Use of a vickrey auction format with a hidden reserve price to discover the value of conservation easements

Use of a Vickrey Auction with a Hidden Reserve Price to Discover the
Value of Conservation Easements
Laura Brown,a Cynthia Edwards,b Brian Gray,c Wanjing Hu,d and Elizabeth Troutte a. Department of Economics, University of Manitoba b. Ducks Unlimited Canada c. Ducks Unlimited Canada (currently on an interchange with Environment Canada) d. Department of Rural Economy, University of Alberta e. Department of Economics, University of Manitoba Abstract

This paper describes the application of a Vickrey auction (second-price sealed bid auction)
with a hidden reserve price mechanism in a pilot project aimed at determining Canadian
prairie landowners' valuation of conservation easements placed on natural areas on their
lands. The main characteristics of the price setting mechanism include revealing the
landowners' true willingness to accept compensation for easements over natural lands
and allocating easements efficiently. The paper reviews the merits of a Vickrey auction
with a hidden reserve price as the theoretical basis for accomplishing these objectives in a
real-world setting. The paper then describes the pilot setting, the resulting auction design,
and the implications of the pilot project for future conservation easement research and
campaigns.

Keywords: conservation easement, Vickrey auction, hidden reserve price, Ducks
Unlimited Canada
(Please do not quote or cite.)
Use of a Vickrey Auction with a Hidden Reserve Price to Discover the
Value of Conservation Easements

I. Introduction

Along with the implementation of sustainable development strategies, policy makers and
practitioners have increasingly focused on coordinating the development of economy,
society and ecology. In this context, questions have arisen about how to protect the land-
based environment, especially the privately owned land-based environment. In the past
few decades, most efforts toward protecting biodiversity and ecosystems have been
directed at publicly owned land through the creation of national and provincial parks or
ecological reserves. That is, although nearly 60 percent of the land in the U.S. and likely
a similar percent of the land in Canada is privately owned, few effective tools for
protecting privately owned grassland, forestland, wetland and other valuable ecosystems
have been implemented (Morrisette, 2001). Conservation easements (CEs) offer an
answer to the dearth of tools to preserve ecosystem resources that exist on land owned by
private individuals.
A CE is a voluntary contractual agreement in which a landowner transfers a subset of
(usually particular use) rights over a defined area of land to a governmental or nonprofit
agency in order to limit the type and/or amount of use of the defined area. CEs require
landowners to limit the types and/or amounts of uses that would destroy or otherwise
threaten the viability of natural, scenic or historic areas on their property, while still
allowing landowners to retain ownership and certain use rights over the areas.
CEs typically take the form of written agreements between landowners and other entities
that are eligible to hold CEs. The principal holders of CEs include government agencies,
land trusts such as Nature Conservancy Canada, and other qualified non-profit
organizations such as Ducks Unlimited Canada (DUC). The objects of CEs are lands that
possess special value due to their ecological, historic or agricultural attributes. The
duration of a CE may be limited or perpetual (Silver, Attridge, MacRae, and Cox, 1995).
Depending on the CE's duration, it can be a useful tool for ensuring that lands are
preserved beyond the life of the landowner who enters into the CE agreement.
In establishing a CE, landowners may either donate or sell land rights to the recipient
agencies that become CE holders. Many governments provide tax benefits to landowners
who donate land rights to a CE holder. In this case, the landowner transfers rights under
the CE agreement, an approved appraiser estimates the value of the rights transferred, and
the landowner receives a receipt for making a charitable donation of that amount to the
1 A land trust is a private, nonprofit conservation organization. Land trusts' main missions include protecting natural resources such as productive farm and forest land, natural areas, historic structures and recreational areas; educating the public about the need to conserve land; and providing land use and estate planning services to local governments and individuals. The most useful tool of land trusts is purchasing and accepting donations of conservation easements. CE holder (even if the CE holder is a government agency). The landowner then qualifies
for a tax deduction whose magnitude is determined by tax rules, but which will be less
than the estimated value of the rights transferred. For instance, Canada's Ecological Gifts
Program offers landowners who donate CEs a credit of up to 17% of the first $200 of the
value of the land placed under the CE, and 29% of the remaining value; additionally,
landowners can use these credits to lower their income for income tax purposes
(http://www.ec.gc.ca/press/001004-2_b_e.htm).
Alternatively, a landowner may sell rights to a CE holder, provided the parties can
negotiate a mutually agreeable price. In recent years, governments and conservation
organizations in North America have increasingly sought to implement purchased CEs
due to a low incidence of donated CEs. Legislation allowing purchased CEs has only
emerged relatively recently, with conservation organizations being quick to take
advantage of the legislative changes. For example, Nature Conservancy Canada (NCC)
began purchasing CEs almost immediately in response to governmental allowances of
paid CEs.
However, even as governments' and conservation organizations' interest in CEs grows,
there remains considerable uncertainty regarding the value of rights transferred under a
CE, and thus the prices that purchased CEs should carry. The lack of knowledge about
CEs, especially about CE values, is not only a barrier to the development of CE programs
by CE implementation agencies, but is also one of the significant reasons that landowners
have, to date, demonstrated limited interest in CE programs. Thus, determining rational
prices for purchased CEs has become essential to fostering the CE market and the
protection of valuable ecosystems.
This paper describes the theoretical underpinnings of an auction process used in a pilot
project for the purchase of CEs, how these were implemented in an actual Ducks
Unlimited Canada (DUC) project, and how the outcomes of this experiment could
illuminate future attempts at CE price discovery. Following short descriptions of the
legislative and programmatic history of CEs and the DUC pilot project, the paper reviews
the theoretical elements of price discovery in the context of CEs. It next explains the
suitability of an auction mechanism to discover CE prices. The paper then illustrates why
a Vickrey auction with a hidden reserve price, which was implemented in the DUC pilot,
is an appropriate device for CE price revelation. The final section of the paper
summarizes the results of the DUC pilot, concluding with a discussion of the pilot's
implications for the design of future CE price discovery exercises.
II. Legislative and programmatic background of CEs and the struggle to price them

Even though most Canadian provinces introduced statutes for CEs following the 1973
Historic Sites Protection Act in New Brunswick (Silver, Attridge, MacRae, and Cox,
(1995), much of the legislation gave only governments authority to hold CEs (Attridge,
2 For example, Saskatchewan, and Manitoba have only had such legislation since 1997 and 1998, respectively. 1997). Early CE legislation took the form of resource acts such as Saskatchewan's
Heritage Property Act (1979), the Manitoba Heritage Resources Act (1985), Alberta's
Heritage Resources Act (1985), Prince Edward Island's Natural Areas Protection Act
(1988), and so on (Silver, Attridge, MacRae, and Cox, 1995). Initially, the statutes
authorized only governments to hold CEs in Canada. As the tool became more familiar,
especially in the past decade, governments enacted legislative changes allowing non-
profit organizations to negotiate CEs with private landowners (Attridge, 1997). The
eligible non-profit organizations include Ducks Unlimited Canada, Nature Conservancy
of Canada, Rocky Mountain Elk Foundation, Canadian Nature Federation, Evergreen,
Land Stewardship Centre of Canada, Manitoba Habitat Heritage Corporation, and
hundreds of land trusts.
The United States' record of CE statutes is longer than Canada's. California became the
first state to enact a CE statute in 1959, and New York followed closely with legislation
in 1960 (Morrisette, 2001). Despite the enactment of similar legislation by some other
states, CE statutes did not achieve marked promotion until the passage of the Uniform
Conservation Easement Act (UCEA) in 1981 (Gustanski and Squires et al 2000, P.13).
The UCEA allows the federal government and nonprofit organizations to hold CEs. It
also offers a model for states to enact CEs. Currently, only Wyoming, Pennsylvania,
North Dakota, and Oklahoma do not have CE statutes (Morrisette, 2001). At present,
even though CEs have achieved significant popularity in North America, a detailed
survey about CE implementation is sorely needed.
As more paid CEs are applied, especially by nonprofit environmental organizations,
different programs have experimented with various price discovery mechanisms. Three
examples illustrate some of the practices currently in force. Nature Conservancy Canada
(NCC) has been buying CEs from landowners for less than a decade. Currently, NCC
uses standard-rate payments of the defined land's assessment value to determine a CE's
price, usually paying 20% to 25% of the assessed value for a CE placed on that land.
Generally, no negotiation occurs between NCC and landowners, and the price rate is
fixed; landowners simply accept or reject the standard-rate payment. Manitoba Habitat
Heritage Corporation (MHHC), the leading CE buyer in Manitoba, also uses a fixed-rate
payment system. Both MHHC and NCC suspect that their fixed-rate price programs are
unattractive to landowners. Both NCC and MHHC purchase only perpetual CEs; in fact,
Canadian landowners currently have no option to donate or sell CEs of limited duration.
On the other hand, the United States' Conservation Reserve Program (CRP), launched in
1985, purchases ten- to 15-year CEs using a different price determination mechanism
than the fixed-rate system of NCC and MHHC. As a voluntary long-term cropland
retirement program (Osborn and Ribaudo, 1998) enforced by U.S. Department of
Agriculture (USDA), CRP uses a simple auction with a reserve price to determine which
CEs to purchase within targeted areas. It sets its reserve price according to an
environmental benefit index combined with private sector annual rental rates for similar
land (Osborn and Ribaudo, 1998).

3 As per telephone conversations at the time of project planning and implementation. As paid CE programs operate and desire to improve their ecosystem protection results,
much work remains in determining CE values for the purpose of setting prices for paid
CEs. With this challenge in mind, Ducks Unlimited Canada (DUC) undertook a pilot
experiment with the objective of shedding light on a landowner's private value of a CE
and the determinants of that value.
Overview of DUC's experiment

DUC has been conserving habitats for the benefit of waterfowl, other wildlife and
humans for more than 64 years. In late 2000, DUC conducted an experiment in Alberta,
Saskatchewan and Manitoba to learn about how landowners value the placement of CEs
on their lands to determine the true and defendable monetary value of CEs for perpetual
protection of threatened habitats on private land. Researchers recognized that the pilot
would also increase landowners' awareness and understanding of CEs. By the late 1990s,
research showed that 70% of Canada's original wetlands have been lost through
conversion to other uses, and that western Canadian native grasslands are under similar
threat of conversion (http://www.ducks.ca/aboutduc/index.html). DUC chose its Alberta,
Saskatchewan, and Manitoba sites based on their rapid conversion rates, so that the pilot
targeted areas where wetland and grassland habitats were at particular risk.
The pilot had two stages. In the first stage, rural landowners from a total of four sites in
Canada's prairie provinces were invited to submit bids expressing the amount of
compensation they would accept in exchange for placing a perpetual CE on areas of land
they owned that contained natural wetland or grassland. Landowners could bid for two
types of perpetual easements: agricultural use CEs and no-agricultural use CEs. Under
either type, DUC would be the CE holder, with rights and responsibilities distributed
differently between landowners and DUC depending on the type of CE contracted.
Agriculture use CEs allow compatible agricultural uses of the land, such as haying,
grazing, and watering livestock. However, they do not allow any breaking, cultivation,
burning or conversion of those lands (both uplands and wetlands). Under agricultural use
CEs, landowners remain responsible for and have sole discretion over management
decisions on lands under CEs. No-agriculture use CEs optimize the land's quality as
waterfowl and wildlife habitat by prohibiting breaking, draining and any agricultural use.
As such, under a no-agricultural use CE, the landowner relinquishes a greater number and
range of use and management rights, with DUC assuming responsibility for management
decisions and their implementation costs.
The second stage of the pilot consisted of a follow-up survey of landowners to learn
about their views on CEs and the reasons for their choices in the first stage. The survey
population consisted of all 3,665 landowners in the four sites who had received bid
materials in the first stage regardless of whether or not they had submitted bids to sell
4 This pilot study was conducted in four sites that were of interest to DUC due to their varied habitats, their historic high rates of land conversion, and their consequent high potential for conservation. Two sites were located in Saskatchewan (Lake Alma and Yorkton), and one in each of Manitoba (Killarney) and Alberta (Torlea). CEs. The survey instrument contained questions designed to collect data that would
indicate the factors that had affected landowners' decisions about whether or not to bid,
that would allow examination of the factors responsible for differences in bid amounts,
and that would provide insights into landowners' attitudes toward conservation.
The bidding process used in the first stage of the DUC pilot was based on auction theory
that has been fairly well developed in the economics literature. A review of this theory
provides the underpinning for how it influenced the design of the price determination
mechanism used in the DUC pilot.
III. Price discovery mechanism design in DUC's pilot

Why use an auction mechanism to discover CE prices?

As mentioned previously, there is no generally accepted price discovery mechanism for
CE's. CEs are quite new, have characteristics of nonmarket goods, and are not yet well
understood by landowners. Therefore, a price discovery mechanism is needed to enable
conservation agencies to have greater confidence that they know what prices to offer in
order to induce CE uptake while not overpaying for CEs relative to landowners'
willingness to accept. Since the objective is to discover the true minimum compensation
that landowners would be willing to accept in exchange for placing CEs on their lands,
the core factor that must be considered during the price determination process is how to
establish the price equal to landowners' true value of CEs. This subsection will provide
the theoretical foundation to the decisions made about auction design in the pilot.
In economics, market value is defined by the consumer's willingness to pay and the
supplier's willingness to accept. Where these two are equal, the exchange can be made
and the price of the exchange is the value of the item. However, there are very specific
conditions on the nature of the market and the exchange that must be met for this price to
reflect value in any meaningful way. First, there must be a market. Second, there must
be clear property rights to the item so that it can be exchanged in the market. Third, the
market must be perfectly competitive. A competitive market requires that there be many
buyers and sellers, and none must have power over setting the price. Nor can any actor
or group of actors force an exchange to be made. Fourth, the consumers and producers
must have full information about the items being exchanged. Fifth, there must be zero
transaction costs. Sixth, the item should only have value to the people who own it. In
this case the private value to the owners (buyers and sellers) is equal to the social value to
the community at large. If the item has value to persons not involved in the market
exchange, then an externality exists and the price in the market will not equal the value
of the item to society. For example, a seller can sell the right to drain his lake, but by
doing so, may cause the wells of many others to run dry. In this case, the price for the
right to drain that the seller may accept is lower than the value to society of preserving
this lake (not selling).
5 Externality is defined as an unintended and uncompensated side effect of economic activities on parties outside the transaction (Sterner, 2001). The characteristics of CEs and their novelty in law mean that there is no market for CEs that can fit the requirements for conventional market valuation. Because there has only been a legal right in Canada for nonprofit organizations to purchase CEs since 1990 (Silver, Attridge, MacRae and Cox, 1995), the existing CE market is in the infancy of its evolution, and there is no clear market price as yet. While the property rights for CEs have been established in law, there is a lack of clarity concerning rights that could affect the value of CEs to landowners. For example, in Saskatchewan landowners do not have the right to drain wetlands without prior permission from the provincial environment ministry. However, in practice, there is no penalty for wholesale violation of this rule. Therefore, it is unclear whether or not landowners have the right to drain wetlands. This raises a landowner's minimum willingness to accept for a CE placed on a wetland relative to what it would be if the anti-draining law was enforced. The result is a reduction in the number of CEs landowners are willing to sell and an increase in the cost of protecting valuable ecosystems. The market for CEs is limited in participation, and so it does not possess the features of a competitive market. The consumers of environmental benefits are society in general and future generations. However, these people are not the purchasers of the CEs. If they were, the market would have a larger number of buyers than it does at present. It would still not meet the criteria of a competitive market, because it is impossible to limit the benefit of a CE to the purchaser. In this way, the purchase of CEs is vulnerable to 'free ridership.' That is, because a person can benefit without paying, he will be tempted to pay less than he would if this were not the case. It is also almost impossible for the government to police the maintenance of CEs if individuals could purchase them. For both these reasons, there are a limited number of organizations that are permitted to purchase CEs. These organizations must have habitat conservation as their mandate. Usually, a small number of buyers would indicate that they have market power in the face of a large number of landowners who are prospective sellers of CEs. However, as shown below this is often not the case for purchasers of environmental goods. Because CE purchasing organizations are small in number, the sellers can easily identify the purchasers and can therefore try to get a price that is based on the purchasers' willingness to pay for the CEs, rather than the landowner's own valuation of the land. Nor does the large number of landowners weaken their bargaining power. On the contrary, the purchaser's objective to preserve the land gives the seller monopoly power. It is often not just any land that is desired, but specific lands that contain specific ecosystem features, some of which are geographical. The landowner quickly recognizes that he owns a unique good and is a monopoly seller of that good. The non-divisibility of the environmental good produced by CEs also contributes to landowners' monopoly power. The purchaser cannot buy just one or two units of land in an area if the environmental goal requires that a certain ecosystem remains intact. Each of the landowners owns a crucial part of a whole, and each has monopoly power over the sale of that part. The CE market is therefore a market in which two powerful players -- the buyer and the seller -- bargain, and the outcome determines whether the price is closer to the purchaser's maximum willingness to pay or the landowner's minimum willingness to accept. The range for the equilibrium price can be quite wide because the valuation of the CE for each party is completely different. The landowner's private valuation of the land is based on the present value of its agricultural use, its discounted future sale value, and the value of any other personal benefit derived from its ownership. In the DUC pilot, the lands eligible for CEs were lands that had not been used for agriculture in the more than a century in which agriculture has been developed on the prairies. Therefore, eligible areas were basically scrap land. If they had any real agricultural value, odds are they would have been converted to agricultural use some time in the modern history of Canada. Nevertheless, some landowners in the pilot perceived that certain wetlands had a high potential value if drained. In these cases, the undetermined right to drain makes the valuation of such land extremely difficult. (It is also quite possible that landowners realize that the threat to drain raises the market value of ecologically significant lands.) Furthermore, landowners, both in the pilot and in general, have a valid concern about the unknown effects of a CE on their ability to sell and on the sale price of CE lands and adjacent lands in the future. Because the market is new, and there is not yet information on the future price effects of CEs in land markets, landowners will require a higher price for the CE than the agricultural value of the land on which the CE would be placed. On the other hand, the ecological value of lands usually targeted for CEs is quite high. Such lands serve important environmental functions, including preservation of habitat, contribution to rainfall, maintenance of underground water tables, cleaning of water through filtration, moderation of microclimates, and so on. These ecological benefits are known to be the basis of the environmental organizations' willingness to pay for CEs. For example, the upper Assiniboine area, which was targeted for the CE pilot project, is known for its value in feeding the Assiniboine River, the major source of clean water for the city of Brandon, Manitoba. Draining wetlands in the upper Assiniboine could seriously affect both the quantity and quality of water for downstream communities. In sum, the complexity of the effects of CEs on land values means that there is no strictly determined value that can be predicted for landowners' willingness to accept as a price for CEs. Therefore, even if environmental organizations had complete market power, they do not have the necessary information to estimate a value for landowners' willingness to accept. On the other hand, the organizations' willingness to pay is based on complex environmental evaluations that are limited by science and an uncertain future. Furthermore, because these organizations are working on behalf of future generations (and are funded at a level that is below the social optimum), a socially efficient price would be closer to the landowner's willingness to accept than the organizations' willingness to pay. 6 It is only the desperate plight of today's farmers that makes them even contemplate using these marginal lands for agriculture.
These features of CEs, markets, and the buyers and sellers of CEs preclude the use of
conventional price setting through a market to determine a socially optimal price for the
purchase of CEs from individual landowners by environmental organizations.
Therefore, it is important for organizations to try to determine landowners' true
valuations by some other mechanism. For this reason, the experiment implemented by
DUC to determine landowner valuations of CEs used an auction process, with features
selected according to auction theory.
Auction theory of value revelation

Auctions have the power to reveal, through a bidding process, the true valuation of an
item for which a market does not exist (Vickrey, 1961). Value revelation was in fact the
paramount goal of the DUC pilot. Thus, an important question was which auction format
would best fulfill this objective.
Because auctions can be useful where prices do not exist or are not well defined, they are
often the tool of choice for the sale of unique items (art) or items for which a market is
not yet established. Auctions have been used in the distribution of broadcast spectrum
rights by government (Levin, 1970), treasury bills (Milgrom and Weber, 1982), for the
purchase of construction contracts, and other goods or services where a market price is
difficult to establish. In the U.S., an auction mechanism is used for the purchase of
conservation contracts by the Department of Agriculture under the Conservation Reserve
Program (CRP).
Auctions offer both buyers and sellers a mechanism that reveals information about the
valuation of a product whose market value is unknown and for which a market has not
been clearly established. A CE auction introduces competition between landowners,
thereby decreasing their monopoly power and contributing to revelation of information
on valuation to a CE buyer that would otherwise be known only to the landowner.
Auction theory has identified four basic structures for auction design. Each has its own
strengths and weaknesses in terms of leading to "truth telling" by auction participants.
Truth telling means that the participants reveal their own valuation of the good being
auctioned through their bid. The design of a specific auction is derived from one of these
four basic structures, often with specific features whose purpose is to account for
particularities of the goods or of the participants in order to enhance truth telling. This
section examines the four basic auction types and discusses why the particular features of
the DUC pilot auction were chosen.
The first auction structure is known as an English auction or open-bid ascending auction.
Besides barter, it is perhaps one of the oldest known mechanisms for the exchange of
goods. In an open auction, all bidders are aware of the bids made by other bidders. In an
English auction, bids increase until no bidder chooses to offer a higher price than the
highest bid already offered. The good goes to the participant who has made the highest
bid. The amount paid for the good is the amount of the highest bid. The winner may not
pay the highest price she was willing to bid, because once all other bidders drop out, there is no need to increase the amount bid. The most popular contemporary example of an English auction is EBAY. The second auction structure is known as the first-price sealed bid auction. In this auction, as in the English auction, the highest bidder receives the item being auctioned, and pays a price equal to the winning bid. However, in this case, bidders do not see other bids; they only know their own bid amount. One problem with this auction is the fact that the highest bidder may suffer what is known as the "winner's curse" (Milgrom and Weber, 1982). The winner's curse is a result of the fact that an item for sale by auction has an uncertain value. In the face of this uncertainty the winner has likely paid a price higher than the item's actual value. The most common example of the winner's curse is found in the auction for unproven oil fields. Because the actual value of the land depends on the future sale of oil, which is unknown at the time of auction, some bidders will overestimate the value, win the auction, and pay an amount greater than the actual value of the lands. The winner's curse is also a common problem in contracts for public works. The winner often is a company that has bid too low for a contract, and then finds it impossible to complete the project within the specified budget. The third auction structure is called a Dutch auction. The Dutch auction operates as a descending price auction. The price is lowered until the item is purchased. By its nature, buyers cannot see the valuations of other potential bidders, because as soon as the highest bidder faces a price at or below his own valuation, the item is purchased and the auction is over. The last auction structure is called a Vickrey auction, or second-price sealed bid auction. The name derives from the economist who first described this auction and analyzed its implications for truth-revelation. In this auction, all bids are submitted independently, and, as in the first-price sealed bid auction, other bidders are not aware of any other bids submitted. In this case, however, the highest bidder pays a price for the good equal to the second highest bid received (that is the winning bidder pays the amount of the highest losing bid). Vickrey showed that, if a large number of bidders participate in the auction, this format will induce bidders to reveal their own most accurate valuation of a good, partly because bidders only pay the second highest bid, and so will not suffer the winner's curse (Vickrey, 1961). One question that arises is why the auctioneer would be willing to receive only the second highest bid in second-price auctions since they can get the highest bid in first-price auctions. Vickrey derived a feature of these four auction formats, called the 'revenue equivalence theorem.' According to this theorem, if bidders are risk-neutral and have independent private values, all auctions will provide the same revenue to the auctioneer, and the person with the highest valuation will receive the good (Vickrey, 1961). However, the revenue equivalence theorem only holds when bidders are risk-neutral and have independent private values. A risk-neutral bidder does not care about the risk of losing the auction and is only sensitive to the expected return. For risk-neutral bidders, the main concern is how to avoid the winner's curse and maximize expected revenue. So they bid less in the first price auction than their own valuation. Therefore the seller receives the same revenue in any auction for a single item, provided buyers are risk neutral and each buyer has his own private valuation for the good auctioned. In contrast, risk-averse bidders are afraid of losing the auction. Therefore, they bid more aggressively in the first price auction even though they have to pay the amount they bid. In the second-price auction, there is no significant bidding strategy difference between risk-neutral and risk-averse bidders since the amount they pay depends on the second-highest bid. The above comparison leads to the conclusion that with risk aversion, the first-price sealed bid auction and the Dutch auction will earn higher revenue for the seller than an ascending auction or a second-price sealed bid auction. The second condition for 'revenue equivalence' across the auction types is that bidders have independent private values, which means that each bidder only has information on his own valuation of the item. If he values the item very highly, he will place a high bid in a first-price sealed bid auction and would bid up to almost his own valuation in an ascending price auction. If he won the item, we would expect him to pay the same amount in all four auction structures. This condition ensures that the person who has the highest valuation will get the item regardless of which auction format the auctioneer chooses. In contrast, bidders may form a common valuation on an item. In this case, their own valuation depends, at least in part, on what they perceive to be others' valuation of the object. In this case, the first-price sealed bid, the second-price sealed bid, and the Dutch auctions provide bidders with no information on other bids. However, the open ascending price auction provides bidders with information on other bidders' valuation of the item. If many bidders drop from the auction at a low price, then the remaining bidders will lower their valuation of the object. If some competing bidders stay in at a very high price, the remaining bidders raise their valuation. With common values, the ascending auction may raise more or less revenue than the other three types of auction, depending on the values of all other bidders. The revenue equivalence theorem is not an auction goal; it describes an auction outcome. Auction goals can vary. They can include maximizing revenue, distributing goods efficiently, as well as revealing values. The meaning of revenue maximization is self-evident, and value revelation has been discussed above. Efficient allocation refers to the case where winners of an auction are most likely to be those bidders who most want to sell their CEs and who assign the lowest values to CEs placed on their lands (for a sale). In certain auction types, for example an English auction, it is possible for a strong bidder to deter entry into the bidding process. If this deterrence occurs, the strong bidder may receive the benefits of the auction even though a weaker bidder should have won. Of these three goals, DUC's primary goal for the pilot was to reveal values. Therefore, it was deemed reasonable, because this was a pilot, to sacrifice other potential goals if necessary in order to design an auction that offered a high probability of attaining the revelation goal. Three features of the pilot setting are also important in order to understand the resulting auction design. First, this was an auction in which landowners bid to sell CEs, not purchase them. In this case, winning bidders (landowners) received payment for the CEs, with DUC paying. In a reverse auction such as this, a buyer (DUC) might choose as a goal to minimize its total cost. In this case, DUC had as a secondary goal to maximize the land area protected within a fixed budget, but its primary goal was to reveal landowners' values. Second, DUC wished to purchase many CEs. This was not an auction for a single item, but a multi-unit auction. An additional feature of auctions is the role of the auctioneer. In many reverse auctions, the purchaser also serves as auctioneer. This was the case in the DUC pilot. Based on these considerations, a Vickrey auction with a hidden reserve price was chosen for the pilot. The characteristics of the landowners and the CEs as well as anecdotal information about past attempts at a CE auction, led the designers to conclude that this particular auction structure was most likely to lead to revelation of landowners' valuations of CEs. The second-price sealed bid or Vickrey auction was originally proposed as the best auction to reveal the bidder's true valuation of an item for sale (Vickrey, 1961). This same result holds whether the bidder is a seller or a buyer. The Vickrey auction possesses this feature because the seller (in the case of the DUC pilot) does not receive his or her own bid for the CE, but receives more than he/she bid for it. Therefore the seller will not suffer from the winner's curse if his bid is a lot lower than other bids for the sale of the CE. In this particular auction, sellers were very uncertain of the market value of a CE, and so reducing the risk of suffering from the winner's curse was central to convincing landowners to bid according to their actual valuation rather than strategically. The Vickrey auction is also efficient (Vickrey, 1961). Another important consideration, especially in reverse multi-unit auctions, is the potential for bidder collusion to influence the final price. In an English auction, bidders exchange information openly while bidding occurs. This can lead to collusion, where landowners could work together to raise the price of CEs above their actual valuations. It could also lead to adverse social consequences for landowners who refuse to collude. The Vickrey auction with sealed bid can still be subject to collusion, but only where there are a small number of potential bidders. This particular concern, however, was addressed through the setting of a reserve price in the pilot auction. The reserve price reduced the opportunity for collusion because no landowner would be paid an amount higher than the reserve price. The reserve price was hidden in the pilot because it was believed that a revealed reserve price would have the effect of reducing the auction to a fixed price offer, and all bids received would be at that price. Indeed, the U.S. uses this format in the Conservation Reserve Program, and does find that most bids are very close to its publicly disclosed reserve price in a first-price sealed bid auction.
The hidden reserve price also served several other purposes besides reducing collusion
possibilities. Anecdotal reports of a previous attempt at selling CEs by first-price auction
led to a result where all bids were incredibly high (often greater than the assessed value
of the land itself) and no purchases were made. It was believed that landowners tried to
discover DUC's willingness to pay through their bids, and did not in any way reveal their
own valuation of CEs. In contrast, the hidden reserve price used in the pilot signalled to
landowners that there did exist a maximum price beyond which CEs would not be
purchased, thereby providing landowners with an incentive to make reasonable bids
based on their own valuation.
The hidden reserve price, together with the second-price feature of the auction, were
supposed to provide the greatest probability that landowners would bid according to their
actual valuation of placing a CE on their land, thus achieving the paramount goal of the
pilot. The second-price aspect of the auction design encouraged landowners to reveal
their true valuation by guaranteeing that winners would receive payment that was higher
than their bid. The existence of the reserve price meant that the incentive for landowners
was to bid an amount low enough to be in the winning group. This auction design
therefore reduced the landowner's problem to one of bidding an amount that would put
him in the winning group, with the amount based on his own valuation for the sale of a
CE. Each member of the winning group then received the same rate of payment for their
CE.
One difficulty with the use of a hidden reserve price is that it is possible for the
auctioneer to change the reserve price once the bids are in. There is no real way to
prevent this in a one-shot pilot project such as this. In the DUC pilot, even with this
potential weakness in mind, the Vickrey auction with a hidden reserve price format was
deemed to be the most likely to induce landowners to reveal their true valuations.
IV. Model of the DUC pilot

A formal modeling of the Vickrey auction provides support for its use in this project.
The main objective of the project was to induce landowners to reveal the minimum
amount of compensation they were willing to accept to sell CEs to DUC. This section
provides a mathematical proof that the Vickrey auction should meet this objective.
More formally, we can describe the model as follows:
Let: bi denote the bid that the ith landowner submits;
xi denote the true valuation of the ith landowner for placing CEs on his land; ci denote the opportunity cost of placing CEs on the lands; r denote the hidden reserve price (known to DUC but not to the landowner); 7 Bids were evaluated in terms of the percentage they represented of the corresponding land parcel's assessed value. Winning bids and consequent payments were thus determined as a percentage of assessed value. The actual amount of money paid to winning landowners differed depending on the assessed value of their land parcel. ∏i denote the payoff (expected benefit) of the ith landowner. Suppose that the ith landowner submits bid bi. The amount xi is his true valuation of the CEs to be placed on his land. We assume that the landowner's estimate xi is based on the opportunity cost (ci) of placing CEs on his land. In other words, this is a private independent value model. The landowner estimates his true value based the opportunity cost, which consists of the land's agriculture use value, its discounted future sale value and any other benefits, but he does not care or have information about other landowners' valuations. The payoff for the landowner is: If the landowner bids low enough to enter into winning group, he receives DUC's reserve price, which is higher than his bid. Alternatively, if the landowner bids too high to qualify for the auction's winning group, he keeps the land use rights and retains his option to sell unencumbered land at a future date.
The question is whether this mechanism can discover the landowner's true valuation of a
CE. Thus, we must now show that, if the landowner follows a truth-telling strategy in the
auction, he has no incentive to deviate. In other words, if the landowner chooses to bid
his true value, he will not become better off if he moves from this decision. If his best
strategy is to bid his true value, then the equilibrium result for the auction is where each
landowner bids his true value. Our conclusion is that, under the Vickrey auction with a
hidden reserve price mechanism, truth-telling is the landowner's weakly dominant
strategy. In order to prove this, let us consider the two possible cases of lying:
(1) the landowner bids lower than his true valuation (bi < xi);
(2) the landowner bids higher than his true valuation (bi > xi);
Case (1): Landowner bids lower than his true valuation (bi < xi)

If the landowner bids lower than his true value, there are three possible results.
If xi > bi > r, the landowner has a high valuation for the placement of aCEon his land. The
bid is lower than his true value but still higher than the reserve price. In this case, the
landowner would not be able to sell a CE. His payoff from this strategy is the
opportunity cost (ci). Even if the landowner bids his true value, which is higher than the
reserve price in this case, he still loses the game and gains the opportunity cost (ci). Since
the landowner's true valuation is higher than the reserve price, he would not regret losing
the game. In this case, the landowner's payoffs from truth telling and bidding lower than
his true value are equal. The landowner would not be better off if he lied.
If xi > r >bi, the landowner bids lower than the reserve price, while his true valuation is
higher than the reserve price. Following this strategy, the landowner would win the
auction and receive r. However, his gain from winning is lower than his true valuation
(xi). In this case, the landowner would suffer from the winner's curse. If he bid truly,
losing the auction would be more beneficial than winning. Thus, here again the
landowner would be worse off by bidding lower than his true value.
Finally, if r > xi > bi the landowner bids lower than his true value and his true valuation is
lower than the reserve price. Consequently, the landowner would win the auction with a
payoff of the reserve price r. Since telling the truth by bidding according to his actual
value would bring the same result, the landowner could not become better off by lying in
this case.
Based on the above three cases, we conclude that if the landowner bids lower than his
true valuation, he would either be worse off or receive the same expected benefit as the
payoff from adopting a truth-telling strategy. There is thus no incentive for the landowner
to bid lower than his true value for a CE.
Case (2) Landowner bids higher than his true valuation (bi > xi)

If this is the case, we can also consider three possible results.
If bi >xi > r, the landowner bids higher than the reserve price and loses the auction. This
strategy would not make any difference from the truth-telling strategy because the
landowner's true value is also higher than the auction reserve price. Under either of these
strategies, the landowner's payoff is the opportunity cost, ci, since the landowner loses
the auction in both cases.
If bi > r > xi, the landowner bids higher than the reserve price and he loses the auction.
His payoff is the opportunity cost. However, if he bid the true value (xi.), which is lower
than the reserve price, he would win the game and receive the payoff r. Recall, we
assume throughout this exercise that the true valuation is equal to opportunity cost. The
reserve price is higher than opportunity cost in this case. This implies that a truth-telling
strategy would bring the landowner greater benefit than would lying since, if he bid his
opportunity cost, he would be able to sell a CE and gain the (greater) reserve price. In this
case, lying by bidding higher than his true value and losing the auction makes the
landowner worse off.
If r > bi > xi, the landowner's bid is lower than the auction reserve price but higher than
his true value. The landowner would win and be paid the reserve price. A truth-telling
8 Winner's curse: In a regular auction, it means that the winner paid too much for the item relative to its value to him. In a reverse auction, it means that the winner is paid less than he should be paid. strategy would not lower his payoff; rather, it would yield the same result. Therefore,
there is no incentive for the landowner to bid a value higher than his true value.
For case (2), then, we conclude that if the landowner lies by bidding higher than his true
value, he would not suffer from the winner's curse. However, neither would lying in this
direction generate a higher payoff than bidding his true value.
Under the Vickrey auction with a hidden reserve price mechanism, therefore, the
landowner does not benefit from lying. So he would not have an incentive to deviate from
the truth-telling strategy. Truth-telling is a weakly dominant strategy for landowners.
V. Pilot Implementation and Implications

On the basis of the result that, in theory, the Vickrey auction should elicit truth telling in
the valuation of conservation easements from the landowners' perspectives, we now turn
to the implementation of the auction stage of the pilot. The results of the survey (second
stage of the DUC pilot) will be presented in a future paper. Here, we discuss various
factors, both foreseen and unforeseen, and how they affected landowners' participation in
the auction and/or their bids. That is, we describe what happened when we implemented
the auction design, and what can be learned from this experiment. Selected results from
the follow-up survey will elaborate on these factors and auction results.which affected the
pilot's results and examine the implications of the results and the factors that affected
them for future projects and research in this area.
Participation in the auction was remarkably low. Of 3,665 landowners who received
auction materials inviting them to participate, only 46 submitted bids. According to the
survey results, there were three main reasons for this low participation rate: the
perpetuity of CEs in the pilot, a general lack of knowledge about CEs on the part of most
landowners, and fear. First, it became clear during the pilot that landowner knowledge
about CEs was in its early stages, and this was confirmed in the survey responses. Only
about 6 % of survey respondents said they know a lot about CEs, while over 54 %
reported knowing nothing at all about CEs before the pilot. For instance, a sizeable
minority of both bidders and nonbidders expressed concern that placing a CE on their
land would affect their property taxes. Second, there was an unanticipated reaction to the
auction stage of the pilot from some sites, increasing landowner fears concerning sales of
CEs. In two of the four sites, the leaders of the Rural Municipalities initiated active
campaigns to discourage landowners from participating in the auction. These campaigns
included mailings and media announcements, and contributed to landowner's concerns
and fears about entering into CE contracts.
But the leading impediment to landowner participation in the auction, as well as general
barrier to landowner openness to the idea of placing CEs on their land, is the fact that
only perpetual CEs are possible in Canada at this time. There is currently no CE holder
offering to accept limited-duration CEs. In this pilot, perpetuity was the major reason landowners gave for not bidding in the auction. Many landowners - nonbidders and bidders alike -- reported that they are too uncertain about the long-run effects of a perpetual CE on their land's resale value; additionally, some survey respondents mentioned that they did not want to limit their production and land use options over an infinite time horizon. The lack of information naturally led to trepidation concerning participation in the auction, especially among risk-averse landowners. Because landowners were unfamiliar with CE contracts and the contracts' potential effects on land values, many were unwilling to be first-movers in the CE market. They could choose to pass up this pilot opportunity to sell a CE, then, if neighbours participated, they could get information on the costs and benefits of the contract before approaching a conservation organization or participating in a program in the future. Of these three leading reasons for low landowner participation in the auction, the one most in DUC's or any other conservation agency's control is that of landowner understanding about CEs. While CEs were introduced over a decade ago, for many years they were only acquired by donation. Therefore, unless a landowner already had a strong desire to ensure the long-term protection of natural lands, he/she had no reason to learn about CEs. Also, because only a few CE contracts were written each year, DUC had neither standard contract formats nor general information materials prepared. As part of the auction implementation, it was therefore necessary to produce materials outlining the basics of CEs, such as what a CE is, what types of CE contracts were available, and how a CE contract works. These materials were all sent to landowners as part of the bid package, along with additional materials describing the auction format and bidding procedures. In spite of the barriers to participation in the auction, 46 landowners bid in the CE pilot. The bids were dispersed, with some quite high and others very low. The bid values were affected by lack of prior knowledge of CEs, the auction design, factors that were site specific, and personal preferences. In addition to affecting auction participation, landowners' lack of prior knowledge of CEs also affected their bid amounts. In theory, the price a landowner is willing to accept in exchange for placing a CE on his/her land would be based on the foregone revenue from potential conversion of that land to agricultural or other productive use(s) and the discounted value of the land's reduced resale value. However, at this time, both of these are unknown by landowners. In actuality, the remaining areas of natural wetland and grassland ecosystems are likely on land that is extremely marginal land for agriculture or they would have already been converted to agricultural use in these areas of high conversion rates. Thus, this factor should add very little to landowner's minimum willingness to accept to place CEs on these lands. But the potential effects on the land's market value cannot be as easily dismissed. CEs are still both new enough and rare enough that there is little empirical evidence as to their land market effects. It may be that in the relatively short or medium term, a CE will reduce land's resale value, while in the longer-term the presence of a CE could boost a land parcel's resale value as natural ecosystem areas become scarce enough to make CEs highly valuable. At present, however, landowner's face great uncertainty as to the longer-term financial effects of placing CEs on their lands, and can thus be expected to have no idea how to bid for CEs. As such, the wide dispersion of bids received in the pilot is not at all surprising. The fear that CEs might affect future land values seems to have led many landowners to bid quite high. The issue of trust arose in a focus group session prior to the implementation of the project. The hidden reserve price was required to prevent farmers from using the bid process as an opportunity to try to reveal the organization's willingness to pay. However, the hidden reserve price discouraged some farmers from participating because it added another layer of uncertainty to the bidding process. A large component of this uncertainty consisted of landowners' suspicion that the CE buyer could change the reserve price at its convenience. In order to reduce this uncertainty and suspicion, CE buyers would need to put in place outside binding agreements to ensure the reserve price would be fixed, at least downward. It is impossible to prevent the reserve price from rising because it is impossible to prohibit renegotiation between buyer and seller after the bid process is completed. In addition to affecting participation, trust in a fixed reserve price, or the lack of such, could also affect bid amounts. If landowners believe there is the potential for the CE buyer to move the reserve price, some of them may bid quite high rather than according to their true valuation in order to induce the organization to raise the reserve price. In this pilot, strong signals were sent to landowners that the reserve price would not change. However, DUC did in fact raise the reserve price once it observed the bids received and considered factors affecting the different sites in the pilot. Another factor affecting bid amounts was local variation in land values. Landowners' bids were expressed as a percentage of land value (assessed value of the quarter on which the CE would be located). However, the market value of the specific land on which the CE would be placed is affected by local practices that are not reflected in assessed values. For example, in Saskatchewan, it is illegal to drain wetlands without prior approval of the Ministry of the Environment. This means that wetlands should have a very low value to a grain farmer who cannot plant there. However, in several municipalities, the local government had unilaterally assumed responsibility for draining wetlands, or for granting permissions for landowners to do so. Therefore, the assessed value did not reflect the de facto legal status of these lands, as they could, in practice, be readily drained. Furthermore, because landowners generally believed the wetlands covered rich soil, they perceived this land to have a much higher potential market value (if drained) than the assessment would indicate. This example highlights the fact that CEs in some areas must be purchased at a higher percentage of assessed value than CEs in other areas; that is, landowners in different areas will make CEs available at different prices, depending on local conditions. In DUC's experiment, it became obvious that DUC's locally based field officers possessed excellent knowledge of these local conditions and expectations. The bids received from these areas supported assertions that field officers had made during the design phase concerning local variations in values and the need for locally specific CE prices. The implication that local knowledge is important to determine price guidelines was perhaps the most important conclusion of this project. There is no "one size fits all" price that will adequately guide the purchase of CEs, in either absolute or percentage terms. An auction format to purchase CEs may still be the best allocative mechanism in terms of developing local pricing guidelines. Because the CE market is thin, once a pilot such as DUC's is complete, the information collected can be used to devise guidelines that can then be used as part of the bargaining process for individual purchases negotiated on a case-by-case basis. That said, no price-determination method for CEs is likely to work well, at least in the Canadian prairies, until CE contracts are far better understood by a reasonable number of landowners. Landowner lack of knowledge about what CEs are, how they work, and their value presented a clear impediment to auction participation, thereby limiting the amount of information this experimental auction collected. This in turn limited the amount of guidance the pilot could provide for future CE pricing. Landowner uncertainty also led to widely disperse bids by auction participants, which may have limited the usefulness of the pricing data collected. Thus, governments and conservation agencies wishing to expand CE programs in the prairies will first need to conduct CE education initiatives. This will serve to increase landowner openness to placing CEs on their lands, as well as smooth the CE market's operation in terms of participation and pricing. In sum, DUC's auction experiment unveiled many previously unknown features of both CE markets and the use of auctions in an area where the product has no established market and encompasses many levels of uncertainty. This pilot has shown that, while an auction may have low participation, it can still provide useful information for future bargaining processes, as well as be a vehicle for increasing the level of knowledge and discussion about the product. As for the CE market in the prairies, we conclude that greater education of landowners is a top priority, while the setting of one price is not only unnecessary, but likely a mistake. References
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Source: http://economics.ca/2006/papers/0372.pdf