Evaluating Conservation Auctions with Unknown Bidder Costs: The Scottish Fishing Vessel Decommissioning Program

I. Introduction

To address market failures in the use of natural resources, governments often appropriate public funds for achieving conservation objectives, paying private agents to mitigate their impact on the environment (Ferraro and Simpson 2002). In land-based conservation programs, governments have often made use of fixed-price schemes, offering all eligible producers a predetermined flat-rate payment irrespective of their compliance costs or resource settings (Baylis et al. 2008). In marine resource conservation programs, by contrast, where the goal is to buy out fishing vessels to conserve fish stocks, government agencies have typically relied on competitive bidding to allocate funds. Competitive bidding in this context means that fishermen compete for buy-out grants by submitting financial bids to the regulating agency, indicating the payment they demand for retiring their vessel from the fishery. Bids are selected on a value-for-money basis until the budget is exhausted. Examples include the Northeast Groundfish Fishery Buyout Program in the United States (Walden, Kirkley, and Kitts 2003) and the various decommissioning schemes established under the European Union's Multi-Annual Guidance Program.¹

To the best of the authors' knowledge, it has so far been the sealed-bid discriminatory-price (DP) auction that has been used to buy out fishing capacity. Under this pay-as-you-bid pricing rule, winning bidders are paid their own winning bids. An alternative pricing rule is the uniform-price (UP) auction, whereby winning bidders are all paid the same price: either the highest winning bid or the lowest rejected bid. It is not clear why conservation agencies have so far preferred the discriminatory format; in particular, it is not clear which of the two auction formats generates the greatest value for money. Auction theory has established that DP auctions, like all first-price auctions, generate bid shading; that is, bidders' optimal bidding strategy is to put in bids (i.e., payment demands) that are in excess of their costs (Cox, Roberson, and Smith 1982; Cox, Smith, and Walker 1984). The resulting rents deteriorate the performance of the auction. By contrast, the dominant bidding strategy in a UP auction, as first shown by Vickrey (1961) for the simplest case of a second-price auction, is to put in a bid equal, in a buy-out auction, to one's opportunity cost. Because all successful bidders are paid the same price, that of the highest winning or the lowest rejected bid, they also earn a rent equal to the difference between the uniform price and their own cost (Vickrey 1976).

Auction theory suggests that the two auction formats will yield the same expenditures for the procurer only under a set of restrictive assumptions such as bidder risk-neutrality (Milgrom 2004). Conservation auctions, however, are more complex in practice and do not abide by the theory's restrictive assumptions; as a result, we cannot expect expenditure equivalence. Whether government expenditure and bidder rents are higher under a uniform price, based on true opportunity costs, or under differentiated prices, based on inflated opportunity costs, turns out to be an empirical question (Tenorio 1993, 1999). Because theory does not offer sufficient guidance, economists have turned to laboratory experiments and agent-based modeling to study the economic performance of the different pricing rules. In laboratory experiments, McKee and Berrens (2001) and Cason and Gangadharan (2005) find DP auctions to be less costly than UP auctions for a given environmental budget. In other experiments, where bidders were allowed to revise their bids, Cummings, Holt, and Laury (2004) find that average prices are initially lower in the DP auction, but that the difference vanishes as bidders revise their offers. Using agent-based modeling of multiunit auctions, Hailu and Thoyer (2006, 2007, and 2010) find that, over multiple rounds and when bidders are allowed to learn over time, the relative performance, in terms of budgetary cost-effectiveness, of the two auction formats depended on bidder heterogeneity and on the degree of competition intensity. Studies based on actual field data are very few (e.g., Jack, Leimona, and Ferraro 2009), probably because the uniform pricing rule has not until very recently been seriously considered by governments as an alternative to the pay-as-you-bid auction. As a result, the relative performance of the DP versus the UP auctions remains in practice an open question for conservation-oriented procurement authorities.

A number of studies have used field data from pilot conservation auctions to assess auction performance relative to fixed-price schemes, which offer landholders a predetermined, fixed payment on a take-it-or-leave-it basis (e.g., Stoneham et al. 2003; Connor, Ward, and Bryan 2008). These studies demonstrate the superiority of the DP auction to the fixed-payment scheme. A critical assumption in these studies is that bids represent bidders' costs. This is not the case, however, since price discriminating auctions generate bid shading. One cannot therefore equate bids and costs. Doing so results in an overestimation of the auction's performance advantage.

Against this background, this paper has an empirical and a methodological objective. The empirical aim is to investigate the relative performance of the DP and the UP auctions based on data from two auctions carried out in the field: the fishing vessel decommissioning auctions run by the Scottish government in 2001 and 2003. Both auctions used the DP rule. The methodological objective is to develop a methodology for assessing the performance of an equivalent UP auction. This requires an estimate of the costs underlying the fishermen's bids in the two Scottish DP auctions. Unlike previous evaluations of field conservation auctions (Stoneham et al. 2003; Connor, Ward, and Bryan 2008; Jack, Leimona, and Ferraro 2009), the present study uses isomorphic experimental auctions—that is, auction setups that mimicked the Scottish vessel decommissioning mechanisms—to derive an estimate of bid shading and thereby of the underlying costs.

In analyzing the bids and estimated costs, we find that the DP format outperformed the UP in the 2001 auction, but obtain the opposite result for the 2003 auction. This is intriguing, given that the auction rules in the two cases were the same. Given that the literature does not provide sufficient guidance to explain this contrast, a third objective of this paper is to clarify the factors that underlie these contrasting performances. In this way we are able to shed some light on the conditions under which conservation agencies should benefit from the use of one or the other auction format.

II. The Scottish Fishing Vessel Decommissioning Auctions

The Scottish fishing vessel decommissioning auctions were run by the then Scottish Executive Environment and Rural Affairs Department (SEERAD).² The decommissioning schemes intended to buy out both vessel capacity and an amount of fishing activity. Capacity reduction aims at the longer-term impact on fish stock conservation, whereas activity reduction aims at shorter-term outcomes. Capacity referred to a vessel's gross tonnage (a measure of the hull's volume), to its engine power (measured in kW installed), or to some combination of the two, while fishing activity referred to both days at sea and quantity of fish landed, of which there were several species (cod, haddock, scallops, etc.). Fishing vessel owners were eligible to apply if their vessels met a set of criteria relating to the type of license held, the port of registration, vessel length and age, and minimum activity level in terms of days at sea in the two years preceding the auction. Vessels decommissioned under the scheme had to be destroyed or permanently removed from the fishery, although all equipment could be removed prior to destruction. Bidders were informed that applications would be evaluated and ranked according to some or all of the following considerations:

• The bid amount asked

• The size (tonnage and/or engine power) of the vessel

• The level of recorded fishing activity (days out on fishing trips) and the recorded landings made in respect of the vessel during the two years preceding the auction

Fishermen were not told the weights that the agency put on the different criteria, but the overall budget (•25m in 2001 and •31m in 2003) was announced before the auctions. The weights were set by SEERAD ex post, after bids had been received, and were such that priority was given in the 2001 auction to buying out vessel capacity, measured using a formula combining gross tonnage and engine power.³ The weighting was different in the 2003 auction, as it focused specifically on reducing cod landings, in terms of both activity (days at sea) and landings (metric tons of cod).

The data set provided by SEERAD consisted of the technical characteristics of the vessels that participated in the two auctions and of the bids submitted by the fishers. Out of a catchment of 607 eligible vessels, 198 (or 33%) were put up for decommissioning through the 2001 auction. In the 2003 program, bids were received for 159 vessels. Table 1 summarizes the key characteristics of the vessels for which bids were submitted. Vessel capacity in Table 1 is measured by gross tonnage, which represents the volume of the vessel's hull. Fishing activity was measured as number of days at sea fishing in the two years preceding the auction (1999–2000 for the 2001 auction and 2001–2002 for the 2003 auction). Types of fish landings (not shown in Table 1) were white fish, nephrops, and scallops, each of which fetch different market prices per unit weight.

Comparing the two auctions, it is clear from Table 1 that, on average, larger and more active vessels were offered in the 2003 exercise at a higher bid per gross ton. This may reflect higher average productivities and thus higher average profits forgone from scrapping the vessels (i.e., higher opportunity costs). Using SEERAD's bid rankings as well as the total budgets, we were able, as explained below, to compute for each auction the number of vessels decommissioned.

The difference in emphasis of the two auctions, with the 2001 auction focusing on capacity buy-outs and the 2003 auction specifically targeting cod landings, is important in that it would have affected how bids were ranked and which bidders were selected. The fact that SEERAD did not disclose the specific weights used for ranking bids made it necessary to explore different weightings to see which weighting function corresponded to the ranking made by SEERAD. We therefore explored and compared several weighting functions, contrasting a focus on vessel capacity and one on fishing activity. In the 2001 auction, we ended up giving a 60% weight to capacity and the remaining 40% to activity. In the 2003 auction, we gave a 20% weight to capacity and an equal weight of 40% each to cod fishing activity (days at sea) and cod landings (in tons). These weights were used to construct a unit of service, or UoS, a measure of the quantity the decommissioning agency was willing to pay for through the auction. Contrary to appearances, each of the two UoS metrics is specific to each auction and cannot directly be compared.

The auction-specific UoS was the metric used to rank bids and select bidders. In Appendix A, bidders in both auctions are ranked according to the selection criterion, • bid per UoS offered (third column). Vessels with the lowest • bid per UoS were selected until the buy-out funds of •25 million in 2001 and •31 million in 2003 were exhausted. In order to make the UoS scale-insensitive, we normalized all measurements such that the average of each measurement (such as gross tonnage, days at sea, fish landings) was set equal to 100. For each of the two auctions, the measurements for individual vessels were then expressed in percent of the auction's average values.

Because the two SEERAD auctions targeted different outcomes (capacity reduction in 2001 versus cod landings in 2003), we have treated them in our analysis as independent events. It is conceivable, however, that bidders used information from the 2001 auction to update their priors about potential weights and rival bidders' behavior for the 2003 auction. This would have affected bidding strategies.

III. Evaluating Auction Performance

Deriving the Underlying Cost Curve

Auctions are typically held because bidder costs are unknown. In fact, a key function of auctions is to reveal bidders' costs to the auctioneer. The cost revelation powers of the DP and UP auction formats differ, however. Under the uniform pricing rule, the dominant strategy is to bid one's cost (Vickrey 1961, 1976). The UP auction can thus be considered a perfect cost revelation mechanism. Under the discriminatory pricing rule, by contrast, bidders face an incentive to shade their bids above costs (Cox, Roberson, and Smith 1982; Cox, Smith, and Walker 1984). Since the Scottish fishing vessel decommissioning auctions used the DP rule, bids received do not reflect true opportunity costs: the cost revelation property of the auction is blurred by the fact that bids contain an element of rent.

This poses a problem for our analysis to the extent that (1) auction performance evaluation requires, in one way or another, bids to be compared with costs, and (2) the outcome of an equivalent UP auction can be simulated only when the analyst knows the bidders' underlying costs. Ex-post auction evaluation thus requires some procedure for deriving bidder costs, given their DP bids. Clearly, this cannot be done without making some assumptions, and depending on these assumptions, the derived cost curve may differ. As a result, one cannot speak of “the” underlying cost curve, but of “an” underlying cost curve: given the available information, it cannot be considered as being unique.

We used controlled laboratory experiments to derive a cost curve underlying the SEERAD's DP bids. The experiments, carried out as part of another research program (Schilizzi and Latacz-Lohmann 2007), implemented the same auction mechanism as those held in the field: an environmental procurement auction with a fixed budget and a sealed-bid discriminatory pricing rule, from which an estimate of bid shading can be made. In this case, costs are known, by design, as well as bids, and bid shading can be calculated directly.

Laboratory experiments were carried out with university students in two different countries in identical conditions, each auction implementing the sealed-bid discriminatory price mechanism under informational conditions similar to those of SEERAD. This allowed us to make one key assumption: the invariance of bid-shading ratios, that is, the ratio of a bidder's bid request to his or her underlying cost, known to the experimenter by design.

The lab auctions were calibrated in such a way that bidding competition in the lab reflected bidding competition in the SEERAD auctions. This required the lab budget to be set such that roughly the same percentage of “service” would be traded as in the SEERAD auctions. Clearly, this required some guesswork, but the result was very satisfactory: while the 2001 and 2003 SEERAD auctions bought, respectively, 65% and 66%of the UoS offered by the fishermen, the lab auctions resulted in 66% of the UoS offered being accepted.

The cost curve was finally derived from the DP bids in a three-step procedure. The first step involved computing rent rates, or rent-over-bid (R/B) ratios for the 44 experimental subjects. The R/B ratio [R/B = (bid-cost)/ bid] measures the share of rent per unit bid.⁴This ranged from 0.02 to 0.93 with an average of 0.31 (see Appendix A). The R/B ratio was, as the theory of discriminative (first-price) auctions predicts, a decreasing function of bidder costs (Latacz-Lohmann and Van der Hamsvoort 1997), that is, bid shading was more pronounced for low-cost bidders: the average R/B for the bidders in the lowest-cost quartile was 0.57, and that for the highest-cost quartile was 0.13.

The second step involved exporting the experimental R/B ratios to the SEERAD auctions. This required some gaps to be filled, due to the fact that the data sets were very different in size: 44 experimental bids compared to 198 in the 2001 data set and 159 in the 2003 data set. The 44 experimental R/B ratios were first distributed equally across the two larger SEERAD data sets. The gaps were then filled by linearly interpolating between the nearest experimental R/B ratios. This procedure ensures that the average R/B ratios for any cost quantiles are conserved.

In the third step, costs were computed by solving the R/B formula (above) for cost: cost = bid × (1 −R/B). This procedure thus yields an individual cost estimate for each bidder in each of the two SEERAD auctions. By joining these estimates up along the quantity (UoS) axis, one obtains a cost curve underlying the bids. This is shown in Figure 1 for the 2001 and 2003 auctions. A small number of very high bids and costs are not shown, as they would obscure the exact run of the curves.

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Figure 1

Bid and Estimated Cost Curves for the 2001 (left) and 2003 (right) Auctions (The Two Units of Service [UoS]Measures Are Specific to Each Auction)

Although the lab experiments were calibrated to reflect bidding competition in the field, two differences between lab and field auctions remain. The lab auctions were set up as one-shot tenders (without repetition). We used the bid-shading calibrations from that one-shot auction to infer the cost curves for the two SEERAD auctions, which may or may not represent fully independent events. As explained above, bidding strategies in the 2003 auction may have been affected by bidder learning that would not have been captured by the single lab auctions. This must be borne in mind when interpreting the results.

DP and UP Auction Performance

At first sight, the buy-out performance of the two SEERAD auctions may appear to differ considerably: whereas the 2001 auction bought out 65% of the vessels up for decommissioning, the 2003 auction only bought out 43%. However, one must remember that the two auctions had different objectives and so cannot be directly compared relative to the number of vessels. Instead, they must be compared on their own terms: measured in terms of Units of Service (UoS), the two auctions, as shown in the DP section of Table 2, buy out nearly identical percentages: 65% and 66%, respectively. These percentages are also, as previously noted, very similar to our experimental auctions (66%).

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TABLE 2

DP-and UP-Equivalent Performance Indicators for 2001 and 2003 Auctions

In terms of cost-effectiveness, that is, the amount paid per UoS obtained, the 2001 and 2003 auctions do seem to perform differently: •1,928 and •2,935, respectively. However, although both auctions are labeled in UoS, each metric is in fact different and corresponds, one, to a focus on fishing vessel capacity, and the other, on the amount of cod fish caught and days at sea. On the other hand, the two auctions can be directly compared in terms of payments relative to underlying costs, as estimated in the previous section. From Table 2, section DP, it is clear that bidder rents were much higher in the 2003 auction than in the 2001 auction: 56% compared to 37% in terms of the proportion of rent in the payment (R/B), and by a factor 2.27 compared to 1.57 in terms of payment over estimated cost. We carried out Kolmogorov-Smirnov tests of differences in the distributions of all important auction performance indicators between the 2001 and 2003 auctions and, more importantly, between the DP and UP formats. The results are reported in Table 2.

How would the two auctions have performed under an equivalent UP pricing rule instead of a DP rule? Recall that under the DP pricing rule, each bidder is paid his or her own bid. Under the UP pricing rule, bidders are all paid the same price per unit of UoS, either that of the last accepted bidder, or that of the first rejected bidder. The Scottish government did not carry out any UP auctions in this field, but we can construct a UP auction equivalent to the DP auction. That is, given the fixed budgets of •25 million in 2001 and of •31 million in 2003, how many UoS would each auction buy out using a UP pricing rule, assuming the same population of bidders? To do this, an important assumption must be made, based on auction theory for second-price and UP auctions (Vickrey 1961, 1976): that UP auction formats are incentive-compatible and bidders have an incentive to bid their true costs. Experiments carried out by Cason and Gangadharan (2005) and by Sasaki et al. (2011) tend to show that, on average, this is indeed the case.

In our UP-equivalent simulation, we paid all accepted bidders the price of the first rejected bidder, but using the price of the last accepted bidder hardly changed the results. In Figure 2, the budget-constrained UP-equivalent auctions are constructed such that the area of the rectangles touching the estimated cost curve up to UP equals the area under the bid curve up to DP. This reflects the same budget constraint under UP and DP. The 2001 auction reveals the same performance of the DP relative to the UP, as reported in previous work (Cason and Gangadharan 2005, and Sasaki et al. 2011), where the DP appears to perform better: Table 2, section UP, shows that the DP auction is 17% more cost-effective than the UP (smaller payment per UoS). Hailu and Thoyer (2006, 2007, and 2010) did report contrasting performances, but with simulated virtual agents learning over time with identically repeated auction rounds; here we are interested in single-round auction performance.

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Figure 2

Construction of DP-Equivalent UP Auctions for 2001 (left) and 2003 (right) Auctions (Rectangle Areas Up to F Are Equal to Areas under Bid Curve Up to C)

Until the present study, it appeared that single-round DP auctions must always perform better on the cost-effectiveness criterion than their UP equivalent. As the 2003 auction reveals, however (see Figure 2), the generality of this statement is not borne out by our results. Now the UP vertical line is to the right of the DP instead of to the left as in the 2001 auction, indicating that, for the same budget, the UP auction obtains more UoS than the DP: in the 2003 auction, the UP performs slightly better than the DP in cost-effectiveness by 4% (see Table 2). In addition, the rent paid out to bidders in the UP is also less, and the actual proportion of vessels or UoS bought out relative to those eligible (UoS/Max) is higher, by 6% and 5%, respectively.

Although statistically significant differences exist only with respect to the rent paid out to bidders, the previous presumption regarding the superiority of the DP format over the UP does not seem to be general. This raises the question as to when either is superior to the other, at least in terms of cost-effectiveness, which tends to be the main criterion by which conservation auctions are evaluated.

IV. Factors Affecting Relative Auction Performance

The contrasting auction performance results observed in Section III are likely to be sensitive to (1) the degree of bid shading in the DP auction and (2) the heterogeneity of bidder costs (Hailu and Thoyer: 2006, 2007, and 2010). While the degree of bid shading is reflected by the vertical distance between the bid and the cost curves (the further apart these two curves, the greater the bid shading), cost heterogeneity is reflected by the shape of the cost curve (the steeper the curve, the more heterogeneous are bidder costs). Whereas the shape of cost curves is determined by the SEERAD bids, the bid-shading ratios (R/B) were imported from isomorphic experimental auctions. Such an extrapolation assumes bid competition in the lab to roughly match bidding competition in the field. Although the experiments were designed and calibrated to achieve a close match, this is by no means guaranteed. It is thus important to explore the sensitivity of the performances of the two auction formats to variations in bid shading and bidder heterogeneity.

Bid Shading

To explore the extent to which the relative performance of the two auction formats might be affected by errors in the bid-shading ratios imported from the experiments, we ask, for each auction, by how much the cost curve should be shifted, up or down, so that the DP format performs exactly as well, in terms of cost-effectiveness (payment per UoS), as its equivalent UP. This means that, for a given identical budget, both DP and UP supply the same quantity of UoS. The resulting degree of bid shading is thus made independent of the specific values imported from the experiments: instead, it reflects the structure of the original bid data in terms of min-max range, steepness, and shape, which have been kept unchanged.

Starting with the 2003 auction, we are interested in the direction of the curve shift and in how much the rent-to-bid ratio (R/B) must change to make both auction formats perform equally well. The right-hand panel of Figure 3 summarizes the results. First, the cost curve must shift up: given that with the bid-shading ratios directly imported from the experiments, the DP auction performs worse than its equivalent UP, as per the corresponding panel in Figure 2, we need to worsen UP's relative performance by reducing the bid-shading for DP. This translates into a smaller distance between the bid and cost curves in Figure 3. Secondly, we wish to know by how much the cost curve shifts up. We used two summary statistics to measure this shift, the mean and the median bid-shading ratio R/B. Both measures show similar declines, the mean by 9% and the median by 10% (Table 3, third column).

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Figure 3

Minimal Cost Curve Shift Compatible with DP-UP Auction Equivalence: 2001 Curve (left) Shifts Down, 2003 Curve (right) Shifts Up (Note Reversed Positions of Points C and F in the Two Panels)

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TABLE 3

Changes in Bid-Shading Ratios Needed to Make DP and UP Formats Perform Equally Well in Both SEERAD Auctions

We can interpret these results by saying that an error greater than 10% in the estimate of the experimental bid-shading ratio would be needed for the relative performance of the two auction formats to be reversed. Whether this should be interpreted as a small or a large value will be investigated below. Meanwhile, in the 2001 auction, the needed shift of the cost curve is down, and the corresponding change in the mean and median bid-shading ratios are both 26% (Table 3, second column). Clearly, the superiority of the DP auction in the 2001 auction is more robust than its inferiority in the 2003 auction: the error in the R/B ratio imported from the experiments would need to be greater than 26%. Again, whether this value of 26% can be interpreted as small or large, that is, whether the relative performance of the DP and UP formats in the two auctions can be considered as robust to errors in bid-shading extrapolation, now needs to be investigated.

Our experimental DP auctions involved subjects in two different countries, Australia and Germany, each with its own specific culture. In both contexts, by design, we knew the bidders' costs as well as their bids. We first established the extent to which bid shading differed in both cases. It differed by a mere 1 percentage point: the average R/B ratio was 32% in Germany and 31% in Australia. We then proceeded to apply the SEERAD extrapolation procedure to our experiments, first from the German auction to the Australian auction, then from the Australian to the German. Contrary to the SEERAD case, we here had the means to measure the accuracy of the extrapolation; that is, we could compare the extrapolated cost curve to the actual experimental cost curve. Thus, in the Germany to Australia case, we exported Germany's R/B ratios to the Australian bid data, assuming Australian costs unknown, and vice versa in the Australian to the German case. The question was, how large were the errors compared to the threshold percentage errors underlying the robustness of the SEERAD cost extrapolations?

The results were as follows: the extrapolation error in the average R/B ratio extrapolated from Germany to Australia was + 8% and that from Australia to Germany was − 7%. By comparison, the 10% and 26% threshold errors in the two SEERAD auctions are greater than 7% or 8%, indicating that the relative performance of the DP and UP formats in the SEERAD auctions can be considered as robust to errors in bid-shading extrapolation. This was the purpose of this subsection. We may conclude by saying that the degree of bid shading, all else equal, is alone a sufficient factor for determining whether the DP format performs better or worse than the UP format.

V. Conclusion

As an alternative to the more traditional fixed-price schemes, several governments, for example, the United States, Australia, the United Kingdom, and Germany, have started using auctions, or tenders, to purchase environmental services from private agents. In doing so they have had to choose between the sealed-bid DP format (a multiple-unit first-price mechanism), and the sealed-bid UP format (a multiple-unit second-price mechanism). For reasons that have mostly to do with transparency and political expedience, the DP has so far always been the preferred format. One may question, however, if it is economically the most efficient and whether the UP format might not, under certain conditions, be a preferable policy tool. Previous theoretical and experimental studies have shown that in terms of economic cost-effectiveness the single round DP format consistently outperforms the UP.

No comparison of this nature has to date been done with conservation auction field data. It was therefore worth checking whether this higher performance of the DP over the UP format would also be observed in the field. In the context of an ongoing effort to conserve marine fish stocks, the then Scottish Executive Environment and Rural Affairs Department (SEERAD) carried out two vessel decommissioning auctions in 2001 and 2003, the data of which were made available to us. Using a new procedure for deriving the unobserved bidder costs underlying the bid curve, we found that while the 2001 auction confirmed the findings in the literature, the 2003 auction did not. Instead, in 2003 the UP performed slightly better than the DP.

Two factors have been found to strongly influence the relative performance of the DP and UP auction formats: the degree of bid shading and the heterogeneity of bidders' costs. Each alone is sufficient to reverse the relative performance of the two auction formats. This finding sheds some light on the previous literature, in that the bid curves as a rule had the textbook convex shape. In the case of the SEERAD auctions, the shape was of the logit S-type. Using a median-preserving pivot function, we found that giving the bid and cost curves the standard convex shape indeed restored the superior performance of the DP format.

The confidence in deciding which auction format performs better rests of course with the robustness of the method employed. In this study, we used isomorphic experimental auctions—that is, auction setups that mimicked the Scottish vessel decommissioning mechanisms—to derive an estimate of bid shading and thereby of the underlying costs. We ran a protocol for examining whether such an extrapolation was robust and sufficiently accurate by carrying out the experiments in two different countries. Only if the lab auctions are believed to properly reflect bidding conditions in the field can the extrapolated cost curve of the field auctions be taken as a reliable estimate. In future extensions, the credibility of the cost extrapolation from lab data could be enhanced by drawing lab bidders from the same population as the field auction. Along the lines of Cummings, Holt, and Laury (2004), one could supplement student bidder sessions with fisher bidder sessions to examine external validity.⁵

The findings in this paper should allow policy makers to better evaluate the performance of a conservation auction relative to an equivalent alternative format. In a Land Economics paper published in 2007, Schilizzi and Latacz-Lohmann evaluated conservation auctions relative to an equivalent fixed price scheme; here we evaluate a DP auction relative to an equivalent UP auction. In a series of three papers, Hailu and Thoyer (2006, 2007, and 2010) compared the performance of the DP, the UP, and the generalized Vickrey auctions using an agent-based model of simulated agents learning over many auction rounds. They concluded that the superiority of the DP format depended on bidder heterogeneity and on the intensity of bidder competition. Here we conclude for nonrepeated auctions that the superiority of the DP depends on bidder heterogeneity and on the degree of bid shading. The present study thus contributes to the gradual buildup of understanding in the literature of the conditions under which the different auction mechanisms perform most cost-effectively.

In interpreting the results of this study it is important to recall that the 2001 and 2003 auctions may not have been completely independent events. It is therefore conceivable that interdependent behavior of bidders, which would not have been captured by our bid-shading extrapolation, may have influenced the relative performance of the DP and UP auction formats. Erring on the side of caution, we conclude that, for the time being, conservation agencies should in practice continue using the DP as the default format for conservation auctions. This conclusion is reinforced by the observation that the superiority of the DP auction in 2001 is more robust than its inferiority in the 2003 auction. More research is needed before more robust policy recommendations can be made.

Appendix A