables. These two variables would appear to have an ambiguous impact on the see-and-be-seen bidders or the bidders seeking to increase seller's revenue, with one exception. Bidders wanting to increase revenue to the seller might not be as aggressive when they see that the ratio of bid to value is high. These variables may have implications for impatient bidders. As "minimum increment/value" increases, jump bidding should decline (because small minimum increments would be most likely to understate the bidders' desired pace of the auction). One might make an argument either way for "bid/ value." The same predicted effects, but for slightly different reasoning, would be true for bidders worried about crowding in the final seconds. (24)

These expected effects are summarized in Table 2 for each of the models. The estimation results are presented in Table 3. (25) A comparison between the expected effects and the actual effects is produced in Table 4 (where an x indicates an inconsistency between prediction and estimate).

The follow observations can be drawn from the estimations.

* The number of bidders appears to have a negative effect on the incidence of jump bidding and on the magnitude of the jump bids. There is a negative sign on the coefficient in five of the six estimations (four of the five are significant at [alpha] = 0.05).

* Being the first bid (particularly as measured by the "Dummy 2" variable) is positively associated with both the incidence and the magnitude of jump bidding (significant in only two cases). The coefficient on the last bid dummy is of mixed sign and significance (positive in five cases, significant in only one).

* The variables relating to craft items appear to be playing a statistically significant role in several of the coefficients in the second church auction, but not the first. In terms of the sign, in the second church auction the craft auctions appear to generate a greater jump on the first and last bids but a smaller jump in between.

* Lag bids play a significant role in church auction estimations, but with the opposite signs in the church rather than the school auctions. In the church auctions, as the previous bid went up, so did the subsequent jump bid. The opposite (and insignificant) effects in the school could be due to the fact that the school auctions had enough observations with an announced value that we incorporated in the regression several value variables not included in the church auctions.

* The lag of jump bids does not appear to be a consistently signed or consistently significant factor.

The value variables were estimated only for the school auctions, where they show up significantly (the ratio of bid to value positive and significant, the ratio of minimum increment to value negative and significant).

Interpretation of the Statistical Results

We now turn to interpretations of the statistical results. Both the descriptive and parametric analyses suggest several broad conclusions. First, the data suggest that no single model significantly describes all the data, and there are results consistent with each model. (26) This should be expected. There is no reason that any one bidder could not simultaneously be a charitable bidder who also is worried about final-seconds crowding, and so forth. Different bidders may have different characteristics within a category (such as differences in degree of charitable preferences). The differences between the church auction and the private school auction also stand out, and we will discuss them separately.

In the church auctions, a striking result is the predominance of (often significant) negative coefficients on the number of bidders. As the number of final bidders goes up, we find less jump bidding. This is a relatively supportive result for the charitable model (one can free ride more on a multiplicity of other bidders). It is a negative result for the proposition that bidders want to be seen raising the price (why jump more when you are seen by fewer people?). It is also a negative result for the model of final-seconds crowding (more bidders should induce more crowding and hence more jump bidding). We had said that the effect was ambiguous for the model of impatient bidders. The negative sign suggests that if the price is moving up steadily due to a stream of bids from a large number of bidders, there is less need to jump.

Similarly, all "Dummy Second" coefficients are positive, although the coefficients are not statistically significant. This weakly supports the charitable, see-and-be-seen, and impatience models. There are mixed results on the question of final bid effects.

There is not much else in the estimations for the church auctions that provide consistent support for the charitable model or the see-and-be-seen model. Especially in the 1999 auction, the models of bidder impatience seem to work the best. However, there is some indication in the 2000 church auction that the net effect of a craft item was to lead to more jump bidding in auctions with fewer bidders (compare the direct effects of the craft coefficient with the crossed effects). This effect is somewhat plausible. If a craft is produced by fifth-graders, it may get a big jump out of the gate and again at the last if it has not seen a lot of action during the auction. This suggests a modified form of the charitable model in that some bidders care that some specific goods receive a high price.

We turn next to the school auctions. Recall that the descriptive statistics reveal that jump bidding is substantially less common. In the parametric results, there are both similarities and differences with the church auctions. As in the church auctions, the number of bidders is also significantly negatively related to jump bidding, and the dummy variables for first effects are positive and significant. There are no craft variables in the school auctions. "Lagbid" has the opposite sign (negative and insignificant) in the school auction, but that needs to be interpreted in light of the additional information available in the school auction regression, namely, a stated value for each item. The existence of the stated retail values allows us to include value-related variables directly in the estimation ("lagbid" may have been a proxy for value in the church auction estimations). In the school auctions, jump bids are negatively and significantly associated with the ratio of minimum increment of bidding to stated value. This is consistent with an argument that impatient bidders can substitute jump bids or higher minimum increments as a way of speeding up the pace of an auction or for dealing with final-seconds crowding. Also, jump bids increased as the ratio of bid to value increased. This seems to argue against only the charitable model.

As in the church auctions, the estimated coefficients coincide well with the predictions of the model of bidder impatience. In addition, it seems that it is only in the school auctions that the see-and-be-seen model performs well. The additional evidence for this assertion is that in the school auction 4-5% of the items sold at prices exceeding the stated value by more than one bidding increment. We believe that it would not be controversial to describe the school auction as more of a social event, drawing more secular philanthropic leaders. The church auction was more informal, and bidders were largely church members and affiliates who interacted frequently. Finally, a noticeable difference between the two locales is that the final-seconds crowding model appears to work less well in the school auction. This is interesting because the school auction managers closed the auction in slightly divergent rounds (staggered approximately 10 minutes or so) by clusters of tables. This system was known to the bidders. The strategic problems of a single closing time in geographically dispersed auctions may have been ameliorated in comparison with the church auctions, which used a single closing time for all items.

In summary, the behavior of bidders in all of these auctions meets minimum standards of rationality. There are many jump bids, especially in the church auctions, but they are largely clustered at smaller levels where their economic significance is likely to be minimal. However, in each of the auctions, there are a small number of bidders averaging higher levels of jump bidding. Jump bids seem to be a means by which impatient bidders can accelerate the pace of the auction and/or deal with end period effects. There is some evidence of the two types of charitable behavior, but it is limited.

V. SILENT AUCTION LABORATORY EXPERIMENTS

Experimental Design

One of the most binding limitations of field data is that we do not know the values that the bidders placed on any of the items. (27) Value information is needed to answer such questions as: "Do bidders in a silent auction bid over their values?" and "Is the auction efficient?" and "Is there something in the nature of the bidders' values that explains jump bidding?" Also, idiosyncratic effects of individual bidders are difficult to address without value information.

From our discussion of the nature of the silent auction and what we hope to learn from experiments (informed by the field data), we conclude that there are four obvious potential treatments of an experimental design for ascending auctions, as follows: single or multiple units at auction, exogenous or endogenous tick size, clock close or activity close, public goods valuation or not. (28) The silent auction, by its very nature, solves some of these choices. Silent auctions are invariably multiple good, have an exogenous minimum bid increment but allow bidding beyond that increment, close auctions by a clock (or similar device), and typically occur in the context of a public good or charity. Therefore, our choice of an experimental design will stay within those parameters.

Values of each of the aforementioned attributes could be varied systematically as a design treatment or held fixed throughout the research. In addition, the induced bidder values are a critical consideration. In the experiments reported here, we chose and held constant the number of bidders in each session (8), the number of goods at auction (16), the number of auctions per session (5), and the clock time for each auction (12 minutes). Within a session, random draws were used to assign the number and identity of bidders who valued a good (redrawn for each good and each period) and the values themselves (redrawn for each bidder, for each good, and each period). These valuations were replicated in each of the six sessions. We chose two treatments for this phase of the research: minimum bidding increment (varied between sessions) and the extent of induced charitable public goods value on seller's revenue (varied within a session by period). The across-session comparison on minimum increment is represented by three sessions with a 25-cent minimum and three sessions with a 50-cent minimum (maximum value on each good was $20). The within-session comparison on public goods value was instituted by a NNYYN sequence in each session, where N represents an auction period in which there is no induced public goods value and Y represents that there is for some bidders an induced public goods value. In the Y periods (that is, periods 3 and 4), each bidder received a privately disclosed additional earnings amount, which was a percentage of the total seller revenue for that period. Four individuals had no induced public goods value, two received 1%, and two received 5%. In other words, the total induced "charitable" public goods value was 12% of whatever total revenues were received by the seller for that period. (29) Table 5 is a summary table of the experimental design. Figure 2 presents the standard geographical dispersion of auction stations we used during the experiments. Sample instructions are available online at http://mailer. fsu.edu/~misaac/rsrcinst.pdf.

[FIGURE 2 OMITTED]

Experimental Results

Descriptive Results. We begin by presenting in Table 6 descriptive results with the field data compared side by side with the experimental data. We also present statistics that are available only from the laboratory data: market efficiency and relative revenue generation. The index of efficiency is calculated by looking at actual resale values for the winners divided by the maximum of the induced values. For the public goods periods, we do not include the induced public goods values. The revenue comparison is actual seller revenue received divided by the second highest value. For these calculations, we make the calculations primarily at a level of aggregation such that one period in one session is one observation. However, in parentheses, we have included the same calculations where each individual auction is an observation. Figures 3 and 4 present the same histogram as Figure 1 for the field data; that is, an observation is the mean level of bid increments for a single bidder across all the bids that bidder placed in all the auctions that session. The distribution is on percentage of all. bidders in the auctions. The data are disaggregated into Figures 3 and 4 because the 0.25 minimum increment sessions display a different pattern than the 0.5 minimum increment sessions, as we will discuss later. Finally, in Figure 5 we present the time series of the number of jump bids across time (coded into 15-second intervals). Note that Figure 5 presents the number of jump bids, whereas Table 6 talks about the percentage of bids that are jump bids.

[FIGURES 3-5 OMITTED]

The following is a statement and discussion of observations about the descriptive statistics.

* Bidders seldom jump their own bids.

* Bidders seldom bid over their induced values for items.

* Bidders frequently submit jump bids, and the frequency depends on the treatment.

These observations are essentially the same as with the field data. Note that the existence of the public goods values seems to make little difference in either jumping one's own value or in bidding in excess of induced value. In terms of the incidence of jump bidding, inspection of the four treatments suggests some variation. A chi-squared test easily shows at the 0.05 level of significance that the individual frequencies are not replicates of the overall mean. The difference in means indicates that there is less incidence of jump bidding with the higher minimum bidding increment and a greater incidence of jump bidding with the public goods values. A similar test indicates that the differences in the proportion of bids that are a jump of the bidder's own bid or which are in excess of value are not significant.

* These auctions are moderately efficient, and the level of aggregation makes little difference.

Although the efficiencies (~95-98%) may be slightly lower than we might expect from other experiments with single object ascending auctions (~99%), (30) they are still capturing about 91-95% of the surplus relative to random assignment. Recall that these auctions are allocating 16 goods in 12 minutes. A two-way analysis of variance on the efficiency results yields the following. The p-value for the public goods treatment was 0.57; the p for the minimum increment treatment was 0.07. The 0.5 minimum increment auctions had higher efficiencies, on average, than the 0.25 minimum increment auctions. (31)

* The revenue index is highly dependant on the level of aggregation.

With the greatest level of disaggregation, the calculations are especially sensitive to a small number of cases in which a winning bidder pays well above a low second-highest value. Greater aggregation is arguably more useful to anyone wishing to choose an auction mechanism, and at this level we see that the silent auction entails a nontrivial amount of absolute revenue loss. In a two-way analysis of variance, the p on the public goods treatment is 0.77; the p on the minimum increment treatment is 0.02. The 0.5 minimum increment auctions had higher revenue, on average, than the 0.25 minimum increment auctions. Of course, although we cannot measure here the forgone revenue against cost saving features of the charity auction, it does suggest that it would be interesting for future research to consider changes in the silent auction that might enhance revenue while preserving its favorable attributes. (32)

* Bidders use jump bidding more aggressively in the experiments with the lower minimum bid increment. This is seen clearly in Figures 3 and 4.

* Jump bids occur throughout the auction; the experiments with the higher minimum increment are more "front loaded."

Contrary to the family of signaling models, jump bids are not confined to the very first bids in an auction. In fact, Figure 5 shows that jump bids occur throughout the auctions. It is interesting that the auctions with the higher minimum increment appear to peak earlier in the auction. This is a pattern that appears to be consistent with the Isaac et al. (2005) model of jump bidding, which features strategic and impatience motives for jump biddings.

Parametric Results. Tables 7 and 8 present the companion regressions to those we ran on the field data. These estimations are conducted with a random effects framework. The overall goodness of fit is measured using a pseudo-[R.sup.2] (Wald) measure developed by Magee (1990). Many of the variables are constructed in the same fashion as in the field (e.g., number of active bidders, dummy last, and so forth). Some of the variables are modified (values are now known and controlled by the experimenter and we now know actual clock time). (33) Many of the results are strikingly uniform across the four categories. Jump bidding decreases as the bid on the floor gets closer to the bidder's value (eight coefficients significant). This is very consistent with an impatience model of bidding. There is a similar effect that jump bidding declines as time remaining in the auction decreases (five coefficients significant), which argues against final-seconds crowding explanations. However, last bids tend to have higher jumps (four coefficients positive and significant), which is more consistent with final-seconds crowding. In addition, we were able to construct a variable that measures how "occupied" a bidder was; that is, how many items each bidder had in play elsewhere when making a bid. This variable is labeled "N of Objects." The crowding model would predict a positive relationship, which indeed is the case in six of the estimations. However, that coefficient is statistically significant in only three cases. Finally, the effect of the number of active bidders is negative in seven of the eight regressions, and it is significant in roughly half.

The remaining values present more heterogeneous results. The first-period effects are mixed. The effect of previous jump bidding is usually negative but seldom significant. Surprisingly, the intragroup effect of minimum increment related to object value is typically negative but not significant.

We summarize our conclusions about the laboratory experiments as follows. The strong tendency is for jump bids to decrease as the bid on the floor approaches value, the tendency is for bids to decline across clock time, and the intergroup minimum increment effects are all suggestive that something in the nature of silent auctions induces a type of impatience on the bidders. The evidence is mixed on whether there is a separate effect due to end-period crowding. Indicators for the charitable model are that the number of bidders has a negative effect, and there is an intergroup effect on jump bidding based on induced public goods values. However, there is no similar intergroup difference on bidding over value. (34) It is doubtful that there would be any home-grown motivation for see-and-be-seen behavior.

VI. COMPARISON OF THE FIELD AND EXPERIMENTAL SILENT AUCTIONS

There are numerous similarities between the field data and the experimental data. In both environments, bidders seldom raise their own bids, but jump bids are common throughout the auctions. In terms of the parametric estimations, jump bidding is negatively associated with the number of bidders and with measures of progression of the auction.

A few differences between the field data and the experimental data stand out. First, in the school auction a respectable number of bids were above the stated values. This could be because the stated values did not correctly capture a true value, or those values could be accurate and these bids could, in fact, be above value. If the latter is correct, this could be direct evidence of either charitable behavior or of the desire to be seen as being a high bidder in the school auctions. Second, the distribution of jump bidding by bidders in the field auctions looks more like the 0.5 minimum increment experimental auctions.

As a summary comparison, we present in Table 9 the regression results from the two comparable environments: the 2000 church data and the 0.5 public goods experiments. We chose a church session because the incidence of jump bidding is closer to the laboratory sessions. We chose the 0.5 laboratory data because the distribution of bidders by jumping activity is more similar to the field pattern. For the laboratory data, we present two different regressions. The first is the laboratory data using only regressors we had in the field. The second is the laboratory data taking advantage of our additional possibilities of observation and control in the laboratory experiments; that is, the last column represents both the different data and the difference in our ability to observe and define regressors. Notice that field and laboratory estimations look similar when using the "field" form of the estimation. This suggests that the model we used in the field captures similar patterns in the laboratory data. However, notice that, in the third column, two of the new variables about individual bidder values and items in play are statistically significant, and the pseudo-[R.sup.2] is higher. This demonstrates the value of the additional and more disaggregated information of the laboratory that was not available in the field.

VII. SUMMARY AND CONCLUSIONS

The silent auction is a staple of American charitable fundraising. Given economists' recent experiences with and interests in the evaluation of auctions, it would seem logical to visit the silent auction. Obtaining data from three silent auctions, we have documented that this is a mechanism that transacts the sale of a large number of items in a short period of time, without the expense of professional auctioneers or auction designers. However, the field data do not allow for direct observation of bidder values, so that efficiency and revenue performance are unobservable. What we can observe is bidding. A striking feature is the presence of jump bidding. There is no reason to believe that only one model describes regularities in the jump bidding, however, there is persistent support for the conjecture that bidders jump because they are impatient. (35) There is some support for models of direct and indirect charitable activity. Our inability to observe value directly also hinders our ability to model jump bidding.

Laboratory experiments allow us to recreate essential features of a field silent auction in an environment of greater control and observability. The data from the experiments are remarkably similar to the field data in those dimensions that can be observed in both. In the laboratory alone we can measure efficiency and relative revenue generation of the auctions. We found that the silent auctions were moderately efficient but were somewhat under the standard competitive benchmark, a benchmark that has been approximated in previous single-item auctions with both single and multiple units. Finally, several of the outcomes differed depending on the minimum bid increment in the auction. For our design, the 0.5 minimum increment experiments had higher efficiencies, greater revenues, and a different time path and distribution of jump bidding than did the experiments with a 0.25 minimum bid increment. In general, it is the 0.5 minimum increment data that seem to most resemble our field data.

In addition to what we have learned immediately, these experiments establish that it is possible to construct a laboratory experimental design that acts as a credible test for research on silent auctions. Having done so, one can turn to additional research on such topics in silent auction design as the effects (on efficiency and revenue) of larger minimum increments, more extensive public goods preferences, alternative structures of public goods preferences, staggered closing times, or changes in the silent auction itself. We are currently investigating the performance of a sealed-bid version of the silent auction.

REFERENCES

Andreoni, J. "Impure Altruism and Donations to Public Goods: A Theory of Warm Glow Giving." Economic Journal, 100, 1993, 464-77.

Avery, C. "Strategic Jump Bidding in English Auctions." Review of Economic Studies, 65, 1998, 185-210.

Borgers, T., and C. Dustmann. "Strange Bids: Bidding Behavior in the United Kingdom's Third Generation Spectrum Auction." Economic Journal, 115, 2005, 551-78.

Coppinger, V. M., V. L. Smith, and J. A. Titus. "Incentives and Behavior in English, Dutch, and Sealed-Bid Auctions." Economic Inquiry, 18, 1980, 1-22.

Cox, J. C., B. Roberson, and V. L. Smith. "Theory and Behavior of Single Object Auctions," in Research in Experimental Economics, vol. 2, edited by V. L. Smith. Greenwich, Conn.: JAI Press, 1982, 1-44.

Daniel, K., and D. Hirshleifer. "A Theory of Costly Sequential Bidding." University of California, Los Angeles, 1977.

Davis, D. D., L. Razzolini, R. Reilly, and B. J. Wilson. "Raising Revenues for Charity: Auctions Versus Lotteries." Virginia Commonwealth University, 2003.

Engelbrecht-Wiggans, R. "Auctions with Price Proportional Benefits to Bidders." Games and Economic Behavior, 6, 1994, 339-46.

Engers, M., and McManus, B. "Charity Auctions." University of Virginia, 2002.

Isaac, R. M., T. Salmon, and A. Zillante. "A Theory of Jump Bidding in Ascending Auctions." Forthcoming in Journal of Economic Behavior and Organization, 2005.

Isaac, R. M., J. M. Walker, and A. W. Williams. "Group Size and the Voluntary Provision of Public Goods: Experimental Evidence Utilizing Very Large Groups." Journal of Public Economics, 54, 1994, 1-36.

Kagel, J. H., R. M. Harstad, and D. Levin. "Information Impact and Allocation Rules in Auctions With Affiliated Private Values: A Laboratory Study." Econometrica, 55, 1987, 1275-304.

Magee, L. "[R.sup.2] Measures Based on Wald and Likelihood Ratio Joint Significance Tests." American Statistician, 44, 1990, 250-53.

McCabe, K. A., S. J. Rassenti, and V. L. Smith. "Auction Institutional Design: Theory and Behavior of Simultaneous Multiple Unit Generalizations of English Auctions." American Economic Review, 80, 1991, 1276-83.

Morgan, J., and M. Sefton. "Funding Public Goods with Lotteries: Experimental Evidence." Review of Economic Studies, 67, 2000, 785-810.

Plott, C. R., and T. Salmon. "The Simultaneous, Ascending Auction: Dynamics of Price Adjustment in Experiments and in the U.K. 3G Auction." Journal of Economic Behavior and Organization, 53, 2004, 353-83.

Roth, A. E., and A. Ockenfels. "Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet." American Economic Review, 92, 2002, 1093-103.

Rothkopf, M. H., and R. M. Harstad. "On the Role of Discrete Bid Levels in Oral Auctions." European Journal of Operations Research, 74, 1994, 572-81.

Salmon, T., and R. M. Isaac. "Revenue from the Saints, the Show-offs, and the Predators." Florida State University, 2005.

(1.) See Morgan and Sefton (2000) and Davis et al. (2003) for comparisons of institutions for fundraising for charitable activities. Among the factors other than revenue that influence the choice of fundraising institutions are the legal climate and the social and entertainment properties of the process. Though we know of no controlled field study, the word of mouth about silent auctions is that they are pleasant social activities in and of themselves, which draw people to the charitable event. If this is true, comparative revenue for the charities is not simply the static revenue difference for a fixed number of bidders but also depends on how many people are drawn to the event.

(2.) There is another version of the silent auction, which resembles simultaneous sealed bid auctions. In this version, each bidder writes a bid down on a slip of paper and places it in a jar next to the item. All auctions stop by a clock.

(3.) See Cox et al. (1982) and Kagel et al. (1987). The Coppinger et al. (1980) paper suggests that ticks in their English experimental auctions were endogenous. Cox and colleagues support this interpretation.

(4.) Including bidders who bid only on items with only one bidder, there were 91 bidders listed.

(5.) This includes the same restrictions as in the 1999 auction.

(6.) The church auctions lasted about two hours; the school auction lasted about four hours. The church auctions were in the context of a potluck dinner and family activities. The school auction was in the context of other activities, including hors d'oeuvres, wine tasting, and separate sequential oral auctions for a small number of expensive goods.

(7.) As mentioned, we set aside the issue of combinatorial values.

(8.) See Engelbrecht-Wiggans (1994), Engers and McManus (2002), and Salmon and Isaac (2002) for examples from different environments.

(9.) See Isaac et al. (1994). It must be emphasized that the silent auction is not the voluntary contributions mechanism, and the value environments also differ.

(10.) Two very different environments are the signaling models of jump bidding in Avery (1998) and Daniel and Hirshleifer (1997).

(11.) In fact, unlike in the study by Borgers and Dustmann (2004), there are no obvious restrictions to put on the data that give us much in the way of indirect restrictions on bidders value.

(12.) The concept of see and be seen is thereby similar to Andreoni's "warm glow" effect (1993).

(13.) For example, with identical bidders and a uniform distribution of values, see Salmon and Isaac (2005).

(14.) The relationship is not strictly monotonic, and it must be emphasized that their results are just for two bidders.

(15.) Our thanks to Tim Salmon for pointing this out. It is important to note that such a bidder does not know whether he or she is making the final bid among all bidders for that item.

(16.) Quite a few (47.83%) of bids over stated value exceeded value by more than the minimum increment for that item. The values were intended to be retail values, but were often self-reported. We present this figure because if overbids were always less than the minimum increment, then we might simply be observing bidding approximations that were more difficult in the school auctions with larger minimum increments. But this level of overbids looks more like charitable or see-and-be-seen actions. We excluded a small number of items listed as "priceless."

(17.) The x-axis marker on each column is the lower bound of that bin.

(18.) We used a scaling factor across all auctions where a bid equal to the minimum bid increment was a magnitude 1, and the difference between the minimum increment and size of jump divided by the minimum increment present in the auction defined the magnitude for bids that exceeded the minimum increment.

(19.) Clearly, our "number of bidders" measure, the number of bidders who eventually placed a bid, is imperfect. The nature of these auctions is that all bidders are eligible to bid in all of them. The question is how many are going to be practically active in a particular auction? This is an endogenous outcome resulting from bidders' decisions throughout an auction. However, another feature of the silent auction is that bidders can watch the arrival of bidders at an auction station. The idea that bidders can guess which items are drawing the most attention is not far-fetched.

(20.) In fact, first jump bids are a prediction of Daniel and Hirshleifer (1997).

(21.) In the case of the school data, there were no items that could be classified as a craft in the terms used for the church auctions. Therefore, none of the variables using this declaration were used in the school auction estimations.

(22.) For example, looking simply at the time series of the auction, attempts to speed up the generation of information ought to be greatest at the beginning, when bids are lower. On the other hand, looking across goods, those generating higher bids might foster higher jump bids.

(23.) The question is, if I see others submitting large jump bids, and I am interested in speeding up the auction, how should I respond? At our current level of modeling, there does not appear to be an unambiguous answer.

(24.) We are not asserting an exactness of these stated values. However, they should serve as reasonable proxies.

(25.) Since a previous draft, we have corrected a coding error in the bid sequence variable.

(26.) The low pseudo-adjusted R-squares in the probit estimations are consistent with similarly weak results in a predictive accuracy table.

(27.) Whether the announced value on the gift certificates is an exception is unclear.

(28.) Notice that we simplified the design issues by setting aside the issue of combinatorial values.

(29.) Notice that in terms of our discussion in section IV, we are explicitly inducing a charitable rather than a see-and-be-seen model of public goods.

(30.) Coppinger et al. (1980) report that 96% of English auctions in one treatment and 97% of English auctions in another treatment were fully efficient, but they don't calculate the overall average. McCabe et al. (1991) report that a series of multiple unit ascending clock auctions averaged 99.99% efficiency.

(31.) We based the efficiency measure only on the basic induced values on the objects. We did not attempt to factor in the preferences for high prices in the public goods periods.

(32.) An obvious candidate would be the sealed-bid version of the auction.

(33.) We use log of(bid-value) to account for nonlinear front-loading of jump bids.

(34.) It should be emphasized that we might not observe every instance of a bidder willing to bid over his or her value.

(35.) Thus these results are consistent with the theoretical model of Isaac et al. (2005).

R. MARK ISAAC and KURT SCHNIER *

* We thank representatives of a church and a school in Tucson, Arizona, for making their records available. Tim Salmon provided much feedback on earlier drafts, as did seminar participants at the University of Florida and George Mason University. Arthur Zillante, Michael Bailey, and Michael Iachini assisted with conducting the experiments. As usual, the authors are solely responsible for all errors.

Isaac: Professor, Department of Economics, Florida State University, Tallahassee, FL 32306-2180. Phone 1-850-644-7081, Fax 1-850-644-4535, E-mail misaac@mailer. fsu.edu

Schnier: Assistant Professor, Department of Environmental and Natural Resource Economics, University of Rhode Island, Kingston, RI 02881. Phone 1-401-874-4565, Fax 1-401-782-4766, E-mail schnier@uri.edu

TABLE 1
Auction Data Description

 % of % Jumps % Bids >
Auction Jumps Own Bid Stated Value

Church 2000 38.55 0 0
Church 1999 37.09 0 0
School data 8.92 0 9.93

TABLE 2
Predicted Effects for Regressors on Jump Bids

 See-and- Final-Seconds
Variable Charitable Be-Seen Impatience Crowding

N of Bidders - + ? +
Dummy 1st + + + 0
Dummy Last + + 0 +
Dummy Craft + + 0 0
Craft x 1st(2nd) + + 0 0
Craft x Last + + 0 0
Bid Sequence ? 0 - +
Lag Bid -/0 0 ? ?
Lag Jump - 0 ? +
Bid/Value - ? ? ?
Min.Incr./Val. ? ? - -

TABLE 3
Probit and Tobit Estimation of Field Data

 Probit Estimation
(Probability
of Jump Bid) Church 1999 Church 2000 School 2001

Constant -0.246 (-1.22) -0.275 (-1.64) -1.812 (-2.76)
N-Bidders -0.081 (3.56) -0.028 (-1.65) -0.176 (-2.74)
Dummy 1st 0.229 (1.09) -0.394 (-2.10) -0.869 (-1.61)
Dummy 2nd 0.2 (1.23) 0.081 (0.55) 0.595 (2.35)
Dummy Last -0.031 (-0.16) 0.064 (0.39) -0.030 (-0.09)
Dummy Craft -0.151 (-1.80) -0.282 (-2.91) NA
Bid Sequence -0.187 (-0.77) -0.382 (-1.88) -1.213 (-1.74)
Lag Bid 0.016 (6.09) 0.025 (8.12) -0.001 (-1.23)
Lag Jump 0.011 (0.65) -0.035 (-1.59) -0.22 (-1.37)
Craft x Dummy 1st -0.342 (-1.25) 0.438 (1.63) NA
Craft x Dummy 2nd 0.117 (0.46) 0.153 (0.62) NA
Craft x Dummy Last 0.243 (0.94) 0.464 (1.90) NA
Bid/Value NA NA 3.76 (7.03)
Min. Inc./Value NA NA -8.642 (-3.20)
Pseudo-[R.sup.2] 0.0899 0.052 0.1892

 Tobit Estimation
(Magnitude
of Jump Bid) Church 1999 Church 2000 School 2001

Constant 0.615 (0.90) 1.805 (7.43) 0.780 (4.13)
N-Bidders 0.032 (0.42) -0.067 (-2.80) -0.087 (-5.02)
Dummy 1st 1.314 (1.79) -0.139 (-0.05) -0.009 (-0.06)
Dummy 2nd 0.988 (1.68) 0.364 (1.68) 0.30 (4.21)
Dummy Last 0.934 (1.38) 0.491 (2.07) 0.128 (1.27)
Dummy Craft -0.093 (-0.31) -0.235 (-1.67) NA
Bid Sequence -1.18 (-1.40) -0.765 (-2.58) -0.601 (-2.99)
Lag Bid 0.065 (17.06) 0.043 (10.24) -0.0001 (-0.32)
Lag Jump 0.203 (5.82) -0.012 (-0.38) -0.096 (-2.25)
Craft x Dummy 1st -0.51 (-0.56) 0.985 (2.92) NA
Craft x Dummy 2nd -0.65 (-0.70) -0.123 (-0.34) NA
Craft x Dummy Last -.825 (-0.90) 0.552 (1.53) NA
Bid/Value NA NA 1.73 (11.94)
Min. Inc./Value NA NA -3.06 (-5.06)
Pseudo-[R.sup.2] 0.0887 0.0249 0.1066

TABLE 4
Coefficients Inconsistent with Predictions

 Charitable See & Be Seen

Church 1999 Incidence 5 5
11 regressors L,C,Cx1 LagB,LagJ N,C,L,C, 1xC,LagB

 Magnitude 6 5
 N,C,Cx1,CxL LagB,LagJ C,Cx1,CxL, LagB,
 LagJ

Church 2000 Incidence 3 4
11 regressors 1,C,LagB N,1,C,LagB

 Magnitude 2 4
 C,LagB N,C,BidSeq, LagB

School Incidence 2 2
9 regressors L,Bid/Val N,L

 Magnitude 1 3
 Bid/Val N,BidSeq, LagJ

 Impatience Final Seconds

Church 1999 Incidence 0 3
11 regressors N,L,LagB

 Magnitude 0 1

Church 2000 Incidence 2 4
11 regressors 1,C N,CBidSeq, Bid/Val

 Magnitude 2 4
 L,1xC N,Cx1, LagB,LagJ

School Incidence 1 5
9 regressors L N,1,C, LagB,LagJ

 Magnitude 0 4
 N,1,LagB, LagJ

Note: Key to regressors: N = N-bidders; 1 = Dummy 1st; L = Dummy
Last; C = Dummy Craft; Cx1 = Craft x Dummy 1; CxL == Craft x Dummy
Last, BidSeq = Bid Sequence, LagB = Lag Bid, LagJ = Lag Jump,
Bid/Val Bid/Value.

TABLE 5
Experimental Design

Number of sessions 6
Number of auction periods 5
 per session
Number of goods at 16 For geographic dispersion,
 auction in each period see Figure 2
Number of bidders in each 8
 period
Number of bidders who 2-8 Chosen randomly, uniform
 value each good process
Bidder values for those $0-$20 Chosen randomly for each
 who value bidder, item, and period
Charitable public goods NNYYN
 value (yes or no)
Charitable public goods 2 at 5%; 2 at Percent paid on total
 value (amount) 1%; 4 at 0% sales revenue
Charitable public goods How it worked, Y or N
 value (information) period, but not
 distribution
Minimum bidding 0.25 (3 exps),
 increment 0.5 (3 exps)
Clock time per period 12 minutes Displayed

TABLE 6
Comparison of Field and Laboratory Results

 % Jumps % Bids >
Data Set % of Jumps Own Bid Stated Value

Field
Church 1999 data set 37.09 0 NA
Church 2000 data set 38.55 0 NA
SIP 2001 Data Set 8.92 0 9.93 (a)
Laboratory
0.25 No Public Goods 57.42 0.13 1.08
0.25 Public Goods 61.83 0.09 1.25
0.5 No Public Goods 40.16 0.16 1.57
0.5 Public Goods 48.38 0.13 1.43

Data Set Efficiency (c) Revenue Index (c)

Field
Church 1999 data set NA NA
Church 2000 data set NA NA
SIP 2001 Data Set NA NA
Laboratory
0.25 No Public Goods 94.88% (94.58%) (b) 81.31% (87.35%) (b)
0.25 Public Goods 95.30% (95.48%) (b) 86.34% (131.43%) (b)
0.5 No Public Goods 96.87 (96.57%) (b) 92.71 (102.23%) (b)
0.5 Public Goods 97.79% (97.57%) (b) 89.64% (101.63%) (b)

(a) The posted value of the item is used in place of an induced
valuation.

(b) Main numbers are value weighted (aggregated) at the period
level; numbers in parentheses are weighted by individual auctions.

(c) At the period-weighted level, random assignment efficiencies
(including zero values) would be 39.6% for no public goods and
39.48% for the public goods cases.

TABLE 7
Probit Regressions for Laboratory Sessions

 0.25 without 0.25 with
Variable Public Goods Public Goods

Constant -0.404 (-2.21) 0.020 (0.09)
Number of active bidders -0.025 (-1.08) -0.079 (-2.16)
Dummy 1st -0.210 (-1.54) -0.671 (-3.85)
Dummy Last -0.221 (-1.23) 0.151 (0.95)
Seconds Remaining 0.0002 (1.02) 0.001 (4.09)
Log Value Minus Lag Bid 0.156 (3.24) 0.376 (7.24)
Lag Jump 0.037 (1.22) 0.002 (0.05)
Min. Inc./Induced -2.30 (-1.64) 0.358 (0.38)
N of Objects 0.075 (3.90) -.023 (-1.15)
Pseudo-[R.sup.2] 0.0402 0.0865

 0.5 without 0.5 with
Variable Public Goods Public Goods

Constant -1.09 (-5.46) -0.883 (-3.32)
Number of active bidders 0.004 (0.13) -0.008 (-0.22)
Dummy 1st 0.259 (1.67) -0.004 (-0.02)
Dummy Last 0.193 (1.48) 0.439 (2.62)
Seconds Remaining 0.0007 (2.61) 0.0004 (0.88)
Log Value Minus Lag Bid 0.442 (7.81) 0.437 (5.75)
Lag Jump -0.054 (-2.17) -0.023 (-0.70)
Min. Inc./Induced -1.37 (-1.40) -2.686 (-1.58)
N of Objects 0.017 (0.73) 0.062 (2.17)
Pseudo-[R.sup.2] 0.1155 0.1101

Note: Numbers in parentheses are asymptotic t-statistics.

TABLE 8 Tobit Regressions for Laboratory Sessions

 0.25 without 0.25 with
Variable Public Goods Public Goods

Constant 0.271 (0.46) 1.020 (1.70)
Number of active bidders -0.178 (-2.21) -0.221 (-2.24)
Dummy 1st 1.307 (2.74) -0.347 (-0.72)
Dummy Last 1.408 (3.18) 0.850 (1.97)
Seconds Remaining 0.0006 (0.08) 0.003 (3.99)
Log Value Minus Lag Bid 1.07 (7.07) 1.205 (8.35)
Lag Jump -0.035 (-0.34) -0.121 (-1.04)
Min. Inc./Induced -0.364 (-0.33) -0.082 (-0.03)
N of Objects 0.265 (4.23) 0.094 (1.68)
Pseudo-[R.sup.2] 0.0905 0.1404

 0.5 without 0.5 with
Variable Public Goods Public Goods

Constant -0.157 (-0.38) -0.173 (-0.31)
Number of active bidders -0.073 (-1.05) -0.181 (-2.08)
Dummy 1st 1.662 (4.94) -0.216 (-0.52)
Dummy Last 0.945 (3.11) 1.673 (4.41)
Seconds Remaining 0.0006 (3.97) 0.003 (3.29)
Log Value Minus Lag Bid 1.270 (10.98) 1.348 (9.02)
Lag Jump -0.197 (-0.35) -0.028 (-0.38)
Min. Inc./Induced -0.123 (-0.32) 0.317 (0.86)
N of Objects -.030 (-0.60) 0.009 (0.14)
Pseudo-[R.sup.2] 0.1984 0.1897

Note: Numbers in parentheses are r-statistics.

TABLE 9
Comparison of Probit Regression between Field and Laboratory

 Field Variables
 Field Variables 0.5 with
Variable Church 2000 Public Goods

Constant -0.275 (-1.64) -0.165 (-0.69)
Number of active bidders -0.028 (-1.65) -0.038 (-1.00)
Dummy 1st (Dummy 2nd in field) 0.081 (0.55) -0.568 (-0.31)
Dummy Last 0.064 (0.39) 0.40 (2.48)
Seconds Remaining -0.382 (-1.88) 0.0013 (3.71)
 (-1x bid sequence)
Lag Bid 0.025 (8.12) -0.004 (-0.28)
Lag Jump -0.035 (-1.59) -0.165 (-0.69)
Log(Value Minus Lag Bid) NA NA
Min. Inc./Induced NA NA
N of Objects NA NA
Pseudo [R.sup.2] 0.052 0.0395

 Lab Variables
 0.5 with
Variable Public Goods

Constant -0.883 (-3.32)
Number of active bidders -0.008 (-0.022)
Dummy 1st (Dummy 2nd in field) -0.004 (-0.02)
Dummy Last 0.439 (2.62)
Seconds Remaining 0.00004 (0.88)
 (-1x bid sequence)
Lag Bid NA
Lag Jump -0.023 (-0.70)
Log(Value Minus Lag Bid) 0.437 (5.75)
Min. Inc./Induced -2.686 (-1.58)
N of Objects 0.062 (2.17)
Pseudo [R.sup.2] 0.1101

Notes: Numbers in parentheses are asymptotic t-statistics.
Craft variables not displayed.